TSTP Solution File: LAT268-2 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : LAT268-2 : TPTP v8.2.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : do_cvc5 %s %d
% Computer : n018.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 17:22:19 EDT 2024
% Result : Unsatisfiable 0.20s 0.53s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : LAT268-2 : TPTP v8.2.0. Released v3.2.0.
% 0.13/0.14 % Command : do_cvc5 %s %d
% 0.14/0.35 % Computer : n018.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Mon May 27 13:34:23 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.20/0.50 %----Proving TF0_NAR, FOF, or CNF
% 0.20/0.50 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.20/0.53 % SZS status Unsatisfiable for /export/starexec/sandbox/tmp/tmp.wtFAa4pIGx/cvc5---1.0.5_27261.smt2
% 0.20/0.53 % SZS output start Proof for /export/starexec/sandbox/tmp/tmp.wtFAa4pIGx/cvc5---1.0.5_27261.smt2
% 0.20/0.54 (assume a0 (tptp.c_lessequals tptp.v_S tptp.v_A (tptp.tc_set tptp.t_a)))
% 0.20/0.54 (assume a1 (tptp.c_in tptp.v_x tptp.v_S tptp.t_a))
% 0.20/0.54 (assume a2 (not (tptp.c_in (tptp.c_Pair (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.v_x tptp.t_a tptp.t_a) tptp.v_r (tptp.tc_prod tptp.t_a tptp.t_a))))
% 0.20/0.54 (assume a3 (= tptp.v_A (tptp.c_Tarski_Opotype_Opset tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit)))
% 0.20/0.54 (assume a4 (forall ((V_x $$unsorted) (V_S $$unsorted) (T_a $$unsorted) (V_cl $$unsorted)) (or (not (tptp.c_in V_x V_S T_a)) (not (tptp.c_in V_cl tptp.c_Tarski_OCompleteLattice (tptp.tc_Tarski_Opotype_Opotype__ext__type T_a tptp.tc_Product__Type_Ounit))) (not (tptp.c_in V_cl tptp.c_Tarski_OPartialOrder (tptp.tc_Tarski_Opotype_Opotype__ext__type T_a tptp.tc_Product__Type_Ounit))) (not (tptp.c_lessequals V_S (tptp.c_Tarski_Opotype_Opset V_cl T_a tptp.tc_Product__Type_Ounit) (tptp.tc_set T_a))) (tptp.c_in (tptp.c_Pair V_x (tptp.c_Tarski_Olub V_S V_cl T_a) T_a T_a) (tptp.c_Tarski_Opotype_Oorder V_cl T_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod T_a T_a)))))
% 0.20/0.54 (assume a5 (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted) (V_cl $$unsorted)) (or (not (tptp.c_in (tptp.c_Pair V_x V_y T_a T_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual V_cl T_a) T_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod T_a T_a))) (tptp.c_in (tptp.c_Pair V_y V_x T_a T_a) (tptp.c_Tarski_Opotype_Oorder V_cl T_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod T_a T_a)))))
% 0.20/0.54 (assume a6 (tptp.c_in (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.c_Tarski_OCompleteLattice (tptp.tc_Tarski_Opotype_Opotype__ext__type tptp.t_a tptp.tc_Product__Type_Ounit)))
% 0.20/0.54 (assume a7 (tptp.c_in (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.c_Tarski_OPartialOrder (tptp.tc_Tarski_Opotype_Opotype__ext__type tptp.t_a tptp.tc_Product__Type_Ounit)))
% 0.20/0.54 (assume a8 (forall ((V_S $$unsorted) (V_cl $$unsorted) (T_a $$unsorted)) (= (tptp.c_Tarski_Oglb V_S V_cl T_a) (tptp.c_Tarski_Olub V_S (tptp.c_Tarski_Odual V_cl T_a) T_a))))
% 0.20/0.54 (assume a9 (forall ((V_cl $$unsorted) (T_a $$unsorted)) (= (tptp.c_Tarski_Opotype_Opset (tptp.c_Tarski_Odual V_cl T_a) T_a tptp.tc_Product__Type_Ounit) (tptp.c_Tarski_Opotype_Opset V_cl T_a tptp.tc_Product__Type_Ounit))))
% 0.20/0.54 (assume a10 (= tptp.v_r (tptp.c_Tarski_Opotype_Oorder tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit)))
% 0.20/0.54 (step t1 (cl (=> (forall ((V_x $$unsorted) (V_S $$unsorted) (T_a $$unsorted) (V_cl $$unsorted)) (or (not (tptp.c_in V_x V_S T_a)) (not (tptp.c_in V_cl tptp.c_Tarski_OCompleteLattice (tptp.tc_Tarski_Opotype_Opotype__ext__type T_a tptp.tc_Product__Type_Ounit))) (not (tptp.c_in V_cl tptp.c_Tarski_OPartialOrder (tptp.tc_Tarski_Opotype_Opotype__ext__type T_a tptp.tc_Product__Type_Ounit))) (not (tptp.c_lessequals V_S (tptp.c_Tarski_Opotype_Opset V_cl T_a tptp.tc_Product__Type_Ounit) (tptp.tc_set T_a))) (tptp.c_in (tptp.c_Pair V_x (tptp.c_Tarski_Olub V_S V_cl T_a) T_a T_a) (tptp.c_Tarski_Opotype_Oorder V_cl T_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod T_a T_a)))) (or (not (tptp.c_in tptp.v_x tptp.v_S tptp.t_a)) (not (tptp.c_in (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.c_Tarski_OCompleteLattice (tptp.tc_Tarski_Opotype_Opotype__ext__type tptp.t_a tptp.tc_Product__Type_Ounit))) (not (tptp.c_in (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.c_Tarski_OPartialOrder (tptp.tc_Tarski_Opotype_Opotype__ext__type tptp.t_a tptp.tc_Product__Type_Ounit))) (not (tptp.c_lessequals tptp.v_S (tptp.c_Tarski_Opotype_Opset (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_set tptp.t_a))) (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Olub tptp.v_S (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a)))) (forall ((V_x $$unsorted) (V_S $$unsorted) (T_a $$unsorted) (V_cl $$unsorted)) (or (not (tptp.c_in V_x V_S T_a)) (not (tptp.c_in V_cl tptp.c_Tarski_OCompleteLattice (tptp.tc_Tarski_Opotype_Opotype__ext__type T_a tptp.tc_Product__Type_Ounit))) (not (tptp.c_in V_cl tptp.c_Tarski_OPartialOrder (tptp.tc_Tarski_Opotype_Opotype__ext__type T_a tptp.tc_Product__Type_Ounit))) (not (tptp.c_lessequals V_S (tptp.c_Tarski_Opotype_Opset V_cl T_a tptp.tc_Product__Type_Ounit) (tptp.tc_set T_a))) (tptp.c_in (tptp.c_Pair V_x (tptp.c_Tarski_Olub V_S V_cl T_a) T_a T_a) (tptp.c_Tarski_Opotype_Oorder V_cl T_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod T_a T_a))))) :rule implies_neg1)
% 0.20/0.54 (anchor :step t2)
% 0.20/0.54 (assume t2.a0 (forall ((V_x $$unsorted) (V_S $$unsorted) (T_a $$unsorted) (V_cl $$unsorted)) (or (not (tptp.c_in V_x V_S T_a)) (not (tptp.c_in V_cl tptp.c_Tarski_OCompleteLattice (tptp.tc_Tarski_Opotype_Opotype__ext__type T_a tptp.tc_Product__Type_Ounit))) (not (tptp.c_in V_cl tptp.c_Tarski_OPartialOrder (tptp.tc_Tarski_Opotype_Opotype__ext__type T_a tptp.tc_Product__Type_Ounit))) (not (tptp.c_lessequals V_S (tptp.c_Tarski_Opotype_Opset V_cl T_a tptp.tc_Product__Type_Ounit) (tptp.tc_set T_a))) (tptp.c_in (tptp.c_Pair V_x (tptp.c_Tarski_Olub V_S V_cl T_a) T_a T_a) (tptp.c_Tarski_Opotype_Oorder V_cl T_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod T_a T_a)))))
% 0.20/0.54 (step t2.t1 (cl (or (not (forall ((V_x $$unsorted) (V_S $$unsorted) (T_a $$unsorted) (V_cl $$unsorted)) (or (not (tptp.c_in V_x V_S T_a)) (not (tptp.c_in V_cl tptp.c_Tarski_OCompleteLattice (tptp.tc_Tarski_Opotype_Opotype__ext__type T_a tptp.tc_Product__Type_Ounit))) (not (tptp.c_in V_cl tptp.c_Tarski_OPartialOrder (tptp.tc_Tarski_Opotype_Opotype__ext__type T_a tptp.tc_Product__Type_Ounit))) (not (tptp.c_lessequals V_S (tptp.c_Tarski_Opotype_Opset V_cl T_a tptp.tc_Product__Type_Ounit) (tptp.tc_set T_a))) (tptp.c_in (tptp.c_Pair V_x (tptp.c_Tarski_Olub V_S V_cl T_a) T_a T_a) (tptp.c_Tarski_Opotype_Oorder V_cl T_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod T_a T_a))))) (or (not (tptp.c_in tptp.v_x tptp.v_S tptp.t_a)) (not (tptp.c_in (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.c_Tarski_OCompleteLattice (tptp.tc_Tarski_Opotype_Opotype__ext__type tptp.t_a tptp.tc_Product__Type_Ounit))) (not (tptp.c_in (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.c_Tarski_OPartialOrder (tptp.tc_Tarski_Opotype_Opotype__ext__type tptp.t_a tptp.tc_Product__Type_Ounit))) (not (tptp.c_lessequals tptp.v_S (tptp.c_Tarski_Opotype_Opset (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_set tptp.t_a))) (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Olub tptp.v_S (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a))))) :rule forall_inst :args ((:= V_x tptp.v_x) (:= V_S tptp.v_S) (:= T_a tptp.t_a) (:= V_cl (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a))))
% 0.20/0.54 (step t2.t2 (cl (not (forall ((V_x $$unsorted) (V_S $$unsorted) (T_a $$unsorted) (V_cl $$unsorted)) (or (not (tptp.c_in V_x V_S T_a)) (not (tptp.c_in V_cl tptp.c_Tarski_OCompleteLattice (tptp.tc_Tarski_Opotype_Opotype__ext__type T_a tptp.tc_Product__Type_Ounit))) (not (tptp.c_in V_cl tptp.c_Tarski_OPartialOrder (tptp.tc_Tarski_Opotype_Opotype__ext__type T_a tptp.tc_Product__Type_Ounit))) (not (tptp.c_lessequals V_S (tptp.c_Tarski_Opotype_Opset V_cl T_a tptp.tc_Product__Type_Ounit) (tptp.tc_set T_a))) (tptp.c_in (tptp.c_Pair V_x (tptp.c_Tarski_Olub V_S V_cl T_a) T_a T_a) (tptp.c_Tarski_Opotype_Oorder V_cl T_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod T_a T_a))))) (or (not (tptp.c_in tptp.v_x tptp.v_S tptp.t_a)) (not (tptp.c_in (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.c_Tarski_OCompleteLattice (tptp.tc_Tarski_Opotype_Opotype__ext__type tptp.t_a tptp.tc_Product__Type_Ounit))) (not (tptp.c_in (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.c_Tarski_OPartialOrder (tptp.tc_Tarski_Opotype_Opotype__ext__type tptp.t_a tptp.tc_Product__Type_Ounit))) (not (tptp.c_lessequals tptp.v_S (tptp.c_Tarski_Opotype_Opset (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_set tptp.t_a))) (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Olub tptp.v_S (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a)))) :rule or :premises (t2.t1))
% 0.20/0.54 (step t2.t3 (cl (or (not (tptp.c_in tptp.v_x tptp.v_S tptp.t_a)) (not (tptp.c_in (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.c_Tarski_OCompleteLattice (tptp.tc_Tarski_Opotype_Opotype__ext__type tptp.t_a tptp.tc_Product__Type_Ounit))) (not (tptp.c_in (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.c_Tarski_OPartialOrder (tptp.tc_Tarski_Opotype_Opotype__ext__type tptp.t_a tptp.tc_Product__Type_Ounit))) (not (tptp.c_lessequals tptp.v_S (tptp.c_Tarski_Opotype_Opset (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_set tptp.t_a))) (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Olub tptp.v_S (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a)))) :rule resolution :premises (t2.t2 t2.a0))
% 0.20/0.54 (step t2 (cl (not (forall ((V_x $$unsorted) (V_S $$unsorted) (T_a $$unsorted) (V_cl $$unsorted)) (or (not (tptp.c_in V_x V_S T_a)) (not (tptp.c_in V_cl tptp.c_Tarski_OCompleteLattice (tptp.tc_Tarski_Opotype_Opotype__ext__type T_a tptp.tc_Product__Type_Ounit))) (not (tptp.c_in V_cl tptp.c_Tarski_OPartialOrder (tptp.tc_Tarski_Opotype_Opotype__ext__type T_a tptp.tc_Product__Type_Ounit))) (not (tptp.c_lessequals V_S (tptp.c_Tarski_Opotype_Opset V_cl T_a tptp.tc_Product__Type_Ounit) (tptp.tc_set T_a))) (tptp.c_in (tptp.c_Pair V_x (tptp.c_Tarski_Olub V_S V_cl T_a) T_a T_a) (tptp.c_Tarski_Opotype_Oorder V_cl T_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod T_a T_a))))) (or (not (tptp.c_in tptp.v_x tptp.v_S tptp.t_a)) (not (tptp.c_in (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.c_Tarski_OCompleteLattice (tptp.tc_Tarski_Opotype_Opotype__ext__type tptp.t_a tptp.tc_Product__Type_Ounit))) (not (tptp.c_in (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.c_Tarski_OPartialOrder (tptp.tc_Tarski_Opotype_Opotype__ext__type tptp.t_a tptp.tc_Product__Type_Ounit))) (not (tptp.c_lessequals tptp.v_S (tptp.c_Tarski_Opotype_Opset (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_set tptp.t_a))) (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Olub tptp.v_S (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a)))) :rule subproof :discharge (t2.a0))
% 0.20/0.54 (step t3 (cl (=> (forall ((V_x $$unsorted) (V_S $$unsorted) (T_a $$unsorted) (V_cl $$unsorted)) (or (not (tptp.c_in V_x V_S T_a)) (not (tptp.c_in V_cl tptp.c_Tarski_OCompleteLattice (tptp.tc_Tarski_Opotype_Opotype__ext__type T_a tptp.tc_Product__Type_Ounit))) (not (tptp.c_in V_cl tptp.c_Tarski_OPartialOrder (tptp.tc_Tarski_Opotype_Opotype__ext__type T_a tptp.tc_Product__Type_Ounit))) (not (tptp.c_lessequals V_S (tptp.c_Tarski_Opotype_Opset V_cl T_a tptp.tc_Product__Type_Ounit) (tptp.tc_set T_a))) (tptp.c_in (tptp.c_Pair V_x (tptp.c_Tarski_Olub V_S V_cl T_a) T_a T_a) (tptp.c_Tarski_Opotype_Oorder V_cl T_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod T_a T_a)))) (or (not (tptp.c_in tptp.v_x tptp.v_S tptp.t_a)) (not (tptp.c_in (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.c_Tarski_OCompleteLattice (tptp.tc_Tarski_Opotype_Opotype__ext__type tptp.t_a tptp.tc_Product__Type_Ounit))) (not (tptp.c_in (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.c_Tarski_OPartialOrder (tptp.tc_Tarski_Opotype_Opotype__ext__type tptp.t_a tptp.tc_Product__Type_Ounit))) (not (tptp.c_lessequals tptp.v_S (tptp.c_Tarski_Opotype_Opset (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_set tptp.t_a))) (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Olub tptp.v_S (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a)))) (or (not (tptp.c_in tptp.v_x tptp.v_S tptp.t_a)) (not (tptp.c_in (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.c_Tarski_OCompleteLattice (tptp.tc_Tarski_Opotype_Opotype__ext__type tptp.t_a tptp.tc_Product__Type_Ounit))) (not (tptp.c_in (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.c_Tarski_OPartialOrder (tptp.tc_Tarski_Opotype_Opotype__ext__type tptp.t_a tptp.tc_Product__Type_Ounit))) (not (tptp.c_lessequals tptp.v_S (tptp.c_Tarski_Opotype_Opset (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_set tptp.t_a))) (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Olub tptp.v_S (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a)))) :rule resolution :premises (t1 t2))
