TSTP Solution File: SCT120+1 by cvc5---1.0.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SCT120+1 : TPTP v8.2.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : do_cvc5 %s %d
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed May 29 17:42:50 EDT 2024
% Result : Theorem 26.93s 27.23s
% Output : Proof 27.02s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.18 % Problem : SCT120+1 : TPTP v8.2.0. Released v5.2.0.
% 0.18/0.19 % Command : do_cvc5 %s %d
% 0.19/0.40 % Computer : n014.cluster.edu
% 0.19/0.40 % Model : x86_64 x86_64
% 0.19/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.40 % Memory : 8042.1875MB
% 0.19/0.40 % OS : Linux 3.10.0-693.el7.x86_64
% 0.19/0.40 % CPULimit : 300
% 0.19/0.40 % WCLimit : 300
% 0.19/0.40 % DateTime : Mon May 27 17:38:39 EDT 2024
% 0.19/0.40 % CPUTime :
% 0.52/0.67 %----Proving TF0_NAR, FOF, or CNF
% 26.93/27.23 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 26.93/27.23 --- Run --no-e-matching --full-saturate-quant at 5...
% 26.93/27.23 --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 26.93/27.23 --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 26.93/27.23 --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 26.93/27.23 % SZS status Theorem for /export/starexec/sandbox2/tmp/tmp.d4ordS8rn2/cvc5---1.0.5_14261.smt2
% 26.93/27.23 % SZS output start Proof for /export/starexec/sandbox2/tmp/tmp.d4ordS8rn2/cvc5---1.0.5_14261.smt2
% 26.93/27.23 (assume a0 (forall ((V_g_2 $$unsorted) (V_f_2 $$unsorted)) (=> (forall ((B_x $$unsorted)) (= (tptp.hAPP V_f_2 B_x) (tptp.hAPP V_g_2 B_x))) (= V_f_2 V_g_2))))
% 26.93/27.23 (assume a1 (forall ((V_x_2 $$unsorted) (T_a $$unsorted)) (tptp.c_member T_a V_x_2 (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_HOL_Obool)))))
% 26.93/27.23 (assume a2 (forall ((V_r_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_Oirrefl T_a V_r_2) (forall ((B_x $$unsorted)) (not (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a B_x B_x) V_r_2))))))
% 26.93/27.23 (assume a3 (forall ((V_r_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_Ototal__on T_a V_A_2 V_r_2) (forall ((B_x $$unsorted)) (=> (tptp.c_member T_a B_x V_A_2) (forall ((B_xa $$unsorted)) (=> (tptp.c_member T_a B_xa V_A_2) (=> (not (= B_x B_xa)) (or (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a B_x B_xa) V_r_2) (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a B_xa B_x) V_r_2))))))))))
% 26.93/27.23 (assume a4 (forall ((V_r_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_Otrans T_a V_r_2) (forall ((B_x $$unsorted) (B_y $$unsorted)) (=> (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a B_x B_y) V_r_2) (forall ((B_z $$unsorted)) (=> (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a B_y B_z) V_r_2) (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a B_x B_z) V_r_2))))))))
% 26.93/27.23 (assume a5 (forall ((V_c_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (V_r_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Relation_Otrans T_a V_r_2) (=> (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_a_2 V_b_2) V_r_2) (=> (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_b_2 V_c_2) V_r_2) (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_a_2 V_c_2) V_r_2))))))
% 26.93/27.23 (assume a6 (forall ((V_x_2 $$unsorted) (T_a $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_HOL_Obool)) V_x_2))))
% 26.93/27.23 (assume a7 (forall ((V_c_2 $$unsorted) (T_a $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted)) (=> (= V_A_2 V_B_2) (=> (=> (tptp.c_member T_a V_c_2 V_A_2) (not (tptp.c_member T_a V_c_2 V_B_2))) (not (=> (not (tptp.c_member T_a V_c_2 V_A_2)) (tptp.c_member T_a V_c_2 V_B_2)))))))
% 26.93/27.23 (assume a8 (forall ((V_z_2 $$unsorted) (V_L_2 $$unsorted) (V_y_2 $$unsorted) (V_x_2 $$unsorted)) (= (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt V_x_2 V_y_2) (tptp.c_Arrow__Order__Mirabelle_Omkbot V_L_2 V_z_2)) (and (not (= V_y_2 V_z_2)) (=> (= V_x_2 V_z_2) (not (= V_x_2 V_y_2))) (=> (not (= V_x_2 V_z_2)) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt V_x_2 V_y_2) V_L_2))))))
% 26.93/27.23 (assume a9 (forall ((V_z_2 $$unsorted) (V_L_2 $$unsorted) (V_y_2 $$unsorted) (V_x_2 $$unsorted)) (= (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt V_x_2 V_y_2) (tptp.c_Arrow__Order__Mirabelle_Omktop V_L_2 V_z_2)) (and (not (= V_x_2 V_z_2)) (=> (= V_y_2 V_z_2) (not (= V_x_2 V_y_2))) (=> (not (= V_y_2 V_z_2)) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt V_x_2 V_y_2) V_L_2))))))
% 26.93/27.23 (assume a10 (forall ((V_r_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Order__Relation_Ostrict__linear__order__on T_a V_A_2 V_r_2) (and (tptp.c_Relation_Otrans T_a V_r_2) (tptp.c_Relation_Oirrefl T_a V_r_2) (tptp.c_Relation_Ototal__on T_a V_A_2 V_r_2)))))
% 26.93/27.23 (assume a11 (forall ((V_x_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Otop T_a) (= (tptp.hAPP (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_b T_a)) V_x_2) (tptp.c_Orderings_Otop__class_Otop T_a)))))
% 26.93/27.23 (assume a12 (forall ((V_x_2 $$unsorted) (T_a $$unsorted)) (tptp.c_member T_a V_x_2 (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_HOL_Obool)))))
% 26.93/27.23 (assume a13 (forall ((V_A_2 $$unsorted) (T_a $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted)) (=> (= V_a_2 V_b_2) (=> (tptp.c_member T_a V_b_2 V_A_2) (tptp.c_member T_a V_a_2 V_A_2)))))
% 26.93/27.23 (assume a14 (forall ((V_A_2 $$unsorted) (T_a $$unsorted) (V_y_2 $$unsorted) (V_x_2 $$unsorted)) (=> (= V_x_2 V_y_2) (= (tptp.c_member T_a V_x_2 V_A_2) (tptp.c_member T_a V_y_2 V_A_2)))))
% 26.93/27.23 (assume a15 (forall ((V_x_2 $$unsorted) (T_a $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted)) (=> (= V_A_2 V_B_2) (= (tptp.c_member T_a V_x_2 V_A_2) (tptp.c_member T_a V_x_2 V_B_2)))))
% 26.93/27.23 (assume a16 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_member T_a V_x_2 (tptp.c_fequal V_y_2)) (= V_x_2 V_y_2))))
% 26.93/27.23 (assume a17 (forall ((V_A_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_member T_a V_x_2 V_A_2) (tptp.hBOOL (tptp.hAPP V_A_2 V_x_2)))))
% 26.93/27.23 (assume a18 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (V_R_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_FunDef_Oin__rel T_a T_b V_R_2 V_x_2 V_y_2) (tptp.c_member (tptp.tc_prod T_a T_b) (tptp.c_Product__Type_OPair T_a T_b V_x_2 V_y_2) V_R_2))))
% 26.93/27.23 (assume a19 (forall ((T_a $$unsorted) (V_R_2 $$unsorted) (V_y_2 $$unsorted) (V_y_H_2 $$unsorted) (T_b $$unsorted) (V_x_2 $$unsorted) (V_P_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP V_P_2 V_x_2)) (=> (tptp.c_member (tptp.tc_prod T_b T_b) (tptp.c_Product__Type_OPair T_b T_b V_y_H_2 V_y_2) (tptp.hAPP V_R_2 V_x_2)) (tptp.c_member (tptp.tc_prod (tptp.tc_prod T_a T_b) (tptp.tc_prod T_a T_b)) (tptp.c_Product__Type_OPair (tptp.tc_prod T_a T_b) (tptp.tc_prod T_a T_b) (tptp.c_Product__Type_OPair T_a T_b V_x_2 V_y_H_2) (tptp.c_Product__Type_OPair T_a T_b V_x_2 V_y_2)) (tptp.c_Recdef_Osame__fst T_a T_b V_P_2 V_R_2))))))
% 26.93/27.23 (assume a20 (forall ((V_r_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (=> (tptp.c_member (tptp.tc_prod T_a T_b) (tptp.c_Product__Type_OPair T_a T_b V_a_2 V_b_2) V_r_2) (tptp.c_member T_b V_b_2 (tptp.c_Relation_ORange T_a T_b V_r_2)))))
% 26.93/27.23 (assume a21 (forall ((V_A_2 $$unsorted) (T_a $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted)) (=> (= V_a_2 V_b_2) (=> (tptp.c_member T_a V_a_2 V_A_2) (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_a_2 V_b_2) (tptp.c_Relation_OId__on T_a V_A_2))))))
% 26.93/27.23 (assume a22 (forall ((V_A_2 $$unsorted) (V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_x_2 V_y_2) (tptp.c_Relation_OId__on T_a V_A_2)) (and (= V_x_2 V_y_2) (tptp.c_member T_a V_x_2 V_A_2)))))
% 26.93/27.23 (assume a23 (forall ((V_r_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (=> (tptp.c_member (tptp.tc_prod T_a T_b) (tptp.c_Product__Type_OPair T_a T_b V_a_2 V_b_2) V_r_2) (tptp.c_member T_a V_a_2 (tptp.c_Relation_ODomain T_a T_b V_r_2)))))
% 26.93/27.23 (assume a24 (forall ((V_r_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Nitpick_Orefl_H T_a V_r_2) (forall ((B_x $$unsorted)) (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a B_x B_x) V_r_2)))))
% 26.93/27.23 (assume a25 (forall ((V_r_2 $$unsorted) (T_a $$unsorted)) (=> (forall ((B_x $$unsorted) (B_y $$unsorted)) (=> (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a B_x B_y) V_r_2) (forall ((B_z $$unsorted)) (=> (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a B_y B_z) V_r_2) (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a B_x B_z) V_r_2))))) (tptp.c_Relation_Otrans T_a V_r_2))))
% 26.93/27.23 (assume a26 (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (V_L_2 $$unsorted)) (=> (tptp.c_member (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_HOL_Obool) V_L_2 tptp.c_Arrow__Order__Mirabelle_OLin) (=> (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt V_a_2 V_b_2) V_L_2) (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt V_b_2 V_a_2) V_L_2))))))
% 26.93/27.23 (assume a27 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (V_L_2 $$unsorted)) (=> (tptp.c_member (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_HOL_Obool) V_L_2 tptp.c_Arrow__Order__Mirabelle_OLin) (=> (not (= V_x_2 V_y_2)) (= (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt V_x_2 V_y_2) V_L_2)) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt V_y_2 V_x_2) V_L_2))))))
% 26.93/27.23 (assume a28 (forall ((V_f_2 $$unsorted) (V_r_2 $$unsorted) (T_b $$unsorted) (V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_x_2 V_y_2) (tptp.c_Relation_Oinv__image T_b T_a V_r_2 V_f_2)) (tptp.c_member (tptp.tc_prod T_b T_b) (tptp.c_Product__Type_OPair T_b T_b (tptp.hAPP V_f_2 V_x_2) (tptp.hAPP V_f_2 V_y_2)) V_r_2))))
% 26.93/27.23 (assume a29 (forall ((V_A_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_ORange T_a T_a (tptp.c_Relation_OId__on T_a V_A_2)) V_A_2)))
% 26.93/27.23 (assume a30 (forall ((V_A_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_ODomain T_a T_a (tptp.c_Relation_OId__on T_a V_A_2)) V_A_2)))
% 26.93/27.23 (assume a31 (forall ((V_A_2 $$unsorted) (T_a $$unsorted)) (tptp.c_Relation_Otrans T_a (tptp.c_Relation_OId__on T_a V_A_2))))
% 26.93/27.23 (assume a32 (forall ((V_f_2 $$unsorted) (T_b $$unsorted) (V_r_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Relation_Otrans T_a V_r_2) (tptp.c_Relation_Otrans T_b (tptp.c_Relation_Oinv__image T_a T_b V_r_2 V_f_2)))))
% 26.93/27.23 (assume a33 (forall ((V_x_2 $$unsorted) (V_L_2 $$unsorted)) (=> (tptp.c_member (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_HOL_Obool) V_L_2 tptp.c_Arrow__Order__Mirabelle_OLin) (tptp.c_member (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_HOL_Obool) (tptp.c_Arrow__Order__Mirabelle_Omktop V_L_2 V_x_2) tptp.c_Arrow__Order__Mirabelle_OLin))))
% 26.93/27.23 (assume a34 (forall ((V_x_2 $$unsorted) (V_L_2 $$unsorted)) (=> (tptp.c_member (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_HOL_Obool) V_L_2 tptp.c_Arrow__Order__Mirabelle_OLin) (tptp.c_member (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_HOL_Obool) (tptp.c_Arrow__Order__Mirabelle_Omkbot V_L_2 V_x_2) tptp.c_Arrow__Order__Mirabelle_OLin))))
% 26.93/27.23 (assume a35 (forall ((V_r_2 $$unsorted) (T_b $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_member T_a V_a_2 (tptp.c_Relation_ODomain T_a T_b V_r_2)) (exists ((B_y $$unsorted)) (tptp.c_member (tptp.tc_prod T_a T_b) (tptp.c_Product__Type_OPair T_a T_b V_a_2 B_y) V_r_2)))))
% 26.93/27.23 (assume a36 (forall ((V_r_2 $$unsorted) (T_b $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_member T_a V_a_2 (tptp.c_Relation_ORange T_b T_a V_r_2)) (exists ((B_y $$unsorted)) (tptp.c_member (tptp.tc_prod T_b T_a) (tptp.c_Product__Type_OPair T_b T_a B_y V_a_2) V_r_2)))))
% 26.93/27.23 (assume a37 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (V_L_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted)) (=> (not (= V_a_2 V_b_2)) (=> (tptp.c_member (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_HOL_Obool) V_L_2 tptp.c_Arrow__Order__Mirabelle_OLin) (= (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt V_x_2 V_y_2) (tptp.c_Arrow__Order__Mirabelle_Oabove V_L_2 V_a_2 V_b_2)) (and (not (= V_x_2 V_y_2)) (=> (= V_x_2 V_b_2) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt V_a_2 V_y_2) V_L_2)) (=> (not (= V_x_2 V_b_2)) (and (=> (= V_y_2 V_b_2) (or (= V_x_2 V_a_2) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt V_x_2 V_a_2) V_L_2))) (=> (not (= V_y_2 V_b_2)) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt V_x_2 V_y_2) V_L_2))))))))))
% 26.93/27.23 (assume a38 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (V_L_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted)) (=> (not (= V_a_2 V_b_2)) (=> (tptp.c_member (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_HOL_Obool) V_L_2 tptp.c_Arrow__Order__Mirabelle_OLin) (= (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt V_x_2 V_y_2) (tptp.c_Arrow__Order__Mirabelle_Obelow V_L_2 V_a_2 V_b_2)) (and (not (= V_x_2 V_y_2)) (=> (= V_y_2 V_a_2) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt V_x_2 V_b_2) V_L_2)) (=> (not (= V_y_2 V_a_2)) (and (=> (= V_x_2 V_a_2) (or (= V_y_2 V_b_2) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt V_b_2 V_y_2) V_L_2))) (=> (not (= V_x_2 V_a_2)) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt V_x_2 V_y_2) V_L_2))))))))))
% 26.93/27.23 (assume a39 (forall ((V_L_2 $$unsorted) (V_y_2 $$unsorted) (V_x_2 $$unsorted)) (=> (not (= V_x_2 V_y_2)) (=> (tptp.c_member (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_HOL_Obool) V_L_2 tptp.c_Arrow__Order__Mirabelle_OLin) (tptp.c_member (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_HOL_Obool) (tptp.c_Arrow__Order__Mirabelle_Oabove V_L_2 V_x_2 V_y_2) tptp.c_Arrow__Order__Mirabelle_OLin)))))
% 26.93/27.23 (assume a40 (forall ((V_L_2 $$unsorted) (V_y_2 $$unsorted) (V_x_2 $$unsorted)) (=> (not (= V_x_2 V_y_2)) (=> (tptp.c_member (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_HOL_Obool) V_L_2 tptp.c_Arrow__Order__Mirabelle_OLin) (tptp.c_member (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_HOL_Obool) (tptp.c_Arrow__Order__Mirabelle_Obelow V_L_2 V_x_2 V_y_2) tptp.c_Arrow__Order__Mirabelle_OLin)))))
% 26.93/27.23 (assume a41 (forall ((V_s_2 $$unsorted) (V_r_2 $$unsorted) (V_b_H_2 $$unsorted) (V_a_H_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_member (tptp.tc_prod (tptp.tc_prod T_a T_b) (tptp.tc_prod T_a T_b)) (tptp.c_Product__Type_OPair (tptp.tc_prod T_a T_b) (tptp.tc_prod T_a T_b) (tptp.c_Product__Type_OPair T_a T_b V_a_2 V_b_2) (tptp.c_Product__Type_OPair T_a T_b V_a_H_2 V_b_H_2)) (tptp.c_Wellfounded_Olex__prod T_a T_b V_r_2 V_s_2)) (or (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_a_2 V_a_H_2) V_r_2) (and (= V_a_2 V_a_H_2) (tptp.c_member (tptp.tc_prod T_b T_b) (tptp.c_Product__Type_OPair T_b T_b V_b_2 V_b_H_2) V_s_2))))))
% 26.93/27.23 (assume a42 (forall ((V_A_2 $$unsorted) (V_c_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_member (tptp.tc_prod T_a T_a) V_c_2 (tptp.c_Relation_OId__on T_a V_A_2)) (not (forall ((B_x $$unsorted)) (=> (tptp.c_member T_a B_x V_A_2) (not (= V_c_2 (tptp.c_Product__Type_OPair T_a T_a B_x B_x)))))))))
% 26.93/27.23 (assume a43 (forall ((V_r_2 $$unsorted) (T_b $$unsorted) (V_b_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_member T_a V_b_2 (tptp.c_Relation_ORange T_b T_a V_r_2)) (not (forall ((B_x $$unsorted)) (not (tptp.c_member (tptp.tc_prod T_b T_a) (tptp.c_Product__Type_OPair T_b T_a B_x V_b_2) V_r_2)))))))
% 26.93/27.23 (assume a44 (forall ((V_r_2 $$unsorted) (T_b $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_member T_a V_a_2 (tptp.c_Relation_ODomain T_a T_b V_r_2)) (not (forall ((B_y $$unsorted)) (not (tptp.c_member (tptp.tc_prod T_a T_b) (tptp.c_Product__Type_OPair T_a T_b V_a_2 B_y) V_r_2)))))))
% 26.93/27.23 (assume a45 (forall ((V_a_2 $$unsorted) (V_r_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Relation_Orefl__on T_a V_A_2 V_r_2) (=> (tptp.c_member T_a V_a_2 V_A_2) (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_a_2 V_a_2) V_r_2)))))
% 26.93/27.23 (assume a46 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (V_r_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Relation_Orefl__on T_a V_A_2 V_r_2) (=> (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_x_2 V_y_2) V_r_2) (tptp.c_member T_a V_x_2 V_A_2)))))
% 26.93/27.23 (assume a47 (forall ((V_R2_2 $$unsorted) (T_b $$unsorted) (V_R1_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Relation_Otrans T_a V_R1_2) (=> (tptp.c_Relation_Otrans T_b V_R2_2) (tptp.c_Relation_Otrans (tptp.tc_prod T_a T_b) (tptp.c_Wellfounded_Olex__prod T_a T_b V_R1_2 V_R2_2))))))
% 26.93/27.23 (assume a48 (forall ((V_A_2 $$unsorted) (T_a $$unsorted)) (tptp.c_Relation_Orefl__on T_a V_A_2 (tptp.c_Relation_OId__on T_a V_A_2))))
% 26.93/27.23 (assume a49 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (V_r_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Relation_Orefl__on T_a V_A_2 V_r_2) (=> (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_x_2 V_y_2) V_r_2) (tptp.c_member T_a V_y_2 V_A_2)))))
% 26.93/27.23 (assume a50 (forall ((V_r_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Order__Relation_Opreorder__on T_a V_A_2 V_r_2) (and (tptp.c_Relation_Orefl__on T_a V_A_2 V_r_2) (tptp.c_Relation_Otrans T_a V_r_2)))))
% 26.93/27.23 (assume a51 (forall ((V_a_2 $$unsorted) (V_r_2 $$unsorted) (V_b_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_member T_a V_b_2 (tptp.c_Wellfounded_Oacc T_a V_r_2)) (=> (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_a_2 V_b_2) V_r_2) (tptp.c_member T_a V_a_2 (tptp.c_Wellfounded_Oacc T_a V_r_2))))))
% 26.93/27.23 (assume a52 (forall ((V_r_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_member T_a V_a_2 (tptp.c_Wellfounded_Oacc T_a V_r_2)) (forall ((B_x $$unsorted)) (=> (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a B_x V_a_2) V_r_2) (tptp.c_member T_a B_x (tptp.c_Wellfounded_Oacc T_a V_r_2)))))))
% 26.93/27.23 (assume a53 (forall ((V_a2_2 $$unsorted) (V_a1_2 $$unsorted) (V_Fa_2 $$unsorted) (V_R_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_Recdef_Owfrec__rel T_a T_b V_R_2 V_Fa_2 V_a1_2 (tptp.hAPP (tptp.hAPP V_Fa_2 V_a2_2) V_a1_2)) (exists ((B_g $$unsorted)) (and (= (tptp.hAPP (tptp.hAPP V_Fa_2 V_a2_2) V_a1_2) (tptp.hAPP (tptp.hAPP V_Fa_2 B_g) V_a1_2)) (forall ((B_z $$unsorted)) (=> (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a B_z V_a1_2) V_R_2) (tptp.c_Recdef_Owfrec__rel T_a T_b V_R_2 V_Fa_2 B_z (tptp.hAPP B_g B_z)))))))))
% 26.93/27.23 (assume a54 (forall ((V_z_2 $$unsorted) (V_y_2 $$unsorted) (V_x_2 $$unsorted) (V_r_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Relation_Osingle__valued T_a T_b V_r_2) (=> (tptp.c_member (tptp.tc_prod T_a T_b) (tptp.c_Product__Type_OPair T_a T_b V_x_2 V_y_2) V_r_2) (=> (tptp.c_member (tptp.tc_prod T_a T_b) (tptp.c_Product__Type_OPair T_a T_b V_x_2 V_z_2) V_r_2) (= V_y_2 V_z_2))))))
% 26.93/27.23 (assume a55 (forall ((V_r_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_Osingle__valued T_a T_b V_r_2) (forall ((B_x $$unsorted) (B_y $$unsorted)) (=> (tptp.c_member (tptp.tc_prod T_a T_b) (tptp.c_Product__Type_OPair T_a T_b B_x B_y) V_r_2) (forall ((B_z $$unsorted)) (=> (tptp.c_member (tptp.tc_prod T_a T_b) (tptp.c_Product__Type_OPair T_a T_b B_x B_z) V_r_2) (= B_y B_z))))))))
% 26.93/27.23 (assume a56 (forall ((V_f_2 $$unsorted) (T_b $$unsorted) (V_r_2 $$unsorted) (V_a_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_x_2 V_a_2) V_r_2) (= (tptp.hAPP (tptp.c_Recdef_Ocut T_a T_b V_f_2 V_r_2 V_a_2) V_x_2) (tptp.hAPP V_f_2 V_x_2)))))
% 26.93/27.23 (assume a57 (forall ((V_g_2 $$unsorted) (V_x_2 $$unsorted) (V_r_2 $$unsorted) (V_f_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (= (tptp.c_Recdef_Ocut T_a T_b V_f_2 V_r_2 V_x_2) (tptp.c_Recdef_Ocut T_a T_b V_g_2 V_r_2 V_x_2)) (forall ((B_y $$unsorted)) (=> (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a B_y V_x_2) V_r_2) (= (tptp.hAPP V_f_2 B_y) (tptp.hAPP V_g_2 B_y)))))))
% 26.93/27.23 (assume a58 (forall ((T_b $$unsorted) (V_a_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted) (B_f $$unsorted) (B_R $$unsorted)) (=> (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_x_2 V_a_2) B_R) (= (tptp.hAPP (tptp.c_Recdef_Ocut T_a T_b B_f B_R V_a_2) V_x_2) (tptp.hAPP B_f V_x_2)))))
% 26.93/27.23 (assume a59 (forall ((V_A_2 $$unsorted) (T_a $$unsorted)) (tptp.c_Relation_Osingle__valued T_a T_a (tptp.c_Relation_OId__on T_a V_A_2))))
% 26.93/27.23 (assume a60 (forall ((V_r_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (forall ((B_y $$unsorted)) (=> (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a B_y V_x_2) V_r_2) (tptp.c_member T_a B_y (tptp.c_Wellfounded_Oacc T_a V_r_2)))) (tptp.c_member T_a V_x_2 (tptp.c_Wellfounded_Oacc T_a V_r_2)))))
% 26.93/27.23 (assume a61 (forall ((V_R_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (not (tptp.c_member T_a V_x_2 (tptp.c_Wellfounded_Oacc T_a V_R_2))) (not (forall ((B_z $$unsorted)) (=> (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a B_z V_x_2) V_R_2) (tptp.c_member T_a B_z (tptp.c_Wellfounded_Oacc T_a V_R_2))))))))
% 26.93/27.23 (assume a62 (forall ((V_a2_2 $$unsorted) (V_a1_2 $$unsorted) (V_Fa_2 $$unsorted) (V_R_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_Recdef_Owfrec__rel T_a T_b V_R_2 V_Fa_2 V_a1_2 V_a2_2) (exists ((B_g $$unsorted)) (and (= V_a2_2 (tptp.hAPP (tptp.hAPP V_Fa_2 B_g) V_a1_2)) (forall ((B_z $$unsorted)) (=> (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a B_z V_a1_2) V_R_2) (tptp.c_Recdef_Owfrec__rel T_a T_b V_R_2 V_Fa_2 B_z (tptp.hAPP B_g B_z)))))))))
% 26.93/27.23 (assume a63 (forall ((V_g_2 $$unsorted) (V_Fa_2 $$unsorted) (T_b $$unsorted) (V_R_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (forall ((B_z $$unsorted)) (=> (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a B_z V_x_2) V_R_2) (tptp.c_Recdef_Owfrec__rel T_a T_b V_R_2 V_Fa_2 B_z (tptp.hAPP V_g_2 B_z)))) (tptp.c_Recdef_Owfrec__rel T_a T_b V_R_2 V_Fa_2 V_x_2 (tptp.hAPP (tptp.hAPP V_Fa_2 V_g_2) V_x_2)))))
% 26.93/27.23 (assume a64 (forall ((V_r_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (=> (forall ((B_x $$unsorted) (B_y $$unsorted)) (=> (tptp.c_member (tptp.tc_prod T_a T_b) (tptp.c_Product__Type_OPair T_a T_b B_x B_y) V_r_2) (forall ((B_z $$unsorted)) (=> (tptp.c_member (tptp.tc_prod T_a T_b) (tptp.c_Product__Type_OPair T_a T_b B_x B_z) V_r_2) (= B_y B_z))))) (tptp.c_Relation_Osingle__valued T_a T_b V_r_2))))
% 26.93/27.23 (assume a65 (forall ((V_b_2 $$unsorted) (V_r_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_member T_a V_a_2 (tptp.c_Wellfounded_Oacc T_a V_r_2)) (=> (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_b_2 V_a_2) (tptp.c_Transitive__Closure_Ortrancl T_a V_r_2)) (tptp.c_member T_a V_b_2 (tptp.c_Wellfounded_Oacc T_a V_r_2))))))
% 26.93/27.23 (assume a66 (forall ((V_r_2 $$unsorted) (V_a_2 $$unsorted) (V_b_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_b_2 V_a_2) (tptp.c_Transitive__Closure_Ortrancl T_a V_r_2)) (=> (tptp.c_member T_a V_a_2 (tptp.c_Wellfounded_Oacc T_a V_r_2)) (tptp.c_member T_a V_b_2 (tptp.c_Wellfounded_Oacc T_a V_r_2))))))
% 26.93/27.23 (assume a67 (forall ((V_x_2 $$unsorted) (V_Fa_2 $$unsorted) (V_R_2 $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (= (tptp.c_Nitpick_Owf__wfrec_H T_b T_a V_R_2 V_Fa_2 V_x_2) (tptp.hAPP (tptp.hAPP V_Fa_2 (tptp.c_Recdef_Ocut T_b T_a (tptp.c_Nitpick_Owf__wfrec T_b T_a V_R_2 V_Fa_2) V_R_2 V_x_2)) V_x_2))))
% 26.93/27.23 (assume a68 (forall ((V_a_2 $$unsorted) (T_a $$unsorted)) (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_a_2 V_a_2) (tptp.c_Relation_OId T_a))))
% 26.93/27.23 (assume a69 (forall ((T_a $$unsorted)) (tptp.c_Relation_Otrans T_a (tptp.c_Relation_OId T_a))))
% 26.93/27.23 (assume a70 (forall ((T_a $$unsorted)) (tptp.c_Relation_Osingle__valued T_a T_a (tptp.c_Relation_OId T_a))))
% 26.93/27.23 (assume a71 (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_a_2 V_b_2) (tptp.c_Relation_OId T_a)) (= V_a_2 V_b_2))))
% 26.93/27.23 (assume a72 (forall ((T_a $$unsorted)) (= (tptp.c_Relation_ODomain T_a T_a (tptp.c_Relation_OId T_a)) (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_HOL_Obool)))))
% 26.93/27.23 (assume a73 (forall ((T_a $$unsorted)) (= (tptp.c_Relation_ORange T_a T_a (tptp.c_Relation_OId T_a)) (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_HOL_Obool)))))
% 26.93/27.23 (assume a74 (forall ((T_a $$unsorted)) (tptp.c_Relation_Orefl__on T_a (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_HOL_Obool)) (tptp.c_Relation_OId T_a))))
% 26.93/27.23 (assume a75 (forall ((V_r_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_a_2 V_a_2) (tptp.c_Transitive__Closure_Ortrancl T_a V_r_2))))
% 26.93/27.23 (assume a76 (forall ((V_r_2 $$unsorted) (V_p_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_member (tptp.tc_prod T_a T_a) V_p_2 V_r_2) (tptp.c_member (tptp.tc_prod T_a T_a) V_p_2 (tptp.c_Transitive__Closure_Ortrancl T_a V_r_2)))))
% 26.93/27.23 (assume a77 (forall ((V_y_2 $$unsorted) (V_R_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (not (tptp.c_member T_a V_x_2 (tptp.c_Relation_ODomain T_a T_a V_R_2))) (= (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_x_2 V_y_2) (tptp.c_Transitive__Closure_Ortrancl T_a V_R_2)) (= V_x_2 V_y_2)))))
% 26.93/27.23 (assume a78 (forall ((V_z_2 $$unsorted) (V_y_2 $$unsorted) (V_x_2 $$unsorted) (V_r_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Relation_Osingle__valued T_a T_a V_r_2) (=> (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_x_2 V_y_2) (tptp.c_Transitive__Closure_Ortrancl T_a V_r_2)) (=> (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_x_2 V_z_2) (tptp.c_Transitive__Closure_Ortrancl T_a V_r_2)) (or (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_y_2 V_z_2) (tptp.c_Transitive__Closure_Ortrancl T_a V_r_2)) (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_z_2 V_y_2) (tptp.c_Transitive__Closure_Ortrancl T_a V_r_2))))))))
% 26.93/27.23 (assume a79 (forall ((V_r_2 $$unsorted) (T_a $$unsorted)) (tptp.c_Relation_Orefl__on T_a (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_HOL_Obool)) (tptp.c_Transitive__Closure_Ortrancl T_a V_r_2))))
% 26.93/27.23 (assume a80 (forall ((V_R_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_ORange T_a T_a (tptp.c_Transitive__Closure_Ortrancl T_a V_R_2)) (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_HOL_Obool)))))
% 26.93/27.23 (assume a81 (forall ((V_R_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_ODomain T_a T_a (tptp.c_Transitive__Closure_Ortrancl T_a V_R_2)) (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_HOL_Obool)))))
% 26.93/27.23 (assume a82 (forall ((V_c_2 $$unsorted) (V_r_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_a_2 V_b_2) (tptp.c_Transitive__Closure_Ortrancl T_a V_r_2)) (=> (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_b_2 V_c_2) (tptp.c_Transitive__Closure_Ortrancl T_a V_r_2)) (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_a_2 V_c_2) (tptp.c_Transitive__Closure_Ortrancl T_a V_r_2))))))
% 26.93/27.23 (assume a83 (forall ((V_c_2 $$unsorted) (V_r_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_a_2 V_b_2) (tptp.c_Transitive__Closure_Ortrancl T_a V_r_2)) (=> (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_b_2 V_c_2) V_r_2) (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_a_2 V_c_2) (tptp.c_Transitive__Closure_Ortrancl T_a V_r_2))))))
% 26.93/27.23 (assume a84 (forall ((V_r_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Transitive__Closure_Ortrancl T_a (tptp.c_Transitive__Closure_Ortrancl T_a V_r_2)) (tptp.c_Transitive__Closure_Ortrancl T_a V_r_2))))
% 26.93/27.23 (assume a85 (forall ((V_r_2 $$unsorted) (T_a $$unsorted)) (tptp.c_Relation_Otrans T_a (tptp.c_Transitive__Closure_Ortrancl T_a V_r_2))))
% 26.93/27.23 (assume a86 (forall ((V_c_2 $$unsorted) (V_r_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_a_2 V_b_2) V_r_2) (=> (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_b_2 V_c_2) (tptp.c_Transitive__Closure_Ortrancl T_a V_r_2)) (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_a_2 V_c_2) (tptp.c_Transitive__Closure_Ortrancl T_a V_r_2))))))
% 26.93/27.23 (assume a87 (forall ((V_p_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_member (tptp.tc_prod T_a T_a) V_p_2 (tptp.c_Relation_OId T_a)) (not (forall ((B_x $$unsorted)) (not (= V_p_2 (tptp.c_Product__Type_OPair T_a T_a B_x B_x))))))))
% 26.93/27.23 (assume a88 (forall ((V_P_2 $$unsorted) (V_r_2 $$unsorted) (V_by_2 $$unsorted) (V_bx_2 $$unsorted) (V_ay_2 $$unsorted) (V_ax_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (=> (tptp.c_member (tptp.tc_prod (tptp.tc_prod T_a T_b) (tptp.tc_prod T_a T_b)) (tptp.c_Product__Type_OPair (tptp.tc_prod T_a T_b) (tptp.tc_prod T_a T_b) (tptp.c_Product__Type_OPair T_a T_b V_ax_2 V_ay_2) (tptp.c_Product__Type_OPair T_a T_b V_bx_2 V_by_2)) (tptp.c_Transitive__Closure_Ortrancl (tptp.tc_prod T_a T_b) V_r_2)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_P_2 V_ax_2) V_ay_2)) (=> (forall ((B_a $$unsorted) (B_b $$unsorted)) (=> (tptp.c_member (tptp.tc_prod (tptp.tc_prod T_a T_b) (tptp.tc_prod T_a T_b)) (tptp.c_Product__Type_OPair (tptp.tc_prod T_a T_b) (tptp.tc_prod T_a T_b) (tptp.c_Product__Type_OPair T_a T_b V_ax_2 V_ay_2) (tptp.c_Product__Type_OPair T_a T_b B_a B_b)) (tptp.c_Transitive__Closure_Ortrancl (tptp.tc_prod T_a T_b) V_r_2)) (forall ((B_aa $$unsorted) (B_ba $$unsorted)) (=> (tptp.c_member (tptp.tc_prod (tptp.tc_prod T_a T_b) (tptp.tc_prod T_a T_b)) (tptp.c_Product__Type_OPair (tptp.tc_prod T_a T_b) (tptp.tc_prod T_a T_b) (tptp.c_Product__Type_OPair T_a T_b B_a B_b) (tptp.c_Product__Type_OPair T_a T_b B_aa B_ba)) V_r_2) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_P_2 B_a) B_b)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_P_2 B_aa) B_ba))))))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_P_2 V_bx_2) V_by_2)))))))
% 26.93/27.23 (assume a89 (forall ((V_P_2 $$unsorted) (V_r_2 $$unsorted) (V_by_2 $$unsorted) (V_bx_2 $$unsorted) (V_ay_2 $$unsorted) (V_ax_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (=> (tptp.c_member (tptp.tc_prod (tptp.tc_prod T_a T_b) (tptp.tc_prod T_a T_b)) (tptp.c_Product__Type_OPair (tptp.tc_prod T_a T_b) (tptp.tc_prod T_a T_b) (tptp.c_Product__Type_OPair T_a T_b V_ax_2 V_ay_2) (tptp.c_Product__Type_OPair T_a T_b V_bx_2 V_by_2)) (tptp.c_Transitive__Closure_Ortrancl (tptp.tc_prod T_a T_b) V_r_2)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_P_2 V_bx_2) V_by_2)) (=> (forall ((B_a $$unsorted) (B_b $$unsorted) (B_aa $$unsorted) (B_ba $$unsorted)) (=> (tptp.c_member (tptp.tc_prod (tptp.tc_prod T_a T_b) (tptp.tc_prod T_a T_b)) (tptp.c_Product__Type_OPair (tptp.tc_prod T_a T_b) (tptp.tc_prod T_a T_b) (tptp.c_Product__Type_OPair T_a T_b B_a B_b) (tptp.c_Product__Type_OPair T_a T_b B_aa B_ba)) V_r_2) (=> (tptp.c_member (tptp.tc_prod (tptp.tc_prod T_a T_b) (tptp.tc_prod T_a T_b)) (tptp.c_Product__Type_OPair (tptp.tc_prod T_a T_b) (tptp.tc_prod T_a T_b) (tptp.c_Product__Type_OPair T_a T_b B_aa B_ba) (tptp.c_Product__Type_OPair T_a T_b V_bx_2 V_by_2)) (tptp.c_Transitive__Closure_Ortrancl (tptp.tc_prod T_a T_b) V_r_2)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_P_2 B_aa) B_ba)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_P_2 B_a) B_b)))))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_P_2 V_ax_2) V_ay_2)))))))
% 26.93/27.23 (assume a90 (forall ((V_r_2 $$unsorted) (V_zb_2 $$unsorted) (V_za_2 $$unsorted) (V_xb_2 $$unsorted) (V_xa_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (=> (tptp.c_member (tptp.tc_prod (tptp.tc_prod T_a T_b) (tptp.tc_prod T_a T_b)) (tptp.c_Product__Type_OPair (tptp.tc_prod T_a T_b) (tptp.tc_prod T_a T_b) (tptp.c_Product__Type_OPair T_a T_b V_xa_2 V_xb_2) (tptp.c_Product__Type_OPair T_a T_b V_za_2 V_zb_2)) (tptp.c_Transitive__Closure_Ortrancl (tptp.tc_prod T_a T_b) V_r_2)) (=> (not (= (tptp.c_Product__Type_OPair T_a T_b V_xa_2 V_xb_2) (tptp.c_Product__Type_OPair T_a T_b V_za_2 V_zb_2))) (not (forall ((B_a $$unsorted) (B_b $$unsorted)) (=> (tptp.c_member (tptp.tc_prod (tptp.tc_prod T_a T_b) (tptp.tc_prod T_a T_b)) (tptp.c_Product__Type_OPair (tptp.tc_prod T_a T_b) (tptp.tc_prod T_a T_b) (tptp.c_Product__Type_OPair T_a T_b V_xa_2 V_xb_2) (tptp.c_Product__Type_OPair T_a T_b B_a B_b)) V_r_2) (not (tptp.c_member (tptp.tc_prod (tptp.tc_prod T_a T_b) (tptp.tc_prod T_a T_b)) (tptp.c_Product__Type_OPair (tptp.tc_prod T_a T_b) (tptp.tc_prod T_a T_b) (tptp.c_Product__Type_OPair T_a T_b B_a B_b) (tptp.c_Product__Type_OPair T_a T_b V_za_2 V_zb_2)) (tptp.c_Transitive__Closure_Ortrancl (tptp.tc_prod T_a T_b) V_r_2))))))))))
% 26.93/27.23 (assume a91 (forall ((V_P_2 $$unsorted) (V_r_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_a_2 V_b_2) (tptp.c_Transitive__Closure_Ortrancl T_a V_r_2)) (=> (tptp.hBOOL (tptp.hAPP V_P_2 V_a_2)) (=> (forall ((B_y $$unsorted)) (=> (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_a_2 B_y) (tptp.c_Transitive__Closure_Ortrancl T_a V_r_2)) (forall ((B_z $$unsorted)) (=> (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a B_y B_z) V_r_2) (=> (tptp.hBOOL (tptp.hAPP V_P_2 B_y)) (tptp.hBOOL (tptp.hAPP V_P_2 B_z))))))) (tptp.hBOOL (tptp.hAPP V_P_2 V_b_2)))))))
% 26.93/27.23 (assume a92 (forall ((V_P_2 $$unsorted) (V_r_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_a_2 V_b_2) (tptp.c_Transitive__Closure_Ortrancl T_a V_r_2)) (=> (tptp.hBOOL (tptp.hAPP V_P_2 V_b_2)) (=> (forall ((B_y $$unsorted) (B_z $$unsorted)) (=> (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a B_y B_z) V_r_2) (=> (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a B_z V_b_2) (tptp.c_Transitive__Closure_Ortrancl T_a V_r_2)) (=> (tptp.hBOOL (tptp.hAPP V_P_2 B_z)) (tptp.hBOOL (tptp.hAPP V_P_2 B_y)))))) (tptp.hBOOL (tptp.hAPP V_P_2 V_a_2)))))))
% 26.93/27.23 (assume a93 (forall ((V_r_2 $$unsorted) (V_z_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_x_2 V_z_2) (tptp.c_Transitive__Closure_Ortrancl T_a V_r_2)) (=> (not (= V_x_2 V_z_2)) (not (forall ((B_y $$unsorted)) (=> (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_x_2 B_y) V_r_2) (not (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a B_y V_z_2) (tptp.c_Transitive__Closure_Ortrancl T_a V_r_2))))))))))
% 26.93/27.23 (assume a94 (forall ((V_r_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_a_2 V_b_2) (tptp.c_Transitive__Closure_Ortrancl T_a V_r_2)) (=> (not (= V_a_2 V_b_2)) (not (forall ((B_y $$unsorted)) (=> (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_a_2 B_y) (tptp.c_Transitive__Closure_Ortrancl T_a V_r_2)) (not (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a B_y V_b_2) V_r_2)))))))))
% 26.93/27.23 (assume a95 (forall ((V_r_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_a_2 V_b_2) (tptp.c_Transitive__Closure_Otrancl T_a V_r_2)) (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_a_2 V_b_2) (tptp.c_Transitive__Closure_Ortrancl T_a V_r_2)))))
% 26.93/27.23 (assume a96 (forall ((V_r_2 $$unsorted) (T_a $$unsorted)) (tptp.c_Relation_Orefl__on T_a (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_HOL_Obool)) (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_HOL_Obool) V_r_2 (tptp.c_Relation_OId T_a)))))
% 26.93/27.23 (assume a97 (exists ((B_L $$unsorted)) (tptp.c_member (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_HOL_Obool) B_L tptp.c_Arrow__Order__Mirabelle_OLin)))
% 26.93/27.23 (assume a98 (forall ((V_b_H $$unsorted) (V_a_H $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (=> (= (tptp.c_Product__Type_OPair T_a T_b V_a V_b) (tptp.c_Product__Type_OPair T_a T_b V_a_H V_b_H)) (not (=> (= V_a V_a_H) (not (= V_b V_b_H)))))))
% 26.93/27.23 (assume a99 (forall ((V_b_H_2 $$unsorted) (V_a_H_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (= (tptp.c_Product__Type_OPair T_a T_b V_a_2 V_b_2) (tptp.c_Product__Type_OPair T_a T_b V_a_H_2 V_b_H_2)) (and (= V_a_2 V_a_H_2) (= V_b_2 V_b_H_2)))))
% 26.93/27.23 (assume a100 (forall ((T_b $$unsorted) (T_a $$unsorted) (V_P_2 $$unsorted)) (= (forall ((B_x1 $$unsorted)) (tptp.hBOOL (tptp.hAPP V_P_2 B_x1))) (forall ((B_a $$unsorted) (B_b $$unsorted)) (tptp.hBOOL (tptp.hAPP V_P_2 (tptp.c_Product__Type_OPair T_a T_b B_a B_b)))))))
% 26.93/27.23 (assume a101 (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (V_r_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Relation_Oantisym T_a V_r_2) (=> (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_a_2 V_b_2) V_r_2) (=> (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_b_2 V_a_2) V_r_2) (= V_a_2 V_b_2))))))
% 26.93/27.23 (assume a102 (forall ((V_r_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_Oantisym T_a V_r_2) (forall ((B_x $$unsorted) (B_y $$unsorted)) (=> (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a B_x B_y) V_r_2) (=> (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a B_y B_x) V_r_2) (= B_x B_y)))))))
% 26.93/27.23 (assume a103 (forall ((V_x_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2) V_x_2)) (=> (not (tptp.hBOOL (tptp.hAPP V_A_2 V_x_2))) (tptp.hBOOL (tptp.hAPP V_B_2 V_x_2))))))
% 26.93/27.23 (assume a104 (forall ((T_a $$unsorted) (V_A_2 $$unsorted) (V_x_2 $$unsorted) (V_B_2 $$unsorted)) (=> (=> (not (tptp.hBOOL (tptp.hAPP V_B_2 V_x_2))) (tptp.hBOOL (tptp.hAPP V_A_2 V_x_2))) (tptp.hBOOL (tptp.hAPP (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2) V_x_2)))))
% 26.93/27.23 (assume a105 (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_c_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_member T_a V_c_2 (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2)) (=> (not (tptp.c_member T_a V_c_2 V_A_2)) (tptp.c_member T_a V_c_2 V_B_2)))))
% 26.93/27.23 (assume a106 (forall ((V_A_2 $$unsorted) (V_B_2 $$unsorted) (V_c_2 $$unsorted) (T_a $$unsorted)) (=> (=> (not (tptp.c_member T_a V_c_2 V_B_2)) (tptp.c_member T_a V_c_2 V_A_2)) (tptp.c_member T_a V_c_2 (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2)))))
% 26.93/27.23 (assume a107 (forall ((V_r_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_a_2 V_b_2) V_r_2) (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_a_2 V_b_2) (tptp.c_Transitive__Closure_Otrancl T_a V_r_2)))))
% 26.93/27.23 (assume a108 (forall ((V_r_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_Oantisym T_a (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_HOL_Obool) V_r_2 (tptp.c_Relation_OId T_a))) (tptp.c_Relation_Oantisym T_a V_r_2))))
% 26.93/27.23 (assume a109 (forall ((V_A_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_A_2) V_A_2)))
% 26.93/27.23 (assume a110 (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2) (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_B_2 V_A_2))))
% 26.93/27.23 (assume a111 (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2)) (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2))))
% 26.93/27.23 (assume a112 (forall ((V_C_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_B_2 V_C_2)) (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_B_2 (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_C_2)))))
% 26.93/27.23 (assume a113 (forall ((V_C_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2) V_C_2) (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_B_2 V_C_2)))))
% 26.93/27.23 (assume a114 (forall ((V_P_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (= (exists ((B_x $$unsorted)) (and (tptp.c_member T_a B_x (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2)) (tptp.hBOOL (tptp.hAPP V_P_2 B_x)))) (or (exists ((B_x $$unsorted)) (and (tptp.c_member T_a B_x V_A_2) (tptp.hBOOL (tptp.hAPP V_P_2 B_x)))) (exists ((B_x $$unsorted)) (and (tptp.c_member T_a B_x V_B_2) (tptp.hBOOL (tptp.hAPP V_P_2 B_x))))))))
% 26.93/27.23 (assume a115 (forall ((V_P_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (= (forall ((B_x $$unsorted)) (=> (tptp.c_member T_a B_x (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2)) (tptp.hBOOL (tptp.hAPP V_P_2 B_x)))) (and (forall ((B_x $$unsorted)) (=> (tptp.c_member T_a B_x V_A_2) (tptp.hBOOL (tptp.hAPP V_P_2 B_x)))) (forall ((B_x $$unsorted)) (=> (tptp.c_member T_a B_x V_B_2) (tptp.hBOOL (tptp.hAPP V_P_2 B_x))))))))
% 26.93/27.23 (assume a116 (forall ((V_B_2 $$unsorted) (T_a $$unsorted) (V_x_2 $$unsorted) (V_A_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP V_A_2 V_x_2)) (tptp.hBOOL (tptp.hAPP (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2) V_x_2)))))
% 26.93/27.23 (assume a117 (forall ((V_A_2 $$unsorted) (T_a $$unsorted) (V_x_2 $$unsorted) (V_B_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP V_B_2 V_x_2)) (tptp.hBOOL (tptp.hAPP (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2) V_x_2)))))
% 26.93/27.23 (assume a118 (forall ((V_s_2 $$unsorted) (V_B_2 $$unsorted) (V_r_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Relation_Orefl__on T_a V_A_2 V_r_2) (=> (tptp.c_Relation_Orefl__on T_a V_B_2 V_s_2) (tptp.c_Relation_Orefl__on T_a (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2) (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_HOL_Obool) V_r_2 V_s_2))))))
% 26.93/27.23 (assume a119 (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (= (tptp.c_Relation_ORange T_b T_a (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun (tptp.tc_prod T_b T_a) tptp.tc_HOL_Obool) V_A_2 V_B_2)) (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_Relation_ORange T_b T_a V_A_2) (tptp.c_Relation_ORange T_b T_a V_B_2)))))
% 26.93/27.23 (assume a120 (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_ODomain T_a T_b (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun (tptp.tc_prod T_a T_b) tptp.tc_HOL_Obool) V_A_2 V_B_2)) (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_Relation_ODomain T_a T_b V_A_2) (tptp.c_Relation_ODomain T_a T_b V_B_2)))))
% 26.93/27.23 (assume a121 (forall ((V_r_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_HOL_Obool) (tptp.c_Transitive__Closure_Otrancl T_a V_r_2) (tptp.c_Relation_OId T_a)) (tptp.c_Transitive__Closure_Ortrancl T_a V_r_2))))
% 26.93/27.23 (assume a122 (forall ((V_r_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Transitive__Closure_Otrancl T_a (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_HOL_Obool) V_r_2 (tptp.c_Relation_OId T_a))) (tptp.c_Transitive__Closure_Ortrancl T_a V_r_2))))
% 26.93/27.23 (assume a123 (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_c_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_member T_a V_c_2 (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2)) (or (tptp.c_member T_a V_c_2 V_A_2) (tptp.c_member T_a V_c_2 V_B_2)))))
% 26.93/27.23 (assume a124 (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_c_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_member T_a V_c_2 V_A_2) (tptp.c_member T_a V_c_2 (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2)))))
% 26.93/27.23 (assume a125 (forall ((V_A_2 $$unsorted) (V_B_2 $$unsorted) (V_c_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_member T_a V_c_2 V_B_2) (tptp.c_member T_a V_c_2 (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2)))))
% 26.93/27.23 (assume a126 (forall ((V_r_2 $$unsorted) (V_p_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_member (tptp.tc_prod T_a T_a) V_p_2 V_r_2) (tptp.c_member (tptp.tc_prod T_a T_a) V_p_2 (tptp.c_Transitive__Closure_Otrancl T_a V_r_2)))))
% 26.93/27.23 (assume a127 (forall ((V_B_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_HOL_Obool)) V_B_2) (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_HOL_Obool)))))
% 26.93/27.23 (assume a128 (forall ((V_A_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_HOL_Obool)))))
% 26.93/27.23 (assume a129 (forall ((V_R_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Transitive__Closure_Otrancl T_a (tptp.c_Transitive__Closure_Ortrancl T_a V_R_2)) (tptp.c_Transitive__Closure_Ortrancl T_a V_R_2))))
% 26.93/27.23 (assume a130 (forall ((V_R_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Transitive__Closure_Ortrancl T_a (tptp.c_Transitive__Closure_Otrancl T_a V_R_2)) (tptp.c_Transitive__Closure_Ortrancl T_a V_R_2))))
% 26.93/27.23 (assume a131 (forall ((V_S_2 $$unsorted) (V_R_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Transitive__Closure_Ortrancl T_a (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_HOL_Obool) (tptp.c_Transitive__Closure_Ortrancl T_a V_R_2) (tptp.c_Transitive__Closure_Ortrancl T_a V_S_2))) (tptp.c_Transitive__Closure_Ortrancl T_a (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_HOL_Obool) V_R_2 V_S_2)))))
% 26.93/27.23 (assume a132 (forall ((V_r_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_ODomain T_a T_a (tptp.c_Transitive__Closure_Otrancl T_a V_r_2)) (tptp.c_Relation_ODomain T_a T_a V_r_2))))
% 26.93/27.23 (assume a133 (forall ((V_r_2 $$unsorted) (T_a $$unsorted)) (tptp.c_Relation_Otrans T_a (tptp.c_Transitive__Closure_Otrancl T_a V_r_2))))
% 26.93/27.23 (assume a134 (forall ((V_r_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Relation_Otrans T_a V_r_2) (= (tptp.c_Transitive__Closure_Otrancl T_a V_r_2) V_r_2))))
% 26.93/27.23 (assume a135 (forall ((V_r_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_ORange T_a T_a (tptp.c_Transitive__Closure_Otrancl T_a V_r_2)) (tptp.c_Relation_ORange T_a T_a V_r_2))))
% 26.93/27.23 (assume a136 (forall ((V_c_2 $$unsorted) (V_R_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_a_2 V_b_2) V_R_2) (=> (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_b_2 V_c_2) V_R_2) (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_a_2 V_c_2) (tptp.c_Transitive__Closure_Otrancl T_a V_R_2))))))
% 26.93/27.23 (assume a137 (forall ((V_c_2 $$unsorted) (V_r_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_a_2 V_b_2) V_r_2) (=> (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_b_2 V_c_2) (tptp.c_Transitive__Closure_Otrancl T_a V_r_2)) (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_a_2 V_c_2) (tptp.c_Transitive__Closure_Otrancl T_a V_r_2))))))
% 26.93/27.23 (assume a138 (forall ((V_c_2 $$unsorted) (V_r_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_a_2 V_b_2) (tptp.c_Transitive__Closure_Otrancl T_a V_r_2)) (=> (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_b_2 V_c_2) V_r_2) (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_a_2 V_c_2) (tptp.c_Transitive__Closure_Otrancl T_a V_r_2))))))
% 26.93/27.23 (assume a139 (forall ((V_c_2 $$unsorted) (V_r_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_a_2 V_b_2) (tptp.c_Transitive__Closure_Otrancl T_a V_r_2)) (=> (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_b_2 V_c_2) (tptp.c_Transitive__Closure_Otrancl T_a V_r_2)) (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_a_2 V_c_2) (tptp.c_Transitive__Closure_Otrancl T_a V_r_2))))))
% 26.93/27.23 (assume a140 (forall ((T_a $$unsorted)) (tptp.c_Relation_Oantisym T_a (tptp.c_Relation_OId T_a))))
% 26.93/27.23 (assume a141 (forall ((V_S_2 $$unsorted) (V_R_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (or (tptp.c_member (tptp.tc_prod T_a T_a) V_x_2 (tptp.c_Transitive__Closure_Ortrancl T_a V_R_2)) (tptp.c_member (tptp.tc_prod T_a T_a) V_x_2 (tptp.c_Transitive__Closure_Ortrancl T_a V_S_2))) (tptp.c_member (tptp.tc_prod T_a T_a) V_x_2 (tptp.c_Transitive__Closure_Ortrancl T_a (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_HOL_Obool) V_R_2 V_S_2))))))
% 26.93/27.23 (assume a142 (forall ((V_A_2 $$unsorted) (T_a $$unsorted)) (tptp.c_Relation_Oantisym T_a (tptp.c_Relation_OId__on T_a V_A_2))))
% 26.93/27.23 (assume a143 (forall ((V_R_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_HOL_Obool) (tptp.c_Transitive__Closure_Ortrancl T_a V_R_2) (tptp.c_Relation_OId T_a)) (tptp.c_Transitive__Closure_Ortrancl T_a V_R_2))))
% 26.93/27.23 (assume a144 (forall ((V_R_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Transitive__Closure_Ortrancl T_a (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_HOL_Obool) V_R_2 (tptp.c_Relation_OId T_a))) (tptp.c_Transitive__Closure_Ortrancl T_a V_R_2))))
% 26.93/27.23 (assume a145 (forall ((V_r_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Relation_Otrans T_a V_r_2) (tptp.c_Relation_Otrans T_a (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_HOL_Obool) V_r_2 (tptp.c_Relation_OId T_a))))))
% 26.93/27.23 (assume a146 (forall ((V_R_2 $$unsorted) (V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_x_2 V_y_2) (tptp.c_Transitive__Closure_Ortrancl T_a V_R_2)) (or (= V_x_2 V_y_2) (and (not (= V_x_2 V_y_2)) (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_x_2 V_y_2) (tptp.c_Transitive__Closure_Otrancl T_a V_R_2)))))))
% 26.93/27.23 (assume a147 (forall ((V_c_2 $$unsorted) (V_r_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_a_2 V_b_2) V_r_2) (=> (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_b_2 V_c_2) (tptp.c_Transitive__Closure_Ortrancl T_a V_r_2)) (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_a_2 V_c_2) (tptp.c_Transitive__Closure_Otrancl T_a V_r_2))))))
% 26.93/27.23 (assume a148 (forall ((V_R_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_a_2 V_b_2) (tptp.c_Transitive__Closure_Ortrancl T_a V_R_2)) (or (= V_a_2 V_b_2) (and (not (= V_a_2 V_b_2)) (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_a_2 V_b_2) (tptp.c_Transitive__Closure_Otrancl T_a V_R_2)))))))
% 26.93/27.23 (assume a149 (forall ((V_c_2 $$unsorted) (V_r_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_a_2 V_b_2) (tptp.c_Transitive__Closure_Ortrancl T_a V_r_2)) (=> (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_b_2 V_c_2) V_r_2) (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_a_2 V_c_2) (tptp.c_Transitive__Closure_Otrancl T_a V_r_2))))))
% 26.93/27.23 (assume a150 (forall ((V_c_2 $$unsorted) (V_r_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_a_2 V_b_2) (tptp.c_Transitive__Closure_Otrancl T_a V_r_2)) (=> (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_b_2 V_c_2) (tptp.c_Transitive__Closure_Ortrancl T_a V_r_2)) (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_a_2 V_c_2) (tptp.c_Transitive__Closure_Otrancl T_a V_r_2))))))
% 26.93/27.23 (assume a151 (forall ((V_z_2 $$unsorted) (V_r_2 $$unsorted) (V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_x_2 V_y_2) (tptp.c_Transitive__Closure_Ortrancl T_a V_r_2)) (=> (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_y_2 V_z_2) (tptp.c_Transitive__Closure_Otrancl T_a V_r_2)) (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_x_2 V_z_2) (tptp.c_Transitive__Closure_Otrancl T_a V_r_2))))))
% 26.93/27.23 (assume a152 (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (V_f1_2 $$unsorted) (T_a $$unsorted) (T_c $$unsorted) (T_b $$unsorted)) (= (tptp.c_Product__Type_Oprod_Oprod__rec T_b T_c T_a V_f1_2 (tptp.c_Product__Type_OPair T_b T_c V_a_2 V_b_2)) (tptp.hAPP (tptp.hAPP V_f1_2 V_a_2) V_b_2))))
% 26.93/27.23 (assume a153 (forall ((V_x_2 $$unsorted) (V_g_2 $$unsorted) (V_f_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Olattice T_a) (= (tptp.hAPP (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_b T_a) V_f_2 V_g_2) V_x_2) (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a (tptp.hAPP V_f_2 V_x_2) (tptp.hAPP V_g_2 V_x_2))))))
% 26.93/27.23 (assume a154 (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Obounded__lattice__top T_a) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_x (tptp.c_Orderings_Otop__class_Otop T_a)) (tptp.c_Orderings_Otop__class_Otop T_a)))))
% 26.93/27.23 (assume a155 (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Obounded__lattice__top T_a) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a (tptp.c_Orderings_Otop__class_Otop T_a) V_x) (tptp.c_Orderings_Otop__class_Otop T_a)))))
% 26.93/27.23 (assume a156 (forall ((V_r_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Order__Relation_Opartial__order__on T_a V_A_2 V_r_2) (and (tptp.c_Order__Relation_Opreorder__on T_a V_A_2 V_r_2) (tptp.c_Relation_Oantisym T_a V_r_2)))))
% 26.93/27.23 (assume a157 (forall ((V_Q_2 $$unsorted) (V_P_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_a_2 V_b_2) (tptp.c_Transitive__Closure_Ortrancl T_a (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_HOL_Obool) V_P_2 V_Q_2))) (=> (forall ((B_x $$unsorted)) (=> (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a B_x V_b_2) (tptp.c_Transitive__Closure_Ortrancl T_a V_P_2)) (forall ((B_y $$unsorted)) (=> (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a B_y B_x) V_Q_2) (= B_y B_x))))) (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_a_2 V_b_2) (tptp.c_Transitive__Closure_Ortrancl T_a V_P_2))))))
% 26.93/27.23 (assume a158 (forall ((V_Q_2 $$unsorted) (V_P_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_a_2 V_b_2) (tptp.c_Transitive__Closure_Ortrancl T_a (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_HOL_Obool) V_P_2 V_Q_2))) (=> (forall ((B_x $$unsorted)) (=> (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_a_2 B_x) (tptp.c_Transitive__Closure_Ortrancl T_a V_P_2)) (forall ((B_y $$unsorted)) (=> (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a B_x B_y) V_Q_2) (= B_x B_y))))) (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_a_2 V_b_2) (tptp.c_Transitive__Closure_Ortrancl T_a V_P_2))))))
% 26.93/27.23 (assume a159 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__sup T_a) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_a V_a) V_a))))
% 26.93/27.23 (assume a160 (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__sup T_a) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_x V_x) V_x))))
% 26.93/27.23 (assume a161 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__sup T_a) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_a V_b) (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_b V_a)))))
% 26.93/27.23 (assume a162 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Olattice T_a) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_x V_y) (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_y V_x)))))
% 26.93/27.23 (assume a163 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__sup T_a) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_x V_y) (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_y V_x)))))
% 26.93/27.23 (assume a164 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__sup T_a) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_a (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_a V_b)) (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_a V_b)))))
% 26.93/27.23 (assume a165 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Olattice T_a) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_x (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_x V_y)) (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_x V_y)))))
% 26.93/27.23 (assume a166 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__sup T_a) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_x (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_x V_y)) (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_x V_y)))))
% 26.93/27.23 (assume a167 (forall ((V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__sup T_a) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_b (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_a V_c)) (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_a (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_b V_c))))))
% 26.93/27.23 (assume a168 (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Olattice T_a) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_x (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_y V_z)) (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_y (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_x V_z))))))
% 26.93/27.23 (assume a169 (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__sup T_a) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_x (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_y V_z)) (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_y (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_x V_z))))))
% 26.93/27.23 (assume a170 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__sup T_a) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_a V_b) V_c) (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_a (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_b V_c))))))
% 26.93/27.23 (assume a171 (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Olattice T_a) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_x V_y) V_z) (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_x (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_y V_z))))))
% 26.93/27.23 (assume a172 (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__sup T_a) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_x V_y) V_z) (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_x (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_y V_z))))))
% 26.93/27.23 (assume a173 (forall ((V_r_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Order__Relation_Olinear__order__on T_a V_A_2 V_r_2) (and (tptp.c_Order__Relation_Opartial__order__on T_a V_A_2 V_r_2) (tptp.c_Relation_Ototal__on T_a V_A_2 V_r_2)))))
% 26.93/27.23 (assume a174 (forall ((V_R_2 $$unsorted) (V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_x_2 V_y_2) (tptp.c_Transitive__Closure_Otrancl T_a V_R_2)) (exists ((B_z $$unsorted)) (and (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_x_2 B_z) V_R_2) (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a B_z V_y_2) (tptp.c_Transitive__Closure_Ortrancl T_a V_R_2)))))))
% 26.93/27.23 (assume a175 (forall ((V_R_2 $$unsorted) (V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_x_2 V_y_2) (tptp.c_Transitive__Closure_Otrancl T_a V_R_2)) (exists ((B_z $$unsorted)) (and (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_x_2 B_z) (tptp.c_Transitive__Closure_Ortrancl T_a V_R_2)) (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a B_z V_y_2) V_R_2))))))
% 26.93/27.23 (assume a176 (forall ((V_r_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Wellfounded_Oacyclic T_a V_r_2) (forall ((B_x $$unsorted)) (not (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a B_x B_x) (tptp.c_Transitive__Closure_Otrancl T_a V_r_2)))))))
% 26.93/27.23 (assume a177 (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (V_c_2 $$unsorted) (T_a $$unsorted) (T_c $$unsorted) (T_b $$unsorted)) (= (tptp.c_Product__Type_Ointernal__split T_b T_c T_a V_c_2 (tptp.c_Product__Type_OPair T_b T_c V_a_2 V_b_2)) (tptp.hAPP (tptp.hAPP V_c_2 V_a_2) V_b_2))))
% 26.93/27.23 (assume a178 (forall ((V_r_2 $$unsorted) (T_a $$unsorted)) (=> (forall ((B_x $$unsorted) (B_y $$unsorted)) (=> (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a B_x B_y) V_r_2) (=> (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a B_y B_x) V_r_2) (= B_x B_y)))) (tptp.c_Relation_Oantisym T_a V_r_2))))
% 26.93/27.23 (assume a179 (forall ((V_r_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Wellfounded_Oacyclic T_a V_r_2) (tptp.c_Relation_Oantisym T_a (tptp.c_Transitive__Closure_Ortrancl T_a V_r_2)))))
% 26.93/27.23 (assume a180 (forall ((V_r_2 $$unsorted) (T_a $$unsorted)) (=> (forall ((B_x $$unsorted)) (not (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a B_x B_x) (tptp.c_Transitive__Closure_Otrancl T_a V_r_2)))) (tptp.c_Wellfounded_Oacyclic T_a V_r_2))))
% 26.93/27.23 (assume a181 (forall ((V_r_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Order__Relation_Olinear__order__on T_a V_A_2 V_r_2) (tptp.c_Order__Relation_Ostrict__linear__order__on T_a V_A_2 (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_HOL_Obool) V_r_2 (tptp.c_Relation_OId T_a))))))
% 26.93/27.23 (assume a182 (forall ((V_r_2 $$unsorted) (V_x_2 $$unsorted) (V_y_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Wellfounded_Oacyclic T_a (tptp.c_Set_Oinsert (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_y_2 V_x_2) V_r_2)) (and (tptp.c_Wellfounded_Oacyclic T_a V_r_2) (not (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_x_2 V_y_2) (tptp.c_Transitive__Closure_Ortrancl T_a V_r_2)))))))
% 26.93/27.23 (assume a183 (forall ((V_r_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_OField T_a V_r_2) (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_Relation_ODomain T_a T_a V_r_2) (tptp.c_Relation_ORange T_a T_a V_r_2)))))
% 26.93/27.23 (assume a184 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (V_r_2 $$unsorted) (T_a $$unsorted)) (=> (forall ((B_x $$unsorted)) (not (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a B_x B_x) (tptp.c_Transitive__Closure_Otrancl T_a V_r_2)))) (=> (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_x_2 V_y_2) V_r_2) (not (= V_x_2 V_y_2))))))
% 26.93/27.23 (assume a185 (forall ((V_b_2 $$unsorted) (V_B_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (=> (not (tptp.c_member T_a V_a_2 V_B_2)) (= V_a_2 V_b_2)) (tptp.c_member T_a V_a_2 (tptp.c_Set_Oinsert T_a V_b_2 V_B_2)))))
% 26.93/27.23 (assume a186 (forall ((V_A_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_member T_a V_a_2 (tptp.c_Set_Oinsert T_a V_b_2 V_A_2)) (=> (not (= V_a_2 V_b_2)) (tptp.c_member T_a V_a_2 V_A_2)))))
% 26.93/27.23 (assume a187 (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_c_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_member T_a V_c_2 (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2)) (not (=> (tptp.c_member T_a V_c_2 V_A_2) (tptp.c_member T_a V_c_2 V_B_2))))))
% 26.93/27.23 (assume a188 (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_c_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_member T_a V_c_2 V_A_2) (=> (not (tptp.c_member T_a V_c_2 V_B_2)) (tptp.c_member T_a V_c_2 (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2))))))
% 26.93/27.23 (assume a189 (forall ((V_r_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_ODomain T_a T_b (tptp.c_Set_Oinsert (tptp.tc_prod T_a T_b) (tptp.c_Product__Type_OPair T_a T_b V_a_2 V_b_2) V_r_2)) (tptp.c_Set_Oinsert T_a V_a_2 (tptp.c_Relation_ODomain T_a T_b V_r_2)))))
% 26.93/27.23 (assume a190 (forall ((V_r_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (= (tptp.c_Relation_ORange T_b T_a (tptp.c_Set_Oinsert (tptp.tc_prod T_b T_a) (tptp.c_Product__Type_OPair T_b T_a V_a_2 V_b_2) V_r_2)) (tptp.c_Set_Oinsert T_a V_b_2 (tptp.c_Relation_ORange T_b T_a V_r_2)))))
% 26.93/27.23 (assume a191 (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_c_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_member T_a V_c_2 (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2)) (and (tptp.c_member T_a V_c_2 V_A_2) (not (tptp.c_member T_a V_c_2 V_B_2))))))
% 26.93/27.23 (assume a192 (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_c_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_member T_a V_c_2 (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2)) (tptp.c_member T_a V_c_2 V_A_2))))
% 26.93/27.23 (assume a193 (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_c_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_member T_a V_c_2 (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2)) (not (tptp.c_member T_a V_c_2 V_B_2)))))
% 26.93/27.23 (assume a194 (forall ((V_B_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (tptp.c_member T_a V_a_2 (tptp.c_Set_Oinsert T_a V_a_2 V_B_2))))
% 26.93/27.23 (assume a195 (forall ((V_A_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_member T_a V_a_2 (tptp.c_Set_Oinsert T_a V_b_2 V_A_2)) (or (= V_a_2 V_b_2) (tptp.c_member T_a V_a_2 V_A_2)))))
% 26.93/27.23 (assume a196 (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (not (tptp.c_member T_a V_x_2 V_A_2)) (=> (not (tptp.c_member T_a V_x_2 V_B_2)) (= (= (tptp.c_Set_Oinsert T_a V_x_2 V_A_2) (tptp.c_Set_Oinsert T_a V_x_2 V_B_2)) (= V_A_2 V_B_2))))))
% 26.93/27.23 (assume a197 (forall ((V_b_2 $$unsorted) (V_B_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_member T_a V_a_2 V_B_2) (tptp.c_member T_a V_a_2 (tptp.c_Set_Oinsert T_a V_b_2 V_B_2)))))
% 26.93/27.23 (assume a198 (forall ((V_A_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_member T_a V_a_2 V_A_2) (= (tptp.c_Set_Oinsert T_a V_a_2 V_A_2) V_A_2))))
% 26.93/27.23 (assume a199 (forall ((V_A_2 $$unsorted) (V_B_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_member T_a V_x_2 V_B_2) (= (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_Set_Oinsert T_a V_x_2 V_A_2) V_B_2) (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2)))))
% 26.93/27.23 (assume a200 (forall ((V_A_2 $$unsorted) (V_B_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (and (=> (tptp.c_member T_a V_x_2 V_B_2) (= (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_Set_Oinsert T_a V_x_2 V_A_2) V_B_2) (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2))) (=> (not (tptp.c_member T_a V_x_2 V_B_2)) (= (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_Set_Oinsert T_a V_x_2 V_A_2) V_B_2) (tptp.c_Set_Oinsert T_a V_x_2 (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2)))))))
% 26.93/27.23 (assume a201 (forall ((V_x_2 $$unsorted) (V_A_2 $$unsorted) (V_y_2 $$unsorted) (T_a $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Set_Oinsert T_a V_y_2 V_A_2) V_x_2)) (or (= V_y_2 V_x_2) (tptp.hBOOL (tptp.hAPP V_A_2 V_x_2))))))
% 26.93/27.23 (assume a202 (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2) V_B_2) (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2))))
% 26.93/27.23 (assume a203 (forall ((V_A_2 $$unsorted) (V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Set_Oinsert T_a V_x_2 (tptp.c_Set_Oinsert T_a V_y_2 V_A_2)) (tptp.c_Set_Oinsert T_a V_y_2 (tptp.c_Set_Oinsert T_a V_x_2 V_A_2)))))
% 26.93/27.23 (assume a204 (forall ((V_A_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Set_Oinsert T_a V_x_2 (tptp.c_Set_Oinsert T_a V_x_2 V_A_2)) (tptp.c_Set_Oinsert T_a V_x_2 V_A_2))))
% 26.93/27.23 (assume a205 (forall ((V_x_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ominus T_a) (= (tptp.hAPP (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_fun T_b T_a) V_A_2 V_B_2) V_x_2) (tptp.c_Groups_Ominus__class_Ominus T_a (tptp.hAPP V_A_2 V_x_2) (tptp.hAPP V_B_2 V_x_2))))))
% 26.93/27.23 (assume a206 (forall ((V_C_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2) V_C_2) (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_C_2) (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_B_2 V_C_2)))))
% 26.93/27.23 (assume a207 (forall ((V_A_2 $$unsorted) (V_B_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_B_2 V_A_2) V_A_2) (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_B_2 V_A_2))))
% 26.93/27.23 (assume a208 (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_B_2 V_A_2)) (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2))))
% 26.93/27.23 (assume a209 (forall ((V_C_2 $$unsorted) (V_B_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_Set_Oinsert T_a V_a_2 V_B_2) V_C_2) (tptp.c_Set_Oinsert T_a V_a_2 (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_B_2 V_C_2)))))
% 26.93/27.23 (assume a210 (forall ((V_B_2 $$unsorted) (V_a_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 (tptp.c_Set_Oinsert T_a V_a_2 V_B_2)) (tptp.c_Set_Oinsert T_a V_a_2 (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2)))))
% 26.93/27.23 (assume a211 (forall ((V_r_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Transitive__Closure_Ortrancl T_a (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_HOL_Obool) V_r_2 (tptp.c_Relation_OId T_a))) (tptp.c_Transitive__Closure_Ortrancl T_a V_r_2))))
% 26.93/27.23 (assume a212 (forall ((V_r_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_Ototal__on T_a V_A_2 (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_HOL_Obool) V_r_2 (tptp.c_Relation_OId T_a))) (tptp.c_Relation_Ototal__on T_a V_A_2 V_r_2))))
% 26.93/27.23 (assume a213 (forall ((V_s_2 $$unsorted) (V_r_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_OField T_a (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_HOL_Obool) V_r_2 V_s_2)) (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_Relation_OField T_a V_r_2) (tptp.c_Relation_OField T_a V_s_2)))))
% 26.93/27.23 (assume a214 (forall ((V_r_2 $$unsorted) (T_a $$unsorted)) (tptp.c_Relation_Oirrefl T_a (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_HOL_Obool) V_r_2 (tptp.c_Relation_OId T_a)))))
% 26.93/27.23 (assume a215 (forall ((V_r_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Relation_Otrans T_a V_r_2) (=> (tptp.c_Relation_Oantisym T_a V_r_2) (tptp.c_Relation_Otrans T_a (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_HOL_Obool) V_r_2 (tptp.c_Relation_OId T_a)))))))
% 26.93/27.23 (assume a216 (forall ((V_r_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_OField T_a (tptp.c_Set_Oinsert (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_a_2 V_b_2) V_r_2)) (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_Set_Oinsert T_a V_a_2 (tptp.c_Set_Oinsert T_a V_b_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)))) (tptp.c_Relation_OField T_a V_r_2)))))
% 26.93/27.23 (assume a217 (forall ((V_r_2 $$unsorted) (V_x_2 $$unsorted) (V_y_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Wellfounded_Owf T_a (tptp.c_Set_Oinsert (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_y_2 V_x_2) V_r_2)) (and (tptp.c_Wellfounded_Owf T_a V_r_2) (not (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_x_2 V_y_2) (tptp.c_Transitive__Closure_Ortrancl T_a V_r_2)))))))
% 26.93/27.23 (assume a218 (forall ((V_r_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_a_2 V_b_2) (tptp.c_Transitive__Closure_Otrancl T_a V_r_2)) (=> (not (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_a_2 V_b_2) V_r_2)) (not (forall ((B_c $$unsorted)) (=> (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_a_2 B_c) (tptp.c_Transitive__Closure_Otrancl T_a V_r_2)) (not (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a B_c V_b_2) V_r_2)))))))))
% 26.93/27.23 (assume a219 (forall ((V_r_2 $$unsorted) (V_z_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_x_2 V_z_2) (tptp.c_Transitive__Closure_Otrancl T_a V_r_2)) (=> (not (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_x_2 V_z_2) V_r_2)) (not (forall ((B_y $$unsorted)) (=> (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_x_2 B_y) V_r_2) (not (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a B_y V_z_2) (tptp.c_Transitive__Closure_Otrancl T_a V_r_2))))))))))
% 26.93/27.23 (assume a220 (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_Relation_ORange T_b T_a V_A_2) (tptp.c_Relation_ORange T_b T_a V_B_2)) (tptp.c_Relation_ORange T_b T_a (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_fun (tptp.tc_prod T_b T_a) tptp.tc_HOL_Obool) V_A_2 V_B_2)))))
% 26.93/27.23 (assume a221 (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Opreorder T_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x V_x))))
% 26.93/27.23 (assume a222 (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_B_2 V_A_2) (= V_A_2 V_B_2)))))
% 26.93/27.23 (assume a223 (forall ((T_a $$unsorted)) (tptp.c_Wellfounded_Owf T_a (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_HOL_Obool)))))
% 26.93/27.23 (assume a224 (forall ((V_a_2 $$unsorted) (T_a $$unsorted)) (not (tptp.c_member T_a V_a_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool))))))
% 26.93/27.23 (assume a225 (forall ((V_c_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2) (=> (tptp.c_member T_a V_c_2 V_A_2) (tptp.c_member T_a V_c_2 V_B_2)))))
% 26.93/27.23 (assume a226 (forall ((V_A_2 $$unsorted) (T_a $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)) V_A_2)))
% 26.93/27.23 (assume a227 (forall ((V_f_2 $$unsorted) (T_b $$unsorted) (V_r_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Wellfounded_Owf T_a V_r_2) (tptp.c_Wellfounded_Owf T_b (tptp.c_Relation_Oinv__image T_a T_b V_r_2 V_f_2)))))
% 26.93/27.23 (assume a228 (forall ((V_rb_2 $$unsorted) (T_b $$unsorted) (V_ra_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Wellfounded_Owf T_a V_ra_2) (=> (tptp.c_Wellfounded_Owf T_b V_rb_2) (tptp.c_Wellfounded_Owf (tptp.tc_prod T_a T_b) (tptp.c_Wellfounded_Olex__prod T_a T_b V_ra_2 V_rb_2))))))
% 26.93/27.23 (assume a229 (forall ((V_x_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 (tptp.c_Set_Oinsert T_a V_x_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)))) (or (= V_A_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (= V_A_2 (tptp.c_Set_Oinsert T_a V_x_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool))))))))
% 26.93/27.23 (assume a230 (forall ((V_s_2 $$unsorted) (V_r_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_HOL_Obool) V_r_2 V_s_2) (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_Relation_OField T_a V_r_2) (tptp.c_Relation_OField T_a V_s_2)))))
% 26.93/27.23 (assume a231 (forall ((T_a $$unsorted)) (= (tptp.c_Relation_OField T_a (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_HOL_Obool))) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)))))
% 26.93/27.23 (assume a232 (forall ((V_x_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2) (=> (tptp.c_member T_a V_x_2 V_A_2) (tptp.c_member T_a V_x_2 V_B_2)))))
% 26.93/27.23 (assume a233 (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_member T_a V_x_2 V_A_2) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2) (tptp.c_member T_a V_x_2 V_B_2)))))
% 26.93/27.23 (assume a234 (forall ((V_x_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2) (=> (tptp.c_member T_a V_x_2 V_A_2) (tptp.c_member T_a V_x_2 V_B_2)))))
% 26.93/27.23 (assume a235 (forall ((T_a $$unsorted)) (tptp.c_Order__Relation_Opartial__order__on T_a (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_HOL_Obool)))))
% 26.93/27.23 (assume a236 (forall ((T_a $$unsorted)) (tptp.c_Order__Relation_Opreorder__on T_a (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_HOL_Obool)))))
% 26.93/27.23 (assume a237 (forall ((V_R2_2 $$unsorted) (V_R1_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_HOL_Obool) V_R1_2 V_R2_2) (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_Wellfounded_Oacc T_a V_R2_2) (tptp.c_Wellfounded_Oacc T_a V_R1_2)))))
% 26.93/27.23 (assume a238 (forall ((V_r_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (= (tptp.c_Relation_ODomain T_a T_b V_r_2) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (= V_r_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun (tptp.tc_prod T_a T_b) tptp.tc_HOL_Obool))))))
% 26.93/27.23 (assume a239 (forall ((T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_ODomain T_a T_b (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun (tptp.tc_prod T_a T_b) tptp.tc_HOL_Obool))) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)))))
% 26.93/27.23 (assume a240 (forall ((V_r_2 $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (= (= (tptp.c_Relation_ORange T_b T_a V_r_2) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (= V_r_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun (tptp.tc_prod T_b T_a) tptp.tc_HOL_Obool))))))
% 26.93/27.23 (assume a241 (forall ((T_a $$unsorted) (T_b $$unsorted)) (= (tptp.c_Relation_ORange T_b T_a (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun (tptp.tc_prod T_b T_a) tptp.tc_HOL_Obool))) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)))))
% 26.93/27.23 (assume a242 (forall ((T_a $$unsorted)) (tptp.c_Relation_Orefl__on T_a (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_HOL_Obool)))))
% 26.93/27.23 (assume a243 (forall ((V_p_2 $$unsorted) (V_r_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Wellfounded_Owf T_a V_r_2) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_HOL_Obool) V_p_2 V_r_2) (tptp.c_Wellfounded_Owf T_a V_p_2)))))
% 26.93/27.23 (assume a244 (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Obot T_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Orderings_Obot__class_Obot T_a) V_x))))
% 26.93/27.23 (assume a245 (forall ((V_A_2 $$unsorted) (T_a $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_A_2)))
% 26.93/27.23 (assume a246 (forall ((V_x_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Obot T_a) (= (tptp.hAPP (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b T_a)) V_x_2) (tptp.c_Orderings_Obot__class_Obot T_a)))))
% 26.93/27.23 (assume a247 (forall ((V_A_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (= V_A_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool))))))
% 26.93/27.23 (assume a248 (forall ((V_g_2 $$unsorted) (V_f_2 $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (=> (tptp.class_Orderings_Oord T_b) (= (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a T_b) V_f_2 V_g_2) (forall ((B_x $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq T_b (tptp.hAPP V_f_2 B_x) (tptp.hAPP V_g_2 B_x)))))))
% 26.93/27.23 (assume a249 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (or (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x V_y) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y V_x)))))
% 26.93/27.23 (assume a250 (forall ((T_a $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted)) (= (= V_A_2 V_B_2) (and (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2) (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_B_2 V_A_2)))))
% 26.93/27.23 (assume a251 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (= (= V_x_2 V_y_2) (and (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x_2 V_y_2) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y_2 V_x_2))))))
% 26.93/27.23 (assume a252 (forall ((V_Q_2 $$unsorted) (T_a $$unsorted) (V_x_2 $$unsorted) (V_P_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP V_P_2 V_x_2)) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_P_2 V_Q_2) (tptp.hBOOL (tptp.hAPP V_Q_2 V_x_2))))))
% 26.93/27.23 (assume a253 (forall ((T_a $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted)) (=> (= V_A_2 V_B_2) (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2))))
% 26.93/27.23 (assume a254 (forall ((T_a $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted)) (=> (= V_A_2 V_B_2) (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_B_2 V_A_2))))
% 26.93/27.23 (assume a255 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Opreorder T_a) (=> (= V_x V_y) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x V_y)))))
% 26.93/27.23 (assume a256 (forall ((V_x_2 $$unsorted) (V_g_2 $$unsorted) (V_f_2 $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (=> (tptp.class_Orderings_Oord T_b) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a T_b) V_f_2 V_g_2) (tptp.c_Orderings_Oord__class_Oless__eq T_b (tptp.hAPP V_f_2 V_x_2) (tptp.hAPP V_g_2 V_x_2))))))
% 26.93/27.23 (assume a257 (forall ((V_x_2 $$unsorted) (V_y_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y_2 V_x_2) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x_2 V_y_2) (= V_x_2 V_y_2))))))
% 26.93/27.23 (assume a258 (forall ((V_x_2 $$unsorted) (V_Q_2 $$unsorted) (V_P_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_P_2 V_Q_2) (=> (tptp.hBOOL (tptp.hAPP V_P_2 V_x_2)) (tptp.hBOOL (tptp.hAPP V_Q_2 V_x_2))))))
% 26.93/27.23 (assume a259 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oord T_a) (=> (= V_a V_b) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b V_c) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_c))))))
% 26.93/27.23 (assume a260 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (=> (= V_a V_b) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_c V_b) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_c V_a))))))
% 26.93/27.23 (assume a261 (forall ((V_C_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_B_2 V_C_2) (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_C_2)))))
% 26.93/27.23 (assume a262 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oord T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_b) (=> (= V_b V_c) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_c))))))
% 26.93/27.23 (assume a263 (forall ((V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b V_a) (=> (= V_b V_c) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_c V_a))))))
% 26.93/27.23 (assume a264 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x V_y) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y V_x) (= V_x V_y))))))
% 26.93/27.23 (assume a265 (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Opreorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x V_y) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y V_z) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x V_z))))))
% 26.93/27.23 (assume a266 (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y V_x) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x V_y) (= V_x V_y))))))
% 26.93/27.23 (assume a267 (forall ((V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y V_x) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_z V_y) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_z V_x))))))
% 26.93/27.23 (assume a268 (forall ((T_a $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted)) (=> (= V_A_2 V_B_2) (not (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2) (not (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_B_2 V_A_2)))))))
% 26.93/27.23 (assume a269 (forall ((V_x_2 $$unsorted) (V_g_2 $$unsorted) (V_f_2 $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (=> (tptp.class_Orderings_Oord T_b) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a T_b) V_f_2 V_g_2) (tptp.c_Orderings_Oord__class_Oless__eq T_b (tptp.hAPP V_f_2 V_x_2) (tptp.hAPP V_g_2 V_x_2))))))
% 26.93/27.23 (assume a270 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (=> (not (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x V_y)) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y V_x)))))
% 26.93/27.23 (assume a271 (forall ((V_s_2 $$unsorted) (V_r_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun (tptp.tc_prod T_a T_b) tptp.tc_HOL_Obool) V_r_2 V_s_2) (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_Relation_ODomain T_a T_b V_r_2) (tptp.c_Relation_ODomain T_a T_b V_s_2)))))
% 26.93/27.23 (assume a272 (forall ((T_a $$unsorted)) (= (tptp.c_Relation_OId__on T_a (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_HOL_Obool)))))
% 26.93/27.23 (assume a273 (forall ((T_a $$unsorted)) (tptp.c_Order__Relation_Olinear__order__on T_a (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_HOL_Obool)))))
% 26.93/27.23 (assume a274 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Olattice T_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_x V_y)))))
% 26.93/27.23 (assume a275 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__sup T_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_x V_y)))))
% 26.93/27.23 (assume a276 (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Olattice T_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_x V_y)))))
% 26.93/27.23 (assume a277 (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__sup T_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_x V_y)))))
% 26.93/27.23 (assume a278 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__sup T_a) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x_2 V_y_2) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_x_2 V_y_2) V_y_2)))))
% 26.93/27.23 (assume a279 (forall ((V_z_2 $$unsorted) (V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__sup T_a) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_x_2 V_y_2) V_z_2) (and (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x_2 V_z_2) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y_2 V_z_2))))))
% 26.93/27.23 (assume a280 (forall ((V_b $$unsorted) (V_a $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__sup T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x V_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_a V_b))))))
% 26.93/27.23 (assume a281 (forall ((V_a $$unsorted) (V_b $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__sup T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x V_b) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_a V_b))))))
% 26.93/27.23 (assume a282 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__sup T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x V_y) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_x V_y) V_y)))))
% 26.93/27.23 (assume a283 (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__sup T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y V_x) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_x V_y) V_x)))))
% 26.93/27.23 (assume a284 (forall ((V_b $$unsorted) (V_x $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__sup T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_x) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b V_x) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_a V_b) V_x))))))
% 26.93/27.23 (assume a285 (forall ((V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__sup T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y V_x) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_z V_x) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_y V_z) V_x))))))
% 26.93/27.23 (assume a286 (forall ((V_d $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__sup T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_c) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b V_d) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_a V_b) (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_c V_d)))))))
% 26.93/27.23 (assume a287 (forall ((V_x $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__sup T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_a V_b) V_x) (not (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_x) (not (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b V_x))))))))
% 26.93/27.23 (assume a288 (forall ((V_A_2 $$unsorted) (T_a $$unsorted)) (= (forall ((B_x $$unsorted)) (not (tptp.c_member T_a B_x V_A_2))) (= V_A_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool))))))