% 0.20/0.54 (step t4 (cl (=> (forall ((V_x $$unsorted) (V_S $$unsorted) (T_a $$unsorted) (V_cl $$unsorted)) (or (not (tptp.c_in V_x V_S T_a)) (not (tptp.c_in V_cl tptp.c_Tarski_OCompleteLattice (tptp.tc_Tarski_Opotype_Opotype__ext__type T_a tptp.tc_Product__Type_Ounit))) (not (tptp.c_in V_cl tptp.c_Tarski_OPartialOrder (tptp.tc_Tarski_Opotype_Opotype__ext__type T_a tptp.tc_Product__Type_Ounit))) (not (tptp.c_lessequals V_S (tptp.c_Tarski_Opotype_Opset V_cl T_a tptp.tc_Product__Type_Ounit) (tptp.tc_set T_a))) (tptp.c_in (tptp.c_Pair V_x (tptp.c_Tarski_Olub V_S V_cl T_a) T_a T_a) (tptp.c_Tarski_Opotype_Oorder V_cl T_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod T_a T_a)))) (or (not (tptp.c_in tptp.v_x tptp.v_S tptp.t_a)) (not (tptp.c_in (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.c_Tarski_OCompleteLattice (tptp.tc_Tarski_Opotype_Opotype__ext__type tptp.t_a tptp.tc_Product__Type_Ounit))) (not (tptp.c_in (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.c_Tarski_OPartialOrder (tptp.tc_Tarski_Opotype_Opotype__ext__type tptp.t_a tptp.tc_Product__Type_Ounit))) (not (tptp.c_lessequals tptp.v_S (tptp.c_Tarski_Opotype_Opset (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_set tptp.t_a))) (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Olub tptp.v_S (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a)))) (not (or (not (tptp.c_in tptp.v_x tptp.v_S tptp.t_a)) (not (tptp.c_in (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.c_Tarski_OCompleteLattice (tptp.tc_Tarski_Opotype_Opotype__ext__type tptp.t_a tptp.tc_Product__Type_Ounit))) (not (tptp.c_in (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.c_Tarski_OPartialOrder (tptp.tc_Tarski_Opotype_Opotype__ext__type tptp.t_a tptp.tc_Product__Type_Ounit))) (not (tptp.c_lessequals tptp.v_S (tptp.c_Tarski_Opotype_Opset (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_set tptp.t_a))) (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Olub tptp.v_S (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a))))) :rule implies_neg2)
% 0.20/0.54 (step t5 (cl (=> (forall ((V_x $$unsorted) (V_S $$unsorted) (T_a $$unsorted) (V_cl $$unsorted)) (or (not (tptp.c_in V_x V_S T_a)) (not (tptp.c_in V_cl tptp.c_Tarski_OCompleteLattice (tptp.tc_Tarski_Opotype_Opotype__ext__type T_a tptp.tc_Product__Type_Ounit))) (not (tptp.c_in V_cl tptp.c_Tarski_OPartialOrder (tptp.tc_Tarski_Opotype_Opotype__ext__type T_a tptp.tc_Product__Type_Ounit))) (not (tptp.c_lessequals V_S (tptp.c_Tarski_Opotype_Opset V_cl T_a tptp.tc_Product__Type_Ounit) (tptp.tc_set T_a))) (tptp.c_in (tptp.c_Pair V_x (tptp.c_Tarski_Olub V_S V_cl T_a) T_a T_a) (tptp.c_Tarski_Opotype_Oorder V_cl T_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod T_a T_a)))) (or (not (tptp.c_in tptp.v_x tptp.v_S tptp.t_a)) (not (tptp.c_in (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.c_Tarski_OCompleteLattice (tptp.tc_Tarski_Opotype_Opotype__ext__type tptp.t_a tptp.tc_Product__Type_Ounit))) (not (tptp.c_in (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.c_Tarski_OPartialOrder (tptp.tc_Tarski_Opotype_Opotype__ext__type tptp.t_a tptp.tc_Product__Type_Ounit))) (not (tptp.c_lessequals tptp.v_S (tptp.c_Tarski_Opotype_Opset (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_set tptp.t_a))) (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Olub tptp.v_S (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a)))) (=> (forall ((V_x $$unsorted) (V_S $$unsorted) (T_a $$unsorted) (V_cl $$unsorted)) (or (not (tptp.c_in V_x V_S T_a)) (not (tptp.c_in V_cl tptp.c_Tarski_OCompleteLattice (tptp.tc_Tarski_Opotype_Opotype__ext__type T_a tptp.tc_Product__Type_Ounit))) (not (tptp.c_in V_cl tptp.c_Tarski_OPartialOrder (tptp.tc_Tarski_Opotype_Opotype__ext__type T_a tptp.tc_Product__Type_Ounit))) (not (tptp.c_lessequals V_S (tptp.c_Tarski_Opotype_Opset V_cl T_a tptp.tc_Product__Type_Ounit) (tptp.tc_set T_a))) (tptp.c_in (tptp.c_Pair V_x (tptp.c_Tarski_Olub V_S V_cl T_a) T_a T_a) (tptp.c_Tarski_Opotype_Oorder V_cl T_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod T_a T_a)))) (or (not (tptp.c_in tptp.v_x tptp.v_S tptp.t_a)) (not (tptp.c_in (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.c_Tarski_OCompleteLattice (tptp.tc_Tarski_Opotype_Opotype__ext__type tptp.t_a tptp.tc_Product__Type_Ounit))) (not (tptp.c_in (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.c_Tarski_OPartialOrder (tptp.tc_Tarski_Opotype_Opotype__ext__type tptp.t_a tptp.tc_Product__Type_Ounit))) (not (tptp.c_lessequals tptp.v_S (tptp.c_Tarski_Opotype_Opset (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_set tptp.t_a))) (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Olub tptp.v_S (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a))))) :rule resolution :premises (t3 t4))
% 0.20/0.54 (step t6 (cl (=> (forall ((V_x $$unsorted) (V_S $$unsorted) (T_a $$unsorted) (V_cl $$unsorted)) (or (not (tptp.c_in V_x V_S T_a)) (not (tptp.c_in V_cl tptp.c_Tarski_OCompleteLattice (tptp.tc_Tarski_Opotype_Opotype__ext__type T_a tptp.tc_Product__Type_Ounit))) (not (tptp.c_in V_cl tptp.c_Tarski_OPartialOrder (tptp.tc_Tarski_Opotype_Opotype__ext__type T_a tptp.tc_Product__Type_Ounit))) (not (tptp.c_lessequals V_S (tptp.c_Tarski_Opotype_Opset V_cl T_a tptp.tc_Product__Type_Ounit) (tptp.tc_set T_a))) (tptp.c_in (tptp.c_Pair V_x (tptp.c_Tarski_Olub V_S V_cl T_a) T_a T_a) (tptp.c_Tarski_Opotype_Oorder V_cl T_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod T_a T_a)))) (or (not (tptp.c_in tptp.v_x tptp.v_S tptp.t_a)) (not (tptp.c_in (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.c_Tarski_OCompleteLattice (tptp.tc_Tarski_Opotype_Opotype__ext__type tptp.t_a tptp.tc_Product__Type_Ounit))) (not (tptp.c_in (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.c_Tarski_OPartialOrder (tptp.tc_Tarski_Opotype_Opotype__ext__type tptp.t_a tptp.tc_Product__Type_Ounit))) (not (tptp.c_lessequals tptp.v_S (tptp.c_Tarski_Opotype_Opset (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_set tptp.t_a))) (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Olub tptp.v_S (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a))))) :rule contraction :premises (t5))
% 0.20/0.54 (step t7 (cl (not (forall ((V_x $$unsorted) (V_S $$unsorted) (T_a $$unsorted) (V_cl $$unsorted)) (or (not (tptp.c_in V_x V_S T_a)) (not (tptp.c_in V_cl tptp.c_Tarski_OCompleteLattice (tptp.tc_Tarski_Opotype_Opotype__ext__type T_a tptp.tc_Product__Type_Ounit))) (not (tptp.c_in V_cl tptp.c_Tarski_OPartialOrder (tptp.tc_Tarski_Opotype_Opotype__ext__type T_a tptp.tc_Product__Type_Ounit))) (not (tptp.c_lessequals V_S (tptp.c_Tarski_Opotype_Opset V_cl T_a tptp.tc_Product__Type_Ounit) (tptp.tc_set T_a))) (tptp.c_in (tptp.c_Pair V_x (tptp.c_Tarski_Olub V_S V_cl T_a) T_a T_a) (tptp.c_Tarski_Opotype_Oorder V_cl T_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod T_a T_a))))) (or (not (tptp.c_in tptp.v_x tptp.v_S tptp.t_a)) (not (tptp.c_in (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.c_Tarski_OCompleteLattice (tptp.tc_Tarski_Opotype_Opotype__ext__type tptp.t_a tptp.tc_Product__Type_Ounit))) (not (tptp.c_in (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.c_Tarski_OPartialOrder (tptp.tc_Tarski_Opotype_Opotype__ext__type tptp.t_a tptp.tc_Product__Type_Ounit))) (not (tptp.c_lessequals tptp.v_S (tptp.c_Tarski_Opotype_Opset (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_set tptp.t_a))) (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Olub tptp.v_S (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a)))) :rule implies :premises (t6))
% 0.20/0.54 (step t8 (cl (not (or (not (tptp.c_in tptp.v_x tptp.v_S tptp.t_a)) (not (tptp.c_in (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.c_Tarski_OCompleteLattice (tptp.tc_Tarski_Opotype_Opotype__ext__type tptp.t_a tptp.tc_Product__Type_Ounit))) (not (tptp.c_in (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.c_Tarski_OPartialOrder (tptp.tc_Tarski_Opotype_Opotype__ext__type tptp.t_a tptp.tc_Product__Type_Ounit))) (not (tptp.c_lessequals tptp.v_S (tptp.c_Tarski_Opotype_Opset (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_set tptp.t_a))) (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Olub tptp.v_S (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a)))) (not (tptp.c_in tptp.v_x tptp.v_S tptp.t_a)) (not (tptp.c_in (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.c_Tarski_OCompleteLattice (tptp.tc_Tarski_Opotype_Opotype__ext__type tptp.t_a tptp.tc_Product__Type_Ounit))) (not (tptp.c_in (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.c_Tarski_OPartialOrder (tptp.tc_Tarski_Opotype_Opotype__ext__type tptp.t_a tptp.tc_Product__Type_Ounit))) (not (tptp.c_lessequals tptp.v_S (tptp.c_Tarski_Opotype_Opset (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_set tptp.t_a))) (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Olub tptp.v_S (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a))) :rule or_pos)
% 0.20/0.54 (step t9 (cl (not (tptp.c_in tptp.v_x tptp.v_S tptp.t_a)) (not (tptp.c_in (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.c_Tarski_OCompleteLattice (tptp.tc_Tarski_Opotype_Opotype__ext__type tptp.t_a tptp.tc_Product__Type_Ounit))) (not (tptp.c_in (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.c_Tarski_OPartialOrder (tptp.tc_Tarski_Opotype_Opotype__ext__type tptp.t_a tptp.tc_Product__Type_Ounit))) (not (tptp.c_lessequals tptp.v_S (tptp.c_Tarski_Opotype_Opset (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_set tptp.t_a))) (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Olub tptp.v_S (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a)) (not (or (not (tptp.c_in tptp.v_x tptp.v_S tptp.t_a)) (not (tptp.c_in (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.c_Tarski_OCompleteLattice (tptp.tc_Tarski_Opotype_Opotype__ext__type tptp.t_a tptp.tc_Product__Type_Ounit))) (not (tptp.c_in (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.c_Tarski_OPartialOrder (tptp.tc_Tarski_Opotype_Opotype__ext__type tptp.t_a tptp.tc_Product__Type_Ounit))) (not (tptp.c_lessequals tptp.v_S (tptp.c_Tarski_Opotype_Opset (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_set tptp.t_a))) (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Olub tptp.v_S (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a))))) :rule reordering :premises (t8))
% 0.20/0.54 (step t10 (cl (and (tptp.c_lessequals tptp.v_S tptp.v_A (tptp.tc_set tptp.t_a)) (= tptp.v_A (tptp.c_Tarski_Opotype_Opset tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit)) (= (tptp.c_Tarski_Opotype_Opset tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.c_Tarski_Opotype_Opset (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit))) (not (tptp.c_lessequals tptp.v_S tptp.v_A (tptp.tc_set tptp.t_a))) (not (= tptp.v_A (tptp.c_Tarski_Opotype_Opset tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit))) (not (= (tptp.c_Tarski_Opotype_Opset tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.c_Tarski_Opotype_Opset (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit)))) :rule and_neg)
% 0.20/0.54 (step t11 (cl (=> (and (tptp.c_lessequals tptp.v_S tptp.v_A (tptp.tc_set tptp.t_a)) (= tptp.v_A (tptp.c_Tarski_Opotype_Opset tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit)) (= (tptp.c_Tarski_Opotype_Opset tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.c_Tarski_Opotype_Opset (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit))) (tptp.c_lessequals tptp.v_S (tptp.c_Tarski_Opotype_Opset (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_set tptp.t_a))) (and (tptp.c_lessequals tptp.v_S tptp.v_A (tptp.tc_set tptp.t_a)) (= tptp.v_A (tptp.c_Tarski_Opotype_Opset tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit)) (= (tptp.c_Tarski_Opotype_Opset tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.c_Tarski_Opotype_Opset (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit)))) :rule implies_neg1)
% 0.20/0.54 (anchor :step t12)
% 0.20/0.54 (assume t12.a0 (tptp.c_lessequals tptp.v_S tptp.v_A (tptp.tc_set tptp.t_a)))
% 0.20/0.54 (assume t12.a1 (= tptp.v_A (tptp.c_Tarski_Opotype_Opset tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit)))
% 0.20/0.54 (assume t12.a2 (= (tptp.c_Tarski_Opotype_Opset tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.c_Tarski_Opotype_Opset (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit)))
% 0.20/0.54 (step t12.t1 (cl (=> (and (tptp.c_lessequals tptp.v_S tptp.v_A (tptp.tc_set tptp.t_a)) (= tptp.v_A (tptp.c_Tarski_Opotype_Opset tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit)) (= (tptp.c_Tarski_Opotype_Opset tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.c_Tarski_Opotype_Opset (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit))) (tptp.c_lessequals tptp.v_S (tptp.c_Tarski_Opotype_Opset (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_set tptp.t_a))) (and (tptp.c_lessequals tptp.v_S tptp.v_A (tptp.tc_set tptp.t_a)) (= tptp.v_A (tptp.c_Tarski_Opotype_Opset tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit)) (= (tptp.c_Tarski_Opotype_Opset tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.c_Tarski_Opotype_Opset (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit)))) :rule implies_neg1)
% 0.20/0.54 (anchor :step t12.t2)
% 0.20/0.54 (assume t12.t2.a0 (tptp.c_lessequals tptp.v_S tptp.v_A (tptp.tc_set tptp.t_a)))
% 0.20/0.54 (assume t12.t2.a1 (= tptp.v_A (tptp.c_Tarski_Opotype_Opset tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit)))
% 0.20/0.54 (assume t12.t2.a2 (= (tptp.c_Tarski_Opotype_Opset tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.c_Tarski_Opotype_Opset (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit)))
% 0.20/0.54 (step t12.t2.t1 (cl (= (= (tptp.c_lessequals tptp.v_S (tptp.c_Tarski_Opotype_Opset (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_set tptp.t_a)) true) (tptp.c_lessequals tptp.v_S (tptp.c_Tarski_Opotype_Opset (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_set tptp.t_a)))) :rule equiv_simplify)
% 0.20/0.54 (step t12.t2.t2 (cl (not (= (tptp.c_lessequals tptp.v_S (tptp.c_Tarski_Opotype_Opset (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_set tptp.t_a)) true)) (tptp.c_lessequals tptp.v_S (tptp.c_Tarski_Opotype_Opset (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_set tptp.t_a))) :rule equiv1 :premises (t12.t2.t1))
% 0.20/0.54 (step t12.t2.t3 (cl (= tptp.v_S tptp.v_S)) :rule refl)
% 0.20/0.54 (step t12.t2.t4 (cl (= (tptp.c_Tarski_Opotype_Opset (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.c_Tarski_Opotype_Opset tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit))) :rule symm :premises (t12.t2.a2))
% 0.20/0.54 (step t12.t2.t5 (cl (= (tptp.c_Tarski_Opotype_Opset tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit) tptp.v_A)) :rule symm :premises (t12.t2.a1))