% 26.93/27.23 (assume a289 (forall ((V_A_2 $$unsorted) (T_a $$unsorted)) (= (exists ((B_x $$unsorted)) (tptp.c_member T_a B_x V_A_2)) (not (= V_A_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)))))))
% 26.93/27.23 (assume a290 (forall ((V_c_2 $$unsorted) (T_a $$unsorted)) (not (tptp.c_member T_a V_c_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool))))))
% 26.93/27.23 (assume a291 (forall ((V_a_2 $$unsorted) (T_a $$unsorted) (V_A_2 $$unsorted)) (=> (= V_A_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (not (tptp.c_member T_a V_a_2 V_A_2)))))
% 26.93/27.23 (assume a292 (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Otop T_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x (tptp.c_Orderings_Otop__class_Otop T_a)))))
% 26.93/27.23 (assume a293 (forall ((V_a_2 $$unsorted) (V_B_2 $$unsorted) (T_a $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_B_2 (tptp.c_Set_Oinsert T_a V_a_2 V_B_2))))
% 26.93/27.23 (assume a294 (forall ((V_b_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2) (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 (tptp.c_Set_Oinsert T_a V_b_2 V_B_2)))))
% 26.93/27.23 (assume a295 (forall ((V_a_2 $$unsorted) (V_D_2 $$unsorted) (V_C_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_C_2 V_D_2) (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_Set_Oinsert T_a V_a_2 V_C_2) (tptp.c_Set_Oinsert T_a V_a_2 V_D_2)))))
% 26.93/27.23 (assume a296 (forall ((V_A_2 $$unsorted) (T_a $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_HOL_Obool)))))
% 26.93/27.23 (assume a297 (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2))))
% 26.93/27.23 (assume a298 (forall ((V_A_2 $$unsorted) (V_B_2 $$unsorted) (T_a $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_B_2 (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2))))
% 26.93/27.23 (assume a299 (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2) V_B_2))))
% 26.93/27.23 (assume a300 (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2) V_B_2))))
% 26.93/27.23 (assume a301 (forall ((V_A_2 $$unsorted) (V_B_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_B_2 V_A_2) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2) V_A_2))))
% 26.93/27.23 (assume a302 (forall ((V_B_2 $$unsorted) (V_C_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_C_2) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_B_2 V_C_2) (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2) V_C_2)))))
% 26.93/27.23 (assume a303 (forall ((V_D_2 $$unsorted) (V_B_2 $$unsorted) (V_C_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_C_2) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_B_2 V_D_2) (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2) (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_C_2 V_D_2))))))
% 26.93/27.23 (assume a304 (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2) V_A_2)))
% 26.93/27.23 (assume a305 (forall ((V_B_2 $$unsorted) (V_D_2 $$unsorted) (V_C_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_C_2) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_D_2 V_B_2) (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2) (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_C_2 V_D_2))))))
% 26.93/27.23 (assume a306 (forall ((V_C_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_B_2 V_C_2) (= (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_B_2 (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_C_2 V_A_2)) V_A_2)))))
% 26.93/27.23 (assume a307 (forall ((V_A_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (not (= (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)) (tptp.c_Set_Oinsert T_a V_a_2 V_A_2)))))
% 26.93/27.23 (assume a308 (forall ((V_A_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (not (= (tptp.c_Set_Oinsert T_a V_a_2 V_A_2) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool))))))
% 26.93/27.23 (assume a309 (forall ((V_d_2 $$unsorted) (V_c_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (= (= (tptp.c_Set_Oinsert T_a V_a_2 (tptp.c_Set_Oinsert T_a V_b_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)))) (tptp.c_Set_Oinsert T_a V_c_2 (tptp.c_Set_Oinsert T_a V_d_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool))))) (or (and (= V_a_2 V_c_2) (= V_b_2 V_d_2)) (and (= V_a_2 V_d_2) (= V_b_2 V_c_2))))))
% 26.93/27.23 (assume a310 (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (= (tptp.c_Set_Oinsert T_a V_a_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (tptp.c_Set_Oinsert T_a V_b_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)))) (= V_a_2 V_b_2))))
% 26.93/27.23 (assume a311 (forall ((V_r_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Wellfounded_Owf T_a V_r_2) (tptp.c_Wellfounded_Owf T_a (tptp.c_Transitive__Closure_Otrancl T_a V_r_2)))))
% 26.93/27.23 (assume a312 (forall ((T_a $$unsorted)) (not (= (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_HOL_Obool)) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool))))))
% 26.93/27.23 (assume a313 (forall ((V_B_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)) V_B_2) V_B_2)))
% 26.93/27.23 (assume a314 (forall ((V_A_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool))) V_A_2)))
% 26.93/27.23 (assume a315 (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (= (= (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (and (= V_A_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (= V_B_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)))))))
% 26.93/27.23 (assume a316 (forall ((V_s_2 $$unsorted) (V_r_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_HOL_Obool) V_r_2 (tptp.c_Transitive__Closure_Ortrancl T_a V_s_2)) (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_HOL_Obool) (tptp.c_Transitive__Closure_Ortrancl T_a V_r_2) (tptp.c_Transitive__Closure_Ortrancl T_a V_s_2)))))
% 26.93/27.23 (assume a317 (forall ((V_S_2 $$unsorted) (V_R_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_HOL_Obool) V_R_2 V_S_2) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_HOL_Obool) V_S_2 (tptp.c_Transitive__Closure_Ortrancl T_a V_R_2)) (= (tptp.c_Transitive__Closure_Ortrancl T_a V_S_2) (tptp.c_Transitive__Closure_Ortrancl T_a V_R_2))))))
% 26.93/27.23 (assume a318 (forall ((V_s_2 $$unsorted) (V_r_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_HOL_Obool) V_r_2 V_s_2) (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_HOL_Obool) (tptp.c_Transitive__Closure_Ortrancl T_a V_r_2) (tptp.c_Transitive__Closure_Ortrancl T_a V_s_2)))))
% 26.93/27.23 (assume a319 (forall ((V_A_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)) V_A_2) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)))))
% 26.93/27.23 (assume a320 (forall ((V_A_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool))) V_A_2)))
% 26.93/27.23 (assume a321 (forall ((V_A_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_A_2) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)))))
% 26.93/27.23 (assume a322 (forall ((T_a $$unsorted)) (= (tptp.c_Transitive__Closure_Otrancl T_a (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_HOL_Obool))) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_HOL_Obool)))))
% 26.93/27.23 (assume a323 (forall ((V_r_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Wellfounded_Owf T_a V_r_2) (tptp.c_Wellfounded_Oacyclic T_a V_r_2))))
% 26.93/27.23 (assume a324 (forall ((V_s_2 $$unsorted) (V_r_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_HOL_Obool) V_r_2 V_s_2) (=> (tptp.c_Relation_Oantisym T_a V_s_2) (tptp.c_Relation_Oantisym T_a V_r_2)))))
% 26.93/27.23 (assume a325 (forall ((V_r_2 $$unsorted) (V_s_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Wellfounded_Oacyclic T_a V_s_2) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_HOL_Obool) V_r_2 V_s_2) (tptp.c_Wellfounded_Oacyclic T_a V_r_2)))))
% 26.93/27.23 (assume a326 (forall ((V_s_2 $$unsorted) (V_r_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun (tptp.tc_prod T_a T_b) tptp.tc_HOL_Obool) V_r_2 V_s_2) (=> (tptp.c_Relation_Osingle__valued T_a T_b V_s_2) (tptp.c_Relation_Osingle__valued T_a T_b V_r_2)))))
% 26.93/27.23 (assume a327 (forall ((T_a $$unsorted)) (tptp.c_Relation_Oantisym T_a (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_HOL_Obool)))))
% 26.93/27.23 (assume a328 (forall ((V_B_2 $$unsorted) (V_x_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 (tptp.c_Set_Oinsert T_a V_x_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)))) V_B_2) (=> (tptp.c_member T_a V_x_2 V_A_2) (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 (tptp.c_Set_Oinsert T_a V_x_2 V_B_2))))))
% 26.93/27.23 (assume a329 (forall ((V_B_2 $$unsorted) (V_x_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 (tptp.c_Set_Oinsert T_a V_x_2 V_B_2)) (and (=> (tptp.c_member T_a V_x_2 V_A_2) (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 (tptp.c_Set_Oinsert T_a V_x_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)))) V_B_2)) (=> (not (tptp.c_member T_a V_x_2 V_A_2)) (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2))))))
% 26.93/27.23 (assume a330 (forall ((V_r_2 $$unsorted) (T_a $$unsorted)) (tptp.c_Relation_Ototal__on T_a (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)) V_r_2)))
% 26.93/27.23 (assume a331 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Obounded__lattice__bot T_a) (= (= (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_x_2 V_y_2) (tptp.c_Orderings_Obot__class_Obot T_a)) (and (= V_x_2 (tptp.c_Orderings_Obot__class_Obot T_a)) (= V_y_2 (tptp.c_Orderings_Obot__class_Obot T_a)))))))
% 26.93/27.23 (assume a332 (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Obounded__lattice__bot T_a) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_x (tptp.c_Orderings_Obot__class_Obot T_a)) V_x))))
% 26.93/27.23 (assume a333 (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Obounded__lattice__bot T_a) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a (tptp.c_Orderings_Obot__class_Obot T_a) V_x) V_x))))
% 26.93/27.23 (assume a334 (forall ((V_a_2 $$unsorted) (V_r_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Wellfounded_Owf T_a V_r_2) (not (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_a_2 V_a_2) V_r_2)))))
% 26.93/27.23 (assume a335 (forall ((V_x_2 $$unsorted) (V_a_2 $$unsorted) (V_r_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Wellfounded_Owf T_a V_r_2) (=> (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_a_2 V_x_2) V_r_2) (not (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_x_2 V_a_2) V_r_2))))))
% 26.93/27.23 (assume a336 (forall ((V_x_2 $$unsorted) (V_a_2 $$unsorted) (V_r_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Wellfounded_Owf T_a V_r_2) (=> (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_a_2 V_x_2) V_r_2) (not (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_x_2 V_a_2) V_r_2))))))
% 26.93/27.23 (assume a337 (forall ((V_a_2 $$unsorted) (V_r_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Wellfounded_Owf T_a V_r_2) (not (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_a_2 V_a_2) V_r_2)))))
% 26.93/27.23 (assume a338 (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_Set_Oinsert T_a V_x_2 V_A_2) V_B_2) (and (tptp.c_member T_a V_x_2 V_B_2) (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2)))))
% 26.93/27.23 (assume a339 (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (not (tptp.c_member T_a V_x_2 V_A_2)) (= (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 (tptp.c_Set_Oinsert T_a V_x_2 V_B_2)) (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2)))))
% 26.93/27.23 (assume a340 (forall ((V_a_2 $$unsorted) (V_b_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_member T_a V_b_2 (tptp.c_Set_Oinsert T_a V_a_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)))) (= V_b_2 V_a_2))))
% 26.93/27.23 (assume a341 (forall ((V_a_2 $$unsorted) (V_b_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_member T_a V_b_2 (tptp.c_Set_Oinsert T_a V_a_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)))) (= V_b_2 V_a_2))))
% 26.93/27.23 (assume a342 (forall ((V_C_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2) V_C_2) (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_B_2 V_C_2)))))
% 26.93/27.23 (assume a343 (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_B_2 V_A_2)) V_B_2))))
% 26.93/27.23 (assume a344 (forall ((V_r_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Wellfounded_Owf T_a V_r_2) (forall ((B_x $$unsorted)) (tptp.c_member T_a B_x (tptp.c_Wellfounded_Oacc T_a V_r_2))))))
% 26.93/27.23 (assume a345 (forall ((V_x_2 $$unsorted) (V_r_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Wellfounded_Owf T_a V_r_2) (tptp.c_member T_a V_x_2 (tptp.c_Wellfounded_Oacc T_a V_r_2)))))
% 26.93/27.23 (assume a346 (forall ((V_A_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Set_Oinsert T_a V_a_2 V_A_2) (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_Set_Oinsert T_a V_a_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool))) V_A_2))))
% 26.93/27.23 (assume a347 (forall ((V_s_2 $$unsorted) (V_r_2 $$unsorted) (V_p_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_member (tptp.tc_prod T_a T_a) V_p_2 (tptp.c_Transitive__Closure_Otrancl T_a V_r_2)) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_HOL_Obool) V_r_2 V_s_2) (tptp.c_member (tptp.tc_prod T_a T_a) V_p_2 (tptp.c_Transitive__Closure_Otrancl T_a V_s_2))))))
% 26.93/27.23 (assume a348 (forall ((V_B_2 $$unsorted) (V_a_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 (tptp.c_Set_Oinsert T_a V_a_2 V_B_2)) (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2) (tptp.c_Set_Oinsert T_a V_a_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)))))))
% 26.93/27.23 (assume a349 (forall ((V_B_2 $$unsorted) (V_a_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 (tptp.c_Set_Oinsert T_a V_a_2 V_B_2)) (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 (tptp.c_Set_Oinsert T_a V_a_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)))) V_B_2))))
% 26.93/27.23 (assume a350 (forall ((V_A_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Set_Oinsert T_a V_a_2 (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 (tptp.c_Set_Oinsert T_a V_a_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool))))) (tptp.c_Set_Oinsert T_a V_a_2 V_A_2))))
% 26.93/27.23 (assume a351 (forall ((V_A_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)))))
% 26.93/27.23 (assume a352 (forall ((V_S_2 $$unsorted) (V_R_2 $$unsorted) (T_a $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_HOL_Obool) (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_HOL_Obool) (tptp.c_Transitive__Closure_Ortrancl T_a V_R_2) (tptp.c_Transitive__Closure_Ortrancl T_a V_S_2)) (tptp.c_Transitive__Closure_Ortrancl T_a (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_HOL_Obool) V_R_2 V_S_2)))))
% 26.93/27.23 (assume a353 (forall ((T_a $$unsorted)) (= (tptp.c_Transitive__Closure_Ortrancl T_a (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_HOL_Obool))) (tptp.c_Relation_OId T_a))))
% 26.93/27.23 (assume a354 (forall ((V_A_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_member T_a V_a_2 V_A_2) (= (tptp.c_Set_Oinsert T_a V_a_2 (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 (tptp.c_Set_Oinsert T_a V_a_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool))))) V_A_2))))
% 26.93/27.23 (assume a355 (forall ((V_A_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (not (tptp.c_member T_a V_x_2 V_A_2)) (= (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_Set_Oinsert T_a V_x_2 V_A_2) (tptp.c_Set_Oinsert T_a V_x_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)))) V_A_2))))
% 26.93/27.23 (assume a356 (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_Relation_ODomain T_a T_b V_A_2) (tptp.c_Relation_ODomain T_a T_b V_B_2)) (tptp.c_Relation_ODomain T_a T_b (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_fun (tptp.tc_prod T_a T_b) tptp.tc_HOL_Obool) V_A_2 V_B_2)))))
% 26.93/27.23 (assume a357 (forall ((V_r_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Order__Relation_Owell__order__on T_a V_A_2 V_r_2) (and (tptp.c_Order__Relation_Olinear__order__on T_a V_A_2 V_r_2) (tptp.c_Wellfounded_Owf T_a (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_HOL_Obool) V_r_2 (tptp.c_Relation_OId T_a)))))))
% 26.93/27.23 (assume a358 (forall ((V_x_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Set_Othe__elem T_a (tptp.c_Set_Oinsert T_a V_x_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)))) V_x_2)))
% 26.93/27.23 (assume a359 (forall ((V_y_2 $$unsorted) (V_z_2 $$unsorted) (V_f_2 $$unsorted) (T_b $$unsorted) (V_A_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_member T_a V_x_2 V_A_2) (=> (tptp.c_Nitpick_Ofold__graph_H T_a T_b V_f_2 V_z_2 (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 (tptp.c_Set_Oinsert T_a V_x_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)))) V_y_2) (tptp.c_Nitpick_Ofold__graph_H T_a T_b V_f_2 V_z_2 V_A_2 (tptp.hAPP (tptp.hAPP V_f_2 V_x_2) V_y_2))))))
% 26.93/27.23 (assume a360 (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (V_r_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Order__Relation_Opreorder__on T_a (tptp.c_Relation_OField T_a V_r_2) V_r_2) (=> (tptp.c_member T_a V_a_2 (tptp.c_Relation_OField T_a V_r_2)) (=> (tptp.c_member T_a V_b_2 (tptp.c_Relation_OField T_a V_r_2)) (= (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_Relation_OImage T_a T_a V_r_2 (tptp.c_Set_Oinsert T_a V_a_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)))) (tptp.c_Relation_OImage T_a T_a V_r_2 (tptp.c_Set_Oinsert T_a V_b_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool))))) (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_b_2 V_a_2) V_r_2)))))))
% 26.93/27.23 (assume a361 (forall ((V_R_2 $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (= (tptp.c_Relation_OImage T_b T_a V_R_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_HOL_Obool))) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)))))
% 26.93/27.23 (assume a362 (forall ((V_A_2 $$unsorted) (V_A_H_2 $$unsorted) (V_r_2 $$unsorted) (V_r_H_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun (tptp.tc_prod T_a T_b) tptp.tc_HOL_Obool) V_r_H_2 V_r_2) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_H_2 V_A_2) (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_b tptp.tc_HOL_Obool) (tptp.c_Relation_OImage T_a T_b V_r_H_2 V_A_H_2) (tptp.c_Relation_OImage T_a T_b V_r_2 V_A_2))))))
% 26.93/27.23 (assume a363 (forall ((V_B_2 $$unsorted) (T_a $$unsorted) (V_A_2 $$unsorted)) (=> (= V_A_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_HOL_Obool))) (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_HOL_Obool) V_A_2 V_B_2))))
% 26.93/27.23 (assume a364 (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_R_2 $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (= (tptp.c_Relation_OImage T_b T_a V_R_2 (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_b tptp.tc_HOL_Obool) V_A_2 V_B_2)) (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_Relation_OImage T_b T_a V_R_2 V_A_2) (tptp.c_Relation_OImage T_b T_a V_R_2 V_B_2)))))
% 26.93/27.23 (assume a365 (forall ((V_A_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_OImage T_a T_a (tptp.c_Relation_OId T_a) V_A_2) V_A_2)))
% 26.93/27.23 (assume a366 (forall ((V_X_2 $$unsorted) (V_r_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_Relation_OImage T_a T_a V_r_2 V_X_2) V_X_2) (= (tptp.c_Relation_OImage T_a T_a (tptp.c_Transitive__Closure_Ortrancl T_a V_r_2) V_X_2) V_X_2))))
% 26.93/27.23 (assume a367 (forall ((V_A_2 $$unsorted) (V_S_2 $$unsorted) (V_R_2 $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (= (tptp.c_Relation_OImage T_b T_a (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun (tptp.tc_prod T_b T_a) tptp.tc_HOL_Obool) V_R_2 V_S_2) V_A_2) (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_Relation_OImage T_b T_a V_R_2 V_A_2) (tptp.c_Relation_OImage T_b T_a V_S_2 V_A_2)))))
% 26.93/27.23 (assume a368 (forall ((V_z_2 $$unsorted) (V_f_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (tptp.c_Nitpick_Ofold__graph_H T_a T_b V_f_2 V_z_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)) V_z_2)))
% 26.93/27.23 (assume a369 (forall ((V_a2_2 $$unsorted) (V_a1_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (tptp.c_Nitpick_Ofold__graph_H T_a T_b V_a1_2 V_a2_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)) V_a2_2)))
% 26.93/27.23 (assume a370 (forall ((V_r_2 $$unsorted) (V_b_2 $$unsorted) (T_b $$unsorted) (V_A_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_member T_a V_a_2 V_A_2) (=> (tptp.c_member (tptp.tc_prod T_a T_b) (tptp.c_Product__Type_OPair T_a T_b V_a_2 V_b_2) V_r_2) (tptp.c_member T_b V_b_2 (tptp.c_Relation_OImage T_a T_b V_r_2 V_A_2))))))
% 26.93/27.23 (assume a371 (forall ((V_A_2 $$unsorted) (V_r_2 $$unsorted) (T_b $$unsorted) (V_b_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_member T_a V_b_2 (tptp.c_Relation_OImage T_b T_a V_r_2 V_A_2)) (exists ((B_x $$unsorted)) (and (tptp.c_member T_b B_x V_A_2) (tptp.c_member (tptp.tc_prod T_b T_a) (tptp.c_Product__Type_OPair T_b T_a B_x V_b_2) V_r_2))))))
% 26.93/27.23 (assume a372 (forall ((V_A_2 $$unsorted) (V_R_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Wellfounded_Owf T_a V_R_2) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 (tptp.c_Relation_OImage T_a T_a V_R_2 V_A_2)) (= V_A_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)))))))
% 26.93/27.23 (assume a373 (forall ((T_a $$unsorted)) (tptp.c_Order__Relation_Owell__order__on T_a (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_HOL_Obool)))))
% 26.93/27.23 (assume a374 (forall ((V_a_2 $$unsorted) (V_r_2 $$unsorted) (T_b $$unsorted) (V_b_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_member T_a V_b_2 (tptp.c_Relation_OImage T_b T_a V_r_2 (tptp.c_Set_Oinsert T_b V_a_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_HOL_Obool))))) (tptp.c_member (tptp.tc_prod T_b T_a) (tptp.c_Product__Type_OPair T_b T_a V_a_2 V_b_2) V_r_2))))
% 26.93/27.23 (assume a375 (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (V_r_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Order__Relation_Opartial__order__on T_a (tptp.c_Relation_OField T_a V_r_2) V_r_2) (=> (tptp.c_member T_a V_a_2 (tptp.c_Relation_OField T_a V_r_2)) (=> (tptp.c_member T_a V_b_2 (tptp.c_Relation_OField T_a V_r_2)) (= (= (tptp.c_Relation_OImage T_a T_a V_r_2 (tptp.c_Set_Oinsert T_a V_a_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)))) (tptp.c_Relation_OImage T_a T_a V_r_2 (tptp.c_Set_Oinsert T_a V_b_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool))))) (= V_a_2 V_b_2)))))))
% 26.93/27.23 (assume a376 (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (V_r_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Relation_Orefl__on T_a (tptp.c_Relation_OField T_a V_r_2) V_r_2) (=> (tptp.c_Relation_Oantisym T_a V_r_2) (=> (tptp.c_member T_a V_a_2 (tptp.c_Relation_OField T_a V_r_2)) (=> (tptp.c_member T_a V_b_2 (tptp.c_Relation_OField T_a V_r_2)) (= (= (tptp.c_Relation_OImage T_a T_a V_r_2 (tptp.c_Set_Oinsert T_a V_a_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)))) (tptp.c_Relation_OImage T_a T_a V_r_2 (tptp.c_Set_Oinsert T_a V_b_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool))))) (= V_a_2 V_b_2))))))))
% 26.93/27.23 (assume a377 (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_r_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Order__Relation_Opreorder__on T_a (tptp.c_Relation_OField T_a V_r_2) V_r_2) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 (tptp.c_Relation_OField T_a V_r_2)) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_B_2 (tptp.c_Relation_OField T_a V_r_2)) (= (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_Relation_OImage T_a T_a V_r_2 V_A_2) (tptp.c_Relation_OImage T_a T_a V_r_2 V_B_2)) (forall ((B_x $$unsorted)) (=> (tptp.c_member T_a B_x V_A_2) (exists ((B_xa $$unsorted)) (and (tptp.c_member T_a B_xa V_B_2) (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a B_xa B_x) V_r_2)))))))))))
% 26.93/27.23 (assume a378 (forall ((V_f_2 $$unsorted) (T_a $$unsorted)) (tptp.c_Wellfounded_Owf T_a (tptp.c_Wellfounded_Omeasure T_a V_f_2))))
% 26.93/27.23 (assume a379 (forall ((V_a5_2 $$unsorted) (V_a1_2 $$unsorted) (V_a2_2 $$unsorted) (V_a4_2 $$unsorted) (V_a3_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_Nitpick_Ofold__graph_H T_a T_b V_a3_2 V_a4_2 V_a2_2 (tptp.hAPP (tptp.hAPP V_a3_2 V_a1_2) V_a5_2)) (or (and (= V_a2_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (= (tptp.hAPP (tptp.hAPP V_a3_2 V_a1_2) V_a5_2) V_a4_2)) (exists ((B_x $$unsorted) (B_y $$unsorted)) (and (= (tptp.hAPP (tptp.hAPP V_a3_2 V_a1_2) V_a5_2) (tptp.hAPP (tptp.hAPP V_a3_2 B_x) B_y)) (tptp.c_member T_a B_x V_a2_2) (tptp.c_Nitpick_Ofold__graph_H T_a T_b V_a3_2 V_a4_2 (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_a2_2 (tptp.c_Set_Oinsert T_a B_x (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)))) B_y)))))))
% 26.93/27.23 (assume a380 (forall ((V_d_2 $$unsorted) (V_c_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add T_a) (=> (= (tptp.c_Groups_Ominus__class_Ominus T_a V_a_2 V_b_2) (tptp.c_Groups_Ominus__class_Ominus T_a V_c_2 V_d_2)) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a_2 V_b_2) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_c_2 V_d_2))))))
% 26.93/27.23 (assume a381 (forall ((V_d_2 $$unsorted) (V_c_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oab__group__add T_a) (=> (= (tptp.c_Groups_Ominus__class_Ominus T_a V_a_2 V_b_2) (tptp.c_Groups_Ominus__class_Ominus T_a V_c_2 V_d_2)) (= (= V_a_2 V_b_2) (= V_c_2 V_d_2))))))
% 26.93/27.23 (assume a382 (forall ((V_A_2 $$unsorted) (V_r_2 $$unsorted) (T_b $$unsorted) (V_b_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_member T_a V_b_2 (tptp.c_Relation_OImage T_b T_a V_r_2 V_A_2)) (not (forall ((B_x $$unsorted)) (=> (tptp.c_member (tptp.tc_prod T_b T_a) (tptp.c_Product__Type_OPair T_b T_a B_x V_b_2) V_r_2) (not (tptp.c_member T_b B_x V_A_2))))))))
% 26.93/27.23 (assume a383 (forall ((T_a $$unsorted) (V_R_2 $$unsorted) (T_b $$unsorted) (V_P_2 $$unsorted)) (=> (forall ((B_x $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP V_P_2 B_x)) (tptp.c_Wellfounded_Owf T_b (tptp.hAPP V_R_2 B_x)))) (tptp.c_Wellfounded_Owf (tptp.tc_prod T_a T_b) (tptp.c_Recdef_Osame__fst T_a T_b V_P_2 V_R_2)))))
% 26.93/27.23 (assume a384 (forall ((V_a_2 $$unsorted) (V_b_2 $$unsorted) (V_r_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Equiv__Relations_Oequiv T_a V_A_2 V_r_2) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_Relation_OImage T_a T_a V_r_2 (tptp.c_Set_Oinsert T_a V_b_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)))) (tptp.c_Relation_OImage T_a T_a V_r_2 (tptp.c_Set_Oinsert T_a V_a_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool))))) (=> (tptp.c_member T_a V_b_2 V_A_2) (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_a_2 V_b_2) V_r_2))))))
% 26.93/27.23 (assume a385 (forall ((V_a_2 $$unsorted) (V_H_2 $$unsorted) (V_r_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_f_2 $$unsorted)) (=> (= V_f_2 (tptp.c_Recdef_Owfrec T_a T_b V_r_2 V_H_2)) (=> (tptp.c_Wellfounded_Owf T_a V_r_2) (= (tptp.hAPP V_f_2 V_a_2) (tptp.hAPP (tptp.hAPP V_H_2 (tptp.c_Recdef_Ocut T_a T_b V_f_2 V_r_2 V_a_2)) V_a_2))))))
% 26.93/27.23 (assume a386 (forall ((V_a_2 $$unsorted) (V_r_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Equiv__Relations_Oequiv T_a V_A_2 V_r_2) (=> (tptp.c_member T_a V_a_2 V_A_2) (tptp.c_member T_a V_a_2 (tptp.c_Relation_OImage T_a T_a V_r_2 (tptp.c_Set_Oinsert T_a V_a_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)))))))))
% 26.93/27.23 (assume a387 (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (V_r_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Equiv__Relations_Oequiv T_a V_A_2 V_r_2) (=> (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_a_2 V_b_2) V_r_2) (= (tptp.c_Relation_OImage T_a T_a V_r_2 (tptp.c_Set_Oinsert T_a V_a_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)))) (tptp.c_Relation_OImage T_a T_a V_r_2 (tptp.c_Set_Oinsert T_a V_b_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)))))))))
% 26.93/27.23 (assume a388 (forall ((V_A_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (V_r_2 $$unsorted) (T_a $$unsorted)) (=> (= (tptp.c_Relation_OImage T_a T_a V_r_2 (tptp.c_Set_Oinsert T_a V_a_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)))) (tptp.c_Relation_OImage T_a T_a V_r_2 (tptp.c_Set_Oinsert T_a V_b_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool))))) (=> (tptp.c_Equiv__Relations_Oequiv T_a V_A_2 V_r_2) (=> (tptp.c_member T_a V_b_2 V_A_2) (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_a_2 V_b_2) V_r_2))))))
% 26.93/27.23 (assume a389 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (V_r_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Equiv__Relations_Oequiv T_a V_A_2 V_r_2) (=> (tptp.c_member T_a V_x_2 V_A_2) (=> (tptp.c_member T_a V_y_2 V_A_2) (= (= (tptp.c_Relation_OImage T_a T_a V_r_2 (tptp.c_Set_Oinsert T_a V_x_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)))) (tptp.c_Relation_OImage T_a T_a V_r_2 (tptp.c_Set_Oinsert T_a V_y_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool))))) (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_x_2 V_y_2) V_r_2)))))))
% 26.93/27.23 (assume a390 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (V_r_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Equiv__Relations_Oequiv T_a V_A_2 V_r_2) (= (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_x_2 V_y_2) V_r_2) (and (= (tptp.c_Relation_OImage T_a T_a V_r_2 (tptp.c_Set_Oinsert T_a V_x_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)))) (tptp.c_Relation_OImage T_a T_a V_r_2 (tptp.c_Set_Oinsert T_a V_y_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool))))) (tptp.c_member T_a V_x_2 V_A_2) (tptp.c_member T_a V_y_2 V_A_2))))))
% 26.93/27.23 (assume a391 (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (V_r_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Equiv__Relations_Oequiv T_a V_A_2 V_r_2) (=> (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_a_2 V_b_2) V_r_2) (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_Relation_OImage T_a T_a V_r_2 (tptp.c_Set_Oinsert T_a V_a_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)))) (tptp.c_Relation_OImage T_a T_a V_r_2 (tptp.c_Set_Oinsert T_a V_b_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)))))))))
% 26.93/27.23 (assume a392 (forall ((T_b $$unsorted) (T_a $$unsorted) (B_M $$unsorted) (B_R $$unsorted)) (=> (tptp.c_Wellfounded_Owf T_a B_R) (forall ((B_x $$unsorted)) (= (tptp.hAPP (tptp.c_Recdef_Owfrec T_a T_b B_R B_M) B_x) (tptp.hAPP (tptp.hAPP B_M (tptp.c_Recdef_Ocut T_a T_b (tptp.c_Recdef_Owfrec T_a T_b B_R B_M) B_R B_x)) B_x))))))
% 26.93/27.23 (assume a393 (forall ((V_a_2 $$unsorted) (V_H_2 $$unsorted) (T_b $$unsorted) (V_r_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Wellfounded_Owf T_a V_r_2) (= (tptp.hAPP (tptp.c_Recdef_Owfrec T_a T_b V_r_2 V_H_2) V_a_2) (tptp.hAPP (tptp.hAPP V_H_2 (tptp.c_Recdef_Ocut T_a T_b (tptp.c_Recdef_Owfrec T_a T_b V_r_2 V_H_2) V_r_2 V_a_2)) V_a_2)))))
% 26.93/27.23 (assume a394 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (V_r_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Equiv__Relations_Oequiv T_a V_A_2 V_r_2) (=> (tptp.c_member T_a V_x_2 V_A_2) (=> (tptp.c_member T_a V_y_2 V_A_2) (= (= (tptp.c_Equiv__Relations_Oquotient T_a (tptp.c_Set_Oinsert T_a V_x_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool))) V_r_2) (tptp.c_Equiv__Relations_Oquotient T_a (tptp.c_Set_Oinsert T_a V_y_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool))) V_r_2)) (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_x_2 V_y_2) V_r_2)))))))
% 26.93/27.23 (assume a395 (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (V_x_2 $$unsorted) (V_r_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Equiv__Relations_Oequiv T_a V_A_2 V_r_2) (=> (tptp.c_member T_a V_x_2 (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_Relation_OImage T_a T_a V_r_2 (tptp.c_Set_Oinsert T_a V_a_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)))) (tptp.c_Relation_OImage T_a T_a V_r_2 (tptp.c_Set_Oinsert T_a V_b_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)))))) (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_a_2 V_b_2) V_r_2)))))
% 26.93/27.23 (assume a396 (forall ((T_a $$unsorted) (V_B_2 $$unsorted) (V_x_2 $$unsorted) (V_A_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP V_A_2 V_x_2)) (=> (tptp.hBOOL (tptp.hAPP V_B_2 V_x_2)) (tptp.hBOOL (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2) V_x_2))))))
% 26.93/27.23 (assume a397 (forall ((V_x_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2) V_x_2)) (not (=> (tptp.hBOOL (tptp.hAPP V_A_2 V_x_2)) (not (tptp.hBOOL (tptp.hAPP V_B_2 V_x_2))))))))
% 26.93/27.23 (assume a398 (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_c_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_member T_a V_c_2 (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2)) (not (=> (tptp.c_member T_a V_c_2 V_A_2) (not (tptp.c_member T_a V_c_2 V_B_2)))))))
% 26.93/27.23 (assume a399 (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_c_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_member T_a V_c_2 V_A_2) (=> (tptp.c_member T_a V_c_2 V_B_2) (tptp.c_member T_a V_c_2 (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2))))))
% 26.93/27.23 (assume a400 (forall ((V_Y_2 $$unsorted) (V_X_2 $$unsorted) (V_r_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Equiv__Relations_Oequiv T_a V_A_2 V_r_2) (=> (tptp.c_member (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_X_2 (tptp.c_Equiv__Relations_Oquotient T_a V_A_2 V_r_2)) (=> (tptp.c_member (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_Y_2 (tptp.c_Equiv__Relations_Oquotient T_a V_A_2 V_r_2)) (or (= V_X_2 V_Y_2) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_X_2 V_Y_2) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)))))))))
% 26.93/27.23 (assume a401 (forall ((V_r_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Equiv__Relations_Oquotient T_a (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)) V_r_2) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun (tptp.tc_fun T_a tptp.tc_HOL_Obool) tptp.tc_HOL_Obool)))))
% 26.93/27.23 (assume a402 (forall ((V_r_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (= (= (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun (tptp.tc_fun T_a tptp.tc_HOL_Obool) tptp.tc_HOL_Obool)) (tptp.c_Equiv__Relations_Oquotient T_a V_A_2 V_r_2)) (= V_A_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool))))))
% 26.93/27.23 (assume a403 (forall ((V_r_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (= (= (tptp.c_Equiv__Relations_Oquotient T_a V_A_2 V_r_2) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun (tptp.tc_fun T_a tptp.tc_HOL_Obool) tptp.tc_HOL_Obool))) (= V_A_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool))))))
% 26.93/27.23 (assume a404 (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Obounded__lattice__bot T_a) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a (tptp.c_Orderings_Obot__class_Obot T_a) V_x) (tptp.c_Orderings_Obot__class_Obot T_a)))))
% 26.93/27.23 (assume a405 (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Obounded__lattice__bot T_a) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_x (tptp.c_Orderings_Obot__class_Obot T_a)) (tptp.c_Orderings_Obot__class_Obot T_a)))))
% 26.93/27.23 (assume a406 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Olattice T_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_x V_y) V_x))))
% 26.93/27.23 (assume a407 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__inf T_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_x V_y) V_x))))
% 26.93/27.23 (assume a408 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Olattice T_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_x V_y) V_y))))
% 26.93/27.23 (assume a409 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__inf T_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_x V_y) V_y))))
% 26.93/27.23 (assume a410 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__inf T_a) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x_2 V_y_2) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_x_2 V_y_2) V_x_2)))))
% 26.93/27.23 (assume a411 (forall ((V_z_2 $$unsorted) (V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__inf T_a) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x_2 (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_y_2 V_z_2)) (and (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x_2 V_y_2) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x_2 V_z_2))))))
% 26.93/27.23 (assume a412 (forall ((V_b $$unsorted) (V_x $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__inf T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_x) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_a V_b) V_x)))))
% 26.93/27.23 (assume a413 (forall ((V_a $$unsorted) (V_x $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__inf T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b V_x) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_a V_b) V_x)))))
% 26.93/27.23 (assume a414 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__inf T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x V_y) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_x V_y) V_x)))))
% 26.93/27.23 (assume a415 (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__inf T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y V_x) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_x V_y) V_y)))))
% 26.93/27.23 (assume a416 (forall ((V_b $$unsorted) (V_a $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__inf T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x V_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x V_b) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_a V_b)))))))
% 26.93/27.23 (assume a417 (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__inf T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x V_y) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x V_z) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_y V_z)))))))
% 26.93/27.23 (assume a418 (forall ((V_d $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__inf T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_c) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b V_d) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_a V_b) (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_c V_d)))))))
% 26.93/27.23 (assume a419 (forall ((V_b $$unsorted) (V_a $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__inf T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_a V_b)) (not (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x V_a) (not (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x V_b))))))))
% 26.93/27.23 (assume a420 (forall ((V_r_H_2 $$unsorted) (V_r_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Wellfounded_Owf T_a V_r_2) (tptp.c_Wellfounded_Owf T_a (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_HOL_Obool) V_r_2 V_r_H_2)))))
% 26.93/27.23 (assume a421 (forall ((V_r_H_2 $$unsorted) (V_r_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Wellfounded_Owf T_a V_r_2) (tptp.c_Wellfounded_Owf T_a (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_HOL_Obool) V_r_H_2 V_r_2)))))
% 26.93/27.23 (assume a422 (forall ((V_B_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)) V_B_2) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)))))
% 26.93/27.23 (assume a423 (forall ((V_A_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)))))
% 26.93/27.23 (assume a424 (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2) V_A_2)))
% 26.93/27.23 (assume a425 (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2) V_B_2)))
% 26.93/27.23 (assume a426 (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_R_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_Relation_OImage T_b T_a V_R_2 (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_b tptp.tc_HOL_Obool) V_A_2 V_B_2)) (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_Relation_OImage T_b T_a V_R_2 V_A_2) (tptp.c_Relation_OImage T_b T_a V_R_2 V_B_2)))))
% 26.93/27.23 (assume a427 (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (= (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (forall ((B_x $$unsorted)) (=> (tptp.c_member T_a B_x V_A_2) (forall ((B_xa $$unsorted)) (=> (tptp.c_member T_a B_xa V_B_2) (not (= B_x B_xa)))))))))
% 26.93/27.23 (assume a428 (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2) V_A_2))))
% 26.93/27.23 (assume a429 (forall ((V_A_2 $$unsorted) (V_B_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_B_2 V_A_2) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2) V_B_2))))
% 26.93/27.23 (assume a430 (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_C_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_C_2 V_A_2) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_C_2 V_B_2) (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_C_2 (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2))))))
% 26.93/27.23 (assume a431 (forall ((V_D_2 $$unsorted) (V_B_2 $$unsorted) (V_C_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_C_2) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_B_2 V_D_2) (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2) (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_C_2 V_D_2))))))
% 26.93/27.23 (assume a432 (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_Relation_ODomain T_a T_b (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun (tptp.tc_prod T_a T_b) tptp.tc_HOL_Obool) V_A_2 V_B_2)) (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_Relation_ODomain T_a T_b V_A_2) (tptp.c_Relation_ODomain T_a T_b V_B_2)))))
% 26.93/27.23 (assume a433 (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_Relation_ORange T_b T_a (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun (tptp.tc_prod T_b T_a) tptp.tc_HOL_Obool) V_A_2 V_B_2)) (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_Relation_ORange T_b T_a V_A_2) (tptp.c_Relation_ORange T_b T_a V_B_2)))))
% 26.93/27.23 (assume a434 (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Olattice T_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_x (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_y V_z)) (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_x V_y) (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_x V_z))))))
% 26.93/27.23 (assume a435 (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Olattice T_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_x V_y) (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_x V_z)) (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_x (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_y V_z))))))
% 26.93/27.23 (assume a436 (forall ((V_B_2 $$unsorted) (V_C_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_member T_a V_a_2 V_C_2) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_Set_Oinsert T_a V_a_2 V_B_2) V_C_2) (tptp.c_Set_Oinsert T_a V_a_2 (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_B_2 V_C_2))))))
% 26.93/27.23 (assume a437 (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_member T_a V_a_2 V_A_2) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 (tptp.c_Set_Oinsert T_a V_a_2 V_B_2)) (tptp.c_Set_Oinsert T_a V_a_2 (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2))))))
% 26.93/27.23 (assume a438 (forall ((V_B_2 $$unsorted) (V_C_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (not (tptp.c_member T_a V_a_2 V_C_2)) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_Set_Oinsert T_a V_a_2 V_B_2) V_C_2) (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_B_2 V_C_2)))))
% 26.93/27.23 (assume a439 (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (not (tptp.c_member T_a V_a_2 V_A_2)) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 (tptp.c_Set_Oinsert T_a V_a_2 V_B_2)) (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2)))))
% 26.93/27.23 (assume a440 (forall ((V_B_2 $$unsorted) (V_C_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (and (=> (tptp.c_member T_a V_a_2 V_C_2) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_Set_Oinsert T_a V_a_2 V_B_2) V_C_2) (tptp.c_Set_Oinsert T_a V_a_2 (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_B_2 V_C_2)))) (=> (not (tptp.c_member T_a V_a_2 V_C_2)) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_Set_Oinsert T_a V_a_2 V_B_2) V_C_2) (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_B_2 V_C_2))))))
% 26.93/27.23 (assume a441 (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (and (=> (tptp.c_member T_a V_a_2 V_A_2) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 (tptp.c_Set_Oinsert T_a V_a_2 V_B_2)) (tptp.c_Set_Oinsert T_a V_a_2 (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2)))) (=> (not (tptp.c_member T_a V_a_2 V_A_2)) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 (tptp.c_Set_Oinsert T_a V_a_2 V_B_2)) (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2))))))
% 26.93/27.23 (assume a442 (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_B_2 V_A_2)) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)))))
% 26.93/27.23 (assume a443 (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (=> (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (= (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2) V_A_2))))
% 26.93/27.23 (assume a444 (forall ((V_C_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (= (= (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2) V_C_2) (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_B_2 V_C_2))) (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_C_2 V_A_2))))
% 26.93/27.23 (assume a445 (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2) (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2)) V_A_2)))
% 26.93/27.23 (assume a446 (forall ((V_C_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_B_2 V_C_2)) (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2) (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_C_2)))))
% 26.93/27.23 (assume a447 (forall ((V_C_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_B_2 V_C_2)) (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2) (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_C_2)))))
% 26.93/27.23 (assume a448 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__inf T_a) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_a V_a) V_a))))
% 26.93/27.23 (assume a449 (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__inf T_a) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_x V_x) V_x))))
% 26.93/27.23 (assume a450 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__inf T_a) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_a V_b) (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_b V_a)))))
% 26.93/27.23 (assume a451 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Olattice T_a) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_x V_y) (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_y V_x)))))
% 26.93/27.23 (assume a452 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__inf T_a) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_x V_y) (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_y V_x)))))
% 26.93/27.23 (assume a453 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__inf T_a) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_a (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_a V_b)) (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_a V_b)))))
% 26.93/27.23 (assume a454 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Olattice T_a) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_x (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_x V_y)) (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_x V_y)))))
% 26.93/27.23 (assume a455 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__inf T_a) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_x (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_x V_y)) (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_x V_y)))))
% 26.93/27.23 (assume a456 (forall ((V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__inf T_a) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_b (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_a V_c)) (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_a (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_b V_c))))))
% 26.93/27.23 (assume a457 (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Olattice T_a) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_x (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_y V_z)) (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_y (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_x V_z))))))
% 26.93/27.23 (assume a458 (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__inf T_a) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_x (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_y V_z)) (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_y (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_x V_z))))))
% 26.93/27.23 (assume a459 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__inf T_a) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_a V_b) V_c) (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_a (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_b V_c))))))
% 26.93/27.23 (assume a460 (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Olattice T_a) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_x V_y) V_z) (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_x (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_y V_z))))))
% 26.93/27.23 (assume a461 (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__inf T_a) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_x V_y) V_z) (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_x (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_y V_z))))))
% 26.93/27.23 (assume a462 (forall ((V_x_2 $$unsorted) (V_g_2 $$unsorted) (V_f_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Olattice T_a) (= (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_b T_a) V_f_2 V_g_2) V_x_2) (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a (tptp.hAPP V_f_2 V_x_2) (tptp.hAPP V_g_2 V_x_2))))))
% 26.93/27.23 (assume a463 (forall ((V_A_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_A_2) V_A_2)))
% 26.93/27.23 (assume a464 (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2) (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_B_2 V_A_2))))
% 26.93/27.23 (assume a465 (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2)) (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2))))
% 26.93/27.23 (assume a466 (forall ((V_C_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_B_2 V_C_2)) (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_B_2 (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_C_2)))))
% 26.93/27.23 (assume a467 (forall ((V_C_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2) V_C_2) (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_B_2 V_C_2)))))
% 26.93/27.23 (assume a468 (forall ((V_x_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2) V_x_2)) (tptp.hBOOL (tptp.hAPP V_A_2 V_x_2)))))
% 26.93/27.23 (assume a469 (forall ((V_x_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2) V_x_2)) (tptp.hBOOL (tptp.hAPP V_B_2 V_x_2)))))
% 26.93/27.23 (assume a470 (forall ((V_s_2 $$unsorted) (V_B_2 $$unsorted) (V_r_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Relation_Orefl__on T_a V_A_2 V_r_2) (=> (tptp.c_Relation_Orefl__on T_a V_B_2 V_s_2) (tptp.c_Relation_Orefl__on T_a (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2) (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_HOL_Obool) V_r_2 V_s_2))))))
% 26.93/27.23 (assume a471 (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_c_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_member T_a V_c_2 (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2)) (tptp.c_member T_a V_c_2 V_B_2))))
% 26.93/27.23 (assume a472 (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_c_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_member T_a V_c_2 (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2)) (tptp.c_member T_a V_c_2 V_A_2))))
% 26.93/27.23 (assume a473 (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_c_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_member T_a V_c_2 (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2)) (and (tptp.c_member T_a V_c_2 V_A_2) (tptp.c_member T_a V_c_2 V_B_2)))))
% 26.93/27.23 (assume a474 (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Obounded__lattice__top T_a) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a (tptp.c_Orderings_Otop__class_Otop T_a) V_x) V_x))))
% 26.93/27.23 (assume a475 (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Obounded__lattice__top T_a) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_x (tptp.c_Orderings_Otop__class_Otop T_a)) V_x))))
% 26.93/27.23 (assume a476 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Obounded__lattice__top T_a) (= (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_x_2 V_y_2) (tptp.c_Orderings_Otop__class_Otop T_a)) (and (= V_x_2 (tptp.c_Orderings_Otop__class_Otop T_a)) (= V_y_2 (tptp.c_Orderings_Otop__class_Otop T_a)))))))
% 26.93/27.23 (assume a477 (forall ((V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Odistrib__lattice T_a) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_y V_z) V_x) (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_y V_x) (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_z V_x))))))
% 26.93/27.23 (assume a478 (forall ((V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Odistrib__lattice T_a) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_y V_z) V_x) (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_y V_x) (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_z V_x))))))
% 26.93/27.23 (assume a479 (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Odistrib__lattice T_a) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_x (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_y V_z)) (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_x V_y) (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_x V_z))))))
% 26.93/27.23 (assume a480 (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Odistrib__lattice T_a) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_x (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_y V_z)) (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_x V_y) (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_x V_z))))))
% 26.93/27.23 (assume a481 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Olattice T_a) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_x (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_x V_y)) V_x))))
% 26.93/27.23 (assume a482 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Olattice T_a) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_x (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_x V_y)) V_x))))
% 26.93/27.23 (assume a483 (forall ((V_s_2 $$unsorted) (V_r_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Relation_Otrans T_a V_r_2) (=> (tptp.c_Relation_Otrans T_a V_s_2) (tptp.c_Relation_Otrans T_a (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_HOL_Obool) V_r_2 V_s_2))))))
% 26.93/27.23 (assume a484 (forall ((V_B_2 $$unsorted) (V_C_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_C_2) (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_B_2 V_C_2)) (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_C_2) V_B_2))))
% 26.93/27.23 (assume a485 (forall ((V_C_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2) V_C_2) (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_C_2) (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_B_2 V_C_2)))))
% 26.93/27.23 (assume a486 (forall ((V_C_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2) V_C_2) (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_B_2 V_C_2)))))
% 26.93/27.23 (assume a487 (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_C_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_C_2 (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2)) (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_C_2 V_A_2) (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_C_2 V_B_2)))))
% 26.93/27.23 (assume a488 (forall ((V_C_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2) (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_B_2 V_C_2)) (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_C_2 V_A_2)) (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2) (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_B_2 V_C_2)) (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_C_2 V_A_2)))))
% 26.93/27.23 (assume a489 (forall ((V_A_2 $$unsorted) (V_C_2 $$unsorted) (V_B_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_B_2 V_C_2) V_A_2) (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_B_2 V_A_2) (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_C_2 V_A_2)))))
% 26.93/27.23 (assume a490 (forall ((V_A_2 $$unsorted) (V_C_2 $$unsorted) (V_B_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_B_2 V_C_2) V_A_2) (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_B_2 V_A_2) (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_C_2 V_A_2)))))
% 26.93/27.23 (assume a491 (forall ((V_C_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_B_2 V_C_2)) (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2) (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_C_2)))))
% 26.93/27.23 (assume a492 (forall ((V_C_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_B_2 V_C_2)) (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2) (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_C_2)))))
% 26.93/27.23 (assume a493 (forall ((V_A_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_HOL_Obool))) V_A_2)))
% 26.93/27.23 (assume a494 (tptp.class_Lattices_Obounded__lattice tptp.tc_HOL_Obool))
% 26.93/27.23 (assume a495 (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (=> (tptp.class_Lattices_Obounded__lattice T_1) (tptp.class_Lattices_Obounded__lattice (tptp.tc_fun T_2 T_1)))))
% 26.93/27.23 (assume a496 (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (=> (tptp.class_Lattices_Obounded__lattice T_1) (tptp.class_Lattices_Obounded__lattice__top (tptp.tc_fun T_2 T_1)))))
% 26.93/27.23 (assume a497 (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (=> (tptp.class_Lattices_Obounded__lattice T_1) (tptp.class_Lattices_Obounded__lattice__bot (tptp.tc_fun T_2 T_1)))))
% 26.93/27.23 (assume a498 (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (=> (tptp.class_Lattices_Olattice T_1) (tptp.class_Lattices_Osemilattice__sup (tptp.tc_fun T_2 T_1)))))
% 26.93/27.23 (assume a499 (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (=> (tptp.class_Lattices_Olattice T_1) (tptp.class_Lattices_Osemilattice__inf (tptp.tc_fun T_2 T_1)))))
% 26.93/27.23 (assume a500 (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (=> (tptp.class_Lattices_Odistrib__lattice T_1) (tptp.class_Lattices_Odistrib__lattice (tptp.tc_fun T_2 T_1)))))
% 26.93/27.23 (assume a501 (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (=> (tptp.class_Orderings_Opreorder T_1) (tptp.class_Orderings_Opreorder (tptp.tc_fun T_2 T_1)))))
% 26.93/27.23 (assume a502 (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (=> (tptp.class_Lattices_Olattice T_1) (tptp.class_Lattices_Olattice (tptp.tc_fun T_2 T_1)))))
% 26.93/27.23 (assume a503 (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (=> (tptp.class_Orderings_Oorder T_1) (tptp.class_Orderings_Oorder (tptp.tc_fun T_2 T_1)))))
% 26.93/27.23 (assume a504 (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (=> (tptp.class_Orderings_Otop T_1) (tptp.class_Orderings_Otop (tptp.tc_fun T_2 T_1)))))
% 26.93/27.23 (assume a505 (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (=> (tptp.class_Orderings_Oord T_1) (tptp.class_Orderings_Oord (tptp.tc_fun T_2 T_1)))))
% 26.93/27.23 (assume a506 (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (=> (tptp.class_Orderings_Obot T_1) (tptp.class_Orderings_Obot (tptp.tc_fun T_2 T_1)))))
% 26.93/27.23 (assume a507 (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (=> (tptp.class_Groups_Ominus T_1) (tptp.class_Groups_Ominus (tptp.tc_fun T_2 T_1)))))
% 26.93/27.23 (assume a508 (tptp.class_Lattices_Obounded__lattice__top tptp.tc_HOL_Obool))
% 26.93/27.23 (assume a509 (tptp.class_Lattices_Obounded__lattice__bot tptp.tc_HOL_Obool))
% 26.93/27.23 (assume a510 (tptp.class_Lattices_Osemilattice__sup tptp.tc_HOL_Obool))
% 26.93/27.23 (assume a511 (tptp.class_Lattices_Osemilattice__inf tptp.tc_HOL_Obool))
% 26.93/27.23 (assume a512 (tptp.class_Lattices_Odistrib__lattice tptp.tc_HOL_Obool))
% 26.93/27.23 (assume a513 (tptp.class_Orderings_Opreorder tptp.tc_HOL_Obool))
% 26.93/27.23 (assume a514 (tptp.class_Lattices_Olattice tptp.tc_HOL_Obool))
% 26.93/27.23 (assume a515 (tptp.class_Orderings_Oorder tptp.tc_HOL_Obool))
% 26.93/27.23 (assume a516 (tptp.class_Orderings_Otop tptp.tc_HOL_Obool))
% 26.93/27.23 (assume a517 (tptp.class_Orderings_Oord tptp.tc_HOL_Obool))
% 26.93/27.23 (assume a518 (tptp.class_Orderings_Obot tptp.tc_HOL_Obool))
% 26.93/27.23 (assume a519 (tptp.class_Groups_Ominus tptp.tc_HOL_Obool))
% 26.93/27.23 (assume a520 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP (tptp.c_fequal V_x_2) V_y_2))) (= V_x_2 V_y_2))))
% 26.93/27.23 (assume a521 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted)) (or (not (= V_x_2 V_y_2)) (tptp.hBOOL (tptp.hAPP (tptp.c_fequal V_x_2) V_y_2)))))
% 26.93/27.23 (assume a522 (forall ((B_x $$unsorted)) (=> (forall ((B_xa $$unsorted)) (and (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP B_x B_xa)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP B_x B_xa)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP B_x B_xa)))) (and (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.v_F B_x)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.v_F B_x)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.v_F B_x))))))
% 26.93/27.23 (assume a523 (forall ((B_P $$unsorted)) (=> (forall ((B_x $$unsorted)) (and (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP B_P B_x)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP B_P B_x)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP B_P B_x)))) (forall ((B_a $$unsorted) (B_b $$unsorted)) (=> (not (= B_a B_b)) (=> (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt B_a B_b) (tptp.hAPP B_P tptp.v_i)) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt B_a B_b) (tptp.v_F B_P))))))))
% 26.93/27.23 (assume a524 (forall ((B_x $$unsorted)) (and (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP tptp.v_P B_x)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP tptp.v_P B_x)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP tptp.v_P B_x)))))
% 26.93/27.23 (assume a525 (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_b) (tptp.v_F tptp.v_P)))
% 26.93/27.23 (assume a526 (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_b) (tptp.hAPP tptp.v_P tptp.v_i))))
% 26.93/27.23 (assume a527 true)
% 26.93/27.23 (step t1 (cl (=> (forall ((B_x $$unsorted) (BOUND_VARIABLE_7486 $$unsorted)) (or (not (tptp.c_member tptp.tc_Arrow__Order__Mirabelle_Oalt B_x (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)))) (not (tptp.c_member tptp.tc_Arrow__Order__Mirabelle_Oalt BOUND_VARIABLE_7486 (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)))) (= B_x BOUND_VARIABLE_7486) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt B_x BOUND_VARIABLE_7486) (tptp.hAPP tptp.v_P tptp.v_i)) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt BOUND_VARIABLE_7486 B_x) (tptp.hAPP tptp.v_P tptp.v_i)))) (or (not (tptp.c_member tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)))) (not (tptp.c_member tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_b (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)))) (= tptp.v_a tptp.v_b) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_b) (tptp.hAPP tptp.v_P tptp.v_i)) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_b tptp.v_a) (tptp.hAPP tptp.v_P tptp.v_i)))) (forall ((B_x $$unsorted) (BOUND_VARIABLE_7486 $$unsorted)) (or (not (tptp.c_member tptp.tc_Arrow__Order__Mirabelle_Oalt B_x (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)))) (not (tptp.c_member tptp.tc_Arrow__Order__Mirabelle_Oalt BOUND_VARIABLE_7486 (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)))) (= B_x BOUND_VARIABLE_7486) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt B_x BOUND_VARIABLE_7486) (tptp.hAPP tptp.v_P tptp.v_i)) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt BOUND_VARIABLE_7486 B_x) (tptp.hAPP tptp.v_P tptp.v_i))))) :rule implies_neg1)
% 26.93/27.23 (anchor :step t2)
% 26.93/27.23 (assume t2.a0 (forall ((B_x $$unsorted) (BOUND_VARIABLE_7486 $$unsorted)) (or (not (tptp.c_member tptp.tc_Arrow__Order__Mirabelle_Oalt B_x (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)))) (not (tptp.c_member tptp.tc_Arrow__Order__Mirabelle_Oalt BOUND_VARIABLE_7486 (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)))) (= B_x BOUND_VARIABLE_7486) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt B_x BOUND_VARIABLE_7486) (tptp.hAPP tptp.v_P tptp.v_i)) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt BOUND_VARIABLE_7486 B_x) (tptp.hAPP tptp.v_P tptp.v_i)))))
% 26.93/27.23 (step t2.t1 (cl (or (not (forall ((B_x $$unsorted) (BOUND_VARIABLE_7486 $$unsorted)) (or (not (tptp.c_member tptp.tc_Arrow__Order__Mirabelle_Oalt B_x (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)))) (not (tptp.c_member tptp.tc_Arrow__Order__Mirabelle_Oalt BOUND_VARIABLE_7486 (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)))) (= B_x BOUND_VARIABLE_7486) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt B_x BOUND_VARIABLE_7486) (tptp.hAPP tptp.v_P tptp.v_i)) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt BOUND_VARIABLE_7486 B_x) (tptp.hAPP tptp.v_P tptp.v_i))))) (or (not (tptp.c_member tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)))) (not (tptp.c_member tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_b (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)))) (= tptp.v_a tptp.v_b) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_b) (tptp.hAPP tptp.v_P tptp.v_i)) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_b tptp.v_a) (tptp.hAPP tptp.v_P tptp.v_i))))) :rule forall_inst :args ((:= B_x tptp.v_a) (:= BOUND_VARIABLE_7486 tptp.v_b)))
% 26.93/27.23 (step t2.t2 (cl (not (forall ((B_x $$unsorted) (BOUND_VARIABLE_7486 $$unsorted)) (or (not (tptp.c_member tptp.tc_Arrow__Order__Mirabelle_Oalt B_x (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)))) (not (tptp.c_member tptp.tc_Arrow__Order__Mirabelle_Oalt BOUND_VARIABLE_7486 (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)))) (= B_x BOUND_VARIABLE_7486) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt B_x BOUND_VARIABLE_7486) (tptp.hAPP tptp.v_P tptp.v_i)) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt BOUND_VARIABLE_7486 B_x) (tptp.hAPP tptp.v_P tptp.v_i))))) (or (not (tptp.c_member tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)))) (not (tptp.c_member tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_b (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)))) (= tptp.v_a tptp.v_b) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_b) (tptp.hAPP tptp.v_P tptp.v_i)) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_b tptp.v_a) (tptp.hAPP tptp.v_P tptp.v_i)))) :rule or :premises (t2.t1))
% 26.93/27.23 (step t2.t3 (cl (or (not (tptp.c_member tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)))) (not (tptp.c_member tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_b (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)))) (= tptp.v_a tptp.v_b) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_b) (tptp.hAPP tptp.v_P tptp.v_i)) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_b tptp.v_a) (tptp.hAPP tptp.v_P tptp.v_i)))) :rule resolution :premises (t2.t2 t2.a0))
% 26.93/27.23 (step t2 (cl (not (forall ((B_x $$unsorted) (BOUND_VARIABLE_7486 $$unsorted)) (or (not (tptp.c_member tptp.tc_Arrow__Order__Mirabelle_Oalt B_x (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)))) (not (tptp.c_member tptp.tc_Arrow__Order__Mirabelle_Oalt BOUND_VARIABLE_7486 (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)))) (= B_x BOUND_VARIABLE_7486) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt B_x BOUND_VARIABLE_7486) (tptp.hAPP tptp.v_P tptp.v_i)) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt BOUND_VARIABLE_7486 B_x) (tptp.hAPP tptp.v_P tptp.v_i))))) (or (not (tptp.c_member tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)))) (not (tptp.c_member tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_b (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)))) (= tptp.v_a tptp.v_b) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_b) (tptp.hAPP tptp.v_P tptp.v_i)) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_b tptp.v_a) (tptp.hAPP tptp.v_P tptp.v_i)))) :rule subproof :discharge (t2.a0))
% 26.93/27.23 (step t3 (cl (=> (forall ((B_x $$unsorted) (BOUND_VARIABLE_7486 $$unsorted)) (or (not (tptp.c_member tptp.tc_Arrow__Order__Mirabelle_Oalt B_x (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)))) (not (tptp.c_member tptp.tc_Arrow__Order__Mirabelle_Oalt BOUND_VARIABLE_7486 (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)))) (= B_x BOUND_VARIABLE_7486) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt B_x BOUND_VARIABLE_7486) (tptp.hAPP tptp.v_P tptp.v_i)) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt BOUND_VARIABLE_7486 B_x) (tptp.hAPP tptp.v_P tptp.v_i)))) (or (not (tptp.c_member tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)))) (not (tptp.c_member tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_b (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)))) (= tptp.v_a tptp.v_b) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_b) (tptp.hAPP tptp.v_P tptp.v_i)) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_b tptp.v_a) (tptp.hAPP tptp.v_P tptp.v_i)))) (or (not (tptp.c_member tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)))) (not (tptp.c_member tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_b (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)))) (= tptp.v_a tptp.v_b) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_b) (tptp.hAPP tptp.v_P tptp.v_i)) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_b tptp.v_a) (tptp.hAPP tptp.v_P tptp.v_i)))) :rule resolution :premises (t1 t2))
% 26.93/27.23 (step t4 (cl (=> (forall ((B_x $$unsorted) (BOUND_VARIABLE_7486 $$unsorted)) (or (not (tptp.c_member tptp.tc_Arrow__Order__Mirabelle_Oalt B_x (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)))) (not (tptp.c_member tptp.tc_Arrow__Order__Mirabelle_Oalt BOUND_VARIABLE_7486 (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)))) (= B_x BOUND_VARIABLE_7486) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt B_x BOUND_VARIABLE_7486) (tptp.hAPP tptp.v_P tptp.v_i)) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt BOUND_VARIABLE_7486 B_x) (tptp.hAPP tptp.v_P tptp.v_i)))) (or (not (tptp.c_member tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)))) (not (tptp.c_member tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_b (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)))) (= tptp.v_a tptp.v_b) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_b) (tptp.hAPP tptp.v_P tptp.v_i)) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_b tptp.v_a) (tptp.hAPP tptp.v_P tptp.v_i)))) (not (or (not (tptp.c_member tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)))) (not (tptp.c_member tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_b (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)))) (= tptp.v_a tptp.v_b) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_b) (tptp.hAPP tptp.v_P tptp.v_i)) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_b tptp.v_a) (tptp.hAPP tptp.v_P tptp.v_i))))) :rule implies_neg2)
% 26.93/27.23 (step t5 (cl (=> (forall ((B_x $$unsorted) (BOUND_VARIABLE_7486 $$unsorted)) (or (not (tptp.c_member tptp.tc_Arrow__Order__Mirabelle_Oalt B_x (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)))) (not (tptp.c_member tptp.tc_Arrow__Order__Mirabelle_Oalt BOUND_VARIABLE_7486 (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)))) (= B_x BOUND_VARIABLE_7486) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt B_x BOUND_VARIABLE_7486) (tptp.hAPP tptp.v_P tptp.v_i)) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt BOUND_VARIABLE_7486 B_x) (tptp.hAPP tptp.v_P tptp.v_i)))) (or (not (tptp.c_member tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)))) (not (tptp.c_member tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_b (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)))) (= tptp.v_a tptp.v_b) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_b) (tptp.hAPP tptp.v_P tptp.v_i)) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_b tptp.v_a) (tptp.hAPP tptp.v_P tptp.v_i)))) (=> (forall ((B_x $$unsorted) (BOUND_VARIABLE_7486 $$unsorted)) (or (not (tptp.c_member tptp.tc_Arrow__Order__Mirabelle_Oalt B_x (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)))) (not (tptp.c_member tptp.tc_Arrow__Order__Mirabelle_Oalt BOUND_VARIABLE_7486 (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)))) (= B_x BOUND_VARIABLE_7486) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt B_x BOUND_VARIABLE_7486) (tptp.hAPP tptp.v_P tptp.v_i)) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt BOUND_VARIABLE_7486 B_x) (tptp.hAPP tptp.v_P tptp.v_i)))) (or (not (tptp.c_member tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)))) (not (tptp.c_member tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_b (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)))) (= tptp.v_a tptp.v_b) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_b) (tptp.hAPP tptp.v_P tptp.v_i)) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_b tptp.v_a) (tptp.hAPP tptp.v_P tptp.v_i))))) :rule resolution :premises (t3 t4))
% 26.93/27.23 (step t6 (cl (=> (forall ((B_x $$unsorted) (BOUND_VARIABLE_7486 $$unsorted)) (or (not (tptp.c_member tptp.tc_Arrow__Order__Mirabelle_Oalt B_x (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)))) (not (tptp.c_member tptp.tc_Arrow__Order__Mirabelle_Oalt BOUND_VARIABLE_7486 (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)))) (= B_x BOUND_VARIABLE_7486) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt B_x BOUND_VARIABLE_7486) (tptp.hAPP tptp.v_P tptp.v_i)) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt BOUND_VARIABLE_7486 B_x) (tptp.hAPP tptp.v_P tptp.v_i)))) (or (not (tptp.c_member tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)))) (not (tptp.c_member tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_b (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)))) (= tptp.v_a tptp.v_b) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_b) (tptp.hAPP tptp.v_P tptp.v_i)) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_b tptp.v_a) (tptp.hAPP tptp.v_P tptp.v_i))))) :rule contraction :premises (t5))
% 26.93/27.23 (step t7 (cl (not (forall ((B_x $$unsorted) (BOUND_VARIABLE_7486 $$unsorted)) (or (not (tptp.c_member tptp.tc_Arrow__Order__Mirabelle_Oalt B_x (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)))) (not (tptp.c_member tptp.tc_Arrow__Order__Mirabelle_Oalt BOUND_VARIABLE_7486 (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)))) (= B_x BOUND_VARIABLE_7486) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt B_x BOUND_VARIABLE_7486) (tptp.hAPP tptp.v_P tptp.v_i)) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt BOUND_VARIABLE_7486 B_x) (tptp.hAPP tptp.v_P tptp.v_i))))) (or (not (tptp.c_member tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)))) (not (tptp.c_member tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_b (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)))) (= tptp.v_a tptp.v_b) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_b) (tptp.hAPP tptp.v_P tptp.v_i)) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_b tptp.v_a) (tptp.hAPP tptp.v_P tptp.v_i)))) :rule implies :premises (t6))
% 26.93/27.23 (step t8 (cl (not (or (not (tptp.c_member tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)))) (not (tptp.c_member tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_b (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)))) (= tptp.v_a tptp.v_b) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_b) (tptp.hAPP tptp.v_P tptp.v_i)) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_b tptp.v_a) (tptp.hAPP tptp.v_P tptp.v_i)))) (not (tptp.c_member tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)))) (not (tptp.c_member tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_b (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)))) (= tptp.v_a tptp.v_b) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_b) (tptp.hAPP tptp.v_P tptp.v_i)) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_b tptp.v_a) (tptp.hAPP tptp.v_P tptp.v_i))) :rule or_pos)
% 26.93/27.23 (step t9 (cl (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_b) (tptp.hAPP tptp.v_P tptp.v_i)) (= tptp.v_a tptp.v_b) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_b tptp.v_a) (tptp.hAPP tptp.v_P tptp.v_i)) (not (tptp.c_member tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_b (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)))) (not (tptp.c_member tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)))) (not (or (not (tptp.c_member tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)))) (not (tptp.c_member tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_b (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)))) (= tptp.v_a tptp.v_b) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_b) (tptp.hAPP tptp.v_P tptp.v_i)) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_b tptp.v_a) (tptp.hAPP tptp.v_P tptp.v_i))))) :rule reordering :premises (t8))
% 26.93/27.23 (step t10 (cl (not (= (or (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_b) (tptp.v_F tptp.v_P))) (not (= tptp.v_a tptp.v_b)) (not (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_a) (tptp.v_F tptp.v_P))))) (or (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_b) (tptp.v_F tptp.v_P))) (not (= tptp.v_a tptp.v_b)) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_a) (tptp.v_F tptp.v_P))))) (not (or (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_b) (tptp.v_F tptp.v_P))) (not (= tptp.v_a tptp.v_b)) (not (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_a) (tptp.v_F tptp.v_P)))))) (or (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_b) (tptp.v_F tptp.v_P))) (not (= tptp.v_a tptp.v_b)) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_a) (tptp.v_F tptp.v_P)))) :rule equiv_pos2)
% 26.93/27.23 (step t11 (cl (= (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_b) (tptp.v_F tptp.v_P))) (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_b) (tptp.v_F tptp.v_P))))) :rule refl)
% 26.93/27.23 (step t12 (cl (= (not (= tptp.v_a tptp.v_b)) (not (= tptp.v_a tptp.v_b)))) :rule refl)
% 26.93/27.23 (step t13 (cl (= (= (= (not (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_a) (tptp.v_F tptp.v_P)))) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_a) (tptp.v_F tptp.v_P))) true) (= (not (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_a) (tptp.v_F tptp.v_P)))) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_a) (tptp.v_F tptp.v_P))))) :rule equiv_simplify)
% 26.93/27.24 (step t14 (cl (not (= (= (not (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_a) (tptp.v_F tptp.v_P)))) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_a) (tptp.v_F tptp.v_P))) true)) (= (not (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_a) (tptp.v_F tptp.v_P)))) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_a) (tptp.v_F tptp.v_P)))) :rule equiv1 :premises (t13))
% 26.93/27.24 (step t15 (cl (= (= (not (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_a) (tptp.v_F tptp.v_P)))) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_a) (tptp.v_F tptp.v_P))) (= (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_a) (tptp.v_F tptp.v_P)) (not (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_a) (tptp.v_F tptp.v_P))))))) :rule all_simplify)
% 26.93/27.24 (step t16 (cl (= (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_a) (tptp.v_F tptp.v_P)) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_a) (tptp.v_F tptp.v_P)))) :rule refl)
% 26.93/27.24 (step t17 (cl (= (not (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_a) (tptp.v_F tptp.v_P)))) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_a) (tptp.v_F tptp.v_P)))) :rule all_simplify)
% 26.93/27.24 (step t18 (cl (= (= (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_a) (tptp.v_F tptp.v_P)) (not (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_a) (tptp.v_F tptp.v_P))))) (= (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_a) (tptp.v_F tptp.v_P)) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_a) (tptp.v_F tptp.v_P))))) :rule cong :premises (t16 t17))
% 26.93/27.24 (step t19 (cl (= (= (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_a) (tptp.v_F tptp.v_P)) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_a) (tptp.v_F tptp.v_P))) true)) :rule all_simplify)
% 26.93/27.24 (step t20 (cl (= (= (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_a) (tptp.v_F tptp.v_P)) (not (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_a) (tptp.v_F tptp.v_P))))) true)) :rule trans :premises (t18 t19))
% 26.93/27.24 (step t21 (cl (= (= (not (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_a) (tptp.v_F tptp.v_P)))) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_a) (tptp.v_F tptp.v_P))) true)) :rule trans :premises (t15 t20))
% 26.93/27.24 (step t22 (cl (= (not (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_a) (tptp.v_F tptp.v_P)))) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_a) (tptp.v_F tptp.v_P)))) :rule resolution :premises (t14 t21))
% 26.93/27.24 (step t23 (cl (= (or (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_b) (tptp.v_F tptp.v_P))) (not (= tptp.v_a tptp.v_b)) (not (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_a) (tptp.v_F tptp.v_P))))) (or (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_b) (tptp.v_F tptp.v_P))) (not (= tptp.v_a tptp.v_b)) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_a) (tptp.v_F tptp.v_P))))) :rule cong :premises (t11 t12 t22))
% 26.93/27.24 (step t24 (cl (=> (and (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_b) (tptp.v_F tptp.v_P)) (= tptp.v_a tptp.v_b) (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_a) (tptp.v_F tptp.v_P)))) false) (and (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_b) (tptp.v_F tptp.v_P)) (= tptp.v_a tptp.v_b) (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_a) (tptp.v_F tptp.v_P))))) :rule implies_neg1)
% 26.93/27.24 (anchor :step t25)
% 26.93/27.24 (assume t25.a0 (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_b) (tptp.v_F tptp.v_P)))
% 26.93/27.24 (assume t25.a1 (= tptp.v_a tptp.v_b))
% 26.93/27.24 (assume t25.a2 (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_a) (tptp.v_F tptp.v_P))))
% 26.93/27.24 (step t25.t1 (cl (not (= (= false true) false)) (not (= false true)) false) :rule equiv_pos2)
% 26.93/27.24 (step t25.t2 (cl (= (= false true) false)) :rule all_simplify)
% 26.93/27.24 (step t25.t3 (cl (= (= (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_a) (tptp.v_F tptp.v_P)) false) (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_a) (tptp.v_F tptp.v_P))))) :rule equiv_simplify)
% 26.93/27.24 (step t25.t4 (cl (= (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_a) (tptp.v_F tptp.v_P)) false) (not (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_a) (tptp.v_F tptp.v_P))))) :rule equiv2 :premises (t25.t3))
% 26.93/27.24 (step t25.t5 (cl (not (not (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_a) (tptp.v_F tptp.v_P))))) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_a) (tptp.v_F tptp.v_P))) :rule not_not)
% 26.93/27.24 (step t25.t6 (cl (= (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_a) (tptp.v_F tptp.v_P)) false) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_a) (tptp.v_F tptp.v_P))) :rule resolution :premises (t25.t4 t25.t5))
% 26.93/27.24 (step t25.t7 (cl (= (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_a) (tptp.v_F tptp.v_P)) false)) :rule resolution :premises (t25.t6 t25.a2))
% 26.93/27.24 (step t25.t8 (cl (= false (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_a) (tptp.v_F tptp.v_P)))) :rule symm :premises (t25.t7))
% 26.93/27.24 (step t25.t9 (cl (= (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) :rule refl)
% 26.93/27.24 (step t25.t10 (cl (= tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) :rule refl)
% 26.93/27.24 (step t25.t11 (cl (= tptp.v_a tptp.v_a)) :rule refl)
% 26.93/27.24 (step t25.t12 (cl (= tptp.v_b tptp.v_a)) :rule symm :premises (t25.a1))
% 26.93/27.24 (step t25.t13 (cl (= tptp.v_a tptp.v_b)) :rule symm :premises (t25.t12))
% 26.93/27.24 (step t25.t14 (cl (= (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_a) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_b))) :rule cong :premises (t25.t10 t25.t10 t25.t11 t25.t13))