% 0.20/0.54 (step t12.t2.t6 (cl (= (tptp.c_Tarski_Opotype_Opset (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) tptp.v_A)) :rule trans :premises (t12.t2.t4 t12.t2.t5))
% 0.20/0.54 (step t12.t2.t7 (cl (= (tptp.tc_set tptp.t_a) (tptp.tc_set tptp.t_a))) :rule refl)
% 0.20/0.54 (step t12.t2.t8 (cl (= (tptp.c_lessequals tptp.v_S (tptp.c_Tarski_Opotype_Opset (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_set tptp.t_a)) (tptp.c_lessequals tptp.v_S tptp.v_A (tptp.tc_set tptp.t_a)))) :rule cong :premises (t12.t2.t3 t12.t2.t6 t12.t2.t7))
% 0.20/0.54 (step t12.t2.t9 (cl (= (= (tptp.c_lessequals tptp.v_S tptp.v_A (tptp.tc_set tptp.t_a)) true) (tptp.c_lessequals tptp.v_S tptp.v_A (tptp.tc_set tptp.t_a)))) :rule equiv_simplify)
% 0.20/0.54 (step t12.t2.t10 (cl (= (tptp.c_lessequals tptp.v_S tptp.v_A (tptp.tc_set tptp.t_a)) true) (not (tptp.c_lessequals tptp.v_S tptp.v_A (tptp.tc_set tptp.t_a)))) :rule equiv2 :premises (t12.t2.t9))
% 0.20/0.54 (step t12.t2.t11 (cl (= (tptp.c_lessequals tptp.v_S tptp.v_A (tptp.tc_set tptp.t_a)) true)) :rule resolution :premises (t12.t2.t10 t12.t2.a0))
% 0.20/0.54 (step t12.t2.t12 (cl (= (tptp.c_lessequals tptp.v_S (tptp.c_Tarski_Opotype_Opset (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_set tptp.t_a)) true)) :rule trans :premises (t12.t2.t8 t12.t2.t11))
% 0.20/0.54 (step t12.t2.t13 (cl (tptp.c_lessequals tptp.v_S (tptp.c_Tarski_Opotype_Opset (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_set tptp.t_a))) :rule resolution :premises (t12.t2.t2 t12.t2.t12))
% 0.20/0.54 (step t12.t2 (cl (not (tptp.c_lessequals tptp.v_S tptp.v_A (tptp.tc_set tptp.t_a))) (not (= tptp.v_A (tptp.c_Tarski_Opotype_Opset tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit))) (not (= (tptp.c_Tarski_Opotype_Opset tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.c_Tarski_Opotype_Opset (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit))) (tptp.c_lessequals tptp.v_S (tptp.c_Tarski_Opotype_Opset (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_set tptp.t_a))) :rule subproof :discharge (t12.t2.a0 t12.t2.a1 t12.t2.a2))
% 0.20/0.54 (step t12.t3 (cl (not (and (tptp.c_lessequals tptp.v_S tptp.v_A (tptp.tc_set tptp.t_a)) (= tptp.v_A (tptp.c_Tarski_Opotype_Opset tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit)) (= (tptp.c_Tarski_Opotype_Opset tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.c_Tarski_Opotype_Opset (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit)))) (tptp.c_lessequals tptp.v_S tptp.v_A (tptp.tc_set tptp.t_a))) :rule and_pos)
% 0.20/0.54 (step t12.t4 (cl (not (and (tptp.c_lessequals tptp.v_S tptp.v_A (tptp.tc_set tptp.t_a)) (= tptp.v_A (tptp.c_Tarski_Opotype_Opset tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit)) (= (tptp.c_Tarski_Opotype_Opset tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.c_Tarski_Opotype_Opset (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit)))) (= tptp.v_A (tptp.c_Tarski_Opotype_Opset tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit))) :rule and_pos)
% 0.20/0.54 (step t12.t5 (cl (not (and (tptp.c_lessequals tptp.v_S tptp.v_A (tptp.tc_set tptp.t_a)) (= tptp.v_A (tptp.c_Tarski_Opotype_Opset tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit)) (= (tptp.c_Tarski_Opotype_Opset tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.c_Tarski_Opotype_Opset (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit)))) (= (tptp.c_Tarski_Opotype_Opset tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.c_Tarski_Opotype_Opset (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit))) :rule and_pos)
% 0.20/0.54 (step t12.t6 (cl (tptp.c_lessequals tptp.v_S (tptp.c_Tarski_Opotype_Opset (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_set tptp.t_a)) (not (and (tptp.c_lessequals tptp.v_S tptp.v_A (tptp.tc_set tptp.t_a)) (= tptp.v_A (tptp.c_Tarski_Opotype_Opset tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit)) (= (tptp.c_Tarski_Opotype_Opset tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.c_Tarski_Opotype_Opset (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit)))) (not (and (tptp.c_lessequals tptp.v_S tptp.v_A (tptp.tc_set tptp.t_a)) (= tptp.v_A (tptp.c_Tarski_Opotype_Opset tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit)) (= (tptp.c_Tarski_Opotype_Opset tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.c_Tarski_Opotype_Opset (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit)))) (not (and (tptp.c_lessequals tptp.v_S tptp.v_A (tptp.tc_set tptp.t_a)) (= tptp.v_A (tptp.c_Tarski_Opotype_Opset tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit)) (= (tptp.c_Tarski_Opotype_Opset tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.c_Tarski_Opotype_Opset (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit))))) :rule resolution :premises (t12.t2 t12.t3 t12.t4 t12.t5))
% 0.20/0.54 (step t12.t7 (cl (not (and (tptp.c_lessequals tptp.v_S tptp.v_A (tptp.tc_set tptp.t_a)) (= tptp.v_A (tptp.c_Tarski_Opotype_Opset tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit)) (= (tptp.c_Tarski_Opotype_Opset tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.c_Tarski_Opotype_Opset (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit)))) (not (and (tptp.c_lessequals tptp.v_S tptp.v_A (tptp.tc_set tptp.t_a)) (= tptp.v_A (tptp.c_Tarski_Opotype_Opset tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit)) (= (tptp.c_Tarski_Opotype_Opset tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.c_Tarski_Opotype_Opset (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit)))) (not (and (tptp.c_lessequals tptp.v_S tptp.v_A (tptp.tc_set tptp.t_a)) (= tptp.v_A (tptp.c_Tarski_Opotype_Opset tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit)) (= (tptp.c_Tarski_Opotype_Opset tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.c_Tarski_Opotype_Opset (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit)))) (tptp.c_lessequals tptp.v_S (tptp.c_Tarski_Opotype_Opset (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_set tptp.t_a))) :rule reordering :premises (t12.t6))
% 0.20/0.54 (step t12.t8 (cl (not (and (tptp.c_lessequals tptp.v_S tptp.v_A (tptp.tc_set tptp.t_a)) (= tptp.v_A (tptp.c_Tarski_Opotype_Opset tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit)) (= (tptp.c_Tarski_Opotype_Opset tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.c_Tarski_Opotype_Opset (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit)))) (tptp.c_lessequals tptp.v_S (tptp.c_Tarski_Opotype_Opset (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_set tptp.t_a))) :rule contraction :premises (t12.t7))
% 0.20/0.54 (step t12.t9 (cl (=> (and (tptp.c_lessequals tptp.v_S tptp.v_A (tptp.tc_set tptp.t_a)) (= tptp.v_A (tptp.c_Tarski_Opotype_Opset tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit)) (= (tptp.c_Tarski_Opotype_Opset tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.c_Tarski_Opotype_Opset (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit))) (tptp.c_lessequals tptp.v_S (tptp.c_Tarski_Opotype_Opset (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_set tptp.t_a))) (tptp.c_lessequals tptp.v_S (tptp.c_Tarski_Opotype_Opset (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_set tptp.t_a))) :rule resolution :premises (t12.t1 t12.t8))
% 0.20/0.54 (step t12.t10 (cl (=> (and (tptp.c_lessequals tptp.v_S tptp.v_A (tptp.tc_set tptp.t_a)) (= tptp.v_A (tptp.c_Tarski_Opotype_Opset tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit)) (= (tptp.c_Tarski_Opotype_Opset tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.c_Tarski_Opotype_Opset (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit))) (tptp.c_lessequals tptp.v_S (tptp.c_Tarski_Opotype_Opset (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_set tptp.t_a))) (not (tptp.c_lessequals tptp.v_S (tptp.c_Tarski_Opotype_Opset (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_set tptp.t_a)))) :rule implies_neg2)
% 0.20/0.54 (step t12.t11 (cl (=> (and (tptp.c_lessequals tptp.v_S tptp.v_A (tptp.tc_set tptp.t_a)) (= tptp.v_A (tptp.c_Tarski_Opotype_Opset tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit)) (= (tptp.c_Tarski_Opotype_Opset tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.c_Tarski_Opotype_Opset (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit))) (tptp.c_lessequals tptp.v_S (tptp.c_Tarski_Opotype_Opset (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_set tptp.t_a))) (=> (and (tptp.c_lessequals tptp.v_S tptp.v_A (tptp.tc_set tptp.t_a)) (= tptp.v_A (tptp.c_Tarski_Opotype_Opset tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit)) (= (tptp.c_Tarski_Opotype_Opset tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.c_Tarski_Opotype_Opset (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit))) (tptp.c_lessequals tptp.v_S (tptp.c_Tarski_Opotype_Opset (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_set tptp.t_a)))) :rule resolution :premises (t12.t9 t12.t10))
% 0.20/0.54 (step t12.t12 (cl (=> (and (tptp.c_lessequals tptp.v_S tptp.v_A (tptp.tc_set tptp.t_a)) (= tptp.v_A (tptp.c_Tarski_Opotype_Opset tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit)) (= (tptp.c_Tarski_Opotype_Opset tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.c_Tarski_Opotype_Opset (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit))) (tptp.c_lessequals tptp.v_S (tptp.c_Tarski_Opotype_Opset (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_set tptp.t_a)))) :rule contraction :premises (t12.t11))
% 0.20/0.54 (step t12.t13 (cl (not (and (tptp.c_lessequals tptp.v_S tptp.v_A (tptp.tc_set tptp.t_a)) (= tptp.v_A (tptp.c_Tarski_Opotype_Opset tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit)) (= (tptp.c_Tarski_Opotype_Opset tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.c_Tarski_Opotype_Opset (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit)))) (tptp.c_lessequals tptp.v_S (tptp.c_Tarski_Opotype_Opset (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_set tptp.t_a))) :rule implies :premises (t12.t12))
% 0.20/0.54 (step t12.t14 (cl (and (tptp.c_lessequals tptp.v_S tptp.v_A (tptp.tc_set tptp.t_a)) (= tptp.v_A (tptp.c_Tarski_Opotype_Opset tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit)) (= (tptp.c_Tarski_Opotype_Opset tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.c_Tarski_Opotype_Opset (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit))) (not (tptp.c_lessequals tptp.v_S tptp.v_A (tptp.tc_set tptp.t_a))) (not (= tptp.v_A (tptp.c_Tarski_Opotype_Opset tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit))) (not (= (tptp.c_Tarski_Opotype_Opset tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.c_Tarski_Opotype_Opset (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit)))) :rule and_neg)
% 0.20/0.54 (step t12.t15 (cl (and (tptp.c_lessequals tptp.v_S tptp.v_A (tptp.tc_set tptp.t_a)) (= tptp.v_A (tptp.c_Tarski_Opotype_Opset tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit)) (= (tptp.c_Tarski_Opotype_Opset tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.c_Tarski_Opotype_Opset (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit)))) :rule resolution :premises (t12.t14 t12.a0 t12.a1 t12.a2))
% 0.20/0.54 (step t12.t16 (cl (tptp.c_lessequals tptp.v_S (tptp.c_Tarski_Opotype_Opset (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_set tptp.t_a))) :rule resolution :premises (t12.t13 t12.t15))
% 0.20/0.54 (step t12 (cl (not (tptp.c_lessequals tptp.v_S tptp.v_A (tptp.tc_set tptp.t_a))) (not (= tptp.v_A (tptp.c_Tarski_Opotype_Opset tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit))) (not (= (tptp.c_Tarski_Opotype_Opset tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.c_Tarski_Opotype_Opset (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit))) (tptp.c_lessequals tptp.v_S (tptp.c_Tarski_Opotype_Opset (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_set tptp.t_a))) :rule subproof :discharge (t12.a0 t12.a1 t12.a2))
% 0.20/0.54 (step t13 (cl (not (and (tptp.c_lessequals tptp.v_S tptp.v_A (tptp.tc_set tptp.t_a)) (= tptp.v_A (tptp.c_Tarski_Opotype_Opset tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit)) (= (tptp.c_Tarski_Opotype_Opset tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.c_Tarski_Opotype_Opset (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit)))) (tptp.c_lessequals tptp.v_S tptp.v_A (tptp.tc_set tptp.t_a))) :rule and_pos)
% 0.20/0.54 (step t14 (cl (not (and (tptp.c_lessequals tptp.v_S tptp.v_A (tptp.tc_set tptp.t_a)) (= tptp.v_A (tptp.c_Tarski_Opotype_Opset tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit)) (= (tptp.c_Tarski_Opotype_Opset tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.c_Tarski_Opotype_Opset (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit)))) (= tptp.v_A (tptp.c_Tarski_Opotype_Opset tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit))) :rule and_pos)
% 0.20/0.54 (step t15 (cl (not (and (tptp.c_lessequals tptp.v_S tptp.v_A (tptp.tc_set tptp.t_a)) (= tptp.v_A (tptp.c_Tarski_Opotype_Opset tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit)) (= (tptp.c_Tarski_Opotype_Opset tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.c_Tarski_Opotype_Opset (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit)))) (= (tptp.c_Tarski_Opotype_Opset tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.c_Tarski_Opotype_Opset (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit))) :rule and_pos)
% 0.20/0.54 (step t16 (cl (tptp.c_lessequals tptp.v_S (tptp.c_Tarski_Opotype_Opset (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_set tptp.t_a)) (not (and (tptp.c_lessequals tptp.v_S tptp.v_A (tptp.tc_set tptp.t_a)) (= tptp.v_A (tptp.c_Tarski_Opotype_Opset tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit)) (= (tptp.c_Tarski_Opotype_Opset tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.c_Tarski_Opotype_Opset (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit)))) (not (and (tptp.c_lessequals tptp.v_S tptp.v_A (tptp.tc_set tptp.t_a)) (= tptp.v_A (tptp.c_Tarski_Opotype_Opset tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit)) (= (tptp.c_Tarski_Opotype_Opset tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.c_Tarski_Opotype_Opset (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit)))) (not (and (tptp.c_lessequals tptp.v_S tptp.v_A (tptp.tc_set tptp.t_a)) (= tptp.v_A (tptp.c_Tarski_Opotype_Opset tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit)) (= (tptp.c_Tarski_Opotype_Opset tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.c_Tarski_Opotype_Opset (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit))))) :rule resolution :premises (t12 t13 t14 t15))