% 26.93/27.24 (step t25.t15 (cl (= (tptp.v_F tptp.v_P) (tptp.v_F tptp.v_P))) :rule refl)
% 26.93/27.24 (step t25.t16 (cl (= (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_a) (tptp.v_F tptp.v_P)) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_b) (tptp.v_F tptp.v_P)))) :rule cong :premises (t25.t9 t25.t14 t25.t15))
% 26.93/27.24 (step t25.t17 (cl (= (= (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_b) (tptp.v_F tptp.v_P)) true) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_b) (tptp.v_F tptp.v_P)))) :rule equiv_simplify)
% 26.93/27.24 (step t25.t18 (cl (= (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_b) (tptp.v_F tptp.v_P)) true) (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_b) (tptp.v_F tptp.v_P)))) :rule equiv2 :premises (t25.t17))
% 26.93/27.24 (step t25.t19 (cl (= (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_b) (tptp.v_F tptp.v_P)) true)) :rule resolution :premises (t25.t18 t25.a0))
% 26.93/27.24 (step t25.t20 (cl (= false true)) :rule trans :premises (t25.t8 t25.t16 t25.t19))
% 26.93/27.24 (step t25.t21 (cl false) :rule resolution :premises (t25.t1 t25.t2 t25.t20))
% 26.93/27.24 (step t25 (cl (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_b) (tptp.v_F tptp.v_P))) (not (= tptp.v_a tptp.v_b)) (not (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_a) (tptp.v_F tptp.v_P)))) false) :rule subproof :discharge (t25.a0 t25.a1 t25.a2))
% 26.93/27.24 (step t26 (cl (not (and (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_b) (tptp.v_F tptp.v_P)) (= tptp.v_a tptp.v_b) (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_a) (tptp.v_F tptp.v_P))))) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_b) (tptp.v_F tptp.v_P))) :rule and_pos)
% 26.93/27.24 (step t27 (cl (not (and (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_b) (tptp.v_F tptp.v_P)) (= tptp.v_a tptp.v_b) (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_a) (tptp.v_F tptp.v_P))))) (= tptp.v_a tptp.v_b)) :rule and_pos)
% 26.93/27.24 (step t28 (cl (not (and (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_b) (tptp.v_F tptp.v_P)) (= tptp.v_a tptp.v_b) (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_a) (tptp.v_F tptp.v_P))))) (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_a) (tptp.v_F tptp.v_P)))) :rule and_pos)
% 26.93/27.24 (step t29 (cl false (not (and (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_b) (tptp.v_F tptp.v_P)) (= tptp.v_a tptp.v_b) (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_a) (tptp.v_F tptp.v_P))))) (not (and (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_b) (tptp.v_F tptp.v_P)) (= tptp.v_a tptp.v_b) (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_a) (tptp.v_F tptp.v_P))))) (not (and (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_b) (tptp.v_F tptp.v_P)) (= tptp.v_a tptp.v_b) (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_a) (tptp.v_F tptp.v_P)))))) :rule resolution :premises (t25 t26 t27 t28))
% 26.93/27.24 (step t30 (cl (not (and (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_b) (tptp.v_F tptp.v_P)) (= tptp.v_a tptp.v_b) (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_a) (tptp.v_F tptp.v_P))))) (not (and (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_b) (tptp.v_F tptp.v_P)) (= tptp.v_a tptp.v_b) (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_a) (tptp.v_F tptp.v_P))))) (not (and (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_b) (tptp.v_F tptp.v_P)) (= tptp.v_a tptp.v_b) (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_a) (tptp.v_F tptp.v_P))))) false) :rule reordering :premises (t29))
% 26.93/27.24 (step t31 (cl (not (and (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_b) (tptp.v_F tptp.v_P)) (= tptp.v_a tptp.v_b) (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_a) (tptp.v_F tptp.v_P))))) false) :rule contraction :premises (t30))
% 26.93/27.24 (step t32 (cl (=> (and (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_b) (tptp.v_F tptp.v_P)) (= tptp.v_a tptp.v_b) (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_a) (tptp.v_F tptp.v_P)))) false) false) :rule resolution :premises (t24 t31))
% 26.93/27.24 (step t33 (cl (=> (and (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_b) (tptp.v_F tptp.v_P)) (= tptp.v_a tptp.v_b) (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_a) (tptp.v_F tptp.v_P)))) false) (not false)) :rule implies_neg2)
% 26.93/27.24 (step t34 (cl (=> (and (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_b) (tptp.v_F tptp.v_P)) (= tptp.v_a tptp.v_b) (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_a) (tptp.v_F tptp.v_P)))) false) (=> (and (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_b) (tptp.v_F tptp.v_P)) (= tptp.v_a tptp.v_b) (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_a) (tptp.v_F tptp.v_P)))) false)) :rule resolution :premises (t32 t33))
% 26.93/27.24 (step t35 (cl (=> (and (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_b) (tptp.v_F tptp.v_P)) (= tptp.v_a tptp.v_b) (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_a) (tptp.v_F tptp.v_P)))) false)) :rule contraction :premises (t34))
% 26.93/27.24 (step t36 (cl (= (=> (and (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_b) (tptp.v_F tptp.v_P)) (= tptp.v_a tptp.v_b) (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_a) (tptp.v_F tptp.v_P)))) false) (not (and (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_b) (tptp.v_F tptp.v_P)) (= tptp.v_a tptp.v_b) (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_a) (tptp.v_F tptp.v_P))))))) :rule implies_simplify)
% 26.93/27.24 (step t37 (cl (not (=> (and (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_b) (tptp.v_F tptp.v_P)) (= tptp.v_a tptp.v_b) (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_a) (tptp.v_F tptp.v_P)))) false)) (not (and (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_b) (tptp.v_F tptp.v_P)) (= tptp.v_a tptp.v_b) (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_a) (tptp.v_F tptp.v_P)))))) :rule equiv1 :premises (t36))
% 26.93/27.24 (step t38 (cl (not (and (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_b) (tptp.v_F tptp.v_P)) (= tptp.v_a tptp.v_b) (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_a) (tptp.v_F tptp.v_P)))))) :rule resolution :premises (t35 t37))
% 26.93/27.24 (step t39 (cl (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_b) (tptp.v_F tptp.v_P))) (not (= tptp.v_a tptp.v_b)) (not (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_a) (tptp.v_F tptp.v_P))))) :rule not_and :premises (t38))
% 26.93/27.24 (step t40 (cl (or (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_b) (tptp.v_F tptp.v_P))) (not (= tptp.v_a tptp.v_b)) (not (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_a) (tptp.v_F tptp.v_P))))) (not (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_b) (tptp.v_F tptp.v_P))))) :rule or_neg)
% 26.93/27.24 (step t41 (cl (or (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_b) (tptp.v_F tptp.v_P))) (not (= tptp.v_a tptp.v_b)) (not (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_a) (tptp.v_F tptp.v_P))))) (not (not (= tptp.v_a tptp.v_b)))) :rule or_neg)
% 26.93/27.24 (step t42 (cl (or (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_b) (tptp.v_F tptp.v_P))) (not (= tptp.v_a tptp.v_b)) (not (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_a) (tptp.v_F tptp.v_P))))) (not (not (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_a) (tptp.v_F tptp.v_P)))))) :rule or_neg)
% 26.93/27.24 (step t43 (cl (or (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_b) (tptp.v_F tptp.v_P))) (not (= tptp.v_a tptp.v_b)) (not (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_a) (tptp.v_F tptp.v_P))))) (or (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_b) (tptp.v_F tptp.v_P))) (not (= tptp.v_a tptp.v_b)) (not (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_a) (tptp.v_F tptp.v_P))))) (or (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_b) (tptp.v_F tptp.v_P))) (not (= tptp.v_a tptp.v_b)) (not (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_a) (tptp.v_F tptp.v_P)))))) :rule resolution :premises (t39 t40 t41 t42))
% 26.93/27.24 (step t44 (cl (or (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_b) (tptp.v_F tptp.v_P))) (not (= tptp.v_a tptp.v_b)) (not (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_a) (tptp.v_F tptp.v_P)))))) :rule contraction :premises (t43))
% 26.93/27.24 (step t45 (cl (or (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_b) (tptp.v_F tptp.v_P))) (not (= tptp.v_a tptp.v_b)) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_a) (tptp.v_F tptp.v_P)))) :rule resolution :premises (t10 t23 t44))
% 26.93/27.24 (step t46 (cl (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_b) (tptp.v_F tptp.v_P))) (not (= tptp.v_a tptp.v_b)) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_a) (tptp.v_F tptp.v_P))) :rule or :premises (t45))
% 26.93/27.24 (step t47 (cl (=> (forall ((B_x $$unsorted)) (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt B_x B_x) (tptp.v_F tptp.v_P)))) (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_a) (tptp.v_F tptp.v_P)))) (forall ((B_x $$unsorted)) (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt B_x B_x) (tptp.v_F tptp.v_P))))) :rule implies_neg1)
% 26.93/27.24 (anchor :step t48)
% 26.93/27.24 (assume t48.a0 (forall ((B_x $$unsorted)) (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt B_x B_x) (tptp.v_F tptp.v_P)))))
% 26.93/27.24 (step t48.t1 (cl (or (not (forall ((B_x $$unsorted)) (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt B_x B_x) (tptp.v_F tptp.v_P))))) (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_a) (tptp.v_F tptp.v_P))))) :rule forall_inst :args ((:= B_x tptp.v_a)))
% 26.93/27.24 (step t48.t2 (cl (not (forall ((B_x $$unsorted)) (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt B_x B_x) (tptp.v_F tptp.v_P))))) (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_a) (tptp.v_F tptp.v_P)))) :rule or :premises (t48.t1))
% 26.93/27.24 (step t48.t3 (cl (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_a) (tptp.v_F tptp.v_P)))) :rule resolution :premises (t48.t2 t48.a0))
% 26.93/27.24 (step t48 (cl (not (forall ((B_x $$unsorted)) (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt B_x B_x) (tptp.v_F tptp.v_P))))) (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_a) (tptp.v_F tptp.v_P)))) :rule subproof :discharge (t48.a0))
% 26.93/27.24 (step t49 (cl (=> (forall ((B_x $$unsorted)) (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt B_x B_x) (tptp.v_F tptp.v_P)))) (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_a) (tptp.v_F tptp.v_P)))) (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_a) (tptp.v_F tptp.v_P)))) :rule resolution :premises (t47 t48))
% 26.93/27.24 (step t50 (cl (=> (forall ((B_x $$unsorted)) (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt B_x B_x) (tptp.v_F tptp.v_P)))) (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_a) (tptp.v_F tptp.v_P)))) (not (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_a) (tptp.v_F tptp.v_P))))) :rule implies_neg2)
% 26.93/27.24 (step t51 (cl (=> (forall ((B_x $$unsorted)) (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt B_x B_x) (tptp.v_F tptp.v_P)))) (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_a) (tptp.v_F tptp.v_P)))) (=> (forall ((B_x $$unsorted)) (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt B_x B_x) (tptp.v_F tptp.v_P)))) (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_a) (tptp.v_F tptp.v_P))))) :rule resolution :premises (t49 t50))
% 26.93/27.24 (step t52 (cl (=> (forall ((B_x $$unsorted)) (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt B_x B_x) (tptp.v_F tptp.v_P)))) (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_a) (tptp.v_F tptp.v_P))))) :rule contraction :premises (t51))
% 26.93/27.24 (step t53 (cl (not (forall ((B_x $$unsorted)) (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt B_x B_x) (tptp.v_F tptp.v_P))))) (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_a) (tptp.v_F tptp.v_P)))) :rule implies :premises (t52))
% 26.93/27.24 (step t54 (cl (not (= (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.v_F tptp.v_P)) (forall ((B_x $$unsorted)) (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt B_x B_x) (tptp.v_F tptp.v_P)))))) (not (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.v_F tptp.v_P))) (forall ((B_x $$unsorted)) (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt B_x B_x) (tptp.v_F tptp.v_P))))) :rule equiv_pos2)
% 26.93/27.24 (step t55 (cl (not (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.v_F tptp.v_P))) (forall ((B_x $$unsorted)) (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt B_x B_x) (tptp.v_F tptp.v_P)))) (not (= (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.v_F tptp.v_P)) (forall ((B_x $$unsorted)) (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt B_x B_x) (tptp.v_F tptp.v_P))))))) :rule reordering :premises (t54))
% 26.93/27.24 (step t56 (cl (not (and (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.v_F tptp.v_P)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.v_F tptp.v_P)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.v_F tptp.v_P)))) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.v_F tptp.v_P))) :rule and_pos)
% 26.93/27.24 (step t57 (cl (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.v_F tptp.v_P)) (not (and (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.v_F tptp.v_P)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.v_F tptp.v_P)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.v_F tptp.v_P))))) :rule reordering :premises (t56))
% 26.93/27.24 (step t58 (cl (not (or (not (forall ((BOUND_VARIABLE_10414 $$unsorted)) (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP tptp.v_P BOUND_VARIABLE_10414)))) (not (forall ((BOUND_VARIABLE_10420 $$unsorted)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP tptp.v_P BOUND_VARIABLE_10420)))) (not (forall ((BOUND_VARIABLE_10426 $$unsorted)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP tptp.v_P BOUND_VARIABLE_10426)))) (and (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.v_F tptp.v_P)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.v_F tptp.v_P)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.v_F tptp.v_P))))) (not (forall ((BOUND_VARIABLE_10414 $$unsorted)) (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP tptp.v_P BOUND_VARIABLE_10414)))) (not (forall ((BOUND_VARIABLE_10420 $$unsorted)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP tptp.v_P BOUND_VARIABLE_10420)))) (not (forall ((BOUND_VARIABLE_10426 $$unsorted)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP tptp.v_P BOUND_VARIABLE_10426)))) (and (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.v_F tptp.v_P)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.v_F tptp.v_P)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.v_F tptp.v_P)))) :rule or_pos)
% 26.93/27.24 (step t59 (cl (not (forall ((BOUND_VARIABLE_10414 $$unsorted)) (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP tptp.v_P BOUND_VARIABLE_10414)))) (not (forall ((BOUND_VARIABLE_10420 $$unsorted)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP tptp.v_P BOUND_VARIABLE_10420)))) (not (forall ((BOUND_VARIABLE_10426 $$unsorted)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP tptp.v_P BOUND_VARIABLE_10426)))) (and (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.v_F tptp.v_P)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.v_F tptp.v_P)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.v_F tptp.v_P))) (not (or (not (forall ((BOUND_VARIABLE_10414 $$unsorted)) (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP tptp.v_P BOUND_VARIABLE_10414)))) (not (forall ((BOUND_VARIABLE_10420 $$unsorted)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP tptp.v_P BOUND_VARIABLE_10420)))) (not (forall ((BOUND_VARIABLE_10426 $$unsorted)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP tptp.v_P BOUND_VARIABLE_10426)))) (and (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.v_F tptp.v_P)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.v_F tptp.v_P)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.v_F tptp.v_P)))))) :rule reordering :premises (t58))
% 26.93/27.24 (step t60 (cl (= (forall ((BOUND_VARIABLE_10491 $$unsorted)) (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP tptp.v_P BOUND_VARIABLE_10491))) (forall ((BOUND_VARIABLE_10414 $$unsorted)) (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP tptp.v_P BOUND_VARIABLE_10414))))) :rule hole :args ((forall ((BOUND_VARIABLE_10491 $$unsorted)) (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP tptp.v_P BOUND_VARIABLE_10491))) (= BOUND_VARIABLE_10491 BOUND_VARIABLE_10414)))
% 26.93/27.24 (step t61 (cl (not (forall ((BOUND_VARIABLE_10491 $$unsorted)) (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP tptp.v_P BOUND_VARIABLE_10491)))) (forall ((BOUND_VARIABLE_10414 $$unsorted)) (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP tptp.v_P BOUND_VARIABLE_10414)))) :rule equiv1 :premises (t60))
% 26.93/27.24 (step t62 (cl (not (= (forall ((B_x $$unsorted)) (and (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP tptp.v_P B_x)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP tptp.v_P B_x)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP tptp.v_P B_x)))) (and (forall ((BOUND_VARIABLE_10491 $$unsorted)) (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP tptp.v_P BOUND_VARIABLE_10491))) (forall ((BOUND_VARIABLE_10497 $$unsorted)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP tptp.v_P BOUND_VARIABLE_10497))) (forall ((BOUND_VARIABLE_10503 $$unsorted)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP tptp.v_P BOUND_VARIABLE_10503)))))) (not (forall ((B_x $$unsorted)) (and (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP tptp.v_P B_x)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP tptp.v_P B_x)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP tptp.v_P B_x))))) (and (forall ((BOUND_VARIABLE_10491 $$unsorted)) (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP tptp.v_P BOUND_VARIABLE_10491))) (forall ((BOUND_VARIABLE_10497 $$unsorted)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP tptp.v_P BOUND_VARIABLE_10497))) (forall ((BOUND_VARIABLE_10503 $$unsorted)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP tptp.v_P BOUND_VARIABLE_10503))))) :rule equiv_pos2)
% 26.93/27.24 (step t63 (cl (= (forall ((B_x $$unsorted)) (and (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP tptp.v_P B_x)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP tptp.v_P B_x)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP tptp.v_P B_x)))) (and (forall ((BOUND_VARIABLE_10491 $$unsorted)) (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP tptp.v_P BOUND_VARIABLE_10491))) (forall ((BOUND_VARIABLE_10497 $$unsorted)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP tptp.v_P BOUND_VARIABLE_10497))) (forall ((BOUND_VARIABLE_10503 $$unsorted)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP tptp.v_P BOUND_VARIABLE_10503)))))) :rule all_simplify)
% 26.93/27.24 (step t64 (cl (and (forall ((BOUND_VARIABLE_10491 $$unsorted)) (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP tptp.v_P BOUND_VARIABLE_10491))) (forall ((BOUND_VARIABLE_10497 $$unsorted)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP tptp.v_P BOUND_VARIABLE_10497))) (forall ((BOUND_VARIABLE_10503 $$unsorted)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP tptp.v_P BOUND_VARIABLE_10503))))) :rule resolution :premises (t62 t63 a524))
% 26.93/27.24 (step t65 (cl (forall ((BOUND_VARIABLE_10491 $$unsorted)) (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP tptp.v_P BOUND_VARIABLE_10491)))) :rule and :premises (t64))
% 26.93/27.24 (step t66 (cl (forall ((BOUND_VARIABLE_10414 $$unsorted)) (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP tptp.v_P BOUND_VARIABLE_10414)))) :rule resolution :premises (t61 t65))
% 26.93/27.24 (step t67 (cl (= (forall ((BOUND_VARIABLE_10497 $$unsorted)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP tptp.v_P BOUND_VARIABLE_10497))) (forall ((BOUND_VARIABLE_10420 $$unsorted)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP tptp.v_P BOUND_VARIABLE_10420))))) :rule hole :args ((forall ((BOUND_VARIABLE_10497 $$unsorted)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP tptp.v_P BOUND_VARIABLE_10497))) (= BOUND_VARIABLE_10497 BOUND_VARIABLE_10420)))
% 26.93/27.24 (step t68 (cl (not (forall ((BOUND_VARIABLE_10497 $$unsorted)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP tptp.v_P BOUND_VARIABLE_10497)))) (forall ((BOUND_VARIABLE_10420 $$unsorted)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP tptp.v_P BOUND_VARIABLE_10420)))) :rule equiv1 :premises (t67))
% 26.93/27.24 (step t69 (cl (forall ((BOUND_VARIABLE_10497 $$unsorted)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP tptp.v_P BOUND_VARIABLE_10497)))) :rule and :premises (t64))
% 26.93/27.24 (step t70 (cl (forall ((BOUND_VARIABLE_10420 $$unsorted)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP tptp.v_P BOUND_VARIABLE_10420)))) :rule resolution :premises (t68 t69))
% 26.93/27.24 (step t71 (cl (= (forall ((BOUND_VARIABLE_10503 $$unsorted)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP tptp.v_P BOUND_VARIABLE_10503))) (forall ((BOUND_VARIABLE_10426 $$unsorted)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP tptp.v_P BOUND_VARIABLE_10426))))) :rule hole :args ((forall ((BOUND_VARIABLE_10503 $$unsorted)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP tptp.v_P BOUND_VARIABLE_10503))) (= BOUND_VARIABLE_10503 BOUND_VARIABLE_10426)))
% 26.93/27.24 (step t72 (cl (not (forall ((BOUND_VARIABLE_10503 $$unsorted)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP tptp.v_P BOUND_VARIABLE_10503)))) (forall ((BOUND_VARIABLE_10426 $$unsorted)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP tptp.v_P BOUND_VARIABLE_10426)))) :rule equiv1 :premises (t71))
% 26.93/27.24 (step t73 (cl (forall ((BOUND_VARIABLE_10503 $$unsorted)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP tptp.v_P BOUND_VARIABLE_10503)))) :rule and :premises (t64))
% 26.93/27.24 (step t74 (cl (forall ((BOUND_VARIABLE_10426 $$unsorted)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP tptp.v_P BOUND_VARIABLE_10426)))) :rule resolution :premises (t72 t73))
% 26.93/27.24 (step t75 (cl (=> (forall ((B_x $$unsorted)) (or (not (forall ((BOUND_VARIABLE_10414 $$unsorted)) (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP B_x BOUND_VARIABLE_10414)))) (not (forall ((BOUND_VARIABLE_10420 $$unsorted)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP B_x BOUND_VARIABLE_10420)))) (not (forall ((BOUND_VARIABLE_10426 $$unsorted)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP B_x BOUND_VARIABLE_10426)))) (and (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.v_F B_x)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.v_F B_x)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.v_F B_x))))) (or (not (forall ((BOUND_VARIABLE_10414 $$unsorted)) (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP tptp.v_P BOUND_VARIABLE_10414)))) (not (forall ((BOUND_VARIABLE_10420 $$unsorted)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP tptp.v_P BOUND_VARIABLE_10420)))) (not (forall ((BOUND_VARIABLE_10426 $$unsorted)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP tptp.v_P BOUND_VARIABLE_10426)))) (and (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.v_F tptp.v_P)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.v_F tptp.v_P)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.v_F tptp.v_P))))) (forall ((B_x $$unsorted)) (or (not (forall ((BOUND_VARIABLE_10414 $$unsorted)) (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP B_x BOUND_VARIABLE_10414)))) (not (forall ((BOUND_VARIABLE_10420 $$unsorted)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP B_x BOUND_VARIABLE_10420)))) (not (forall ((BOUND_VARIABLE_10426 $$unsorted)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP B_x BOUND_VARIABLE_10426)))) (and (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.v_F B_x)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.v_F B_x)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.v_F B_x)))))) :rule implies_neg1)
% 26.93/27.24 (anchor :step t76)
% 26.93/27.24 (assume t76.a0 (forall ((B_x $$unsorted)) (or (not (forall ((BOUND_VARIABLE_10414 $$unsorted)) (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP B_x BOUND_VARIABLE_10414)))) (not (forall ((BOUND_VARIABLE_10420 $$unsorted)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP B_x BOUND_VARIABLE_10420)))) (not (forall ((BOUND_VARIABLE_10426 $$unsorted)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP B_x BOUND_VARIABLE_10426)))) (and (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.v_F B_x)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.v_F B_x)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.v_F B_x))))))
% 26.93/27.24 (step t76.t1 (cl (or (not (forall ((B_x $$unsorted)) (or (not (forall ((BOUND_VARIABLE_10414 $$unsorted)) (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP B_x BOUND_VARIABLE_10414)))) (not (forall ((BOUND_VARIABLE_10420 $$unsorted)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP B_x BOUND_VARIABLE_10420)))) (not (forall ((BOUND_VARIABLE_10426 $$unsorted)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP B_x BOUND_VARIABLE_10426)))) (and (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.v_F B_x)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.v_F B_x)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.v_F B_x)))))) (or (not (forall ((BOUND_VARIABLE_10414 $$unsorted)) (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP tptp.v_P BOUND_VARIABLE_10414)))) (not (forall ((BOUND_VARIABLE_10420 $$unsorted)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP tptp.v_P BOUND_VARIABLE_10420)))) (not (forall ((BOUND_VARIABLE_10426 $$unsorted)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP tptp.v_P BOUND_VARIABLE_10426)))) (and (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.v_F tptp.v_P)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.v_F tptp.v_P)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.v_F tptp.v_P)))))) :rule forall_inst :args ((:= B_x tptp.v_P)))
% 26.93/27.24 (step t76.t2 (cl (not (forall ((B_x $$unsorted)) (or (not (forall ((BOUND_VARIABLE_10414 $$unsorted)) (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP B_x BOUND_VARIABLE_10414)))) (not (forall ((BOUND_VARIABLE_10420 $$unsorted)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP B_x BOUND_VARIABLE_10420)))) (not (forall ((BOUND_VARIABLE_10426 $$unsorted)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP B_x BOUND_VARIABLE_10426)))) (and (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.v_F B_x)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.v_F B_x)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.v_F B_x)))))) (or (not (forall ((BOUND_VARIABLE_10414 $$unsorted)) (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP tptp.v_P BOUND_VARIABLE_10414)))) (not (forall ((BOUND_VARIABLE_10420 $$unsorted)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP tptp.v_P BOUND_VARIABLE_10420)))) (not (forall ((BOUND_VARIABLE_10426 $$unsorted)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP tptp.v_P BOUND_VARIABLE_10426)))) (and (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.v_F tptp.v_P)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.v_F tptp.v_P)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.v_F tptp.v_P))))) :rule or :premises (t76.t1))
% 26.93/27.24 (step t76.t3 (cl (or (not (forall ((BOUND_VARIABLE_10414 $$unsorted)) (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP tptp.v_P BOUND_VARIABLE_10414)))) (not (forall ((BOUND_VARIABLE_10420 $$unsorted)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP tptp.v_P BOUND_VARIABLE_10420)))) (not (forall ((BOUND_VARIABLE_10426 $$unsorted)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP tptp.v_P BOUND_VARIABLE_10426)))) (and (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.v_F tptp.v_P)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.v_F tptp.v_P)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.v_F tptp.v_P))))) :rule resolution :premises (t76.t2 t76.a0))
% 26.93/27.24 (step t76 (cl (not (forall ((B_x $$unsorted)) (or (not (forall ((BOUND_VARIABLE_10414 $$unsorted)) (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP B_x BOUND_VARIABLE_10414)))) (not (forall ((BOUND_VARIABLE_10420 $$unsorted)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP B_x BOUND_VARIABLE_10420)))) (not (forall ((BOUND_VARIABLE_10426 $$unsorted)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP B_x BOUND_VARIABLE_10426)))) (and (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.v_F B_x)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.v_F B_x)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.v_F B_x)))))) (or (not (forall ((BOUND_VARIABLE_10414 $$unsorted)) (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP tptp.v_P BOUND_VARIABLE_10414)))) (not (forall ((BOUND_VARIABLE_10420 $$unsorted)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP tptp.v_P BOUND_VARIABLE_10420)))) (not (forall ((BOUND_VARIABLE_10426 $$unsorted)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP tptp.v_P BOUND_VARIABLE_10426)))) (and (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.v_F tptp.v_P)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.v_F tptp.v_P)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.v_F tptp.v_P))))) :rule subproof :discharge (t76.a0))
% 26.93/27.24 (step t77 (cl (=> (forall ((B_x $$unsorted)) (or (not (forall ((BOUND_VARIABLE_10414 $$unsorted)) (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP B_x BOUND_VARIABLE_10414)))) (not (forall ((BOUND_VARIABLE_10420 $$unsorted)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP B_x BOUND_VARIABLE_10420)))) (not (forall ((BOUND_VARIABLE_10426 $$unsorted)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP B_x BOUND_VARIABLE_10426)))) (and (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.v_F B_x)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.v_F B_x)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.v_F B_x))))) (or (not (forall ((BOUND_VARIABLE_10414 $$unsorted)) (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP tptp.v_P BOUND_VARIABLE_10414)))) (not (forall ((BOUND_VARIABLE_10420 $$unsorted)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP tptp.v_P BOUND_VARIABLE_10420)))) (not (forall ((BOUND_VARIABLE_10426 $$unsorted)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP tptp.v_P BOUND_VARIABLE_10426)))) (and (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.v_F tptp.v_P)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.v_F tptp.v_P)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.v_F tptp.v_P))))) (or (not (forall ((BOUND_VARIABLE_10414 $$unsorted)) (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP tptp.v_P BOUND_VARIABLE_10414)))) (not (forall ((BOUND_VARIABLE_10420 $$unsorted)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP tptp.v_P BOUND_VARIABLE_10420)))) (not (forall ((BOUND_VARIABLE_10426 $$unsorted)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP tptp.v_P BOUND_VARIABLE_10426)))) (and (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.v_F tptp.v_P)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.v_F tptp.v_P)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.v_F tptp.v_P))))) :rule resolution :premises (t75 t76))
% 26.93/27.24 (step t78 (cl (=> (forall ((B_x $$unsorted)) (or (not (forall ((BOUND_VARIABLE_10414 $$unsorted)) (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP B_x BOUND_VARIABLE_10414)))) (not (forall ((BOUND_VARIABLE_10420 $$unsorted)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP B_x BOUND_VARIABLE_10420)))) (not (forall ((BOUND_VARIABLE_10426 $$unsorted)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP B_x BOUND_VARIABLE_10426)))) (and (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.v_F B_x)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.v_F B_x)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.v_F B_x))))) (or (not (forall ((BOUND_VARIABLE_10414 $$unsorted)) (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP tptp.v_P BOUND_VARIABLE_10414)))) (not (forall ((BOUND_VARIABLE_10420 $$unsorted)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP tptp.v_P BOUND_VARIABLE_10420)))) (not (forall ((BOUND_VARIABLE_10426 $$unsorted)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP tptp.v_P BOUND_VARIABLE_10426)))) (and (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.v_F tptp.v_P)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.v_F tptp.v_P)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.v_F tptp.v_P))))) (not (or (not (forall ((BOUND_VARIABLE_10414 $$unsorted)) (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP tptp.v_P BOUND_VARIABLE_10414)))) (not (forall ((BOUND_VARIABLE_10420 $$unsorted)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP tptp.v_P BOUND_VARIABLE_10420)))) (not (forall ((BOUND_VARIABLE_10426 $$unsorted)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP tptp.v_P BOUND_VARIABLE_10426)))) (and (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.v_F tptp.v_P)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.v_F tptp.v_P)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.v_F tptp.v_P)))))) :rule implies_neg2)
% 26.93/27.24 (step t79 (cl (=> (forall ((B_x $$unsorted)) (or (not (forall ((BOUND_VARIABLE_10414 $$unsorted)) (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP B_x BOUND_VARIABLE_10414)))) (not (forall ((BOUND_VARIABLE_10420 $$unsorted)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP B_x BOUND_VARIABLE_10420)))) (not (forall ((BOUND_VARIABLE_10426 $$unsorted)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP B_x BOUND_VARIABLE_10426)))) (and (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.v_F B_x)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.v_F B_x)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.v_F B_x))))) (or (not (forall ((BOUND_VARIABLE_10414 $$unsorted)) (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP tptp.v_P BOUND_VARIABLE_10414)))) (not (forall ((BOUND_VARIABLE_10420 $$unsorted)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP tptp.v_P BOUND_VARIABLE_10420)))) (not (forall ((BOUND_VARIABLE_10426 $$unsorted)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP tptp.v_P BOUND_VARIABLE_10426)))) (and (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.v_F tptp.v_P)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.v_F tptp.v_P)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.v_F tptp.v_P))))) (=> (forall ((B_x $$unsorted)) (or (not (forall ((BOUND_VARIABLE_10414 $$unsorted)) (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP B_x BOUND_VARIABLE_10414)))) (not (forall ((BOUND_VARIABLE_10420 $$unsorted)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP B_x BOUND_VARIABLE_10420)))) (not (forall ((BOUND_VARIABLE_10426 $$unsorted)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP B_x BOUND_VARIABLE_10426)))) (and (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.v_F B_x)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.v_F B_x)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.v_F B_x))))) (or (not (forall ((BOUND_VARIABLE_10414 $$unsorted)) (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP tptp.v_P BOUND_VARIABLE_10414)))) (not (forall ((BOUND_VARIABLE_10420 $$unsorted)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP tptp.v_P BOUND_VARIABLE_10420)))) (not (forall ((BOUND_VARIABLE_10426 $$unsorted)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP tptp.v_P BOUND_VARIABLE_10426)))) (and (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.v_F tptp.v_P)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.v_F tptp.v_P)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.v_F tptp.v_P)))))) :rule resolution :premises (t77 t78))
% 26.93/27.24 (step t80 (cl (=> (forall ((B_x $$unsorted)) (or (not (forall ((BOUND_VARIABLE_10414 $$unsorted)) (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP B_x BOUND_VARIABLE_10414)))) (not (forall ((BOUND_VARIABLE_10420 $$unsorted)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP B_x BOUND_VARIABLE_10420)))) (not (forall ((BOUND_VARIABLE_10426 $$unsorted)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP B_x BOUND_VARIABLE_10426)))) (and (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.v_F B_x)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.v_F B_x)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.v_F B_x))))) (or (not (forall ((BOUND_VARIABLE_10414 $$unsorted)) (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP tptp.v_P BOUND_VARIABLE_10414)))) (not (forall ((BOUND_VARIABLE_10420 $$unsorted)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP tptp.v_P BOUND_VARIABLE_10420)))) (not (forall ((BOUND_VARIABLE_10426 $$unsorted)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP tptp.v_P BOUND_VARIABLE_10426)))) (and (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.v_F tptp.v_P)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.v_F tptp.v_P)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.v_F tptp.v_P)))))) :rule contraction :premises (t79))
% 26.93/27.24 (step t81 (cl (not (forall ((B_x $$unsorted)) (or (not (forall ((BOUND_VARIABLE_10414 $$unsorted)) (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP B_x BOUND_VARIABLE_10414)))) (not (forall ((BOUND_VARIABLE_10420 $$unsorted)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP B_x BOUND_VARIABLE_10420)))) (not (forall ((BOUND_VARIABLE_10426 $$unsorted)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP B_x BOUND_VARIABLE_10426)))) (and (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.v_F B_x)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.v_F B_x)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.v_F B_x)))))) (or (not (forall ((BOUND_VARIABLE_10414 $$unsorted)) (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP tptp.v_P BOUND_VARIABLE_10414)))) (not (forall ((BOUND_VARIABLE_10420 $$unsorted)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP tptp.v_P BOUND_VARIABLE_10420)))) (not (forall ((BOUND_VARIABLE_10426 $$unsorted)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP tptp.v_P BOUND_VARIABLE_10426)))) (and (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.v_F tptp.v_P)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.v_F tptp.v_P)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.v_F tptp.v_P))))) :rule implies :premises (t80))
% 26.93/27.24 (step t82 (cl (not (= (forall ((B_x $$unsorted)) (=> (forall ((B_xa $$unsorted)) (and (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP B_x B_xa)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP B_x B_xa)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP B_x B_xa)))) (and (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.v_F B_x)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.v_F B_x)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.v_F B_x))))) (forall ((B_x $$unsorted)) (or (not (forall ((BOUND_VARIABLE_10414 $$unsorted)) (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP B_x BOUND_VARIABLE_10414)))) (not (forall ((BOUND_VARIABLE_10420 $$unsorted)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP B_x BOUND_VARIABLE_10420)))) (not (forall ((BOUND_VARIABLE_10426 $$unsorted)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP B_x BOUND_VARIABLE_10426)))) (and (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.v_F B_x)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.v_F B_x)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.v_F B_x))))))) (not (forall ((B_x $$unsorted)) (=> (forall ((B_xa $$unsorted)) (and (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP B_x B_xa)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP B_x B_xa)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP B_x B_xa)))) (and (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.v_F B_x)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.v_F B_x)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.v_F B_x)))))) (forall ((B_x $$unsorted)) (or (not (forall ((BOUND_VARIABLE_10414 $$unsorted)) (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP B_x BOUND_VARIABLE_10414)))) (not (forall ((BOUND_VARIABLE_10420 $$unsorted)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP B_x BOUND_VARIABLE_10420)))) (not (forall ((BOUND_VARIABLE_10426 $$unsorted)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP B_x BOUND_VARIABLE_10426)))) (and (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.v_F B_x)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.v_F B_x)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.v_F B_x)))))) :rule equiv_pos2)
% 26.93/27.24 (anchor :step t83 :args ((B_x $$unsorted) (:= B_x B_x)))
% 26.93/27.24 (step t83.t1 (cl (= B_x B_x)) :rule refl)
% 26.93/27.24 (step t83.t2 (cl (= (forall ((B_xa $$unsorted)) (and (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP B_x B_xa)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP B_x B_xa)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP B_x B_xa)))) (and (forall ((BOUND_VARIABLE_10414 $$unsorted)) (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP B_x BOUND_VARIABLE_10414))) (forall ((BOUND_VARIABLE_10420 $$unsorted)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP B_x BOUND_VARIABLE_10420))) (forall ((BOUND_VARIABLE_10426 $$unsorted)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP B_x BOUND_VARIABLE_10426)))))) :rule all_simplify)
% 26.93/27.24 (step t83.t3 (cl (= (and (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.v_F B_x)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.v_F B_x)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.v_F B_x))) (and (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.v_F B_x)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.v_F B_x)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.v_F B_x))))) :rule refl)