% 0.20/0.54 (step t17 (cl (not (and (tptp.c_lessequals tptp.v_S tptp.v_A (tptp.tc_set tptp.t_a)) (= tptp.v_A (tptp.c_Tarski_Opotype_Opset tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit)) (= (tptp.c_Tarski_Opotype_Opset tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.c_Tarski_Opotype_Opset (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit)))) (not (and (tptp.c_lessequals tptp.v_S tptp.v_A (tptp.tc_set tptp.t_a)) (= tptp.v_A (tptp.c_Tarski_Opotype_Opset tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit)) (= (tptp.c_Tarski_Opotype_Opset tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.c_Tarski_Opotype_Opset (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit)))) (not (and (tptp.c_lessequals tptp.v_S tptp.v_A (tptp.tc_set tptp.t_a)) (= tptp.v_A (tptp.c_Tarski_Opotype_Opset tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit)) (= (tptp.c_Tarski_Opotype_Opset tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.c_Tarski_Opotype_Opset (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit)))) (tptp.c_lessequals tptp.v_S (tptp.c_Tarski_Opotype_Opset (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_set tptp.t_a))) :rule reordering :premises (t16))
% 0.20/0.54 (step t18 (cl (not (and (tptp.c_lessequals tptp.v_S tptp.v_A (tptp.tc_set tptp.t_a)) (= tptp.v_A (tptp.c_Tarski_Opotype_Opset tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit)) (= (tptp.c_Tarski_Opotype_Opset tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.c_Tarski_Opotype_Opset (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit)))) (tptp.c_lessequals tptp.v_S (tptp.c_Tarski_Opotype_Opset (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_set tptp.t_a))) :rule contraction :premises (t17))
% 0.20/0.54 (step t19 (cl (=> (and (tptp.c_lessequals tptp.v_S tptp.v_A (tptp.tc_set tptp.t_a)) (= tptp.v_A (tptp.c_Tarski_Opotype_Opset tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit)) (= (tptp.c_Tarski_Opotype_Opset tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.c_Tarski_Opotype_Opset (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit))) (tptp.c_lessequals tptp.v_S (tptp.c_Tarski_Opotype_Opset (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_set tptp.t_a))) (tptp.c_lessequals tptp.v_S (tptp.c_Tarski_Opotype_Opset (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_set tptp.t_a))) :rule resolution :premises (t11 t18))
% 0.20/0.54 (step t20 (cl (=> (and (tptp.c_lessequals tptp.v_S tptp.v_A (tptp.tc_set tptp.t_a)) (= tptp.v_A (tptp.c_Tarski_Opotype_Opset tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit)) (= (tptp.c_Tarski_Opotype_Opset tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.c_Tarski_Opotype_Opset (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit))) (tptp.c_lessequals tptp.v_S (tptp.c_Tarski_Opotype_Opset (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_set tptp.t_a))) (not (tptp.c_lessequals tptp.v_S (tptp.c_Tarski_Opotype_Opset (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_set tptp.t_a)))) :rule implies_neg2)
% 0.20/0.54 (step t21 (cl (=> (and (tptp.c_lessequals tptp.v_S tptp.v_A (tptp.tc_set tptp.t_a)) (= tptp.v_A (tptp.c_Tarski_Opotype_Opset tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit)) (= (tptp.c_Tarski_Opotype_Opset tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.c_Tarski_Opotype_Opset (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit))) (tptp.c_lessequals tptp.v_S (tptp.c_Tarski_Opotype_Opset (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_set tptp.t_a))) (=> (and (tptp.c_lessequals tptp.v_S tptp.v_A (tptp.tc_set tptp.t_a)) (= tptp.v_A (tptp.c_Tarski_Opotype_Opset tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit)) (= (tptp.c_Tarski_Opotype_Opset tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.c_Tarski_Opotype_Opset (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit))) (tptp.c_lessequals tptp.v_S (tptp.c_Tarski_Opotype_Opset (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_set tptp.t_a)))) :rule resolution :premises (t19 t20))
% 0.20/0.54 (step t22 (cl (=> (and (tptp.c_lessequals tptp.v_S tptp.v_A (tptp.tc_set tptp.t_a)) (= tptp.v_A (tptp.c_Tarski_Opotype_Opset tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit)) (= (tptp.c_Tarski_Opotype_Opset tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.c_Tarski_Opotype_Opset (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit))) (tptp.c_lessequals tptp.v_S (tptp.c_Tarski_Opotype_Opset (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_set tptp.t_a)))) :rule contraction :premises (t21))
% 0.20/0.54 (step t23 (cl (not (and (tptp.c_lessequals tptp.v_S tptp.v_A (tptp.tc_set tptp.t_a)) (= tptp.v_A (tptp.c_Tarski_Opotype_Opset tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit)) (= (tptp.c_Tarski_Opotype_Opset tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.c_Tarski_Opotype_Opset (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit)))) (tptp.c_lessequals tptp.v_S (tptp.c_Tarski_Opotype_Opset (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_set tptp.t_a))) :rule implies :premises (t22))
% 0.20/0.54 (step t24 (cl (not (tptp.c_lessequals tptp.v_S tptp.v_A (tptp.tc_set tptp.t_a))) (not (= tptp.v_A (tptp.c_Tarski_Opotype_Opset tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit))) (not (= (tptp.c_Tarski_Opotype_Opset tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.c_Tarski_Opotype_Opset (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit))) (tptp.c_lessequals tptp.v_S (tptp.c_Tarski_Opotype_Opset (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_set tptp.t_a))) :rule resolution :premises (t10 t23))
% 0.20/0.54 (step t25 (cl (not (= (=> (forall ((V_cl $$unsorted) (T_a $$unsorted)) (= (tptp.c_Tarski_Opotype_Opset (tptp.c_Tarski_Odual V_cl T_a) T_a tptp.tc_Product__Type_Ounit) (tptp.c_Tarski_Opotype_Opset V_cl T_a tptp.tc_Product__Type_Ounit))) (= (tptp.c_Tarski_Opotype_Opset (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.c_Tarski_Opotype_Opset tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit))) (=> (forall ((V_cl $$unsorted) (T_a $$unsorted)) (= (tptp.c_Tarski_Opotype_Opset (tptp.c_Tarski_Odual V_cl T_a) T_a tptp.tc_Product__Type_Ounit) (tptp.c_Tarski_Opotype_Opset V_cl T_a tptp.tc_Product__Type_Ounit))) (= (tptp.c_Tarski_Opotype_Opset tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.c_Tarski_Opotype_Opset (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit))))) (not (=> (forall ((V_cl $$unsorted) (T_a $$unsorted)) (= (tptp.c_Tarski_Opotype_Opset (tptp.c_Tarski_Odual V_cl T_a) T_a tptp.tc_Product__Type_Ounit) (tptp.c_Tarski_Opotype_Opset V_cl T_a tptp.tc_Product__Type_Ounit))) (= (tptp.c_Tarski_Opotype_Opset (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.c_Tarski_Opotype_Opset tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit)))) (=> (forall ((V_cl $$unsorted) (T_a $$unsorted)) (= (tptp.c_Tarski_Opotype_Opset (tptp.c_Tarski_Odual V_cl T_a) T_a tptp.tc_Product__Type_Ounit) (tptp.c_Tarski_Opotype_Opset V_cl T_a tptp.tc_Product__Type_Ounit))) (= (tptp.c_Tarski_Opotype_Opset tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.c_Tarski_Opotype_Opset (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit)))) :rule equiv_pos2)
% 0.20/0.54 (step t26 (cl (= (forall ((V_cl $$unsorted) (T_a $$unsorted)) (= (tptp.c_Tarski_Opotype_Opset (tptp.c_Tarski_Odual V_cl T_a) T_a tptp.tc_Product__Type_Ounit) (tptp.c_Tarski_Opotype_Opset V_cl T_a tptp.tc_Product__Type_Ounit))) (forall ((V_cl $$unsorted) (T_a $$unsorted)) (= (tptp.c_Tarski_Opotype_Opset (tptp.c_Tarski_Odual V_cl T_a) T_a tptp.tc_Product__Type_Ounit) (tptp.c_Tarski_Opotype_Opset V_cl T_a tptp.tc_Product__Type_Ounit))))) :rule refl)
% 0.20/0.54 (step t27 (cl (= (= (tptp.c_Tarski_Opotype_Opset (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.c_Tarski_Opotype_Opset tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit)) (= (tptp.c_Tarski_Opotype_Opset tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.c_Tarski_Opotype_Opset (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit)))) :rule all_simplify)
% 0.20/0.54 (step t28 (cl (= (=> (forall ((V_cl $$unsorted) (T_a $$unsorted)) (= (tptp.c_Tarski_Opotype_Opset (tptp.c_Tarski_Odual V_cl T_a) T_a tptp.tc_Product__Type_Ounit) (tptp.c_Tarski_Opotype_Opset V_cl T_a tptp.tc_Product__Type_Ounit))) (= (tptp.c_Tarski_Opotype_Opset (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.c_Tarski_Opotype_Opset tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit))) (=> (forall ((V_cl $$unsorted) (T_a $$unsorted)) (= (tptp.c_Tarski_Opotype_Opset (tptp.c_Tarski_Odual V_cl T_a) T_a tptp.tc_Product__Type_Ounit) (tptp.c_Tarski_Opotype_Opset V_cl T_a tptp.tc_Product__Type_Ounit))) (= (tptp.c_Tarski_Opotype_Opset tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.c_Tarski_Opotype_Opset (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit))))) :rule cong :premises (t26 t27))
% 0.20/0.54 (step t29 (cl (=> (forall ((V_cl $$unsorted) (T_a $$unsorted)) (= (tptp.c_Tarski_Opotype_Opset (tptp.c_Tarski_Odual V_cl T_a) T_a tptp.tc_Product__Type_Ounit) (tptp.c_Tarski_Opotype_Opset V_cl T_a tptp.tc_Product__Type_Ounit))) (= (tptp.c_Tarski_Opotype_Opset (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.c_Tarski_Opotype_Opset tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit))) (forall ((V_cl $$unsorted) (T_a $$unsorted)) (= (tptp.c_Tarski_Opotype_Opset (tptp.c_Tarski_Odual V_cl T_a) T_a tptp.tc_Product__Type_Ounit) (tptp.c_Tarski_Opotype_Opset V_cl T_a tptp.tc_Product__Type_Ounit)))) :rule implies_neg1)
% 0.20/0.54 (anchor :step t30)
% 0.20/0.54 (assume t30.a0 (forall ((V_cl $$unsorted) (T_a $$unsorted)) (= (tptp.c_Tarski_Opotype_Opset (tptp.c_Tarski_Odual V_cl T_a) T_a tptp.tc_Product__Type_Ounit) (tptp.c_Tarski_Opotype_Opset V_cl T_a tptp.tc_Product__Type_Ounit))))
% 0.20/0.54 (step t30.t1 (cl (or (not (forall ((V_cl $$unsorted) (T_a $$unsorted)) (= (tptp.c_Tarski_Opotype_Opset (tptp.c_Tarski_Odual V_cl T_a) T_a tptp.tc_Product__Type_Ounit) (tptp.c_Tarski_Opotype_Opset V_cl T_a tptp.tc_Product__Type_Ounit)))) (= (tptp.c_Tarski_Opotype_Opset (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.c_Tarski_Opotype_Opset tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit)))) :rule forall_inst :args ((:= V_cl tptp.v_cl) (:= T_a tptp.t_a)))
% 0.20/0.54 (step t30.t2 (cl (not (forall ((V_cl $$unsorted) (T_a $$unsorted)) (= (tptp.c_Tarski_Opotype_Opset (tptp.c_Tarski_Odual V_cl T_a) T_a tptp.tc_Product__Type_Ounit) (tptp.c_Tarski_Opotype_Opset V_cl T_a tptp.tc_Product__Type_Ounit)))) (= (tptp.c_Tarski_Opotype_Opset (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.c_Tarski_Opotype_Opset tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit))) :rule or :premises (t30.t1))
% 0.20/0.54 (step t30.t3 (cl (= (tptp.c_Tarski_Opotype_Opset (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.c_Tarski_Opotype_Opset tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit))) :rule resolution :premises (t30.t2 t30.a0))
% 0.20/0.54 (step t30 (cl (not (forall ((V_cl $$unsorted) (T_a $$unsorted)) (= (tptp.c_Tarski_Opotype_Opset (tptp.c_Tarski_Odual V_cl T_a) T_a tptp.tc_Product__Type_Ounit) (tptp.c_Tarski_Opotype_Opset V_cl T_a tptp.tc_Product__Type_Ounit)))) (= (tptp.c_Tarski_Opotype_Opset (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.c_Tarski_Opotype_Opset tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit))) :rule subproof :discharge (t30.a0))
% 0.20/0.54 (step t31 (cl (=> (forall ((V_cl $$unsorted) (T_a $$unsorted)) (= (tptp.c_Tarski_Opotype_Opset (tptp.c_Tarski_Odual V_cl T_a) T_a tptp.tc_Product__Type_Ounit) (tptp.c_Tarski_Opotype_Opset V_cl T_a tptp.tc_Product__Type_Ounit))) (= (tptp.c_Tarski_Opotype_Opset (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.c_Tarski_Opotype_Opset tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit))) (= (tptp.c_Tarski_Opotype_Opset (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.c_Tarski_Opotype_Opset tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit))) :rule resolution :premises (t29 t30))
% 0.20/0.54 (step t32 (cl (=> (forall ((V_cl $$unsorted) (T_a $$unsorted)) (= (tptp.c_Tarski_Opotype_Opset (tptp.c_Tarski_Odual V_cl T_a) T_a tptp.tc_Product__Type_Ounit) (tptp.c_Tarski_Opotype_Opset V_cl T_a tptp.tc_Product__Type_Ounit))) (= (tptp.c_Tarski_Opotype_Opset (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.c_Tarski_Opotype_Opset tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit))) (not (= (tptp.c_Tarski_Opotype_Opset (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.c_Tarski_Opotype_Opset tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit)))) :rule implies_neg2)
% 0.20/0.54 (step t33 (cl (=> (forall ((V_cl $$unsorted) (T_a $$unsorted)) (= (tptp.c_Tarski_Opotype_Opset (tptp.c_Tarski_Odual V_cl T_a) T_a tptp.tc_Product__Type_Ounit) (tptp.c_Tarski_Opotype_Opset V_cl T_a tptp.tc_Product__Type_Ounit))) (= (tptp.c_Tarski_Opotype_Opset (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.c_Tarski_Opotype_Opset tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit))) (=> (forall ((V_cl $$unsorted) (T_a $$unsorted)) (= (tptp.c_Tarski_Opotype_Opset (tptp.c_Tarski_Odual V_cl T_a) T_a tptp.tc_Product__Type_Ounit) (tptp.c_Tarski_Opotype_Opset V_cl T_a tptp.tc_Product__Type_Ounit))) (= (tptp.c_Tarski_Opotype_Opset (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.c_Tarski_Opotype_Opset tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit)))) :rule resolution :premises (t31 t32))