% 26.93/27.24 (step t83.t4 (cl (= (=> (forall ((B_xa $$unsorted)) (and (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP B_x B_xa)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP B_x B_xa)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP B_x B_xa)))) (and (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.v_F B_x)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.v_F B_x)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.v_F B_x)))) (=> (and (forall ((BOUND_VARIABLE_10414 $$unsorted)) (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP B_x BOUND_VARIABLE_10414))) (forall ((BOUND_VARIABLE_10420 $$unsorted)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP B_x BOUND_VARIABLE_10420))) (forall ((BOUND_VARIABLE_10426 $$unsorted)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP B_x BOUND_VARIABLE_10426)))) (and (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.v_F B_x)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.v_F B_x)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.v_F B_x)))))) :rule cong :premises (t83.t2 t83.t3))
% 26.93/27.24 (step t83 (cl (= (forall ((B_x $$unsorted)) (=> (forall ((B_xa $$unsorted)) (and (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP B_x B_xa)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP B_x B_xa)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP B_x B_xa)))) (and (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.v_F B_x)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.v_F B_x)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.v_F B_x))))) (forall ((B_x $$unsorted)) (=> (and (forall ((BOUND_VARIABLE_10414 $$unsorted)) (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP B_x BOUND_VARIABLE_10414))) (forall ((BOUND_VARIABLE_10420 $$unsorted)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP B_x BOUND_VARIABLE_10420))) (forall ((BOUND_VARIABLE_10426 $$unsorted)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP B_x BOUND_VARIABLE_10426)))) (and (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.v_F B_x)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.v_F B_x)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.v_F B_x))))))) :rule bind)
% 26.93/27.24 (step t84 (cl (= (forall ((B_x $$unsorted)) (=> (and (forall ((BOUND_VARIABLE_10414 $$unsorted)) (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP B_x BOUND_VARIABLE_10414))) (forall ((BOUND_VARIABLE_10420 $$unsorted)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP B_x BOUND_VARIABLE_10420))) (forall ((BOUND_VARIABLE_10426 $$unsorted)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP B_x BOUND_VARIABLE_10426)))) (and (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.v_F B_x)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.v_F B_x)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.v_F B_x))))) (forall ((B_x $$unsorted)) (or (not (forall ((BOUND_VARIABLE_10414 $$unsorted)) (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP B_x BOUND_VARIABLE_10414)))) (not (forall ((BOUND_VARIABLE_10420 $$unsorted)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP B_x BOUND_VARIABLE_10420)))) (not (forall ((BOUND_VARIABLE_10426 $$unsorted)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP B_x BOUND_VARIABLE_10426)))) (and (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.v_F B_x)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.v_F B_x)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.v_F B_x))))))) :rule all_simplify)
% 26.93/27.24 (step t85 (cl (= (forall ((B_x $$unsorted)) (=> (forall ((B_xa $$unsorted)) (and (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP B_x B_xa)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP B_x B_xa)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP B_x B_xa)))) (and (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.v_F B_x)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.v_F B_x)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.v_F B_x))))) (forall ((B_x $$unsorted)) (or (not (forall ((BOUND_VARIABLE_10414 $$unsorted)) (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP B_x BOUND_VARIABLE_10414)))) (not (forall ((BOUND_VARIABLE_10420 $$unsorted)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP B_x BOUND_VARIABLE_10420)))) (not (forall ((BOUND_VARIABLE_10426 $$unsorted)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP B_x BOUND_VARIABLE_10426)))) (and (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.v_F B_x)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.v_F B_x)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.v_F B_x))))))) :rule trans :premises (t83 t84))
% 26.93/27.24 (step t86 (cl (forall ((B_x $$unsorted)) (or (not (forall ((BOUND_VARIABLE_10414 $$unsorted)) (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP B_x BOUND_VARIABLE_10414)))) (not (forall ((BOUND_VARIABLE_10420 $$unsorted)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP B_x BOUND_VARIABLE_10420)))) (not (forall ((BOUND_VARIABLE_10426 $$unsorted)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP B_x BOUND_VARIABLE_10426)))) (and (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.v_F B_x)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.v_F B_x)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.v_F B_x)))))) :rule resolution :premises (t82 t85 a522))
% 26.93/27.24 (step t87 (cl (or (not (forall ((BOUND_VARIABLE_10414 $$unsorted)) (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP tptp.v_P BOUND_VARIABLE_10414)))) (not (forall ((BOUND_VARIABLE_10420 $$unsorted)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP tptp.v_P BOUND_VARIABLE_10420)))) (not (forall ((BOUND_VARIABLE_10426 $$unsorted)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP tptp.v_P BOUND_VARIABLE_10426)))) (and (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.v_F tptp.v_P)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.v_F tptp.v_P)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.v_F tptp.v_P))))) :rule resolution :premises (t81 t86))
% 26.93/27.24 (step t88 (cl (and (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.v_F tptp.v_P)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.v_F tptp.v_P)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.v_F tptp.v_P)))) :rule resolution :premises (t59 t66 t70 t74 t87))
% 26.93/27.24 (step t89 (cl (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.v_F tptp.v_P))) :rule resolution :premises (t57 t88))
% 26.93/27.24 (step t90 (cl (=> (forall ((V_r_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_Oirrefl T_a V_r_2) (forall ((B_x $$unsorted)) (not (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a B_x B_x) V_r_2))))) (= (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.v_F tptp.v_P)) (forall ((B_x $$unsorted)) (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt B_x B_x) (tptp.v_F tptp.v_P)))))) (forall ((V_r_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_Oirrefl T_a V_r_2) (forall ((B_x $$unsorted)) (not (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a B_x B_x) V_r_2)))))) :rule implies_neg1)
% 26.93/27.24 (anchor :step t91)
% 26.93/27.24 (assume t91.a0 (forall ((V_r_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_Oirrefl T_a V_r_2) (forall ((B_x $$unsorted)) (not (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a B_x B_x) V_r_2))))))
% 26.93/27.24 (step t91.t1 (cl (or (not (forall ((V_r_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_Oirrefl T_a V_r_2) (forall ((B_x $$unsorted)) (not (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a B_x B_x) V_r_2)))))) (= (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.v_F tptp.v_P)) (forall ((B_x $$unsorted)) (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt B_x B_x) (tptp.v_F tptp.v_P))))))) :rule forall_inst :args ((:= V_r_2 (tptp.v_F tptp.v_P)) (:= T_a tptp.tc_Arrow__Order__Mirabelle_Oalt)))
% 26.93/27.24 (step t91.t2 (cl (not (forall ((V_r_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_Oirrefl T_a V_r_2) (forall ((B_x $$unsorted)) (not (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a B_x B_x) V_r_2)))))) (= (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.v_F tptp.v_P)) (forall ((B_x $$unsorted)) (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt B_x B_x) (tptp.v_F tptp.v_P)))))) :rule or :premises (t91.t1))
% 26.93/27.24 (step t91.t3 (cl (= (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.v_F tptp.v_P)) (forall ((B_x $$unsorted)) (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt B_x B_x) (tptp.v_F tptp.v_P)))))) :rule resolution :premises (t91.t2 t91.a0))
% 26.93/27.24 (step t91 (cl (not (forall ((V_r_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_Oirrefl T_a V_r_2) (forall ((B_x $$unsorted)) (not (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a B_x B_x) V_r_2)))))) (= (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.v_F tptp.v_P)) (forall ((B_x $$unsorted)) (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt B_x B_x) (tptp.v_F tptp.v_P)))))) :rule subproof :discharge (t91.a0))
% 26.93/27.24 (step t92 (cl (=> (forall ((V_r_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_Oirrefl T_a V_r_2) (forall ((B_x $$unsorted)) (not (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a B_x B_x) V_r_2))))) (= (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.v_F tptp.v_P)) (forall ((B_x $$unsorted)) (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt B_x B_x) (tptp.v_F tptp.v_P)))))) (= (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.v_F tptp.v_P)) (forall ((B_x $$unsorted)) (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt B_x B_x) (tptp.v_F tptp.v_P)))))) :rule resolution :premises (t90 t91))
% 26.93/27.24 (step t93 (cl (=> (forall ((V_r_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_Oirrefl T_a V_r_2) (forall ((B_x $$unsorted)) (not (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a B_x B_x) V_r_2))))) (= (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.v_F tptp.v_P)) (forall ((B_x $$unsorted)) (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt B_x B_x) (tptp.v_F tptp.v_P)))))) (not (= (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.v_F tptp.v_P)) (forall ((B_x $$unsorted)) (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt B_x B_x) (tptp.v_F tptp.v_P))))))) :rule implies_neg2)
% 26.93/27.24 (step t94 (cl (=> (forall ((V_r_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_Oirrefl T_a V_r_2) (forall ((B_x $$unsorted)) (not (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a B_x B_x) V_r_2))))) (= (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.v_F tptp.v_P)) (forall ((B_x $$unsorted)) (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt B_x B_x) (tptp.v_F tptp.v_P)))))) (=> (forall ((V_r_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_Oirrefl T_a V_r_2) (forall ((B_x $$unsorted)) (not (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a B_x B_x) V_r_2))))) (= (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.v_F tptp.v_P)) (forall ((B_x $$unsorted)) (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt B_x B_x) (tptp.v_F tptp.v_P))))))) :rule resolution :premises (t92 t93))
% 26.93/27.24 (step t95 (cl (=> (forall ((V_r_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_Oirrefl T_a V_r_2) (forall ((B_x $$unsorted)) (not (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a B_x B_x) V_r_2))))) (= (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.v_F tptp.v_P)) (forall ((B_x $$unsorted)) (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt B_x B_x) (tptp.v_F tptp.v_P))))))) :rule contraction :premises (t94))
% 26.93/27.24 (step t96 (cl (not (forall ((V_r_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_Oirrefl T_a V_r_2) (forall ((B_x $$unsorted)) (not (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a B_x B_x) V_r_2)))))) (= (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.v_F tptp.v_P)) (forall ((B_x $$unsorted)) (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt B_x B_x) (tptp.v_F tptp.v_P)))))) :rule implies :premises (t95))
% 26.93/27.24 (step t97 (cl (= (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.v_F tptp.v_P)) (forall ((B_x $$unsorted)) (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt B_x B_x) (tptp.v_F tptp.v_P)))))) :rule resolution :premises (t96 a2))
% 26.93/27.24 (step t98 (cl (forall ((B_x $$unsorted)) (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt B_x B_x) (tptp.v_F tptp.v_P))))) :rule resolution :premises (t55 t89 t97))
% 26.93/27.24 (step t99 (cl (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_a) (tptp.v_F tptp.v_P)))) :rule resolution :premises (t53 t98))
% 26.93/27.24 (step t100 (cl (not (= tptp.v_a tptp.v_b))) :rule resolution :premises (t46 t99 a525))
% 26.93/27.24 (step t101 (cl (not (or (not (forall ((BOUND_VARIABLE_10443 $$unsorted)) (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP tptp.v_P BOUND_VARIABLE_10443)))) (not (forall ((BOUND_VARIABLE_10449 $$unsorted)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP tptp.v_P BOUND_VARIABLE_10449)))) (not (forall ((BOUND_VARIABLE_10455 $$unsorted)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP tptp.v_P BOUND_VARIABLE_10455)))) (= tptp.v_a tptp.v_b) (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_b tptp.v_a) (tptp.hAPP tptp.v_P tptp.v_i))) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_b tptp.v_a) (tptp.v_F tptp.v_P)))) (not (forall ((BOUND_VARIABLE_10443 $$unsorted)) (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP tptp.v_P BOUND_VARIABLE_10443)))) (not (forall ((BOUND_VARIABLE_10449 $$unsorted)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP tptp.v_P BOUND_VARIABLE_10449)))) (not (forall ((BOUND_VARIABLE_10455 $$unsorted)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP tptp.v_P BOUND_VARIABLE_10455)))) (= tptp.v_a tptp.v_b) (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_b tptp.v_a) (tptp.hAPP tptp.v_P tptp.v_i))) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_b tptp.v_a) (tptp.v_F tptp.v_P))) :rule or_pos)
% 26.93/27.24 (step t102 (cl (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_b tptp.v_a) (tptp.v_F tptp.v_P)) (= tptp.v_a tptp.v_b) (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_b tptp.v_a) (tptp.hAPP tptp.v_P tptp.v_i))) (not (forall ((BOUND_VARIABLE_10443 $$unsorted)) (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP tptp.v_P BOUND_VARIABLE_10443)))) (not (forall ((BOUND_VARIABLE_10449 $$unsorted)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP tptp.v_P BOUND_VARIABLE_10449)))) (not (forall ((BOUND_VARIABLE_10455 $$unsorted)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP tptp.v_P BOUND_VARIABLE_10455)))) (not (or (not (forall ((BOUND_VARIABLE_10443 $$unsorted)) (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP tptp.v_P BOUND_VARIABLE_10443)))) (not (forall ((BOUND_VARIABLE_10449 $$unsorted)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP tptp.v_P BOUND_VARIABLE_10449)))) (not (forall ((BOUND_VARIABLE_10455 $$unsorted)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP tptp.v_P BOUND_VARIABLE_10455)))) (= tptp.v_a tptp.v_b) (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_b tptp.v_a) (tptp.hAPP tptp.v_P tptp.v_i))) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_b tptp.v_a) (tptp.v_F tptp.v_P))))) :rule reordering :premises (t101))
% 26.93/27.24 (step t103 (cl (not (or (not (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.v_F tptp.v_P))) (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_b) (tptp.v_F tptp.v_P))) (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_b tptp.v_a) (tptp.v_F tptp.v_P))) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_a) (tptp.v_F tptp.v_P)))) (not (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.v_F tptp.v_P))) (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_b) (tptp.v_F tptp.v_P))) (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_b tptp.v_a) (tptp.v_F tptp.v_P))) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_a) (tptp.v_F tptp.v_P))) :rule or_pos)
% 26.93/27.24 (step t104 (cl (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_b) (tptp.v_F tptp.v_P))) (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_b tptp.v_a) (tptp.v_F tptp.v_P))) (not (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.v_F tptp.v_P))) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_a) (tptp.v_F tptp.v_P)) (not (or (not (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.v_F tptp.v_P))) (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_b) (tptp.v_F tptp.v_P))) (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_b tptp.v_a) (tptp.v_F tptp.v_P))) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_a) (tptp.v_F tptp.v_P))))) :rule reordering :premises (t103))
% 26.93/27.24 (step t105 (cl (not (and (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.v_F tptp.v_P)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.v_F tptp.v_P)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.v_F tptp.v_P)))) (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.v_F tptp.v_P))) :rule and_pos)
% 26.93/27.24 (step t106 (cl (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.v_F tptp.v_P)) (not (and (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.v_F tptp.v_P)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.v_F tptp.v_P)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.v_F tptp.v_P))))) :rule reordering :premises (t105))
% 26.93/27.24 (step t107 (cl (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.v_F tptp.v_P))) :rule resolution :premises (t106 t88))
% 26.93/27.24 (step t108 (cl (=> (forall ((V_c_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (V_r_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.c_Relation_Otrans T_a V_r_2)) (not (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_a_2 V_b_2) V_r_2)) (not (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_b_2 V_c_2) V_r_2)) (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_a_2 V_c_2) V_r_2))) (or (not (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.v_F tptp.v_P))) (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_b) (tptp.v_F tptp.v_P))) (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_b tptp.v_a) (tptp.v_F tptp.v_P))) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_a) (tptp.v_F tptp.v_P)))) (forall ((V_c_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (V_r_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.c_Relation_Otrans T_a V_r_2)) (not (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_a_2 V_b_2) V_r_2)) (not (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_b_2 V_c_2) V_r_2)) (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_a_2 V_c_2) V_r_2)))) :rule implies_neg1)
% 26.93/27.24 (anchor :step t109)
% 26.93/27.24 (assume t109.a0 (forall ((V_c_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (V_r_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.c_Relation_Otrans T_a V_r_2)) (not (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_a_2 V_b_2) V_r_2)) (not (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_b_2 V_c_2) V_r_2)) (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_a_2 V_c_2) V_r_2))))
% 26.93/27.24 (step t109.t1 (cl (or (not (forall ((V_c_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (V_r_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.c_Relation_Otrans T_a V_r_2)) (not (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_a_2 V_b_2) V_r_2)) (not (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_b_2 V_c_2) V_r_2)) (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_a_2 V_c_2) V_r_2)))) (or (not (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.v_F tptp.v_P))) (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_b) (tptp.v_F tptp.v_P))) (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_b tptp.v_a) (tptp.v_F tptp.v_P))) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_a) (tptp.v_F tptp.v_P))))) :rule forall_inst :args ((:= V_c_2 tptp.v_a) (:= V_b_2 tptp.v_b) (:= V_a_2 tptp.v_a) (:= V_r_2 (tptp.v_F tptp.v_P)) (:= T_a tptp.tc_Arrow__Order__Mirabelle_Oalt)))
% 26.93/27.24 (step t109.t2 (cl (not (forall ((V_c_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (V_r_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.c_Relation_Otrans T_a V_r_2)) (not (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_a_2 V_b_2) V_r_2)) (not (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_b_2 V_c_2) V_r_2)) (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_a_2 V_c_2) V_r_2)))) (or (not (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.v_F tptp.v_P))) (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_b) (tptp.v_F tptp.v_P))) (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_b tptp.v_a) (tptp.v_F tptp.v_P))) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_a) (tptp.v_F tptp.v_P)))) :rule or :premises (t109.t1))
% 26.93/27.24 (step t109.t3 (cl (or (not (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.v_F tptp.v_P))) (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_b) (tptp.v_F tptp.v_P))) (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_b tptp.v_a) (tptp.v_F tptp.v_P))) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_a) (tptp.v_F tptp.v_P)))) :rule resolution :premises (t109.t2 t109.a0))
% 26.93/27.24 (step t109 (cl (not (forall ((V_c_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (V_r_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.c_Relation_Otrans T_a V_r_2)) (not (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_a_2 V_b_2) V_r_2)) (not (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_b_2 V_c_2) V_r_2)) (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_a_2 V_c_2) V_r_2)))) (or (not (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.v_F tptp.v_P))) (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_b) (tptp.v_F tptp.v_P))) (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_b tptp.v_a) (tptp.v_F tptp.v_P))) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_a) (tptp.v_F tptp.v_P)))) :rule subproof :discharge (t109.a0))
% 26.93/27.24 (step t110 (cl (=> (forall ((V_c_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (V_r_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.c_Relation_Otrans T_a V_r_2)) (not (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_a_2 V_b_2) V_r_2)) (not (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_b_2 V_c_2) V_r_2)) (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_a_2 V_c_2) V_r_2))) (or (not (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.v_F tptp.v_P))) (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_b) (tptp.v_F tptp.v_P))) (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_b tptp.v_a) (tptp.v_F tptp.v_P))) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_a) (tptp.v_F tptp.v_P)))) (or (not (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.v_F tptp.v_P))) (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_b) (tptp.v_F tptp.v_P))) (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_b tptp.v_a) (tptp.v_F tptp.v_P))) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_a) (tptp.v_F tptp.v_P)))) :rule resolution :premises (t108 t109))
% 26.93/27.24 (step t111 (cl (=> (forall ((V_c_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (V_r_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.c_Relation_Otrans T_a V_r_2)) (not (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_a_2 V_b_2) V_r_2)) (not (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_b_2 V_c_2) V_r_2)) (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_a_2 V_c_2) V_r_2))) (or (not (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.v_F tptp.v_P))) (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_b) (tptp.v_F tptp.v_P))) (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_b tptp.v_a) (tptp.v_F tptp.v_P))) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_a) (tptp.v_F tptp.v_P)))) (not (or (not (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.v_F tptp.v_P))) (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_b) (tptp.v_F tptp.v_P))) (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_b tptp.v_a) (tptp.v_F tptp.v_P))) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_a) (tptp.v_F tptp.v_P))))) :rule implies_neg2)
% 26.93/27.24 (step t112 (cl (=> (forall ((V_c_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (V_r_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.c_Relation_Otrans T_a V_r_2)) (not (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_a_2 V_b_2) V_r_2)) (not (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_b_2 V_c_2) V_r_2)) (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_a_2 V_c_2) V_r_2))) (or (not (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.v_F tptp.v_P))) (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_b) (tptp.v_F tptp.v_P))) (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_b tptp.v_a) (tptp.v_F tptp.v_P))) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_a) (tptp.v_F tptp.v_P)))) (=> (forall ((V_c_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (V_r_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.c_Relation_Otrans T_a V_r_2)) (not (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_a_2 V_b_2) V_r_2)) (not (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_b_2 V_c_2) V_r_2)) (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_a_2 V_c_2) V_r_2))) (or (not (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.v_F tptp.v_P))) (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_b) (tptp.v_F tptp.v_P))) (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_b tptp.v_a) (tptp.v_F tptp.v_P))) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_a) (tptp.v_F tptp.v_P))))) :rule resolution :premises (t110 t111))
% 26.93/27.24 (step t113 (cl (=> (forall ((V_c_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (V_r_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.c_Relation_Otrans T_a V_r_2)) (not (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_a_2 V_b_2) V_r_2)) (not (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_b_2 V_c_2) V_r_2)) (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_a_2 V_c_2) V_r_2))) (or (not (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.v_F tptp.v_P))) (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_b) (tptp.v_F tptp.v_P))) (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_b tptp.v_a) (tptp.v_F tptp.v_P))) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_a) (tptp.v_F tptp.v_P))))) :rule contraction :premises (t112))
% 26.93/27.24 (step t114 (cl (not (forall ((V_c_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (V_r_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.c_Relation_Otrans T_a V_r_2)) (not (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_a_2 V_b_2) V_r_2)) (not (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_b_2 V_c_2) V_r_2)) (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_a_2 V_c_2) V_r_2)))) (or (not (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.v_F tptp.v_P))) (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_b) (tptp.v_F tptp.v_P))) (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_b tptp.v_a) (tptp.v_F tptp.v_P))) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_a) (tptp.v_F tptp.v_P)))) :rule implies :premises (t113))
% 26.93/27.24 (step t115 (cl (not (= (forall ((V_c_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (V_r_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Relation_Otrans T_a V_r_2) (=> (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_a_2 V_b_2) V_r_2) (=> (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_b_2 V_c_2) V_r_2) (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_a_2 V_c_2) V_r_2))))) (forall ((V_c_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (V_r_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.c_Relation_Otrans T_a V_r_2)) (not (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_a_2 V_b_2) V_r_2)) (not (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_b_2 V_c_2) V_r_2)) (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_a_2 V_c_2) V_r_2))))) (not (forall ((V_c_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (V_r_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Relation_Otrans T_a V_r_2) (=> (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_a_2 V_b_2) V_r_2) (=> (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_b_2 V_c_2) V_r_2) (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_a_2 V_c_2) V_r_2)))))) (forall ((V_c_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (V_r_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.c_Relation_Otrans T_a V_r_2)) (not (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_a_2 V_b_2) V_r_2)) (not (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_b_2 V_c_2) V_r_2)) (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_a_2 V_c_2) V_r_2)))) :rule equiv_pos2)
% 26.93/27.24 (step t116 (cl (= (forall ((V_c_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (V_r_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Relation_Otrans T_a V_r_2) (=> (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_a_2 V_b_2) V_r_2) (=> (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_b_2 V_c_2) V_r_2) (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_a_2 V_c_2) V_r_2))))) (forall ((V_c_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (V_r_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.c_Relation_Otrans T_a V_r_2)) (not (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_a_2 V_b_2) V_r_2)) (not (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_b_2 V_c_2) V_r_2)) (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_a_2 V_c_2) V_r_2))))) :rule all_simplify)
% 26.93/27.24 (step t117 (cl (forall ((V_c_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (V_r_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.c_Relation_Otrans T_a V_r_2)) (not (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_a_2 V_b_2) V_r_2)) (not (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_b_2 V_c_2) V_r_2)) (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_a_2 V_c_2) V_r_2)))) :rule resolution :premises (t115 t116 a5))
% 26.93/27.24 (step t118 (cl (or (not (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.v_F tptp.v_P))) (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_b) (tptp.v_F tptp.v_P))) (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_b tptp.v_a) (tptp.v_F tptp.v_P))) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_a) (tptp.v_F tptp.v_P)))) :rule resolution :premises (t114 t117))
% 26.93/27.24 (step t119 (cl (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_b tptp.v_a) (tptp.v_F tptp.v_P)))) :rule resolution :premises (t104 a525 t107 t99 t118))
% 26.93/27.24 (step t120 (cl (= (forall ((BOUND_VARIABLE_10491 $$unsorted)) (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP tptp.v_P BOUND_VARIABLE_10491))) (forall ((BOUND_VARIABLE_10443 $$unsorted)) (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP tptp.v_P BOUND_VARIABLE_10443))))) :rule hole :args ((forall ((BOUND_VARIABLE_10491 $$unsorted)) (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP tptp.v_P BOUND_VARIABLE_10491))) (= BOUND_VARIABLE_10491 BOUND_VARIABLE_10443)))
% 26.93/27.24 (step t121 (cl (not (forall ((BOUND_VARIABLE_10491 $$unsorted)) (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP tptp.v_P BOUND_VARIABLE_10491)))) (forall ((BOUND_VARIABLE_10443 $$unsorted)) (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP tptp.v_P BOUND_VARIABLE_10443)))) :rule equiv1 :premises (t120))
% 26.93/27.24 (step t122 (cl (forall ((BOUND_VARIABLE_10443 $$unsorted)) (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP tptp.v_P BOUND_VARIABLE_10443)))) :rule resolution :premises (t121 t65))
% 26.93/27.24 (step t123 (cl (= (forall ((BOUND_VARIABLE_10497 $$unsorted)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP tptp.v_P BOUND_VARIABLE_10497))) (forall ((BOUND_VARIABLE_10449 $$unsorted)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP tptp.v_P BOUND_VARIABLE_10449))))) :rule hole :args ((forall ((BOUND_VARIABLE_10497 $$unsorted)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP tptp.v_P BOUND_VARIABLE_10497))) (= BOUND_VARIABLE_10497 BOUND_VARIABLE_10449)))
% 26.93/27.24 (step t124 (cl (not (forall ((BOUND_VARIABLE_10497 $$unsorted)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP tptp.v_P BOUND_VARIABLE_10497)))) (forall ((BOUND_VARIABLE_10449 $$unsorted)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP tptp.v_P BOUND_VARIABLE_10449)))) :rule equiv1 :premises (t123))
% 26.93/27.24 (step t125 (cl (forall ((BOUND_VARIABLE_10449 $$unsorted)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP tptp.v_P BOUND_VARIABLE_10449)))) :rule resolution :premises (t124 t69))
% 26.93/27.24 (step t126 (cl (= (forall ((BOUND_VARIABLE_10503 $$unsorted)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP tptp.v_P BOUND_VARIABLE_10503))) (forall ((BOUND_VARIABLE_10455 $$unsorted)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP tptp.v_P BOUND_VARIABLE_10455))))) :rule hole :args ((forall ((BOUND_VARIABLE_10503 $$unsorted)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP tptp.v_P BOUND_VARIABLE_10503))) (= BOUND_VARIABLE_10503 BOUND_VARIABLE_10455)))
% 26.93/27.24 (step t127 (cl (not (forall ((BOUND_VARIABLE_10503 $$unsorted)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP tptp.v_P BOUND_VARIABLE_10503)))) (forall ((BOUND_VARIABLE_10455 $$unsorted)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP tptp.v_P BOUND_VARIABLE_10455)))) :rule equiv1 :premises (t126))
% 26.93/27.24 (step t128 (cl (forall ((BOUND_VARIABLE_10455 $$unsorted)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP tptp.v_P BOUND_VARIABLE_10455)))) :rule resolution :premises (t127 t73))
% 26.93/27.24 (step t129 (cl (not (= (=> (forall ((B_P $$unsorted) (BOUND_VARIABLE_10477 $$unsorted) (BOUND_VARIABLE_10475 $$unsorted)) (or (not (forall ((BOUND_VARIABLE_10443 $$unsorted)) (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP B_P BOUND_VARIABLE_10443)))) (not (forall ((BOUND_VARIABLE_10449 $$unsorted)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP B_P BOUND_VARIABLE_10449)))) (not (forall ((BOUND_VARIABLE_10455 $$unsorted)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP B_P BOUND_VARIABLE_10455)))) (= BOUND_VARIABLE_10475 BOUND_VARIABLE_10477) (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt BOUND_VARIABLE_10475 BOUND_VARIABLE_10477) (tptp.hAPP B_P tptp.v_i))) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt BOUND_VARIABLE_10475 BOUND_VARIABLE_10477) (tptp.v_F B_P)))) (or (not (forall ((BOUND_VARIABLE_10443 $$unsorted)) (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP tptp.v_P BOUND_VARIABLE_10443)))) (not (forall ((BOUND_VARIABLE_10449 $$unsorted)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP tptp.v_P BOUND_VARIABLE_10449)))) (not (forall ((BOUND_VARIABLE_10455 $$unsorted)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP tptp.v_P BOUND_VARIABLE_10455)))) (= tptp.v_b tptp.v_a) (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_b tptp.v_a) (tptp.hAPP tptp.v_P tptp.v_i))) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_b tptp.v_a) (tptp.v_F tptp.v_P)))) (=> (forall ((B_P $$unsorted) (BOUND_VARIABLE_10477 $$unsorted) (BOUND_VARIABLE_10475 $$unsorted)) (or (not (forall ((BOUND_VARIABLE_10443 $$unsorted)) (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP B_P BOUND_VARIABLE_10443)))) (not (forall ((BOUND_VARIABLE_10449 $$unsorted)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP B_P BOUND_VARIABLE_10449)))) (not (forall ((BOUND_VARIABLE_10455 $$unsorted)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP B_P BOUND_VARIABLE_10455)))) (= BOUND_VARIABLE_10475 BOUND_VARIABLE_10477) (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt BOUND_VARIABLE_10475 BOUND_VARIABLE_10477) (tptp.hAPP B_P tptp.v_i))) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt BOUND_VARIABLE_10475 BOUND_VARIABLE_10477) (tptp.v_F B_P)))) (or (not (forall ((BOUND_VARIABLE_10443 $$unsorted)) (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP tptp.v_P BOUND_VARIABLE_10443)))) (not (forall ((BOUND_VARIABLE_10449 $$unsorted)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP tptp.v_P BOUND_VARIABLE_10449)))) (not (forall ((BOUND_VARIABLE_10455 $$unsorted)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP tptp.v_P BOUND_VARIABLE_10455)))) (= tptp.v_a tptp.v_b) (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_b tptp.v_a) (tptp.hAPP tptp.v_P tptp.v_i))) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_b tptp.v_a) (tptp.v_F tptp.v_P)))))) (not (=> (forall ((B_P $$unsorted) (BOUND_VARIABLE_10477 $$unsorted) (BOUND_VARIABLE_10475 $$unsorted)) (or (not (forall ((BOUND_VARIABLE_10443 $$unsorted)) (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP B_P BOUND_VARIABLE_10443)))) (not (forall ((BOUND_VARIABLE_10449 $$unsorted)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP B_P BOUND_VARIABLE_10449)))) (not (forall ((BOUND_VARIABLE_10455 $$unsorted)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP B_P BOUND_VARIABLE_10455)))) (= BOUND_VARIABLE_10475 BOUND_VARIABLE_10477) (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt BOUND_VARIABLE_10475 BOUND_VARIABLE_10477) (tptp.hAPP B_P tptp.v_i))) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt BOUND_VARIABLE_10475 BOUND_VARIABLE_10477) (tptp.v_F B_P)))) (or (not (forall ((BOUND_VARIABLE_10443 $$unsorted)) (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP tptp.v_P BOUND_VARIABLE_10443)))) (not (forall ((BOUND_VARIABLE_10449 $$unsorted)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP tptp.v_P BOUND_VARIABLE_10449)))) (not (forall ((BOUND_VARIABLE_10455 $$unsorted)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP tptp.v_P BOUND_VARIABLE_10455)))) (= tptp.v_b tptp.v_a) (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_b tptp.v_a) (tptp.hAPP tptp.v_P tptp.v_i))) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_b tptp.v_a) (tptp.v_F tptp.v_P))))) (=> (forall ((B_P $$unsorted) (BOUND_VARIABLE_10477 $$unsorted) (BOUND_VARIABLE_10475 $$unsorted)) (or (not (forall ((BOUND_VARIABLE_10443 $$unsorted)) (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP B_P BOUND_VARIABLE_10443)))) (not (forall ((BOUND_VARIABLE_10449 $$unsorted)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP B_P BOUND_VARIABLE_10449)))) (not (forall ((BOUND_VARIABLE_10455 $$unsorted)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP B_P BOUND_VARIABLE_10455)))) (= BOUND_VARIABLE_10475 BOUND_VARIABLE_10477) (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt BOUND_VARIABLE_10475 BOUND_VARIABLE_10477) (tptp.hAPP B_P tptp.v_i))) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt BOUND_VARIABLE_10475 BOUND_VARIABLE_10477) (tptp.v_F B_P)))) (or (not (forall ((BOUND_VARIABLE_10443 $$unsorted)) (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP tptp.v_P BOUND_VARIABLE_10443)))) (not (forall ((BOUND_VARIABLE_10449 $$unsorted)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP tptp.v_P BOUND_VARIABLE_10449)))) (not (forall ((BOUND_VARIABLE_10455 $$unsorted)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP tptp.v_P BOUND_VARIABLE_10455)))) (= tptp.v_a tptp.v_b) (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_b tptp.v_a) (tptp.hAPP tptp.v_P tptp.v_i))) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_b tptp.v_a) (tptp.v_F tptp.v_P))))) :rule equiv_pos2)
% 26.93/27.24 (step t130 (cl (= (forall ((B_P $$unsorted) (BOUND_VARIABLE_10477 $$unsorted) (BOUND_VARIABLE_10475 $$unsorted)) (or (not (forall ((BOUND_VARIABLE_10443 $$unsorted)) (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP B_P BOUND_VARIABLE_10443)))) (not (forall ((BOUND_VARIABLE_10449 $$unsorted)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP B_P BOUND_VARIABLE_10449)))) (not (forall ((BOUND_VARIABLE_10455 $$unsorted)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP B_P BOUND_VARIABLE_10455)))) (= BOUND_VARIABLE_10475 BOUND_VARIABLE_10477) (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt BOUND_VARIABLE_10475 BOUND_VARIABLE_10477) (tptp.hAPP B_P tptp.v_i))) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt BOUND_VARIABLE_10475 BOUND_VARIABLE_10477) (tptp.v_F B_P)))) (forall ((B_P $$unsorted) (BOUND_VARIABLE_10477 $$unsorted) (BOUND_VARIABLE_10475 $$unsorted)) (or (not (forall ((BOUND_VARIABLE_10443 $$unsorted)) (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP B_P BOUND_VARIABLE_10443)))) (not (forall ((BOUND_VARIABLE_10449 $$unsorted)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP B_P BOUND_VARIABLE_10449)))) (not (forall ((BOUND_VARIABLE_10455 $$unsorted)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP B_P BOUND_VARIABLE_10455)))) (= BOUND_VARIABLE_10475 BOUND_VARIABLE_10477) (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt BOUND_VARIABLE_10475 BOUND_VARIABLE_10477) (tptp.hAPP B_P tptp.v_i))) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt BOUND_VARIABLE_10475 BOUND_VARIABLE_10477) (tptp.v_F B_P)))))) :rule refl)
% 26.93/27.24 (step t131 (cl (= (not (forall ((BOUND_VARIABLE_10443 $$unsorted)) (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP tptp.v_P BOUND_VARIABLE_10443)))) (not (forall ((BOUND_VARIABLE_10443 $$unsorted)) (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP tptp.v_P BOUND_VARIABLE_10443)))))) :rule refl)
% 26.93/27.24 (step t132 (cl (= (not (forall ((BOUND_VARIABLE_10449 $$unsorted)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP tptp.v_P BOUND_VARIABLE_10449)))) (not (forall ((BOUND_VARIABLE_10449 $$unsorted)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP tptp.v_P BOUND_VARIABLE_10449)))))) :rule refl)
% 26.93/27.24 (step t133 (cl (= (not (forall ((BOUND_VARIABLE_10455 $$unsorted)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP tptp.v_P BOUND_VARIABLE_10455)))) (not (forall ((BOUND_VARIABLE_10455 $$unsorted)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP tptp.v_P BOUND_VARIABLE_10455)))))) :rule refl)
% 26.93/27.24 (step t134 (cl (= (= tptp.v_b tptp.v_a) (= tptp.v_a tptp.v_b))) :rule all_simplify)
% 26.93/27.24 (step t135 (cl (= (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_b tptp.v_a) (tptp.hAPP tptp.v_P tptp.v_i))) (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_b tptp.v_a) (tptp.hAPP tptp.v_P tptp.v_i))))) :rule refl)
% 26.93/27.24 (step t136 (cl (= (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_b tptp.v_a) (tptp.v_F tptp.v_P)) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_b tptp.v_a) (tptp.v_F tptp.v_P)))) :rule refl)