% 0.20/0.54 (step t34 (cl (=> (forall ((V_cl $$unsorted) (T_a $$unsorted)) (= (tptp.c_Tarski_Opotype_Opset (tptp.c_Tarski_Odual V_cl T_a) T_a tptp.tc_Product__Type_Ounit) (tptp.c_Tarski_Opotype_Opset V_cl T_a tptp.tc_Product__Type_Ounit))) (= (tptp.c_Tarski_Opotype_Opset (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.c_Tarski_Opotype_Opset tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit)))) :rule contraction :premises (t33))
% 0.20/0.54 (step t35 (cl (=> (forall ((V_cl $$unsorted) (T_a $$unsorted)) (= (tptp.c_Tarski_Opotype_Opset (tptp.c_Tarski_Odual V_cl T_a) T_a tptp.tc_Product__Type_Ounit) (tptp.c_Tarski_Opotype_Opset V_cl T_a tptp.tc_Product__Type_Ounit))) (= (tptp.c_Tarski_Opotype_Opset tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.c_Tarski_Opotype_Opset (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit)))) :rule resolution :premises (t25 t28 t34))
% 0.20/0.54 (step t36 (cl (not (forall ((V_cl $$unsorted) (T_a $$unsorted)) (= (tptp.c_Tarski_Opotype_Opset (tptp.c_Tarski_Odual V_cl T_a) T_a tptp.tc_Product__Type_Ounit) (tptp.c_Tarski_Opotype_Opset V_cl T_a tptp.tc_Product__Type_Ounit)))) (= (tptp.c_Tarski_Opotype_Opset tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.c_Tarski_Opotype_Opset (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit))) :rule implies :premises (t35))
% 0.20/0.54 (step t37 (cl (= (tptp.c_Tarski_Opotype_Opset tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.c_Tarski_Opotype_Opset (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit))) :rule resolution :premises (t36 a9))
% 0.20/0.54 (step t38 (cl (tptp.c_lessequals tptp.v_S (tptp.c_Tarski_Opotype_Opset (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_set tptp.t_a))) :rule resolution :premises (t24 a0 a3 t37))
% 0.20/0.54 (step t39 (cl (not (= (or (not (not (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a)))) (not (= (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) (tptp.c_Tarski_Olub tptp.v_S (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a))) (not (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Olub tptp.v_S (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a)))) (or (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a)) (not (= (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) (tptp.c_Tarski_Olub tptp.v_S (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a))) (not (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Olub tptp.v_S (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a)))))) (not (or (not (not (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a)))) (not (= (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) (tptp.c_Tarski_Olub tptp.v_S (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a))) (not (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Olub tptp.v_S (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a))))) (or (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a)) (not (= (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) (tptp.c_Tarski_Olub tptp.v_S (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a))) (not (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Olub tptp.v_S (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a))))) :rule equiv_pos2)
% 0.20/0.54 (step t40 (cl (= (= (= (not (not (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a)))) (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a))) true) (= (not (not (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a)))) (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a))))) :rule equiv_simplify)
% 0.20/0.54 (step t41 (cl (not (= (= (not (not (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a)))) (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a))) true)) (= (not (not (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a)))) (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a)))) :rule equiv1 :premises (t40))
% 0.20/0.54 (step t42 (cl (= (= (not (not (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a)))) (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a))) (= (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a)) (not (not (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a))))))) :rule all_simplify)
% 0.20/0.54 (step t43 (cl (= (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a)) (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a)))) :rule refl)
% 0.20/0.54 (step t44 (cl (= (not (not (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a)))) (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a)))) :rule all_simplify)
% 0.20/0.54 (step t45 (cl (= (= (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a)) (not (not (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a))))) (= (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a)) (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a))))) :rule cong :premises (t43 t44))
% 0.20/0.54 (step t46 (cl (= (= (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a)) (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a))) true)) :rule all_simplify)
% 0.20/0.54 (step t47 (cl (= (= (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a)) (not (not (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a))))) true)) :rule trans :premises (t45 t46))
% 0.20/0.54 (step t48 (cl (= (= (not (not (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a)))) (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a))) true)) :rule trans :premises (t42 t47))
% 0.20/0.54 (step t49 (cl (= (not (not (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a)))) (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a)))) :rule resolution :premises (t41 t48))
% 0.20/0.54 (step t50 (cl (= (not (= (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) (tptp.c_Tarski_Olub tptp.v_S (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a))) (not (= (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) (tptp.c_Tarski_Olub tptp.v_S (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a))))) :rule refl)
% 0.20/0.54 (step t51 (cl (= (not (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Olub tptp.v_S (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a))) (not (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Olub tptp.v_S (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a))))) :rule refl)
% 0.20/0.54 (step t52 (cl (= (or (not (not (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a)))) (not (= (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) (tptp.c_Tarski_Olub tptp.v_S (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a))) (not (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Olub tptp.v_S (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a)))) (or (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a)) (not (= (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) (tptp.c_Tarski_Olub tptp.v_S (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a))) (not (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Olub tptp.v_S (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a)))))) :rule cong :premises (t49 t50 t51))
% 0.20/0.54 (step t53 (cl (and (not (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a))) (= (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) (tptp.c_Tarski_Olub tptp.v_S (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a))) (not (not (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a)))) (not (= (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) (tptp.c_Tarski_Olub tptp.v_S (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a)))) :rule and_neg)
% 0.20/0.54 (step t54 (cl (=> (and (not (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a))) (= (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) (tptp.c_Tarski_Olub tptp.v_S (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a))) (not (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Olub tptp.v_S (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a)))) (and (not (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a))) (= (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) (tptp.c_Tarski_Olub tptp.v_S (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a)))) :rule implies_neg1)
% 0.20/0.54 (anchor :step t55)
% 0.20/0.54 (assume t55.a0 (not (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a))))
% 0.20/0.54 (assume t55.a1 (= (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) (tptp.c_Tarski_Olub tptp.v_S (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a)))
% 0.20/0.54 (step t55.t1 (cl (=> (and (not (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a))) (= (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) (tptp.c_Tarski_Olub tptp.v_S (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a))) (not (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Olub tptp.v_S (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a)))) (and (not (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a))) (= (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) (tptp.c_Tarski_Olub tptp.v_S (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a)))) :rule implies_neg1)
% 0.20/0.54 (anchor :step t55.t2)
% 0.20/0.54 (assume t55.t2.a0 (not (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a))))
% 0.20/0.54 (assume t55.t2.a1 (= (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) (tptp.c_Tarski_Olub tptp.v_S (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a)))
% 0.20/0.54 (step t55.t2.t1 (cl (= (= (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Olub tptp.v_S (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a)) false) (not (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Olub tptp.v_S (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a))))) :rule equiv_simplify)
% 0.20/0.54 (step t55.t2.t2 (cl (not (= (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Olub tptp.v_S (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a)) false)) (not (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Olub tptp.v_S (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a)))) :rule equiv1 :premises (t55.t2.t1))
% 0.20/0.54 (step t55.t2.t3 (cl (= tptp.v_x tptp.v_x)) :rule refl)
% 0.20/0.54 (step t55.t2.t4 (cl (= (tptp.c_Tarski_Olub tptp.v_S (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a) (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a))) :rule symm :premises (t55.t2.a1))
% 0.20/0.54 (step t55.t2.t5 (cl (= tptp.t_a tptp.t_a)) :rule refl)
% 0.20/0.54 (step t55.t2.t6 (cl (= (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Olub tptp.v_S (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.t_a tptp.t_a))) :rule cong :premises (t55.t2.t3 t55.t2.t4 t55.t2.t5 t55.t2.t5))
% 0.20/0.54 (step t55.t2.t7 (cl (= (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit))) :rule refl)
% 0.20/0.54 (step t55.t2.t8 (cl (= (tptp.tc_prod tptp.t_a tptp.t_a) (tptp.tc_prod tptp.t_a tptp.t_a))) :rule refl)
% 0.20/0.54 (step t55.t2.t9 (cl (= (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Olub tptp.v_S (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a)) (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a)))) :rule cong :premises (t55.t2.t6 t55.t2.t7 t55.t2.t8))
% 0.20/0.54 (step t55.t2.t10 (cl (= (= (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a)) false) (not (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a))))) :rule equiv_simplify)
% 0.20/0.54 (step t55.t2.t11 (cl (= (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a)) false) (not (not (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a))))) :rule equiv2 :premises (t55.t2.t10))
% 0.20/0.54 (step t55.t2.t12 (cl (not (not (not (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a))))) (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a))) :rule not_not)
% 0.20/0.54 (step t55.t2.t13 (cl (= (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a)) false) (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a))) :rule resolution :premises (t55.t2.t11 t55.t2.t12))
% 0.20/0.54 (step t55.t2.t14 (cl (= (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a)) false)) :rule resolution :premises (t55.t2.t13 t55.t2.a0))
% 0.20/0.54 (step t55.t2.t15 (cl (= (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Olub tptp.v_S (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a)) false)) :rule trans :premises (t55.t2.t9 t55.t2.t14))
% 0.20/0.54 (step t55.t2.t16 (cl (not (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Olub tptp.v_S (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a)))) :rule resolution :premises (t55.t2.t2 t55.t2.t15))
% 0.20/0.54 (step t55.t2 (cl (not (not (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a)))) (not (= (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) (tptp.c_Tarski_Olub tptp.v_S (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a))) (not (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Olub tptp.v_S (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a)))) :rule subproof :discharge (t55.t2.a0 t55.t2.a1))
% 0.20/0.54 (step t55.t3 (cl (not (and (not (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a))) (= (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) (tptp.c_Tarski_Olub tptp.v_S (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a)))) (not (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a)))) :rule and_pos)
% 0.20/0.54 (step t55.t4 (cl (not (and (not (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a))) (= (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) (tptp.c_Tarski_Olub tptp.v_S (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a)))) (= (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) (tptp.c_Tarski_Olub tptp.v_S (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a))) :rule and_pos)
% 0.20/0.54 (step t55.t5 (cl (not (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Olub tptp.v_S (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a))) (not (and (not (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a))) (= (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) (tptp.c_Tarski_Olub tptp.v_S (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a)))) (not (and (not (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a))) (= (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) (tptp.c_Tarski_Olub tptp.v_S (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a))))) :rule resolution :premises (t55.t2 t55.t3 t55.t4))
% 0.20/0.54 (step t55.t6 (cl (not (and (not (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a))) (= (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) (tptp.c_Tarski_Olub tptp.v_S (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a)))) (not (and (not (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a))) (= (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) (tptp.c_Tarski_Olub tptp.v_S (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a)))) (not (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Olub tptp.v_S (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a)))) :rule reordering :premises (t55.t5))
% 0.20/0.54 (step t55.t7 (cl (not (and (not (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a))) (= (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) (tptp.c_Tarski_Olub tptp.v_S (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a)))) (not (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Olub tptp.v_S (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a)))) :rule contraction :premises (t55.t6))
% 0.20/0.54 (step t55.t8 (cl (=> (and (not (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a))) (= (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) (tptp.c_Tarski_Olub tptp.v_S (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a))) (not (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Olub tptp.v_S (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a)))) (not (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Olub tptp.v_S (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a)))) :rule resolution :premises (t55.t1 t55.t7))
% 0.20/0.54 (step t55.t9 (cl (=> (and (not (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a))) (= (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) (tptp.c_Tarski_Olub tptp.v_S (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a))) (not (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Olub tptp.v_S (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a)))) (not (not (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Olub tptp.v_S (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a))))) :rule implies_neg2)
% 0.20/0.54 (step t55.t10 (cl (=> (and (not (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a))) (= (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) (tptp.c_Tarski_Olub tptp.v_S (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a))) (not (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Olub tptp.v_S (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a)))) (=> (and (not (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a))) (= (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) (tptp.c_Tarski_Olub tptp.v_S (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a))) (not (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Olub tptp.v_S (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a))))) :rule resolution :premises (t55.t8 t55.t9))
% 0.20/0.54 (step t55.t11 (cl (=> (and (not (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a))) (= (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) (tptp.c_Tarski_Olub tptp.v_S (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a))) (not (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Olub tptp.v_S (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a))))) :rule contraction :premises (t55.t10))
% 0.20/0.54 (step t55.t12 (cl (not (and (not (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a))) (= (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) (tptp.c_Tarski_Olub tptp.v_S (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a)))) (not (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Olub tptp.v_S (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a)))) :rule implies :premises (t55.t11))
% 0.20/0.54 (step t55.t13 (cl (and (not (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a))) (= (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) (tptp.c_Tarski_Olub tptp.v_S (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a))) (not (not (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a)))) (not (= (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) (tptp.c_Tarski_Olub tptp.v_S (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a)))) :rule and_neg)
% 0.20/0.54 (step t55.t14 (cl (and (not (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a))) (= (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) (tptp.c_Tarski_Olub tptp.v_S (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a)))) :rule resolution :premises (t55.t13 t55.a0 t55.a1))
% 0.20/0.54 (step t55.t15 (cl (not (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Olub tptp.v_S (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a)))) :rule resolution :premises (t55.t12 t55.t14))
% 0.20/0.54 (step t55 (cl (not (not (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a)))) (not (= (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) (tptp.c_Tarski_Olub tptp.v_S (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a))) (not (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Olub tptp.v_S (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a)))) :rule subproof :discharge (t55.a0 t55.a1))
% 0.20/0.54 (step t56 (cl (not (and (not (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a))) (= (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) (tptp.c_Tarski_Olub tptp.v_S (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a)))) (not (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a)))) :rule and_pos)
% 0.20/0.54 (step t57 (cl (not (and (not (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a))) (= (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) (tptp.c_Tarski_Olub tptp.v_S (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a)))) (= (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) (tptp.c_Tarski_Olub tptp.v_S (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a))) :rule and_pos)
% 0.20/0.54 (step t58 (cl (not (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Olub tptp.v_S (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a))) (not (and (not (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a))) (= (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) (tptp.c_Tarski_Olub tptp.v_S (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a)))) (not (and (not (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a))) (= (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) (tptp.c_Tarski_Olub tptp.v_S (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a))))) :rule resolution :premises (t55 t56 t57))
% 0.20/0.54 (step t59 (cl (not (and (not (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a))) (= (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) (tptp.c_Tarski_Olub tptp.v_S (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a)))) (not (and (not (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a))) (= (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) (tptp.c_Tarski_Olub tptp.v_S (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a)))) (not (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Olub tptp.v_S (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a)))) :rule reordering :premises (t58))
% 0.20/0.54 (step t60 (cl (not (and (not (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a))) (= (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) (tptp.c_Tarski_Olub tptp.v_S (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a)))) (not (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Olub tptp.v_S (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a)))) :rule contraction :premises (t59))
% 0.20/0.54 (step t61 (cl (=> (and (not (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a))) (= (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) (tptp.c_Tarski_Olub tptp.v_S (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a))) (not (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Olub tptp.v_S (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a)))) (not (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Olub tptp.v_S (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a)))) :rule resolution :premises (t54 t60))
% 0.20/0.54 (step t62 (cl (=> (and (not (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a))) (= (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) (tptp.c_Tarski_Olub tptp.v_S (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a))) (not (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Olub tptp.v_S (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a)))) (not (not (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Olub tptp.v_S (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a))))) :rule implies_neg2)
% 0.20/0.54 (step t63 (cl (=> (and (not (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a))) (= (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) (tptp.c_Tarski_Olub tptp.v_S (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a))) (not (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Olub tptp.v_S (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a)))) (=> (and (not (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a))) (= (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) (tptp.c_Tarski_Olub tptp.v_S (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a))) (not (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Olub tptp.v_S (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a))))) :rule resolution :premises (t61 t62))
% 0.20/0.54 (step t64 (cl (=> (and (not (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a))) (= (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) (tptp.c_Tarski_Olub tptp.v_S (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a))) (not (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Olub tptp.v_S (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a))))) :rule contraction :premises (t63))
% 0.20/0.54 (step t65 (cl (not (and (not (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a))) (= (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) (tptp.c_Tarski_Olub tptp.v_S (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a)))) (not (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Olub tptp.v_S (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a)))) :rule implies :premises (t64))
% 0.20/0.54 (step t66 (cl (not (not (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a)))) (not (= (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) (tptp.c_Tarski_Olub tptp.v_S (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a))) (not (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Olub tptp.v_S (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a)))) :rule resolution :premises (t53 t65))
% 0.20/0.54 (step t67 (cl (or (not (not (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a)))) (not (= (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) (tptp.c_Tarski_Olub tptp.v_S (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a))) (not (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Olub tptp.v_S (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a)))) (not (not (not (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a)))))) :rule or_neg)
% 0.20/0.54 (step t68 (cl (or (not (not (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a)))) (not (= (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) (tptp.c_Tarski_Olub tptp.v_S (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a))) (not (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Olub tptp.v_S (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a)))) (not (not (= (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) (tptp.c_Tarski_Olub tptp.v_S (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a))))) :rule or_neg)
% 0.20/0.54 (step t69 (cl (or (not (not (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a)))) (not (= (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) (tptp.c_Tarski_Olub tptp.v_S (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a))) (not (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Olub tptp.v_S (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a)))) (not (not (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Olub tptp.v_S (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a))))) :rule or_neg)
% 0.20/0.54 (step t70 (cl (or (not (not (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a)))) (not (= (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) (tptp.c_Tarski_Olub tptp.v_S (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a))) (not (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Olub tptp.v_S (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a)))) (or (not (not (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a)))) (not (= (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) (tptp.c_Tarski_Olub tptp.v_S (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a))) (not (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Olub tptp.v_S (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a)))) (or (not (not (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a)))) (not (= (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) (tptp.c_Tarski_Olub tptp.v_S (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a))) (not (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Olub tptp.v_S (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a))))) :rule resolution :premises (t66 t67 t68 t69))