% 26.93/27.24 (step t137 (cl (= (or (not (forall ((BOUND_VARIABLE_10443 $$unsorted)) (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP tptp.v_P BOUND_VARIABLE_10443)))) (not (forall ((BOUND_VARIABLE_10449 $$unsorted)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP tptp.v_P BOUND_VARIABLE_10449)))) (not (forall ((BOUND_VARIABLE_10455 $$unsorted)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP tptp.v_P BOUND_VARIABLE_10455)))) (= tptp.v_b tptp.v_a) (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_b tptp.v_a) (tptp.hAPP tptp.v_P tptp.v_i))) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_b tptp.v_a) (tptp.v_F tptp.v_P))) (or (not (forall ((BOUND_VARIABLE_10443 $$unsorted)) (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP tptp.v_P BOUND_VARIABLE_10443)))) (not (forall ((BOUND_VARIABLE_10449 $$unsorted)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP tptp.v_P BOUND_VARIABLE_10449)))) (not (forall ((BOUND_VARIABLE_10455 $$unsorted)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP tptp.v_P BOUND_VARIABLE_10455)))) (= tptp.v_a tptp.v_b) (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_b tptp.v_a) (tptp.hAPP tptp.v_P tptp.v_i))) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_b tptp.v_a) (tptp.v_F tptp.v_P))))) :rule cong :premises (t131 t132 t133 t134 t135 t136))
% 26.93/27.24 (step t138 (cl (= (=> (forall ((B_P $$unsorted) (BOUND_VARIABLE_10477 $$unsorted) (BOUND_VARIABLE_10475 $$unsorted)) (or (not (forall ((BOUND_VARIABLE_10443 $$unsorted)) (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP B_P BOUND_VARIABLE_10443)))) (not (forall ((BOUND_VARIABLE_10449 $$unsorted)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP B_P BOUND_VARIABLE_10449)))) (not (forall ((BOUND_VARIABLE_10455 $$unsorted)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP B_P BOUND_VARIABLE_10455)))) (= BOUND_VARIABLE_10475 BOUND_VARIABLE_10477) (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt BOUND_VARIABLE_10475 BOUND_VARIABLE_10477) (tptp.hAPP B_P tptp.v_i))) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt BOUND_VARIABLE_10475 BOUND_VARIABLE_10477) (tptp.v_F B_P)))) (or (not (forall ((BOUND_VARIABLE_10443 $$unsorted)) (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP tptp.v_P BOUND_VARIABLE_10443)))) (not (forall ((BOUND_VARIABLE_10449 $$unsorted)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP tptp.v_P BOUND_VARIABLE_10449)))) (not (forall ((BOUND_VARIABLE_10455 $$unsorted)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP tptp.v_P BOUND_VARIABLE_10455)))) (= tptp.v_b tptp.v_a) (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_b tptp.v_a) (tptp.hAPP tptp.v_P tptp.v_i))) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_b tptp.v_a) (tptp.v_F tptp.v_P)))) (=> (forall ((B_P $$unsorted) (BOUND_VARIABLE_10477 $$unsorted) (BOUND_VARIABLE_10475 $$unsorted)) (or (not (forall ((BOUND_VARIABLE_10443 $$unsorted)) (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP B_P BOUND_VARIABLE_10443)))) (not (forall ((BOUND_VARIABLE_10449 $$unsorted)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP B_P BOUND_VARIABLE_10449)))) (not (forall ((BOUND_VARIABLE_10455 $$unsorted)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP B_P BOUND_VARIABLE_10455)))) (= BOUND_VARIABLE_10475 BOUND_VARIABLE_10477) (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt BOUND_VARIABLE_10475 BOUND_VARIABLE_10477) (tptp.hAPP B_P tptp.v_i))) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt BOUND_VARIABLE_10475 BOUND_VARIABLE_10477) (tptp.v_F B_P)))) (or (not (forall ((BOUND_VARIABLE_10443 $$unsorted)) (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP tptp.v_P BOUND_VARIABLE_10443)))) (not (forall ((BOUND_VARIABLE_10449 $$unsorted)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP tptp.v_P BOUND_VARIABLE_10449)))) (not (forall ((BOUND_VARIABLE_10455 $$unsorted)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP tptp.v_P BOUND_VARIABLE_10455)))) (= tptp.v_a tptp.v_b) (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_b tptp.v_a) (tptp.hAPP tptp.v_P tptp.v_i))) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_b tptp.v_a) (tptp.v_F tptp.v_P)))))) :rule cong :premises (t130 t137))
% 26.93/27.24 (step t139 (cl (=> (forall ((B_P $$unsorted) (BOUND_VARIABLE_10477 $$unsorted) (BOUND_VARIABLE_10475 $$unsorted)) (or (not (forall ((BOUND_VARIABLE_10443 $$unsorted)) (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP B_P BOUND_VARIABLE_10443)))) (not (forall ((BOUND_VARIABLE_10449 $$unsorted)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP B_P BOUND_VARIABLE_10449)))) (not (forall ((BOUND_VARIABLE_10455 $$unsorted)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP B_P BOUND_VARIABLE_10455)))) (= BOUND_VARIABLE_10475 BOUND_VARIABLE_10477) (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt BOUND_VARIABLE_10475 BOUND_VARIABLE_10477) (tptp.hAPP B_P tptp.v_i))) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt BOUND_VARIABLE_10475 BOUND_VARIABLE_10477) (tptp.v_F B_P)))) (or (not (forall ((BOUND_VARIABLE_10443 $$unsorted)) (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP tptp.v_P BOUND_VARIABLE_10443)))) (not (forall ((BOUND_VARIABLE_10449 $$unsorted)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP tptp.v_P BOUND_VARIABLE_10449)))) (not (forall ((BOUND_VARIABLE_10455 $$unsorted)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP tptp.v_P BOUND_VARIABLE_10455)))) (= tptp.v_b tptp.v_a) (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_b tptp.v_a) (tptp.hAPP tptp.v_P tptp.v_i))) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_b tptp.v_a) (tptp.v_F tptp.v_P)))) (forall ((B_P $$unsorted) (BOUND_VARIABLE_10477 $$unsorted) (BOUND_VARIABLE_10475 $$unsorted)) (or (not (forall ((BOUND_VARIABLE_10443 $$unsorted)) (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP B_P BOUND_VARIABLE_10443)))) (not (forall ((BOUND_VARIABLE_10449 $$unsorted)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP B_P BOUND_VARIABLE_10449)))) (not (forall ((BOUND_VARIABLE_10455 $$unsorted)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP B_P BOUND_VARIABLE_10455)))) (= BOUND_VARIABLE_10475 BOUND_VARIABLE_10477) (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt BOUND_VARIABLE_10475 BOUND_VARIABLE_10477) (tptp.hAPP B_P tptp.v_i))) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt BOUND_VARIABLE_10475 BOUND_VARIABLE_10477) (tptp.v_F B_P))))) :rule implies_neg1)
% 26.93/27.24 (anchor :step t140)
% 26.93/27.24 (assume t140.a0 (forall ((B_P $$unsorted) (BOUND_VARIABLE_10477 $$unsorted) (BOUND_VARIABLE_10475 $$unsorted)) (or (not (forall ((BOUND_VARIABLE_10443 $$unsorted)) (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP B_P BOUND_VARIABLE_10443)))) (not (forall ((BOUND_VARIABLE_10449 $$unsorted)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP B_P BOUND_VARIABLE_10449)))) (not (forall ((BOUND_VARIABLE_10455 $$unsorted)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP B_P BOUND_VARIABLE_10455)))) (= BOUND_VARIABLE_10475 BOUND_VARIABLE_10477) (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt BOUND_VARIABLE_10475 BOUND_VARIABLE_10477) (tptp.hAPP B_P tptp.v_i))) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt BOUND_VARIABLE_10475 BOUND_VARIABLE_10477) (tptp.v_F B_P)))))
% 26.93/27.24 (step t140.t1 (cl (or (not (forall ((B_P $$unsorted) (BOUND_VARIABLE_10477 $$unsorted) (BOUND_VARIABLE_10475 $$unsorted)) (or (not (forall ((BOUND_VARIABLE_10443 $$unsorted)) (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP B_P BOUND_VARIABLE_10443)))) (not (forall ((BOUND_VARIABLE_10449 $$unsorted)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP B_P BOUND_VARIABLE_10449)))) (not (forall ((BOUND_VARIABLE_10455 $$unsorted)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP B_P BOUND_VARIABLE_10455)))) (= BOUND_VARIABLE_10475 BOUND_VARIABLE_10477) (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt BOUND_VARIABLE_10475 BOUND_VARIABLE_10477) (tptp.hAPP B_P tptp.v_i))) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt BOUND_VARIABLE_10475 BOUND_VARIABLE_10477) (tptp.v_F B_P))))) (or (not (forall ((BOUND_VARIABLE_10443 $$unsorted)) (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP tptp.v_P BOUND_VARIABLE_10443)))) (not (forall ((BOUND_VARIABLE_10449 $$unsorted)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP tptp.v_P BOUND_VARIABLE_10449)))) (not (forall ((BOUND_VARIABLE_10455 $$unsorted)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP tptp.v_P BOUND_VARIABLE_10455)))) (= tptp.v_b tptp.v_a) (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_b tptp.v_a) (tptp.hAPP tptp.v_P tptp.v_i))) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_b tptp.v_a) (tptp.v_F tptp.v_P))))) :rule forall_inst :args ((:= B_P tptp.v_P) (:= BOUND_VARIABLE_10477 tptp.v_a) (:= BOUND_VARIABLE_10475 tptp.v_b)))
% 26.93/27.24 (step t140.t2 (cl (not (forall ((B_P $$unsorted) (BOUND_VARIABLE_10477 $$unsorted) (BOUND_VARIABLE_10475 $$unsorted)) (or (not (forall ((BOUND_VARIABLE_10443 $$unsorted)) (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP B_P BOUND_VARIABLE_10443)))) (not (forall ((BOUND_VARIABLE_10449 $$unsorted)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP B_P BOUND_VARIABLE_10449)))) (not (forall ((BOUND_VARIABLE_10455 $$unsorted)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP B_P BOUND_VARIABLE_10455)))) (= BOUND_VARIABLE_10475 BOUND_VARIABLE_10477) (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt BOUND_VARIABLE_10475 BOUND_VARIABLE_10477) (tptp.hAPP B_P tptp.v_i))) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt BOUND_VARIABLE_10475 BOUND_VARIABLE_10477) (tptp.v_F B_P))))) (or (not (forall ((BOUND_VARIABLE_10443 $$unsorted)) (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP tptp.v_P BOUND_VARIABLE_10443)))) (not (forall ((BOUND_VARIABLE_10449 $$unsorted)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP tptp.v_P BOUND_VARIABLE_10449)))) (not (forall ((BOUND_VARIABLE_10455 $$unsorted)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP tptp.v_P BOUND_VARIABLE_10455)))) (= tptp.v_b tptp.v_a) (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_b tptp.v_a) (tptp.hAPP tptp.v_P tptp.v_i))) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_b tptp.v_a) (tptp.v_F tptp.v_P)))) :rule or :premises (t140.t1))
% 26.93/27.24 (step t140.t3 (cl (or (not (forall ((BOUND_VARIABLE_10443 $$unsorted)) (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP tptp.v_P BOUND_VARIABLE_10443)))) (not (forall ((BOUND_VARIABLE_10449 $$unsorted)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP tptp.v_P BOUND_VARIABLE_10449)))) (not (forall ((BOUND_VARIABLE_10455 $$unsorted)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP tptp.v_P BOUND_VARIABLE_10455)))) (= tptp.v_b tptp.v_a) (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_b tptp.v_a) (tptp.hAPP tptp.v_P tptp.v_i))) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_b tptp.v_a) (tptp.v_F tptp.v_P)))) :rule resolution :premises (t140.t2 t140.a0))
% 26.93/27.24 (step t140 (cl (not (forall ((B_P $$unsorted) (BOUND_VARIABLE_10477 $$unsorted) (BOUND_VARIABLE_10475 $$unsorted)) (or (not (forall ((BOUND_VARIABLE_10443 $$unsorted)) (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP B_P BOUND_VARIABLE_10443)))) (not (forall ((BOUND_VARIABLE_10449 $$unsorted)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP B_P BOUND_VARIABLE_10449)))) (not (forall ((BOUND_VARIABLE_10455 $$unsorted)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP B_P BOUND_VARIABLE_10455)))) (= BOUND_VARIABLE_10475 BOUND_VARIABLE_10477) (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt BOUND_VARIABLE_10475 BOUND_VARIABLE_10477) (tptp.hAPP B_P tptp.v_i))) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt BOUND_VARIABLE_10475 BOUND_VARIABLE_10477) (tptp.v_F B_P))))) (or (not (forall ((BOUND_VARIABLE_10443 $$unsorted)) (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP tptp.v_P BOUND_VARIABLE_10443)))) (not (forall ((BOUND_VARIABLE_10449 $$unsorted)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP tptp.v_P BOUND_VARIABLE_10449)))) (not (forall ((BOUND_VARIABLE_10455 $$unsorted)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP tptp.v_P BOUND_VARIABLE_10455)))) (= tptp.v_b tptp.v_a) (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_b tptp.v_a) (tptp.hAPP tptp.v_P tptp.v_i))) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_b tptp.v_a) (tptp.v_F tptp.v_P)))) :rule subproof :discharge (t140.a0))
% 26.93/27.24 (step t141 (cl (=> (forall ((B_P $$unsorted) (BOUND_VARIABLE_10477 $$unsorted) (BOUND_VARIABLE_10475 $$unsorted)) (or (not (forall ((BOUND_VARIABLE_10443 $$unsorted)) (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP B_P BOUND_VARIABLE_10443)))) (not (forall ((BOUND_VARIABLE_10449 $$unsorted)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP B_P BOUND_VARIABLE_10449)))) (not (forall ((BOUND_VARIABLE_10455 $$unsorted)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP B_P BOUND_VARIABLE_10455)))) (= BOUND_VARIABLE_10475 BOUND_VARIABLE_10477) (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt BOUND_VARIABLE_10475 BOUND_VARIABLE_10477) (tptp.hAPP B_P tptp.v_i))) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt BOUND_VARIABLE_10475 BOUND_VARIABLE_10477) (tptp.v_F B_P)))) (or (not (forall ((BOUND_VARIABLE_10443 $$unsorted)) (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP tptp.v_P BOUND_VARIABLE_10443)))) (not (forall ((BOUND_VARIABLE_10449 $$unsorted)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP tptp.v_P BOUND_VARIABLE_10449)))) (not (forall ((BOUND_VARIABLE_10455 $$unsorted)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP tptp.v_P BOUND_VARIABLE_10455)))) (= tptp.v_b tptp.v_a) (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_b tptp.v_a) (tptp.hAPP tptp.v_P tptp.v_i))) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_b tptp.v_a) (tptp.v_F tptp.v_P)))) (or (not (forall ((BOUND_VARIABLE_10443 $$unsorted)) (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP tptp.v_P BOUND_VARIABLE_10443)))) (not (forall ((BOUND_VARIABLE_10449 $$unsorted)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP tptp.v_P BOUND_VARIABLE_10449)))) (not (forall ((BOUND_VARIABLE_10455 $$unsorted)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP tptp.v_P BOUND_VARIABLE_10455)))) (= tptp.v_b tptp.v_a) (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_b tptp.v_a) (tptp.hAPP tptp.v_P tptp.v_i))) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_b tptp.v_a) (tptp.v_F tptp.v_P)))) :rule resolution :premises (t139 t140))
% 26.93/27.24 (step t142 (cl (=> (forall ((B_P $$unsorted) (BOUND_VARIABLE_10477 $$unsorted) (BOUND_VARIABLE_10475 $$unsorted)) (or (not (forall ((BOUND_VARIABLE_10443 $$unsorted)) (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP B_P BOUND_VARIABLE_10443)))) (not (forall ((BOUND_VARIABLE_10449 $$unsorted)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP B_P BOUND_VARIABLE_10449)))) (not (forall ((BOUND_VARIABLE_10455 $$unsorted)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP B_P BOUND_VARIABLE_10455)))) (= BOUND_VARIABLE_10475 BOUND_VARIABLE_10477) (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt BOUND_VARIABLE_10475 BOUND_VARIABLE_10477) (tptp.hAPP B_P tptp.v_i))) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt BOUND_VARIABLE_10475 BOUND_VARIABLE_10477) (tptp.v_F B_P)))) (or (not (forall ((BOUND_VARIABLE_10443 $$unsorted)) (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP tptp.v_P BOUND_VARIABLE_10443)))) (not (forall ((BOUND_VARIABLE_10449 $$unsorted)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP tptp.v_P BOUND_VARIABLE_10449)))) (not (forall ((BOUND_VARIABLE_10455 $$unsorted)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP tptp.v_P BOUND_VARIABLE_10455)))) (= tptp.v_b tptp.v_a) (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_b tptp.v_a) (tptp.hAPP tptp.v_P tptp.v_i))) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_b tptp.v_a) (tptp.v_F tptp.v_P)))) (not (or (not (forall ((BOUND_VARIABLE_10443 $$unsorted)) (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP tptp.v_P BOUND_VARIABLE_10443)))) (not (forall ((BOUND_VARIABLE_10449 $$unsorted)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP tptp.v_P BOUND_VARIABLE_10449)))) (not (forall ((BOUND_VARIABLE_10455 $$unsorted)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP tptp.v_P BOUND_VARIABLE_10455)))) (= tptp.v_b tptp.v_a) (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_b tptp.v_a) (tptp.hAPP tptp.v_P tptp.v_i))) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_b tptp.v_a) (tptp.v_F tptp.v_P))))) :rule implies_neg2)
% 26.93/27.24 (step t143 (cl (=> (forall ((B_P $$unsorted) (BOUND_VARIABLE_10477 $$unsorted) (BOUND_VARIABLE_10475 $$unsorted)) (or (not (forall ((BOUND_VARIABLE_10443 $$unsorted)) (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP B_P BOUND_VARIABLE_10443)))) (not (forall ((BOUND_VARIABLE_10449 $$unsorted)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP B_P BOUND_VARIABLE_10449)))) (not (forall ((BOUND_VARIABLE_10455 $$unsorted)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP B_P BOUND_VARIABLE_10455)))) (= BOUND_VARIABLE_10475 BOUND_VARIABLE_10477) (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt BOUND_VARIABLE_10475 BOUND_VARIABLE_10477) (tptp.hAPP B_P tptp.v_i))) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt BOUND_VARIABLE_10475 BOUND_VARIABLE_10477) (tptp.v_F B_P)))) (or (not (forall ((BOUND_VARIABLE_10443 $$unsorted)) (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP tptp.v_P BOUND_VARIABLE_10443)))) (not (forall ((BOUND_VARIABLE_10449 $$unsorted)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP tptp.v_P BOUND_VARIABLE_10449)))) (not (forall ((BOUND_VARIABLE_10455 $$unsorted)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP tptp.v_P BOUND_VARIABLE_10455)))) (= tptp.v_b tptp.v_a) (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_b tptp.v_a) (tptp.hAPP tptp.v_P tptp.v_i))) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_b tptp.v_a) (tptp.v_F tptp.v_P)))) (=> (forall ((B_P $$unsorted) (BOUND_VARIABLE_10477 $$unsorted) (BOUND_VARIABLE_10475 $$unsorted)) (or (not (forall ((BOUND_VARIABLE_10443 $$unsorted)) (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP B_P BOUND_VARIABLE_10443)))) (not (forall ((BOUND_VARIABLE_10449 $$unsorted)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP B_P BOUND_VARIABLE_10449)))) (not (forall ((BOUND_VARIABLE_10455 $$unsorted)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP B_P BOUND_VARIABLE_10455)))) (= BOUND_VARIABLE_10475 BOUND_VARIABLE_10477) (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt BOUND_VARIABLE_10475 BOUND_VARIABLE_10477) (tptp.hAPP B_P tptp.v_i))) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt BOUND_VARIABLE_10475 BOUND_VARIABLE_10477) (tptp.v_F B_P)))) (or (not (forall ((BOUND_VARIABLE_10443 $$unsorted)) (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP tptp.v_P BOUND_VARIABLE_10443)))) (not (forall ((BOUND_VARIABLE_10449 $$unsorted)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP tptp.v_P BOUND_VARIABLE_10449)))) (not (forall ((BOUND_VARIABLE_10455 $$unsorted)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP tptp.v_P BOUND_VARIABLE_10455)))) (= tptp.v_b tptp.v_a) (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_b tptp.v_a) (tptp.hAPP tptp.v_P tptp.v_i))) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_b tptp.v_a) (tptp.v_F tptp.v_P))))) :rule resolution :premises (t141 t142))
% 26.93/27.24 (step t144 (cl (=> (forall ((B_P $$unsorted) (BOUND_VARIABLE_10477 $$unsorted) (BOUND_VARIABLE_10475 $$unsorted)) (or (not (forall ((BOUND_VARIABLE_10443 $$unsorted)) (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP B_P BOUND_VARIABLE_10443)))) (not (forall ((BOUND_VARIABLE_10449 $$unsorted)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP B_P BOUND_VARIABLE_10449)))) (not (forall ((BOUND_VARIABLE_10455 $$unsorted)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP B_P BOUND_VARIABLE_10455)))) (= BOUND_VARIABLE_10475 BOUND_VARIABLE_10477) (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt BOUND_VARIABLE_10475 BOUND_VARIABLE_10477) (tptp.hAPP B_P tptp.v_i))) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt BOUND_VARIABLE_10475 BOUND_VARIABLE_10477) (tptp.v_F B_P)))) (or (not (forall ((BOUND_VARIABLE_10443 $$unsorted)) (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP tptp.v_P BOUND_VARIABLE_10443)))) (not (forall ((BOUND_VARIABLE_10449 $$unsorted)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP tptp.v_P BOUND_VARIABLE_10449)))) (not (forall ((BOUND_VARIABLE_10455 $$unsorted)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP tptp.v_P BOUND_VARIABLE_10455)))) (= tptp.v_b tptp.v_a) (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_b tptp.v_a) (tptp.hAPP tptp.v_P tptp.v_i))) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_b tptp.v_a) (tptp.v_F tptp.v_P))))) :rule contraction :premises (t143))
% 26.93/27.24 (step t145 (cl (=> (forall ((B_P $$unsorted) (BOUND_VARIABLE_10477 $$unsorted) (BOUND_VARIABLE_10475 $$unsorted)) (or (not (forall ((BOUND_VARIABLE_10443 $$unsorted)) (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP B_P BOUND_VARIABLE_10443)))) (not (forall ((BOUND_VARIABLE_10449 $$unsorted)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP B_P BOUND_VARIABLE_10449)))) (not (forall ((BOUND_VARIABLE_10455 $$unsorted)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP B_P BOUND_VARIABLE_10455)))) (= BOUND_VARIABLE_10475 BOUND_VARIABLE_10477) (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt BOUND_VARIABLE_10475 BOUND_VARIABLE_10477) (tptp.hAPP B_P tptp.v_i))) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt BOUND_VARIABLE_10475 BOUND_VARIABLE_10477) (tptp.v_F B_P)))) (or (not (forall ((BOUND_VARIABLE_10443 $$unsorted)) (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP tptp.v_P BOUND_VARIABLE_10443)))) (not (forall ((BOUND_VARIABLE_10449 $$unsorted)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP tptp.v_P BOUND_VARIABLE_10449)))) (not (forall ((BOUND_VARIABLE_10455 $$unsorted)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP tptp.v_P BOUND_VARIABLE_10455)))) (= tptp.v_a tptp.v_b) (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_b tptp.v_a) (tptp.hAPP tptp.v_P tptp.v_i))) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_b tptp.v_a) (tptp.v_F tptp.v_P))))) :rule resolution :premises (t129 t138 t144))
% 26.93/27.24 (step t146 (cl (not (forall ((B_P $$unsorted) (BOUND_VARIABLE_10477 $$unsorted) (BOUND_VARIABLE_10475 $$unsorted)) (or (not (forall ((BOUND_VARIABLE_10443 $$unsorted)) (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP B_P BOUND_VARIABLE_10443)))) (not (forall ((BOUND_VARIABLE_10449 $$unsorted)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP B_P BOUND_VARIABLE_10449)))) (not (forall ((BOUND_VARIABLE_10455 $$unsorted)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP B_P BOUND_VARIABLE_10455)))) (= BOUND_VARIABLE_10475 BOUND_VARIABLE_10477) (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt BOUND_VARIABLE_10475 BOUND_VARIABLE_10477) (tptp.hAPP B_P tptp.v_i))) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt BOUND_VARIABLE_10475 BOUND_VARIABLE_10477) (tptp.v_F B_P))))) (or (not (forall ((BOUND_VARIABLE_10443 $$unsorted)) (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP tptp.v_P BOUND_VARIABLE_10443)))) (not (forall ((BOUND_VARIABLE_10449 $$unsorted)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP tptp.v_P BOUND_VARIABLE_10449)))) (not (forall ((BOUND_VARIABLE_10455 $$unsorted)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP tptp.v_P BOUND_VARIABLE_10455)))) (= tptp.v_a tptp.v_b) (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_b tptp.v_a) (tptp.hAPP tptp.v_P tptp.v_i))) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_b tptp.v_a) (tptp.v_F tptp.v_P)))) :rule implies :premises (t145))
% 26.93/27.24 (step t147 (cl (not (= (forall ((B_P $$unsorted)) (=> (forall ((B_x $$unsorted)) (and (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP B_P B_x)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP B_P B_x)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP B_P B_x)))) (forall ((B_a $$unsorted) (B_b $$unsorted)) (=> (not (= B_a B_b)) (=> (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt B_a B_b) (tptp.hAPP B_P tptp.v_i)) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt B_a B_b) (tptp.v_F B_P))))))) (forall ((B_P $$unsorted) (BOUND_VARIABLE_10477 $$unsorted) (BOUND_VARIABLE_10475 $$unsorted)) (or (not (forall ((BOUND_VARIABLE_10443 $$unsorted)) (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP B_P BOUND_VARIABLE_10443)))) (not (forall ((BOUND_VARIABLE_10449 $$unsorted)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP B_P BOUND_VARIABLE_10449)))) (not (forall ((BOUND_VARIABLE_10455 $$unsorted)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP B_P BOUND_VARIABLE_10455)))) (= BOUND_VARIABLE_10475 BOUND_VARIABLE_10477) (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt BOUND_VARIABLE_10475 BOUND_VARIABLE_10477) (tptp.hAPP B_P tptp.v_i))) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt BOUND_VARIABLE_10475 BOUND_VARIABLE_10477) (tptp.v_F B_P)))))) (not (forall ((B_P $$unsorted)) (=> (forall ((B_x $$unsorted)) (and (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP B_P B_x)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP B_P B_x)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP B_P B_x)))) (forall ((B_a $$unsorted) (B_b $$unsorted)) (=> (not (= B_a B_b)) (=> (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt B_a B_b) (tptp.hAPP B_P tptp.v_i)) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt B_a B_b) (tptp.v_F B_P)))))))) (forall ((B_P $$unsorted) (BOUND_VARIABLE_10477 $$unsorted) (BOUND_VARIABLE_10475 $$unsorted)) (or (not (forall ((BOUND_VARIABLE_10443 $$unsorted)) (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP B_P BOUND_VARIABLE_10443)))) (not (forall ((BOUND_VARIABLE_10449 $$unsorted)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP B_P BOUND_VARIABLE_10449)))) (not (forall ((BOUND_VARIABLE_10455 $$unsorted)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP B_P BOUND_VARIABLE_10455)))) (= BOUND_VARIABLE_10475 BOUND_VARIABLE_10477) (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt BOUND_VARIABLE_10475 BOUND_VARIABLE_10477) (tptp.hAPP B_P tptp.v_i))) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt BOUND_VARIABLE_10475 BOUND_VARIABLE_10477) (tptp.v_F B_P))))) :rule equiv_pos2)
% 26.93/27.24 (anchor :step t148 :args ((B_P $$unsorted) (:= B_P B_P)))
% 26.93/27.24 (step t148.t1 (cl (= B_P B_P)) :rule refl)
% 26.93/27.24 (step t148.t2 (cl (= (forall ((B_x $$unsorted)) (and (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP B_P B_x)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP B_P B_x)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP B_P B_x)))) (and (forall ((BOUND_VARIABLE_10443 $$unsorted)) (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP B_P BOUND_VARIABLE_10443))) (forall ((BOUND_VARIABLE_10449 $$unsorted)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP B_P BOUND_VARIABLE_10449))) (forall ((BOUND_VARIABLE_10455 $$unsorted)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP B_P BOUND_VARIABLE_10455)))))) :rule all_simplify)
% 26.93/27.24 (step t148.t3 (cl (= (forall ((B_a $$unsorted) (B_b $$unsorted)) (=> (not (= B_a B_b)) (=> (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt B_a B_b) (tptp.hAPP B_P tptp.v_i)) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt B_a B_b) (tptp.v_F B_P))))) (forall ((B_a $$unsorted) (B_b $$unsorted)) (or (= B_a B_b) (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt B_a B_b) (tptp.hAPP B_P tptp.v_i))) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt B_a B_b) (tptp.v_F B_P)))))) :rule all_simplify)
% 26.93/27.24 (step t148.t4 (cl (= (=> (forall ((B_x $$unsorted)) (and (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP B_P B_x)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP B_P B_x)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP B_P B_x)))) (forall ((B_a $$unsorted) (B_b $$unsorted)) (=> (not (= B_a B_b)) (=> (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt B_a B_b) (tptp.hAPP B_P tptp.v_i)) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt B_a B_b) (tptp.v_F B_P)))))) (=> (and (forall ((BOUND_VARIABLE_10443 $$unsorted)) (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP B_P BOUND_VARIABLE_10443))) (forall ((BOUND_VARIABLE_10449 $$unsorted)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP B_P BOUND_VARIABLE_10449))) (forall ((BOUND_VARIABLE_10455 $$unsorted)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP B_P BOUND_VARIABLE_10455)))) (forall ((B_a $$unsorted) (B_b $$unsorted)) (or (= B_a B_b) (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt B_a B_b) (tptp.hAPP B_P tptp.v_i))) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt B_a B_b) (tptp.v_F B_P))))))) :rule cong :premises (t148.t2 t148.t3))
% 26.93/27.24 (step t148 (cl (= (forall ((B_P $$unsorted)) (=> (forall ((B_x $$unsorted)) (and (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP B_P B_x)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP B_P B_x)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP B_P B_x)))) (forall ((B_a $$unsorted) (B_b $$unsorted)) (=> (not (= B_a B_b)) (=> (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt B_a B_b) (tptp.hAPP B_P tptp.v_i)) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt B_a B_b) (tptp.v_F B_P))))))) (forall ((B_P $$unsorted)) (=> (and (forall ((BOUND_VARIABLE_10443 $$unsorted)) (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP B_P BOUND_VARIABLE_10443))) (forall ((BOUND_VARIABLE_10449 $$unsorted)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP B_P BOUND_VARIABLE_10449))) (forall ((BOUND_VARIABLE_10455 $$unsorted)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP B_P BOUND_VARIABLE_10455)))) (forall ((B_a $$unsorted) (B_b $$unsorted)) (or (= B_a B_b) (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt B_a B_b) (tptp.hAPP B_P tptp.v_i))) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt B_a B_b) (tptp.v_F B_P)))))))) :rule bind)
% 26.93/27.24 (step t149 (cl (= (forall ((B_P $$unsorted)) (=> (and (forall ((BOUND_VARIABLE_10443 $$unsorted)) (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP B_P BOUND_VARIABLE_10443))) (forall ((BOUND_VARIABLE_10449 $$unsorted)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP B_P BOUND_VARIABLE_10449))) (forall ((BOUND_VARIABLE_10455 $$unsorted)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP B_P BOUND_VARIABLE_10455)))) (forall ((B_a $$unsorted) (B_b $$unsorted)) (or (= B_a B_b) (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt B_a B_b) (tptp.hAPP B_P tptp.v_i))) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt B_a B_b) (tptp.v_F B_P)))))) (forall ((B_P $$unsorted)) (or (not (forall ((BOUND_VARIABLE_10443 $$unsorted)) (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP B_P BOUND_VARIABLE_10443)))) (not (forall ((BOUND_VARIABLE_10449 $$unsorted)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP B_P BOUND_VARIABLE_10449)))) (not (forall ((BOUND_VARIABLE_10455 $$unsorted)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP B_P BOUND_VARIABLE_10455)))) (forall ((B_a $$unsorted) (B_b $$unsorted)) (or (= B_a B_b) (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt B_a B_b) (tptp.hAPP B_P tptp.v_i))) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt B_a B_b) (tptp.v_F B_P)))))))) :rule all_simplify)
% 26.93/27.24 (step t150 (cl (= (forall ((B_P $$unsorted)) (or (not (forall ((BOUND_VARIABLE_10443 $$unsorted)) (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP B_P BOUND_VARIABLE_10443)))) (not (forall ((BOUND_VARIABLE_10449 $$unsorted)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP B_P BOUND_VARIABLE_10449)))) (not (forall ((BOUND_VARIABLE_10455 $$unsorted)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP B_P BOUND_VARIABLE_10455)))) (forall ((B_a $$unsorted) (B_b $$unsorted)) (or (= B_a B_b) (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt B_a B_b) (tptp.hAPP B_P tptp.v_i))) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt B_a B_b) (tptp.v_F B_P)))))) (forall ((B_P $$unsorted) (BOUND_VARIABLE_10477 $$unsorted) (BOUND_VARIABLE_10475 $$unsorted)) (or (not (forall ((BOUND_VARIABLE_10443 $$unsorted)) (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP B_P BOUND_VARIABLE_10443)))) (not (forall ((BOUND_VARIABLE_10449 $$unsorted)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP B_P BOUND_VARIABLE_10449)))) (not (forall ((BOUND_VARIABLE_10455 $$unsorted)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP B_P BOUND_VARIABLE_10455)))) (or (= BOUND_VARIABLE_10475 BOUND_VARIABLE_10477) (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt BOUND_VARIABLE_10475 BOUND_VARIABLE_10477) (tptp.hAPP B_P tptp.v_i))) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt BOUND_VARIABLE_10475 BOUND_VARIABLE_10477) (tptp.v_F B_P))))))) :rule all_simplify)
% 26.93/27.24 (anchor :step t151 :args ((B_P $$unsorted) (:= B_P B_P) (BOUND_VARIABLE_10477 $$unsorted) (:= BOUND_VARIABLE_10477 BOUND_VARIABLE_10477) (BOUND_VARIABLE_10475 $$unsorted) (:= BOUND_VARIABLE_10475 BOUND_VARIABLE_10475)))
% 26.93/27.24 (step t151.t1 (cl (= B_P B_P)) :rule refl)
% 26.93/27.24 (step t151.t2 (cl (= BOUND_VARIABLE_10477 BOUND_VARIABLE_10477)) :rule refl)
% 26.93/27.24 (step t151.t3 (cl (= BOUND_VARIABLE_10475 BOUND_VARIABLE_10475)) :rule refl)
% 26.93/27.24 (step t151.t4 (cl (= (or (not (forall ((BOUND_VARIABLE_10443 $$unsorted)) (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP B_P BOUND_VARIABLE_10443)))) (not (forall ((BOUND_VARIABLE_10449 $$unsorted)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP B_P BOUND_VARIABLE_10449)))) (not (forall ((BOUND_VARIABLE_10455 $$unsorted)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP B_P BOUND_VARIABLE_10455)))) (or (= BOUND_VARIABLE_10475 BOUND_VARIABLE_10477) (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt BOUND_VARIABLE_10475 BOUND_VARIABLE_10477) (tptp.hAPP B_P tptp.v_i))) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt BOUND_VARIABLE_10475 BOUND_VARIABLE_10477) (tptp.v_F B_P)))) (or (not (forall ((BOUND_VARIABLE_10443 $$unsorted)) (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP B_P BOUND_VARIABLE_10443)))) (not (forall ((BOUND_VARIABLE_10449 $$unsorted)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP B_P BOUND_VARIABLE_10449)))) (not (forall ((BOUND_VARIABLE_10455 $$unsorted)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP B_P BOUND_VARIABLE_10455)))) (= BOUND_VARIABLE_10475 BOUND_VARIABLE_10477) (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt BOUND_VARIABLE_10475 BOUND_VARIABLE_10477) (tptp.hAPP B_P tptp.v_i))) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt BOUND_VARIABLE_10475 BOUND_VARIABLE_10477) (tptp.v_F B_P))))) :rule all_simplify)
% 26.93/27.24 (step t151 (cl (= (forall ((B_P $$unsorted) (BOUND_VARIABLE_10477 $$unsorted) (BOUND_VARIABLE_10475 $$unsorted)) (or (not (forall ((BOUND_VARIABLE_10443 $$unsorted)) (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP B_P BOUND_VARIABLE_10443)))) (not (forall ((BOUND_VARIABLE_10449 $$unsorted)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP B_P BOUND_VARIABLE_10449)))) (not (forall ((BOUND_VARIABLE_10455 $$unsorted)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP B_P BOUND_VARIABLE_10455)))) (or (= BOUND_VARIABLE_10475 BOUND_VARIABLE_10477) (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt BOUND_VARIABLE_10475 BOUND_VARIABLE_10477) (tptp.hAPP B_P tptp.v_i))) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt BOUND_VARIABLE_10475 BOUND_VARIABLE_10477) (tptp.v_F B_P))))) (forall ((B_P $$unsorted) (BOUND_VARIABLE_10477 $$unsorted) (BOUND_VARIABLE_10475 $$unsorted)) (or (not (forall ((BOUND_VARIABLE_10443 $$unsorted)) (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP B_P BOUND_VARIABLE_10443)))) (not (forall ((BOUND_VARIABLE_10449 $$unsorted)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP B_P BOUND_VARIABLE_10449)))) (not (forall ((BOUND_VARIABLE_10455 $$unsorted)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP B_P BOUND_VARIABLE_10455)))) (= BOUND_VARIABLE_10475 BOUND_VARIABLE_10477) (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt BOUND_VARIABLE_10475 BOUND_VARIABLE_10477) (tptp.hAPP B_P tptp.v_i))) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt BOUND_VARIABLE_10475 BOUND_VARIABLE_10477) (tptp.v_F B_P)))))) :rule bind)
% 26.93/27.24 (step t152 (cl (= (forall ((B_P $$unsorted)) (or (not (forall ((BOUND_VARIABLE_10443 $$unsorted)) (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP B_P BOUND_VARIABLE_10443)))) (not (forall ((BOUND_VARIABLE_10449 $$unsorted)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP B_P BOUND_VARIABLE_10449)))) (not (forall ((BOUND_VARIABLE_10455 $$unsorted)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP B_P BOUND_VARIABLE_10455)))) (forall ((B_a $$unsorted) (B_b $$unsorted)) (or (= B_a B_b) (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt B_a B_b) (tptp.hAPP B_P tptp.v_i))) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt B_a B_b) (tptp.v_F B_P)))))) (forall ((B_P $$unsorted) (BOUND_VARIABLE_10477 $$unsorted) (BOUND_VARIABLE_10475 $$unsorted)) (or (not (forall ((BOUND_VARIABLE_10443 $$unsorted)) (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP B_P BOUND_VARIABLE_10443)))) (not (forall ((BOUND_VARIABLE_10449 $$unsorted)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP B_P BOUND_VARIABLE_10449)))) (not (forall ((BOUND_VARIABLE_10455 $$unsorted)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP B_P BOUND_VARIABLE_10455)))) (= BOUND_VARIABLE_10475 BOUND_VARIABLE_10477) (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt BOUND_VARIABLE_10475 BOUND_VARIABLE_10477) (tptp.hAPP B_P tptp.v_i))) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt BOUND_VARIABLE_10475 BOUND_VARIABLE_10477) (tptp.v_F B_P)))))) :rule trans :premises (t150 t151))
% 26.93/27.24 (step t153 (cl (= (forall ((B_P $$unsorted)) (=> (and (forall ((BOUND_VARIABLE_10443 $$unsorted)) (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP B_P BOUND_VARIABLE_10443))) (forall ((BOUND_VARIABLE_10449 $$unsorted)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP B_P BOUND_VARIABLE_10449))) (forall ((BOUND_VARIABLE_10455 $$unsorted)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP B_P BOUND_VARIABLE_10455)))) (forall ((B_a $$unsorted) (B_b $$unsorted)) (or (= B_a B_b) (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt B_a B_b) (tptp.hAPP B_P tptp.v_i))) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt B_a B_b) (tptp.v_F B_P)))))) (forall ((B_P $$unsorted) (BOUND_VARIABLE_10477 $$unsorted) (BOUND_VARIABLE_10475 $$unsorted)) (or (not (forall ((BOUND_VARIABLE_10443 $$unsorted)) (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP B_P BOUND_VARIABLE_10443)))) (not (forall ((BOUND_VARIABLE_10449 $$unsorted)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP B_P BOUND_VARIABLE_10449)))) (not (forall ((BOUND_VARIABLE_10455 $$unsorted)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP B_P BOUND_VARIABLE_10455)))) (= BOUND_VARIABLE_10475 BOUND_VARIABLE_10477) (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt BOUND_VARIABLE_10475 BOUND_VARIABLE_10477) (tptp.hAPP B_P tptp.v_i))) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt BOUND_VARIABLE_10475 BOUND_VARIABLE_10477) (tptp.v_F B_P)))))) :rule trans :premises (t149 t152))
% 26.93/27.24 (step t154 (cl (= (forall ((B_P $$unsorted)) (=> (forall ((B_x $$unsorted)) (and (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP B_P B_x)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP B_P B_x)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP B_P B_x)))) (forall ((B_a $$unsorted) (B_b $$unsorted)) (=> (not (= B_a B_b)) (=> (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt B_a B_b) (tptp.hAPP B_P tptp.v_i)) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt B_a B_b) (tptp.v_F B_P))))))) (forall ((B_P $$unsorted) (BOUND_VARIABLE_10477 $$unsorted) (BOUND_VARIABLE_10475 $$unsorted)) (or (not (forall ((BOUND_VARIABLE_10443 $$unsorted)) (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP B_P BOUND_VARIABLE_10443)))) (not (forall ((BOUND_VARIABLE_10449 $$unsorted)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP B_P BOUND_VARIABLE_10449)))) (not (forall ((BOUND_VARIABLE_10455 $$unsorted)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP B_P BOUND_VARIABLE_10455)))) (= BOUND_VARIABLE_10475 BOUND_VARIABLE_10477) (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt BOUND_VARIABLE_10475 BOUND_VARIABLE_10477) (tptp.hAPP B_P tptp.v_i))) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt BOUND_VARIABLE_10475 BOUND_VARIABLE_10477) (tptp.v_F B_P)))))) :rule trans :premises (t148 t153))
% 26.93/27.24 (step t155 (cl (forall ((B_P $$unsorted) (BOUND_VARIABLE_10477 $$unsorted) (BOUND_VARIABLE_10475 $$unsorted)) (or (not (forall ((BOUND_VARIABLE_10443 $$unsorted)) (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP B_P BOUND_VARIABLE_10443)))) (not (forall ((BOUND_VARIABLE_10449 $$unsorted)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP B_P BOUND_VARIABLE_10449)))) (not (forall ((BOUND_VARIABLE_10455 $$unsorted)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP B_P BOUND_VARIABLE_10455)))) (= BOUND_VARIABLE_10475 BOUND_VARIABLE_10477) (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt BOUND_VARIABLE_10475 BOUND_VARIABLE_10477) (tptp.hAPP B_P tptp.v_i))) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt BOUND_VARIABLE_10475 BOUND_VARIABLE_10477) (tptp.v_F B_P))))) :rule resolution :premises (t147 t154 a523))
% 26.93/27.24 (step t156 (cl (or (not (forall ((BOUND_VARIABLE_10443 $$unsorted)) (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP tptp.v_P BOUND_VARIABLE_10443)))) (not (forall ((BOUND_VARIABLE_10449 $$unsorted)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP tptp.v_P BOUND_VARIABLE_10449)))) (not (forall ((BOUND_VARIABLE_10455 $$unsorted)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP tptp.v_P BOUND_VARIABLE_10455)))) (= tptp.v_a tptp.v_b) (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_b tptp.v_a) (tptp.hAPP tptp.v_P tptp.v_i))) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_b tptp.v_a) (tptp.v_F tptp.v_P)))) :rule resolution :premises (t146 t155))
% 26.93/27.24 (step t157 (cl (not (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_b tptp.v_a) (tptp.hAPP tptp.v_P tptp.v_i)))) :rule resolution :premises (t102 t119 t100 t122 t125 t128 t156))
% 26.93/27.24 (step t158 (cl (=> (forall ((V_x_2 $$unsorted) (T_a $$unsorted)) (tptp.c_member T_a V_x_2 (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_HOL_Obool)))) (tptp.c_member tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_b (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)))) (forall ((V_x_2 $$unsorted) (T_a $$unsorted)) (tptp.c_member T_a V_x_2 (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_HOL_Obool))))) :rule implies_neg1)