% 0.20/0.54 (step t71 (cl (or (not (not (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a)))) (not (= (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) (tptp.c_Tarski_Olub tptp.v_S (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a))) (not (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Olub tptp.v_S (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a))))) :rule contraction :premises (t70))
% 0.20/0.54 (step t72 (cl (or (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a)) (not (= (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) (tptp.c_Tarski_Olub tptp.v_S (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a))) (not (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Olub tptp.v_S (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a))))) :rule resolution :premises (t39 t52 t71))
% 0.20/0.54 (step t73 (cl (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a)) (not (= (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) (tptp.c_Tarski_Olub tptp.v_S (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a))) (not (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Olub tptp.v_S (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a)))) :rule or :premises (t72))
% 0.20/0.54 (step t74 (cl (not (or (not (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a))) (tptp.c_in (tptp.c_Pair (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.v_x tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a)))) (not (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a))) (tptp.c_in (tptp.c_Pair (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.v_x tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a))) :rule or_pos)
% 0.20/0.54 (step t75 (cl (not (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a))) (tptp.c_in (tptp.c_Pair (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.v_x tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a)) (not (or (not (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a))) (tptp.c_in (tptp.c_Pair (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.v_x tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a))))) :rule reordering :premises (t74))
% 0.20/0.54 (step t76 (cl (not (= (or (not (not (tptp.c_in (tptp.c_Pair (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.v_x tptp.t_a tptp.t_a) tptp.v_r (tptp.tc_prod tptp.t_a tptp.t_a)))) (not (= tptp.v_r (tptp.c_Tarski_Opotype_Oorder tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit))) (not (tptp.c_in (tptp.c_Pair (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.v_x tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a)))) (or (tptp.c_in (tptp.c_Pair (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.v_x tptp.t_a tptp.t_a) tptp.v_r (tptp.tc_prod tptp.t_a tptp.t_a)) (not (= tptp.v_r (tptp.c_Tarski_Opotype_Oorder tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit))) (not (tptp.c_in (tptp.c_Pair (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.v_x tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a)))))) (not (or (not (not (tptp.c_in (tptp.c_Pair (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.v_x tptp.t_a tptp.t_a) tptp.v_r (tptp.tc_prod tptp.t_a tptp.t_a)))) (not (= tptp.v_r (tptp.c_Tarski_Opotype_Oorder tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit))) (not (tptp.c_in (tptp.c_Pair (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.v_x tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a))))) (or (tptp.c_in (tptp.c_Pair (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.v_x tptp.t_a tptp.t_a) tptp.v_r (tptp.tc_prod tptp.t_a tptp.t_a)) (not (= tptp.v_r (tptp.c_Tarski_Opotype_Oorder tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit))) (not (tptp.c_in (tptp.c_Pair (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.v_x tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a))))) :rule equiv_pos2)
% 0.20/0.54 (step t77 (cl (= (= (= (not (not (tptp.c_in (tptp.c_Pair (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.v_x tptp.t_a tptp.t_a) tptp.v_r (tptp.tc_prod tptp.t_a tptp.t_a)))) (tptp.c_in (tptp.c_Pair (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.v_x tptp.t_a tptp.t_a) tptp.v_r (tptp.tc_prod tptp.t_a tptp.t_a))) true) (= (not (not (tptp.c_in (tptp.c_Pair (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.v_x tptp.t_a tptp.t_a) tptp.v_r (tptp.tc_prod tptp.t_a tptp.t_a)))) (tptp.c_in (tptp.c_Pair (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.v_x tptp.t_a tptp.t_a) tptp.v_r (tptp.tc_prod tptp.t_a tptp.t_a))))) :rule equiv_simplify)
% 0.20/0.54 (step t78 (cl (not (= (= (not (not (tptp.c_in (tptp.c_Pair (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.v_x tptp.t_a tptp.t_a) tptp.v_r (tptp.tc_prod tptp.t_a tptp.t_a)))) (tptp.c_in (tptp.c_Pair (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.v_x tptp.t_a tptp.t_a) tptp.v_r (tptp.tc_prod tptp.t_a tptp.t_a))) true)) (= (not (not (tptp.c_in (tptp.c_Pair (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.v_x tptp.t_a tptp.t_a) tptp.v_r (tptp.tc_prod tptp.t_a tptp.t_a)))) (tptp.c_in (tptp.c_Pair (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.v_x tptp.t_a tptp.t_a) tptp.v_r (tptp.tc_prod tptp.t_a tptp.t_a)))) :rule equiv1 :premises (t77))
% 0.20/0.54 (step t79 (cl (= (= (not (not (tptp.c_in (tptp.c_Pair (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.v_x tptp.t_a tptp.t_a) tptp.v_r (tptp.tc_prod tptp.t_a tptp.t_a)))) (tptp.c_in (tptp.c_Pair (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.v_x tptp.t_a tptp.t_a) tptp.v_r (tptp.tc_prod tptp.t_a tptp.t_a))) (= (tptp.c_in (tptp.c_Pair (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.v_x tptp.t_a tptp.t_a) tptp.v_r (tptp.tc_prod tptp.t_a tptp.t_a)) (not (not (tptp.c_in (tptp.c_Pair (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.v_x tptp.t_a tptp.t_a) tptp.v_r (tptp.tc_prod tptp.t_a tptp.t_a))))))) :rule all_simplify)
% 0.20/0.54 (step t80 (cl (= (tptp.c_in (tptp.c_Pair (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.v_x tptp.t_a tptp.t_a) tptp.v_r (tptp.tc_prod tptp.t_a tptp.t_a)) (tptp.c_in (tptp.c_Pair (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.v_x tptp.t_a tptp.t_a) tptp.v_r (tptp.tc_prod tptp.t_a tptp.t_a)))) :rule refl)
% 0.20/0.54 (step t81 (cl (= (not (not (tptp.c_in (tptp.c_Pair (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.v_x tptp.t_a tptp.t_a) tptp.v_r (tptp.tc_prod tptp.t_a tptp.t_a)))) (tptp.c_in (tptp.c_Pair (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.v_x tptp.t_a tptp.t_a) tptp.v_r (tptp.tc_prod tptp.t_a tptp.t_a)))) :rule all_simplify)
% 0.20/0.54 (step t82 (cl (= (= (tptp.c_in (tptp.c_Pair (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.v_x tptp.t_a tptp.t_a) tptp.v_r (tptp.tc_prod tptp.t_a tptp.t_a)) (not (not (tptp.c_in (tptp.c_Pair (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.v_x tptp.t_a tptp.t_a) tptp.v_r (tptp.tc_prod tptp.t_a tptp.t_a))))) (= (tptp.c_in (tptp.c_Pair (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.v_x tptp.t_a tptp.t_a) tptp.v_r (tptp.tc_prod tptp.t_a tptp.t_a)) (tptp.c_in (tptp.c_Pair (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.v_x tptp.t_a tptp.t_a) tptp.v_r (tptp.tc_prod tptp.t_a tptp.t_a))))) :rule cong :premises (t80 t81))
% 0.20/0.54 (step t83 (cl (= (= (tptp.c_in (tptp.c_Pair (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.v_x tptp.t_a tptp.t_a) tptp.v_r (tptp.tc_prod tptp.t_a tptp.t_a)) (tptp.c_in (tptp.c_Pair (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.v_x tptp.t_a tptp.t_a) tptp.v_r (tptp.tc_prod tptp.t_a tptp.t_a))) true)) :rule all_simplify)
% 0.20/0.54 (step t84 (cl (= (= (tptp.c_in (tptp.c_Pair (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.v_x tptp.t_a tptp.t_a) tptp.v_r (tptp.tc_prod tptp.t_a tptp.t_a)) (not (not (tptp.c_in (tptp.c_Pair (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.v_x tptp.t_a tptp.t_a) tptp.v_r (tptp.tc_prod tptp.t_a tptp.t_a))))) true)) :rule trans :premises (t82 t83))
% 0.20/0.54 (step t85 (cl (= (= (not (not (tptp.c_in (tptp.c_Pair (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.v_x tptp.t_a tptp.t_a) tptp.v_r (tptp.tc_prod tptp.t_a tptp.t_a)))) (tptp.c_in (tptp.c_Pair (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.v_x tptp.t_a tptp.t_a) tptp.v_r (tptp.tc_prod tptp.t_a tptp.t_a))) true)) :rule trans :premises (t79 t84))
% 0.20/0.54 (step t86 (cl (= (not (not (tptp.c_in (tptp.c_Pair (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.v_x tptp.t_a tptp.t_a) tptp.v_r (tptp.tc_prod tptp.t_a tptp.t_a)))) (tptp.c_in (tptp.c_Pair (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.v_x tptp.t_a tptp.t_a) tptp.v_r (tptp.tc_prod tptp.t_a tptp.t_a)))) :rule resolution :premises (t78 t85))
% 0.20/0.54 (step t87 (cl (= (not (= tptp.v_r (tptp.c_Tarski_Opotype_Oorder tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit))) (not (= tptp.v_r (tptp.c_Tarski_Opotype_Oorder tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit))))) :rule refl)
% 0.20/0.54 (step t88 (cl (= (not (tptp.c_in (tptp.c_Pair (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.v_x tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a))) (not (tptp.c_in (tptp.c_Pair (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.v_x tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a))))) :rule refl)
% 0.20/0.54 (step t89 (cl (= (or (not (not (tptp.c_in (tptp.c_Pair (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.v_x tptp.t_a tptp.t_a) tptp.v_r (tptp.tc_prod tptp.t_a tptp.t_a)))) (not (= tptp.v_r (tptp.c_Tarski_Opotype_Oorder tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit))) (not (tptp.c_in (tptp.c_Pair (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.v_x tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a)))) (or (tptp.c_in (tptp.c_Pair (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.v_x tptp.t_a tptp.t_a) tptp.v_r (tptp.tc_prod tptp.t_a tptp.t_a)) (not (= tptp.v_r (tptp.c_Tarski_Opotype_Oorder tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit))) (not (tptp.c_in (tptp.c_Pair (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.v_x tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a)))))) :rule cong :premises (t86 t87 t88))
% 0.20/0.54 (step t90 (cl (and (not (tptp.c_in (tptp.c_Pair (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.v_x tptp.t_a tptp.t_a) tptp.v_r (tptp.tc_prod tptp.t_a tptp.t_a))) (= tptp.v_r (tptp.c_Tarski_Opotype_Oorder tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit))) (not (not (tptp.c_in (tptp.c_Pair (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.v_x tptp.t_a tptp.t_a) tptp.v_r (tptp.tc_prod tptp.t_a tptp.t_a)))) (not (= tptp.v_r (tptp.c_Tarski_Opotype_Oorder tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit)))) :rule and_neg)
% 0.20/0.54 (step t91 (cl (=> (and (not (tptp.c_in (tptp.c_Pair (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.v_x tptp.t_a tptp.t_a) tptp.v_r (tptp.tc_prod tptp.t_a tptp.t_a))) (= tptp.v_r (tptp.c_Tarski_Opotype_Oorder tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit))) (not (tptp.c_in (tptp.c_Pair (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.v_x tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a)))) (and (not (tptp.c_in (tptp.c_Pair (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.v_x tptp.t_a tptp.t_a) tptp.v_r (tptp.tc_prod tptp.t_a tptp.t_a))) (= tptp.v_r (tptp.c_Tarski_Opotype_Oorder tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit)))) :rule implies_neg1)
% 0.20/0.54 (anchor :step t92)
% 0.20/0.54 (assume t92.a0 (not (tptp.c_in (tptp.c_Pair (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.v_x tptp.t_a tptp.t_a) tptp.v_r (tptp.tc_prod tptp.t_a tptp.t_a))))
% 0.20/0.54 (assume t92.a1 (= tptp.v_r (tptp.c_Tarski_Opotype_Oorder tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit)))
% 0.20/0.54 (step t92.t1 (cl (=> (and (not (tptp.c_in (tptp.c_Pair (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.v_x tptp.t_a tptp.t_a) tptp.v_r (tptp.tc_prod tptp.t_a tptp.t_a))) (= tptp.v_r (tptp.c_Tarski_Opotype_Oorder tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit))) (not (tptp.c_in (tptp.c_Pair (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.v_x tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a)))) (and (not (tptp.c_in (tptp.c_Pair (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.v_x tptp.t_a tptp.t_a) tptp.v_r (tptp.tc_prod tptp.t_a tptp.t_a))) (= tptp.v_r (tptp.c_Tarski_Opotype_Oorder tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit)))) :rule implies_neg1)
% 0.20/0.54 (anchor :step t92.t2)
% 0.20/0.54 (assume t92.t2.a0 (not (tptp.c_in (tptp.c_Pair (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.v_x tptp.t_a tptp.t_a) tptp.v_r (tptp.tc_prod tptp.t_a tptp.t_a))))
% 0.20/0.54 (assume t92.t2.a1 (= tptp.v_r (tptp.c_Tarski_Opotype_Oorder tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit)))
% 0.20/0.54 (step t92.t2.t1 (cl (= (= (tptp.c_in (tptp.c_Pair (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.v_x tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a)) false) (not (tptp.c_in (tptp.c_Pair (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.v_x tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a))))) :rule equiv_simplify)
% 0.20/0.54 (step t92.t2.t2 (cl (not (= (tptp.c_in (tptp.c_Pair (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.v_x tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a)) false)) (not (tptp.c_in (tptp.c_Pair (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.v_x tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a)))) :rule equiv1 :premises (t92.t2.t1))
% 0.20/0.54 (step t92.t2.t3 (cl (= (tptp.c_Pair (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.v_x tptp.t_a tptp.t_a) (tptp.c_Pair (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.v_x tptp.t_a tptp.t_a))) :rule refl)
% 0.20/0.54 (step t92.t2.t4 (cl (= (tptp.c_Tarski_Opotype_Oorder tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit) tptp.v_r)) :rule symm :premises (t92.t2.a1))
% 0.20/0.54 (step t92.t2.t5 (cl (= (tptp.tc_prod tptp.t_a tptp.t_a) (tptp.tc_prod tptp.t_a tptp.t_a))) :rule refl)