% 26.93/27.24 (anchor :step t159)
% 26.93/27.24 (assume t159.a0 (forall ((V_x_2 $$unsorted) (T_a $$unsorted)) (tptp.c_member T_a V_x_2 (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_HOL_Obool)))))
% 26.93/27.24 (step t159.t1 (cl (or (not (forall ((V_x_2 $$unsorted) (T_a $$unsorted)) (tptp.c_member T_a V_x_2 (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_HOL_Obool))))) (tptp.c_member tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_b (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool))))) :rule forall_inst :args ((:= V_x_2 tptp.v_b) (:= T_a tptp.tc_Arrow__Order__Mirabelle_Oalt)))
% 26.93/27.24 (step t159.t2 (cl (not (forall ((V_x_2 $$unsorted) (T_a $$unsorted)) (tptp.c_member T_a V_x_2 (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_HOL_Obool))))) (tptp.c_member tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_b (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)))) :rule or :premises (t159.t1))
% 26.93/27.24 (step t159.t3 (cl (tptp.c_member tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_b (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)))) :rule resolution :premises (t159.t2 t159.a0))
% 26.93/27.24 (step t159 (cl (not (forall ((V_x_2 $$unsorted) (T_a $$unsorted)) (tptp.c_member T_a V_x_2 (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_HOL_Obool))))) (tptp.c_member tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_b (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)))) :rule subproof :discharge (t159.a0))
% 26.93/27.24 (step t160 (cl (=> (forall ((V_x_2 $$unsorted) (T_a $$unsorted)) (tptp.c_member T_a V_x_2 (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_HOL_Obool)))) (tptp.c_member tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_b (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)))) (tptp.c_member tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_b (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)))) :rule resolution :premises (t158 t159))
% 26.93/27.24 (step t161 (cl (=> (forall ((V_x_2 $$unsorted) (T_a $$unsorted)) (tptp.c_member T_a V_x_2 (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_HOL_Obool)))) (tptp.c_member tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_b (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)))) (not (tptp.c_member tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_b (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool))))) :rule implies_neg2)
% 26.93/27.24 (step t162 (cl (=> (forall ((V_x_2 $$unsorted) (T_a $$unsorted)) (tptp.c_member T_a V_x_2 (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_HOL_Obool)))) (tptp.c_member tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_b (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)))) (=> (forall ((V_x_2 $$unsorted) (T_a $$unsorted)) (tptp.c_member T_a V_x_2 (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_HOL_Obool)))) (tptp.c_member tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_b (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool))))) :rule resolution :premises (t160 t161))
% 26.93/27.24 (step t163 (cl (=> (forall ((V_x_2 $$unsorted) (T_a $$unsorted)) (tptp.c_member T_a V_x_2 (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_HOL_Obool)))) (tptp.c_member tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_b (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool))))) :rule contraction :premises (t162))
% 26.93/27.24 (step t164 (cl (not (forall ((V_x_2 $$unsorted) (T_a $$unsorted)) (tptp.c_member T_a V_x_2 (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_HOL_Obool))))) (tptp.c_member tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_b (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)))) :rule implies :premises (t163))
% 26.93/27.24 (step t165 (cl (tptp.c_member tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_b (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)))) :rule resolution :premises (t164 a1))
% 26.93/27.24 (step t166 (cl (=> (forall ((V_x_2 $$unsorted) (T_a $$unsorted)) (tptp.c_member T_a V_x_2 (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_HOL_Obool)))) (tptp.c_member tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)))) (forall ((V_x_2 $$unsorted) (T_a $$unsorted)) (tptp.c_member T_a V_x_2 (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_HOL_Obool))))) :rule implies_neg1)
% 26.93/27.24 (anchor :step t167)
% 26.93/27.24 (assume t167.a0 (forall ((V_x_2 $$unsorted) (T_a $$unsorted)) (tptp.c_member T_a V_x_2 (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_HOL_Obool)))))
% 26.93/27.24 (step t167.t1 (cl (or (not (forall ((V_x_2 $$unsorted) (T_a $$unsorted)) (tptp.c_member T_a V_x_2 (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_HOL_Obool))))) (tptp.c_member tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool))))) :rule forall_inst :args ((:= V_x_2 tptp.v_a) (:= T_a tptp.tc_Arrow__Order__Mirabelle_Oalt)))
% 26.93/27.24 (step t167.t2 (cl (not (forall ((V_x_2 $$unsorted) (T_a $$unsorted)) (tptp.c_member T_a V_x_2 (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_HOL_Obool))))) (tptp.c_member tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)))) :rule or :premises (t167.t1))
% 26.93/27.24 (step t167.t3 (cl (tptp.c_member tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)))) :rule resolution :premises (t167.t2 t167.a0))
% 26.93/27.24 (step t167 (cl (not (forall ((V_x_2 $$unsorted) (T_a $$unsorted)) (tptp.c_member T_a V_x_2 (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_HOL_Obool))))) (tptp.c_member tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)))) :rule subproof :discharge (t167.a0))
% 26.93/27.24 (step t168 (cl (=> (forall ((V_x_2 $$unsorted) (T_a $$unsorted)) (tptp.c_member T_a V_x_2 (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_HOL_Obool)))) (tptp.c_member tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)))) (tptp.c_member tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)))) :rule resolution :premises (t166 t167))
% 26.93/27.24 (step t169 (cl (=> (forall ((V_x_2 $$unsorted) (T_a $$unsorted)) (tptp.c_member T_a V_x_2 (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_HOL_Obool)))) (tptp.c_member tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)))) (not (tptp.c_member tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool))))) :rule implies_neg2)
% 26.93/27.24 (step t170 (cl (=> (forall ((V_x_2 $$unsorted) (T_a $$unsorted)) (tptp.c_member T_a V_x_2 (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_HOL_Obool)))) (tptp.c_member tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)))) (=> (forall ((V_x_2 $$unsorted) (T_a $$unsorted)) (tptp.c_member T_a V_x_2 (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_HOL_Obool)))) (tptp.c_member tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool))))) :rule resolution :premises (t168 t169))
% 26.93/27.24 (step t171 (cl (=> (forall ((V_x_2 $$unsorted) (T_a $$unsorted)) (tptp.c_member T_a V_x_2 (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_HOL_Obool)))) (tptp.c_member tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool))))) :rule contraction :premises (t170))
% 26.93/27.24 (step t172 (cl (not (forall ((V_x_2 $$unsorted) (T_a $$unsorted)) (tptp.c_member T_a V_x_2 (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_HOL_Obool))))) (tptp.c_member tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)))) :rule implies :premises (t171))
% 26.93/27.24 (step t173 (cl (tptp.c_member tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)))) :rule resolution :premises (t172 a1))
% 26.93/27.24 (step t174 (cl (not (or (not (tptp.c_member tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)))) (not (tptp.c_member tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_b (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)))) (= tptp.v_a tptp.v_b) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_b) (tptp.hAPP tptp.v_P tptp.v_i)) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_b tptp.v_a) (tptp.hAPP tptp.v_P tptp.v_i))))) :rule resolution :premises (t9 a526 t100 t157 t165 t173))
% 26.93/27.24 (step t175 (cl (not (= (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP tptp.v_P tptp.v_i)) (forall ((B_x $$unsorted) (BOUND_VARIABLE_7486 $$unsorted)) (or (not (tptp.c_member tptp.tc_Arrow__Order__Mirabelle_Oalt B_x (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)))) (not (tptp.c_member tptp.tc_Arrow__Order__Mirabelle_Oalt BOUND_VARIABLE_7486 (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)))) (= B_x BOUND_VARIABLE_7486) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt B_x BOUND_VARIABLE_7486) (tptp.hAPP tptp.v_P tptp.v_i)) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt BOUND_VARIABLE_7486 B_x) (tptp.hAPP tptp.v_P tptp.v_i)))))) (not (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP tptp.v_P tptp.v_i))) (forall ((B_x $$unsorted) (BOUND_VARIABLE_7486 $$unsorted)) (or (not (tptp.c_member tptp.tc_Arrow__Order__Mirabelle_Oalt B_x (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)))) (not (tptp.c_member tptp.tc_Arrow__Order__Mirabelle_Oalt BOUND_VARIABLE_7486 (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)))) (= B_x BOUND_VARIABLE_7486) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt B_x BOUND_VARIABLE_7486) (tptp.hAPP tptp.v_P tptp.v_i)) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt BOUND_VARIABLE_7486 B_x) (tptp.hAPP tptp.v_P tptp.v_i))))) :rule equiv_pos2)
% 26.93/27.24 (step t176 (cl (not (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP tptp.v_P tptp.v_i))) (forall ((B_x $$unsorted) (BOUND_VARIABLE_7486 $$unsorted)) (or (not (tptp.c_member tptp.tc_Arrow__Order__Mirabelle_Oalt B_x (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)))) (not (tptp.c_member tptp.tc_Arrow__Order__Mirabelle_Oalt BOUND_VARIABLE_7486 (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)))) (= B_x BOUND_VARIABLE_7486) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt B_x BOUND_VARIABLE_7486) (tptp.hAPP tptp.v_P tptp.v_i)) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt BOUND_VARIABLE_7486 B_x) (tptp.hAPP tptp.v_P tptp.v_i)))) (not (= (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP tptp.v_P tptp.v_i)) (forall ((B_x $$unsorted) (BOUND_VARIABLE_7486 $$unsorted)) (or (not (tptp.c_member tptp.tc_Arrow__Order__Mirabelle_Oalt B_x (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)))) (not (tptp.c_member tptp.tc_Arrow__Order__Mirabelle_Oalt BOUND_VARIABLE_7486 (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)))) (= B_x BOUND_VARIABLE_7486) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt B_x BOUND_VARIABLE_7486) (tptp.hAPP tptp.v_P tptp.v_i)) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt BOUND_VARIABLE_7486 B_x) (tptp.hAPP tptp.v_P tptp.v_i))))))) :rule reordering :premises (t175))
% 26.93/27.24 (step t177 (cl (=> (forall ((BOUND_VARIABLE_10503 $$unsorted)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP tptp.v_P BOUND_VARIABLE_10503))) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP tptp.v_P tptp.v_i))) (forall ((BOUND_VARIABLE_10503 $$unsorted)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP tptp.v_P BOUND_VARIABLE_10503)))) :rule implies_neg1)
% 26.93/27.24 (anchor :step t178)
% 26.93/27.24 (assume t178.a0 (forall ((BOUND_VARIABLE_10503 $$unsorted)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP tptp.v_P BOUND_VARIABLE_10503))))
% 26.93/27.24 (step t178.t1 (cl (or (not (forall ((BOUND_VARIABLE_10503 $$unsorted)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP tptp.v_P BOUND_VARIABLE_10503)))) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP tptp.v_P tptp.v_i)))) :rule forall_inst :args ((:= BOUND_VARIABLE_10503 tptp.v_i)))
% 26.93/27.24 (step t178.t2 (cl (not (forall ((BOUND_VARIABLE_10503 $$unsorted)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP tptp.v_P BOUND_VARIABLE_10503)))) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP tptp.v_P tptp.v_i))) :rule or :premises (t178.t1))
% 26.93/27.24 (step t178.t3 (cl (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP tptp.v_P tptp.v_i))) :rule resolution :premises (t178.t2 t178.a0))
% 26.93/27.24 (step t178 (cl (not (forall ((BOUND_VARIABLE_10503 $$unsorted)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP tptp.v_P BOUND_VARIABLE_10503)))) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP tptp.v_P tptp.v_i))) :rule subproof :discharge (t178.a0))
% 26.93/27.24 (step t179 (cl (=> (forall ((BOUND_VARIABLE_10503 $$unsorted)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP tptp.v_P BOUND_VARIABLE_10503))) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP tptp.v_P tptp.v_i))) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP tptp.v_P tptp.v_i))) :rule resolution :premises (t177 t178))
% 26.93/27.24 (step t180 (cl (=> (forall ((BOUND_VARIABLE_10503 $$unsorted)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP tptp.v_P BOUND_VARIABLE_10503))) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP tptp.v_P tptp.v_i))) (not (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP tptp.v_P tptp.v_i)))) :rule implies_neg2)
% 26.93/27.24 (step t181 (cl (=> (forall ((BOUND_VARIABLE_10503 $$unsorted)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP tptp.v_P BOUND_VARIABLE_10503))) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP tptp.v_P tptp.v_i))) (=> (forall ((BOUND_VARIABLE_10503 $$unsorted)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP tptp.v_P BOUND_VARIABLE_10503))) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP tptp.v_P tptp.v_i)))) :rule resolution :premises (t179 t180))
% 26.93/27.24 (step t182 (cl (=> (forall ((BOUND_VARIABLE_10503 $$unsorted)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP tptp.v_P BOUND_VARIABLE_10503))) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP tptp.v_P tptp.v_i)))) :rule contraction :premises (t181))
% 26.93/27.24 (step t183 (cl (not (forall ((BOUND_VARIABLE_10503 $$unsorted)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP tptp.v_P BOUND_VARIABLE_10503)))) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP tptp.v_P tptp.v_i))) :rule implies :premises (t182))
% 26.93/27.24 (step t184 (cl (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP tptp.v_P tptp.v_i))) :rule resolution :premises (t183 t73))
% 26.93/27.24 (step t185 (cl (=> (forall ((V_r_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_Ototal__on T_a V_A_2 V_r_2) (forall ((B_x $$unsorted) (BOUND_VARIABLE_7486 $$unsorted)) (or (not (tptp.c_member T_a B_x V_A_2)) (not (tptp.c_member T_a BOUND_VARIABLE_7486 V_A_2)) (= B_x BOUND_VARIABLE_7486) (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a B_x BOUND_VARIABLE_7486) V_r_2) (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a BOUND_VARIABLE_7486 B_x) V_r_2))))) (= (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP tptp.v_P tptp.v_i)) (forall ((B_x $$unsorted) (BOUND_VARIABLE_7486 $$unsorted)) (or (not (tptp.c_member tptp.tc_Arrow__Order__Mirabelle_Oalt B_x (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)))) (not (tptp.c_member tptp.tc_Arrow__Order__Mirabelle_Oalt BOUND_VARIABLE_7486 (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)))) (= B_x BOUND_VARIABLE_7486) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt B_x BOUND_VARIABLE_7486) (tptp.hAPP tptp.v_P tptp.v_i)) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt BOUND_VARIABLE_7486 B_x) (tptp.hAPP tptp.v_P tptp.v_i)))))) (forall ((V_r_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_Ototal__on T_a V_A_2 V_r_2) (forall ((B_x $$unsorted) (BOUND_VARIABLE_7486 $$unsorted)) (or (not (tptp.c_member T_a B_x V_A_2)) (not (tptp.c_member T_a BOUND_VARIABLE_7486 V_A_2)) (= B_x BOUND_VARIABLE_7486) (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a B_x BOUND_VARIABLE_7486) V_r_2) (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a BOUND_VARIABLE_7486 B_x) V_r_2)))))) :rule implies_neg1)
% 26.93/27.24 (anchor :step t186)
% 26.93/27.24 (assume t186.a0 (forall ((V_r_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_Ototal__on T_a V_A_2 V_r_2) (forall ((B_x $$unsorted) (BOUND_VARIABLE_7486 $$unsorted)) (or (not (tptp.c_member T_a B_x V_A_2)) (not (tptp.c_member T_a BOUND_VARIABLE_7486 V_A_2)) (= B_x BOUND_VARIABLE_7486) (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a B_x BOUND_VARIABLE_7486) V_r_2) (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a BOUND_VARIABLE_7486 B_x) V_r_2))))))
% 26.93/27.24 (step t186.t1 (cl (or (not (forall ((V_r_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_Ototal__on T_a V_A_2 V_r_2) (forall ((B_x $$unsorted) (BOUND_VARIABLE_7486 $$unsorted)) (or (not (tptp.c_member T_a B_x V_A_2)) (not (tptp.c_member T_a BOUND_VARIABLE_7486 V_A_2)) (= B_x BOUND_VARIABLE_7486) (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a B_x BOUND_VARIABLE_7486) V_r_2) (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a BOUND_VARIABLE_7486 B_x) V_r_2)))))) (= (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP tptp.v_P tptp.v_i)) (forall ((B_x $$unsorted) (BOUND_VARIABLE_7486 $$unsorted)) (or (not (tptp.c_member tptp.tc_Arrow__Order__Mirabelle_Oalt B_x (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)))) (not (tptp.c_member tptp.tc_Arrow__Order__Mirabelle_Oalt BOUND_VARIABLE_7486 (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)))) (= B_x BOUND_VARIABLE_7486) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt B_x BOUND_VARIABLE_7486) (tptp.hAPP tptp.v_P tptp.v_i)) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt BOUND_VARIABLE_7486 B_x) (tptp.hAPP tptp.v_P tptp.v_i))))))) :rule forall_inst :args ((:= V_r_2 (tptp.hAPP tptp.v_P tptp.v_i)) (:= V_A_2 (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool))) (:= T_a tptp.tc_Arrow__Order__Mirabelle_Oalt)))
% 26.93/27.24 (step t186.t2 (cl (not (forall ((V_r_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_Ototal__on T_a V_A_2 V_r_2) (forall ((B_x $$unsorted) (BOUND_VARIABLE_7486 $$unsorted)) (or (not (tptp.c_member T_a B_x V_A_2)) (not (tptp.c_member T_a BOUND_VARIABLE_7486 V_A_2)) (= B_x BOUND_VARIABLE_7486) (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a B_x BOUND_VARIABLE_7486) V_r_2) (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a BOUND_VARIABLE_7486 B_x) V_r_2)))))) (= (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP tptp.v_P tptp.v_i)) (forall ((B_x $$unsorted) (BOUND_VARIABLE_7486 $$unsorted)) (or (not (tptp.c_member tptp.tc_Arrow__Order__Mirabelle_Oalt B_x (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)))) (not (tptp.c_member tptp.tc_Arrow__Order__Mirabelle_Oalt BOUND_VARIABLE_7486 (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)))) (= B_x BOUND_VARIABLE_7486) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt B_x BOUND_VARIABLE_7486) (tptp.hAPP tptp.v_P tptp.v_i)) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt BOUND_VARIABLE_7486 B_x) (tptp.hAPP tptp.v_P tptp.v_i)))))) :rule or :premises (t186.t1))
% 26.93/27.24 (step t186.t3 (cl (= (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP tptp.v_P tptp.v_i)) (forall ((B_x $$unsorted) (BOUND_VARIABLE_7486 $$unsorted)) (or (not (tptp.c_member tptp.tc_Arrow__Order__Mirabelle_Oalt B_x (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)))) (not (tptp.c_member tptp.tc_Arrow__Order__Mirabelle_Oalt BOUND_VARIABLE_7486 (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)))) (= B_x BOUND_VARIABLE_7486) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt B_x BOUND_VARIABLE_7486) (tptp.hAPP tptp.v_P tptp.v_i)) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt BOUND_VARIABLE_7486 B_x) (tptp.hAPP tptp.v_P tptp.v_i)))))) :rule resolution :premises (t186.t2 t186.a0))
% 26.93/27.24 (step t186 (cl (not (forall ((V_r_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_Ototal__on T_a V_A_2 V_r_2) (forall ((B_x $$unsorted) (BOUND_VARIABLE_7486 $$unsorted)) (or (not (tptp.c_member T_a B_x V_A_2)) (not (tptp.c_member T_a BOUND_VARIABLE_7486 V_A_2)) (= B_x BOUND_VARIABLE_7486) (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a B_x BOUND_VARIABLE_7486) V_r_2) (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a BOUND_VARIABLE_7486 B_x) V_r_2)))))) (= (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP tptp.v_P tptp.v_i)) (forall ((B_x $$unsorted) (BOUND_VARIABLE_7486 $$unsorted)) (or (not (tptp.c_member tptp.tc_Arrow__Order__Mirabelle_Oalt B_x (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)))) (not (tptp.c_member tptp.tc_Arrow__Order__Mirabelle_Oalt BOUND_VARIABLE_7486 (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)))) (= B_x BOUND_VARIABLE_7486) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt B_x BOUND_VARIABLE_7486) (tptp.hAPP tptp.v_P tptp.v_i)) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt BOUND_VARIABLE_7486 B_x) (tptp.hAPP tptp.v_P tptp.v_i)))))) :rule subproof :discharge (t186.a0))
% 26.93/27.24 (step t187 (cl (=> (forall ((V_r_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_Ototal__on T_a V_A_2 V_r_2) (forall ((B_x $$unsorted) (BOUND_VARIABLE_7486 $$unsorted)) (or (not (tptp.c_member T_a B_x V_A_2)) (not (tptp.c_member T_a BOUND_VARIABLE_7486 V_A_2)) (= B_x BOUND_VARIABLE_7486) (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a B_x BOUND_VARIABLE_7486) V_r_2) (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a BOUND_VARIABLE_7486 B_x) V_r_2))))) (= (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP tptp.v_P tptp.v_i)) (forall ((B_x $$unsorted) (BOUND_VARIABLE_7486 $$unsorted)) (or (not (tptp.c_member tptp.tc_Arrow__Order__Mirabelle_Oalt B_x (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)))) (not (tptp.c_member tptp.tc_Arrow__Order__Mirabelle_Oalt BOUND_VARIABLE_7486 (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)))) (= B_x BOUND_VARIABLE_7486) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt B_x BOUND_VARIABLE_7486) (tptp.hAPP tptp.v_P tptp.v_i)) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt BOUND_VARIABLE_7486 B_x) (tptp.hAPP tptp.v_P tptp.v_i)))))) (= (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP tptp.v_P tptp.v_i)) (forall ((B_x $$unsorted) (BOUND_VARIABLE_7486 $$unsorted)) (or (not (tptp.c_member tptp.tc_Arrow__Order__Mirabelle_Oalt B_x (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)))) (not (tptp.c_member tptp.tc_Arrow__Order__Mirabelle_Oalt BOUND_VARIABLE_7486 (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)))) (= B_x BOUND_VARIABLE_7486) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt B_x BOUND_VARIABLE_7486) (tptp.hAPP tptp.v_P tptp.v_i)) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt BOUND_VARIABLE_7486 B_x) (tptp.hAPP tptp.v_P tptp.v_i)))))) :rule resolution :premises (t185 t186))
% 26.93/27.24 (step t188 (cl (=> (forall ((V_r_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_Ototal__on T_a V_A_2 V_r_2) (forall ((B_x $$unsorted) (BOUND_VARIABLE_7486 $$unsorted)) (or (not (tptp.c_member T_a B_x V_A_2)) (not (tptp.c_member T_a BOUND_VARIABLE_7486 V_A_2)) (= B_x BOUND_VARIABLE_7486) (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a B_x BOUND_VARIABLE_7486) V_r_2) (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a BOUND_VARIABLE_7486 B_x) V_r_2))))) (= (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP tptp.v_P tptp.v_i)) (forall ((B_x $$unsorted) (BOUND_VARIABLE_7486 $$unsorted)) (or (not (tptp.c_member tptp.tc_Arrow__Order__Mirabelle_Oalt B_x (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)))) (not (tptp.c_member tptp.tc_Arrow__Order__Mirabelle_Oalt BOUND_VARIABLE_7486 (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)))) (= B_x BOUND_VARIABLE_7486) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt B_x BOUND_VARIABLE_7486) (tptp.hAPP tptp.v_P tptp.v_i)) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt BOUND_VARIABLE_7486 B_x) (tptp.hAPP tptp.v_P tptp.v_i)))))) (not (= (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP tptp.v_P tptp.v_i)) (forall ((B_x $$unsorted) (BOUND_VARIABLE_7486 $$unsorted)) (or (not (tptp.c_member tptp.tc_Arrow__Order__Mirabelle_Oalt B_x (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)))) (not (tptp.c_member tptp.tc_Arrow__Order__Mirabelle_Oalt BOUND_VARIABLE_7486 (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)))) (= B_x BOUND_VARIABLE_7486) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt B_x BOUND_VARIABLE_7486) (tptp.hAPP tptp.v_P tptp.v_i)) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt BOUND_VARIABLE_7486 B_x) (tptp.hAPP tptp.v_P tptp.v_i))))))) :rule implies_neg2)
% 26.93/27.24 (step t189 (cl (=> (forall ((V_r_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_Ototal__on T_a V_A_2 V_r_2) (forall ((B_x $$unsorted) (BOUND_VARIABLE_7486 $$unsorted)) (or (not (tptp.c_member T_a B_x V_A_2)) (not (tptp.c_member T_a BOUND_VARIABLE_7486 V_A_2)) (= B_x BOUND_VARIABLE_7486) (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a B_x BOUND_VARIABLE_7486) V_r_2) (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a BOUND_VARIABLE_7486 B_x) V_r_2))))) (= (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP tptp.v_P tptp.v_i)) (forall ((B_x $$unsorted) (BOUND_VARIABLE_7486 $$unsorted)) (or (not (tptp.c_member tptp.tc_Arrow__Order__Mirabelle_Oalt B_x (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)))) (not (tptp.c_member tptp.tc_Arrow__Order__Mirabelle_Oalt BOUND_VARIABLE_7486 (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)))) (= B_x BOUND_VARIABLE_7486) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt B_x BOUND_VARIABLE_7486) (tptp.hAPP tptp.v_P tptp.v_i)) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt BOUND_VARIABLE_7486 B_x) (tptp.hAPP tptp.v_P tptp.v_i)))))) (=> (forall ((V_r_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_Ototal__on T_a V_A_2 V_r_2) (forall ((B_x $$unsorted) (BOUND_VARIABLE_7486 $$unsorted)) (or (not (tptp.c_member T_a B_x V_A_2)) (not (tptp.c_member T_a BOUND_VARIABLE_7486 V_A_2)) (= B_x BOUND_VARIABLE_7486) (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a B_x BOUND_VARIABLE_7486) V_r_2) (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a BOUND_VARIABLE_7486 B_x) V_r_2))))) (= (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP tptp.v_P tptp.v_i)) (forall ((B_x $$unsorted) (BOUND_VARIABLE_7486 $$unsorted)) (or (not (tptp.c_member tptp.tc_Arrow__Order__Mirabelle_Oalt B_x (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)))) (not (tptp.c_member tptp.tc_Arrow__Order__Mirabelle_Oalt BOUND_VARIABLE_7486 (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)))) (= B_x BOUND_VARIABLE_7486) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt B_x BOUND_VARIABLE_7486) (tptp.hAPP tptp.v_P tptp.v_i)) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt BOUND_VARIABLE_7486 B_x) (tptp.hAPP tptp.v_P tptp.v_i))))))) :rule resolution :premises (t187 t188))
% 26.93/27.24 (step t190 (cl (=> (forall ((V_r_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_Ototal__on T_a V_A_2 V_r_2) (forall ((B_x $$unsorted) (BOUND_VARIABLE_7486 $$unsorted)) (or (not (tptp.c_member T_a B_x V_A_2)) (not (tptp.c_member T_a BOUND_VARIABLE_7486 V_A_2)) (= B_x BOUND_VARIABLE_7486) (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a B_x BOUND_VARIABLE_7486) V_r_2) (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a BOUND_VARIABLE_7486 B_x) V_r_2))))) (= (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP tptp.v_P tptp.v_i)) (forall ((B_x $$unsorted) (BOUND_VARIABLE_7486 $$unsorted)) (or (not (tptp.c_member tptp.tc_Arrow__Order__Mirabelle_Oalt B_x (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)))) (not (tptp.c_member tptp.tc_Arrow__Order__Mirabelle_Oalt BOUND_VARIABLE_7486 (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)))) (= B_x BOUND_VARIABLE_7486) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt B_x BOUND_VARIABLE_7486) (tptp.hAPP tptp.v_P tptp.v_i)) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt BOUND_VARIABLE_7486 B_x) (tptp.hAPP tptp.v_P tptp.v_i))))))) :rule contraction :premises (t189))
% 26.93/27.24 (step t191 (cl (not (forall ((V_r_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_Ototal__on T_a V_A_2 V_r_2) (forall ((B_x $$unsorted) (BOUND_VARIABLE_7486 $$unsorted)) (or (not (tptp.c_member T_a B_x V_A_2)) (not (tptp.c_member T_a BOUND_VARIABLE_7486 V_A_2)) (= B_x BOUND_VARIABLE_7486) (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a B_x BOUND_VARIABLE_7486) V_r_2) (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a BOUND_VARIABLE_7486 B_x) V_r_2)))))) (= (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP tptp.v_P tptp.v_i)) (forall ((B_x $$unsorted) (BOUND_VARIABLE_7486 $$unsorted)) (or (not (tptp.c_member tptp.tc_Arrow__Order__Mirabelle_Oalt B_x (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)))) (not (tptp.c_member tptp.tc_Arrow__Order__Mirabelle_Oalt BOUND_VARIABLE_7486 (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)))) (= B_x BOUND_VARIABLE_7486) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt B_x BOUND_VARIABLE_7486) (tptp.hAPP tptp.v_P tptp.v_i)) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt BOUND_VARIABLE_7486 B_x) (tptp.hAPP tptp.v_P tptp.v_i)))))) :rule implies :premises (t190))
% 26.93/27.24 (step t192 (cl (not (= (forall ((V_r_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_Ototal__on T_a V_A_2 V_r_2) (forall ((B_x $$unsorted)) (=> (tptp.c_member T_a B_x V_A_2) (forall ((B_xa $$unsorted)) (=> (tptp.c_member T_a B_xa V_A_2) (=> (not (= B_x B_xa)) (or (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a B_x B_xa) V_r_2) (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a B_xa B_x) V_r_2))))))))) (forall ((V_r_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_Ototal__on T_a V_A_2 V_r_2) (forall ((B_x $$unsorted) (BOUND_VARIABLE_7486 $$unsorted)) (or (not (tptp.c_member T_a B_x V_A_2)) (not (tptp.c_member T_a BOUND_VARIABLE_7486 V_A_2)) (= B_x BOUND_VARIABLE_7486) (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a B_x BOUND_VARIABLE_7486) V_r_2) (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a BOUND_VARIABLE_7486 B_x) V_r_2))))))) (not (forall ((V_r_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_Ototal__on T_a V_A_2 V_r_2) (forall ((B_x $$unsorted)) (=> (tptp.c_member T_a B_x V_A_2) (forall ((B_xa $$unsorted)) (=> (tptp.c_member T_a B_xa V_A_2) (=> (not (= B_x B_xa)) (or (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a B_x B_xa) V_r_2) (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a B_xa B_x) V_r_2)))))))))) (forall ((V_r_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_Ototal__on T_a V_A_2 V_r_2) (forall ((B_x $$unsorted) (BOUND_VARIABLE_7486 $$unsorted)) (or (not (tptp.c_member T_a B_x V_A_2)) (not (tptp.c_member T_a BOUND_VARIABLE_7486 V_A_2)) (= B_x BOUND_VARIABLE_7486) (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a B_x BOUND_VARIABLE_7486) V_r_2) (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a BOUND_VARIABLE_7486 B_x) V_r_2)))))) :rule equiv_pos2)
% 26.93/27.24 (anchor :step t193 :args ((V_r_2 $$unsorted) (:= V_r_2 V_r_2) (V_A_2 $$unsorted) (:= V_A_2 V_A_2) (T_a $$unsorted) (:= T_a T_a)))
% 26.93/27.24 (step t193.t1 (cl (= V_r_2 V_r_2)) :rule refl)
% 26.93/27.24 (step t193.t2 (cl (= V_A_2 V_A_2)) :rule refl)
% 26.93/27.24 (step t193.t3 (cl (= T_a T_a)) :rule refl)
% 26.93/27.24 (step t193.t4 (cl (= (tptp.c_Relation_Ototal__on T_a V_A_2 V_r_2) (tptp.c_Relation_Ototal__on T_a V_A_2 V_r_2))) :rule refl)
% 26.93/27.24 (anchor :step t193.t5 :args ((B_x $$unsorted) (:= B_x B_x)))
% 26.93/27.24 (step t193.t5.t1 (cl (= B_x B_x)) :rule refl)
% 26.93/27.24 (step t193.t5.t2 (cl (= (tptp.c_member T_a B_x V_A_2) (tptp.c_member T_a B_x V_A_2))) :rule refl)
% 26.93/27.24 (step t193.t5.t3 (cl (= (forall ((B_xa $$unsorted)) (=> (tptp.c_member T_a B_xa V_A_2) (=> (not (= B_x B_xa)) (or (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a B_x B_xa) V_r_2) (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a B_xa B_x) V_r_2))))) (forall ((B_xa $$unsorted)) (or (not (tptp.c_member T_a B_xa V_A_2)) (= B_x B_xa) (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a B_x B_xa) V_r_2) (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a B_xa B_x) V_r_2))))) :rule all_simplify)
% 26.93/27.24 (step t193.t5.t4 (cl (= (=> (tptp.c_member T_a B_x V_A_2) (forall ((B_xa $$unsorted)) (=> (tptp.c_member T_a B_xa V_A_2) (=> (not (= B_x B_xa)) (or (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a B_x B_xa) V_r_2) (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a B_xa B_x) V_r_2)))))) (=> (tptp.c_member T_a B_x V_A_2) (forall ((B_xa $$unsorted)) (or (not (tptp.c_member T_a B_xa V_A_2)) (= B_x B_xa) (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a B_x B_xa) V_r_2) (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a B_xa B_x) V_r_2)))))) :rule cong :premises (t193.t5.t2 t193.t5.t3))
% 26.93/27.24 (step t193.t5 (cl (= (forall ((B_x $$unsorted)) (=> (tptp.c_member T_a B_x V_A_2) (forall ((B_xa $$unsorted)) (=> (tptp.c_member T_a B_xa V_A_2) (=> (not (= B_x B_xa)) (or (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a B_x B_xa) V_r_2) (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a B_xa B_x) V_r_2))))))) (forall ((B_x $$unsorted)) (=> (tptp.c_member T_a B_x V_A_2) (forall ((B_xa $$unsorted)) (or (not (tptp.c_member T_a B_xa V_A_2)) (= B_x B_xa) (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a B_x B_xa) V_r_2) (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a B_xa B_x) V_r_2))))))) :rule bind)
% 26.93/27.24 (step t193.t6 (cl (= (forall ((B_x $$unsorted)) (=> (tptp.c_member T_a B_x V_A_2) (forall ((B_xa $$unsorted)) (or (not (tptp.c_member T_a B_xa V_A_2)) (= B_x B_xa) (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a B_x B_xa) V_r_2) (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a B_xa B_x) V_r_2))))) (forall ((B_x $$unsorted)) (or (not (tptp.c_member T_a B_x V_A_2)) (forall ((B_xa $$unsorted)) (or (not (tptp.c_member T_a B_xa V_A_2)) (= B_x B_xa) (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a B_x B_xa) V_r_2) (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a B_xa B_x) V_r_2))))))) :rule all_simplify)
% 26.93/27.24 (step t193.t7 (cl (= (forall ((B_x $$unsorted)) (or (not (tptp.c_member T_a B_x V_A_2)) (forall ((B_xa $$unsorted)) (or (not (tptp.c_member T_a B_xa V_A_2)) (= B_x B_xa) (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a B_x B_xa) V_r_2) (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a B_xa B_x) V_r_2))))) (forall ((B_x $$unsorted) (BOUND_VARIABLE_7486 $$unsorted)) (or (not (tptp.c_member T_a B_x V_A_2)) (or (not (tptp.c_member T_a BOUND_VARIABLE_7486 V_A_2)) (= B_x BOUND_VARIABLE_7486) (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a B_x BOUND_VARIABLE_7486) V_r_2) (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a BOUND_VARIABLE_7486 B_x) V_r_2)))))) :rule all_simplify)
% 26.93/27.24 (anchor :step t193.t8 :args ((B_x $$unsorted) (:= B_x B_x) (BOUND_VARIABLE_7486 $$unsorted) (:= BOUND_VARIABLE_7486 BOUND_VARIABLE_7486)))
% 26.93/27.24 (step t193.t8.t1 (cl (= B_x B_x)) :rule refl)
% 26.93/27.24 (step t193.t8.t2 (cl (= BOUND_VARIABLE_7486 BOUND_VARIABLE_7486)) :rule refl)
% 26.93/27.24 (step t193.t8.t3 (cl (= (or (not (tptp.c_member T_a B_x V_A_2)) (or (not (tptp.c_member T_a BOUND_VARIABLE_7486 V_A_2)) (= B_x BOUND_VARIABLE_7486) (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a B_x BOUND_VARIABLE_7486) V_r_2) (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a BOUND_VARIABLE_7486 B_x) V_r_2))) (or (not (tptp.c_member T_a B_x V_A_2)) (not (tptp.c_member T_a BOUND_VARIABLE_7486 V_A_2)) (= B_x BOUND_VARIABLE_7486) (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a B_x BOUND_VARIABLE_7486) V_r_2) (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a BOUND_VARIABLE_7486 B_x) V_r_2)))) :rule all_simplify)
% 26.93/27.24 (step t193.t8 (cl (= (forall ((B_x $$unsorted) (BOUND_VARIABLE_7486 $$unsorted)) (or (not (tptp.c_member T_a B_x V_A_2)) (or (not (tptp.c_member T_a BOUND_VARIABLE_7486 V_A_2)) (= B_x BOUND_VARIABLE_7486) (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a B_x BOUND_VARIABLE_7486) V_r_2) (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a BOUND_VARIABLE_7486 B_x) V_r_2)))) (forall ((B_x $$unsorted) (BOUND_VARIABLE_7486 $$unsorted)) (or (not (tptp.c_member T_a B_x V_A_2)) (not (tptp.c_member T_a BOUND_VARIABLE_7486 V_A_2)) (= B_x BOUND_VARIABLE_7486) (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a B_x BOUND_VARIABLE_7486) V_r_2) (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a BOUND_VARIABLE_7486 B_x) V_r_2))))) :rule bind)
% 26.93/27.24 (step t193.t9 (cl (= (forall ((B_x $$unsorted)) (or (not (tptp.c_member T_a B_x V_A_2)) (forall ((B_xa $$unsorted)) (or (not (tptp.c_member T_a B_xa V_A_2)) (= B_x B_xa) (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a B_x B_xa) V_r_2) (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a B_xa B_x) V_r_2))))) (forall ((B_x $$unsorted) (BOUND_VARIABLE_7486 $$unsorted)) (or (not (tptp.c_member T_a B_x V_A_2)) (not (tptp.c_member T_a BOUND_VARIABLE_7486 V_A_2)) (= B_x BOUND_VARIABLE_7486) (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a B_x BOUND_VARIABLE_7486) V_r_2) (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a BOUND_VARIABLE_7486 B_x) V_r_2))))) :rule trans :premises (t193.t7 t193.t8))
% 26.93/27.24 (step t193.t10 (cl (= (forall ((B_x $$unsorted)) (=> (tptp.c_member T_a B_x V_A_2) (forall ((B_xa $$unsorted)) (or (not (tptp.c_member T_a B_xa V_A_2)) (= B_x B_xa) (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a B_x B_xa) V_r_2) (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a B_xa B_x) V_r_2))))) (forall ((B_x $$unsorted) (BOUND_VARIABLE_7486 $$unsorted)) (or (not (tptp.c_member T_a B_x V_A_2)) (not (tptp.c_member T_a BOUND_VARIABLE_7486 V_A_2)) (= B_x BOUND_VARIABLE_7486) (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a B_x BOUND_VARIABLE_7486) V_r_2) (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a BOUND_VARIABLE_7486 B_x) V_r_2))))) :rule trans :premises (t193.t6 t193.t9))
% 26.93/27.24 (step t193.t11 (cl (= (forall ((B_x $$unsorted)) (=> (tptp.c_member T_a B_x V_A_2) (forall ((B_xa $$unsorted)) (=> (tptp.c_member T_a B_xa V_A_2) (=> (not (= B_x B_xa)) (or (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a B_x B_xa) V_r_2) (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a B_xa B_x) V_r_2))))))) (forall ((B_x $$unsorted) (BOUND_VARIABLE_7486 $$unsorted)) (or (not (tptp.c_member T_a B_x V_A_2)) (not (tptp.c_member T_a BOUND_VARIABLE_7486 V_A_2)) (= B_x BOUND_VARIABLE_7486) (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a B_x BOUND_VARIABLE_7486) V_r_2) (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a BOUND_VARIABLE_7486 B_x) V_r_2))))) :rule trans :premises (t193.t5 t193.t10))
% 26.93/27.24 (step t193.t12 (cl (= (= (tptp.c_Relation_Ototal__on T_a V_A_2 V_r_2) (forall ((B_x $$unsorted)) (=> (tptp.c_member T_a B_x V_A_2) (forall ((B_xa $$unsorted)) (=> (tptp.c_member T_a B_xa V_A_2) (=> (not (= B_x B_xa)) (or (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a B_x B_xa) V_r_2) (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a B_xa B_x) V_r_2)))))))) (= (tptp.c_Relation_Ototal__on T_a V_A_2 V_r_2) (forall ((B_x $$unsorted) (BOUND_VARIABLE_7486 $$unsorted)) (or (not (tptp.c_member T_a B_x V_A_2)) (not (tptp.c_member T_a BOUND_VARIABLE_7486 V_A_2)) (= B_x BOUND_VARIABLE_7486) (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a B_x BOUND_VARIABLE_7486) V_r_2) (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a BOUND_VARIABLE_7486 B_x) V_r_2)))))) :rule cong :premises (t193.t4 t193.t11))
% 26.93/27.24 (step t193 (cl (= (forall ((V_r_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_Ototal__on T_a V_A_2 V_r_2) (forall ((B_x $$unsorted)) (=> (tptp.c_member T_a B_x V_A_2) (forall ((B_xa $$unsorted)) (=> (tptp.c_member T_a B_xa V_A_2) (=> (not (= B_x B_xa)) (or (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a B_x B_xa) V_r_2) (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a B_xa B_x) V_r_2))))))))) (forall ((V_r_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_Ototal__on T_a V_A_2 V_r_2) (forall ((B_x $$unsorted) (BOUND_VARIABLE_7486 $$unsorted)) (or (not (tptp.c_member T_a B_x V_A_2)) (not (tptp.c_member T_a BOUND_VARIABLE_7486 V_A_2)) (= B_x BOUND_VARIABLE_7486) (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a B_x BOUND_VARIABLE_7486) V_r_2) (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a BOUND_VARIABLE_7486 B_x) V_r_2))))))) :rule bind)
% 26.93/27.24 (step t194 (cl (forall ((V_r_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_Ototal__on T_a V_A_2 V_r_2) (forall ((B_x $$unsorted) (BOUND_VARIABLE_7486 $$unsorted)) (or (not (tptp.c_member T_a B_x V_A_2)) (not (tptp.c_member T_a BOUND_VARIABLE_7486 V_A_2)) (= B_x BOUND_VARIABLE_7486) (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a B_x BOUND_VARIABLE_7486) V_r_2) (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a BOUND_VARIABLE_7486 B_x) V_r_2)))))) :rule resolution :premises (t192 t193 a3))
% 26.93/27.24 (step t195 (cl (= (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP tptp.v_P tptp.v_i)) (forall ((B_x $$unsorted) (BOUND_VARIABLE_7486 $$unsorted)) (or (not (tptp.c_member tptp.tc_Arrow__Order__Mirabelle_Oalt B_x (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)))) (not (tptp.c_member tptp.tc_Arrow__Order__Mirabelle_Oalt BOUND_VARIABLE_7486 (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)))) (= B_x BOUND_VARIABLE_7486) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt B_x BOUND_VARIABLE_7486) (tptp.hAPP tptp.v_P tptp.v_i)) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt BOUND_VARIABLE_7486 B_x) (tptp.hAPP tptp.v_P tptp.v_i)))))) :rule resolution :premises (t191 t194))
% 26.93/27.24 (step t196 (cl (forall ((B_x $$unsorted) (BOUND_VARIABLE_7486 $$unsorted)) (or (not (tptp.c_member tptp.tc_Arrow__Order__Mirabelle_Oalt B_x (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)))) (not (tptp.c_member tptp.tc_Arrow__Order__Mirabelle_Oalt BOUND_VARIABLE_7486 (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)))) (= B_x BOUND_VARIABLE_7486) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt B_x BOUND_VARIABLE_7486) (tptp.hAPP tptp.v_P tptp.v_i)) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt BOUND_VARIABLE_7486 B_x) (tptp.hAPP tptp.v_P tptp.v_i))))) :rule resolution :premises (t176 t184 t195))
% 27.02/27.24 (step t197 (cl) :rule resolution :premises (t7 t174 t196))
% 27.02/27.24
% 27.02/27.24 % SZS output end Proof for /export/starexec/sandbox2/tmp/tmp.d4ordS8rn2/cvc5---1.0.5_14261.smt2
% 27.02/27.24 % cvc5---1.0.5 exiting
% 27.02/27.25 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------