% 0.20/0.54 (step t92.t2.t6 (cl (= (tptp.c_in (tptp.c_Pair (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.v_x tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a)) (tptp.c_in (tptp.c_Pair (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.v_x tptp.t_a tptp.t_a) tptp.v_r (tptp.tc_prod tptp.t_a tptp.t_a)))) :rule cong :premises (t92.t2.t3 t92.t2.t4 t92.t2.t5))
% 0.20/0.54 (step t92.t2.t7 (cl (= (= (tptp.c_in (tptp.c_Pair (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.v_x tptp.t_a tptp.t_a) tptp.v_r (tptp.tc_prod tptp.t_a tptp.t_a)) false) (not (tptp.c_in (tptp.c_Pair (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.v_x tptp.t_a tptp.t_a) tptp.v_r (tptp.tc_prod tptp.t_a tptp.t_a))))) :rule equiv_simplify)
% 0.20/0.54 (step t92.t2.t8 (cl (= (tptp.c_in (tptp.c_Pair (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.v_x tptp.t_a tptp.t_a) tptp.v_r (tptp.tc_prod tptp.t_a tptp.t_a)) false) (not (not (tptp.c_in (tptp.c_Pair (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.v_x tptp.t_a tptp.t_a) tptp.v_r (tptp.tc_prod tptp.t_a tptp.t_a))))) :rule equiv2 :premises (t92.t2.t7))
% 0.20/0.54 (step t92.t2.t9 (cl (not (not (not (tptp.c_in (tptp.c_Pair (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.v_x tptp.t_a tptp.t_a) tptp.v_r (tptp.tc_prod tptp.t_a tptp.t_a))))) (tptp.c_in (tptp.c_Pair (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.v_x tptp.t_a tptp.t_a) tptp.v_r (tptp.tc_prod tptp.t_a tptp.t_a))) :rule not_not)
% 0.20/0.54 (step t92.t2.t10 (cl (= (tptp.c_in (tptp.c_Pair (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.v_x tptp.t_a tptp.t_a) tptp.v_r (tptp.tc_prod tptp.t_a tptp.t_a)) false) (tptp.c_in (tptp.c_Pair (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.v_x tptp.t_a tptp.t_a) tptp.v_r (tptp.tc_prod tptp.t_a tptp.t_a))) :rule resolution :premises (t92.t2.t8 t92.t2.t9))
% 0.20/0.54 (step t92.t2.t11 (cl (= (tptp.c_in (tptp.c_Pair (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.v_x tptp.t_a tptp.t_a) tptp.v_r (tptp.tc_prod tptp.t_a tptp.t_a)) false)) :rule resolution :premises (t92.t2.t10 t92.t2.a0))
% 0.20/0.54 (step t92.t2.t12 (cl (= (tptp.c_in (tptp.c_Pair (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.v_x tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a)) false)) :rule trans :premises (t92.t2.t6 t92.t2.t11))
% 0.20/0.54 (step t92.t2.t13 (cl (not (tptp.c_in (tptp.c_Pair (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.v_x tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a)))) :rule resolution :premises (t92.t2.t2 t92.t2.t12))
% 0.20/0.54 (step t92.t2 (cl (not (not (tptp.c_in (tptp.c_Pair (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.v_x tptp.t_a tptp.t_a) tptp.v_r (tptp.tc_prod tptp.t_a tptp.t_a)))) (not (= tptp.v_r (tptp.c_Tarski_Opotype_Oorder tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit))) (not (tptp.c_in (tptp.c_Pair (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.v_x tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a)))) :rule subproof :discharge (t92.t2.a0 t92.t2.a1))
% 0.20/0.54 (step t92.t3 (cl (not (and (not (tptp.c_in (tptp.c_Pair (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.v_x tptp.t_a tptp.t_a) tptp.v_r (tptp.tc_prod tptp.t_a tptp.t_a))) (= tptp.v_r (tptp.c_Tarski_Opotype_Oorder tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit)))) (not (tptp.c_in (tptp.c_Pair (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.v_x tptp.t_a tptp.t_a) tptp.v_r (tptp.tc_prod tptp.t_a tptp.t_a)))) :rule and_pos)
% 0.20/0.54 (step t92.t4 (cl (not (and (not (tptp.c_in (tptp.c_Pair (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.v_x tptp.t_a tptp.t_a) tptp.v_r (tptp.tc_prod tptp.t_a tptp.t_a))) (= tptp.v_r (tptp.c_Tarski_Opotype_Oorder tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit)))) (= tptp.v_r (tptp.c_Tarski_Opotype_Oorder tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit))) :rule and_pos)
% 0.20/0.54 (step t92.t5 (cl (not (tptp.c_in (tptp.c_Pair (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.v_x tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a))) (not (and (not (tptp.c_in (tptp.c_Pair (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.v_x tptp.t_a tptp.t_a) tptp.v_r (tptp.tc_prod tptp.t_a tptp.t_a))) (= tptp.v_r (tptp.c_Tarski_Opotype_Oorder tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit)))) (not (and (not (tptp.c_in (tptp.c_Pair (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.v_x tptp.t_a tptp.t_a) tptp.v_r (tptp.tc_prod tptp.t_a tptp.t_a))) (= tptp.v_r (tptp.c_Tarski_Opotype_Oorder tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit))))) :rule resolution :premises (t92.t2 t92.t3 t92.t4))
% 0.20/0.54 (step t92.t6 (cl (not (and (not (tptp.c_in (tptp.c_Pair (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.v_x tptp.t_a tptp.t_a) tptp.v_r (tptp.tc_prod tptp.t_a tptp.t_a))) (= tptp.v_r (tptp.c_Tarski_Opotype_Oorder tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit)))) (not (and (not (tptp.c_in (tptp.c_Pair (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.v_x tptp.t_a tptp.t_a) tptp.v_r (tptp.tc_prod tptp.t_a tptp.t_a))) (= tptp.v_r (tptp.c_Tarski_Opotype_Oorder tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit)))) (not (tptp.c_in (tptp.c_Pair (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.v_x tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a)))) :rule reordering :premises (t92.t5))
% 0.20/0.54 (step t92.t7 (cl (not (and (not (tptp.c_in (tptp.c_Pair (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.v_x tptp.t_a tptp.t_a) tptp.v_r (tptp.tc_prod tptp.t_a tptp.t_a))) (= tptp.v_r (tptp.c_Tarski_Opotype_Oorder tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit)))) (not (tptp.c_in (tptp.c_Pair (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.v_x tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a)))) :rule contraction :premises (t92.t6))
% 0.20/0.54 (step t92.t8 (cl (=> (and (not (tptp.c_in (tptp.c_Pair (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.v_x tptp.t_a tptp.t_a) tptp.v_r (tptp.tc_prod tptp.t_a tptp.t_a))) (= tptp.v_r (tptp.c_Tarski_Opotype_Oorder tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit))) (not (tptp.c_in (tptp.c_Pair (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.v_x tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a)))) (not (tptp.c_in (tptp.c_Pair (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.v_x tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a)))) :rule resolution :premises (t92.t1 t92.t7))
% 0.20/0.54 (step t92.t9 (cl (=> (and (not (tptp.c_in (tptp.c_Pair (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.v_x tptp.t_a tptp.t_a) tptp.v_r (tptp.tc_prod tptp.t_a tptp.t_a))) (= tptp.v_r (tptp.c_Tarski_Opotype_Oorder tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit))) (not (tptp.c_in (tptp.c_Pair (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.v_x tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a)))) (not (not (tptp.c_in (tptp.c_Pair (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.v_x tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a))))) :rule implies_neg2)
% 0.20/0.54 (step t92.t10 (cl (=> (and (not (tptp.c_in (tptp.c_Pair (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.v_x tptp.t_a tptp.t_a) tptp.v_r (tptp.tc_prod tptp.t_a tptp.t_a))) (= tptp.v_r (tptp.c_Tarski_Opotype_Oorder tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit))) (not (tptp.c_in (tptp.c_Pair (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.v_x tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a)))) (=> (and (not (tptp.c_in (tptp.c_Pair (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.v_x tptp.t_a tptp.t_a) tptp.v_r (tptp.tc_prod tptp.t_a tptp.t_a))) (= tptp.v_r (tptp.c_Tarski_Opotype_Oorder tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit))) (not (tptp.c_in (tptp.c_Pair (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.v_x tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a))))) :rule resolution :premises (t92.t8 t92.t9))
% 0.20/0.54 (step t92.t11 (cl (=> (and (not (tptp.c_in (tptp.c_Pair (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.v_x tptp.t_a tptp.t_a) tptp.v_r (tptp.tc_prod tptp.t_a tptp.t_a))) (= tptp.v_r (tptp.c_Tarski_Opotype_Oorder tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit))) (not (tptp.c_in (tptp.c_Pair (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.v_x tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a))))) :rule contraction :premises (t92.t10))
% 0.20/0.54 (step t92.t12 (cl (not (and (not (tptp.c_in (tptp.c_Pair (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.v_x tptp.t_a tptp.t_a) tptp.v_r (tptp.tc_prod tptp.t_a tptp.t_a))) (= tptp.v_r (tptp.c_Tarski_Opotype_Oorder tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit)))) (not (tptp.c_in (tptp.c_Pair (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.v_x tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a)))) :rule implies :premises (t92.t11))
% 0.20/0.54 (step t92.t13 (cl (and (not (tptp.c_in (tptp.c_Pair (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.v_x tptp.t_a tptp.t_a) tptp.v_r (tptp.tc_prod tptp.t_a tptp.t_a))) (= tptp.v_r (tptp.c_Tarski_Opotype_Oorder tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit))) (not (not (tptp.c_in (tptp.c_Pair (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.v_x tptp.t_a tptp.t_a) tptp.v_r (tptp.tc_prod tptp.t_a tptp.t_a)))) (not (= tptp.v_r (tptp.c_Tarski_Opotype_Oorder tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit)))) :rule and_neg)
% 0.20/0.54 (step t92.t14 (cl (and (not (tptp.c_in (tptp.c_Pair (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.v_x tptp.t_a tptp.t_a) tptp.v_r (tptp.tc_prod tptp.t_a tptp.t_a))) (= tptp.v_r (tptp.c_Tarski_Opotype_Oorder tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit)))) :rule resolution :premises (t92.t13 t92.a0 t92.a1))
% 0.20/0.54 (step t92.t15 (cl (not (tptp.c_in (tptp.c_Pair (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.v_x tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a)))) :rule resolution :premises (t92.t12 t92.t14))
% 0.20/0.54 (step t92 (cl (not (not (tptp.c_in (tptp.c_Pair (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.v_x tptp.t_a tptp.t_a) tptp.v_r (tptp.tc_prod tptp.t_a tptp.t_a)))) (not (= tptp.v_r (tptp.c_Tarski_Opotype_Oorder tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit))) (not (tptp.c_in (tptp.c_Pair (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.v_x tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a)))) :rule subproof :discharge (t92.a0 t92.a1))
% 0.20/0.54 (step t93 (cl (not (and (not (tptp.c_in (tptp.c_Pair (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.v_x tptp.t_a tptp.t_a) tptp.v_r (tptp.tc_prod tptp.t_a tptp.t_a))) (= tptp.v_r (tptp.c_Tarski_Opotype_Oorder tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit)))) (not (tptp.c_in (tptp.c_Pair (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.v_x tptp.t_a tptp.t_a) tptp.v_r (tptp.tc_prod tptp.t_a tptp.t_a)))) :rule and_pos)
% 0.20/0.54 (step t94 (cl (not (and (not (tptp.c_in (tptp.c_Pair (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.v_x tptp.t_a tptp.t_a) tptp.v_r (tptp.tc_prod tptp.t_a tptp.t_a))) (= tptp.v_r (tptp.c_Tarski_Opotype_Oorder tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit)))) (= tptp.v_r (tptp.c_Tarski_Opotype_Oorder tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit))) :rule and_pos)
% 0.20/0.54 (step t95 (cl (not (tptp.c_in (tptp.c_Pair (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.v_x tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a))) (not (and (not (tptp.c_in (tptp.c_Pair (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.v_x tptp.t_a tptp.t_a) tptp.v_r (tptp.tc_prod tptp.t_a tptp.t_a))) (= tptp.v_r (tptp.c_Tarski_Opotype_Oorder tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit)))) (not (and (not (tptp.c_in (tptp.c_Pair (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.v_x tptp.t_a tptp.t_a) tptp.v_r (tptp.tc_prod tptp.t_a tptp.t_a))) (= tptp.v_r (tptp.c_Tarski_Opotype_Oorder tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit))))) :rule resolution :premises (t92 t93 t94))
% 0.20/0.54 (step t96 (cl (not (and (not (tptp.c_in (tptp.c_Pair (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.v_x tptp.t_a tptp.t_a) tptp.v_r (tptp.tc_prod tptp.t_a tptp.t_a))) (= tptp.v_r (tptp.c_Tarski_Opotype_Oorder tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit)))) (not (and (not (tptp.c_in (tptp.c_Pair (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.v_x tptp.t_a tptp.t_a) tptp.v_r (tptp.tc_prod tptp.t_a tptp.t_a))) (= tptp.v_r (tptp.c_Tarski_Opotype_Oorder tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit)))) (not (tptp.c_in (tptp.c_Pair (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.v_x tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a)))) :rule reordering :premises (t95))
% 0.20/0.54 (step t97 (cl (not (and (not (tptp.c_in (tptp.c_Pair (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.v_x tptp.t_a tptp.t_a) tptp.v_r (tptp.tc_prod tptp.t_a tptp.t_a))) (= tptp.v_r (tptp.c_Tarski_Opotype_Oorder tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit)))) (not (tptp.c_in (tptp.c_Pair (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.v_x tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a)))) :rule contraction :premises (t96))
% 0.20/0.54 (step t98 (cl (=> (and (not (tptp.c_in (tptp.c_Pair (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.v_x tptp.t_a tptp.t_a) tptp.v_r (tptp.tc_prod tptp.t_a tptp.t_a))) (= tptp.v_r (tptp.c_Tarski_Opotype_Oorder tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit))) (not (tptp.c_in (tptp.c_Pair (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.v_x tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a)))) (not (tptp.c_in (tptp.c_Pair (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.v_x tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a)))) :rule resolution :premises (t91 t97))
% 0.20/0.54 (step t99 (cl (=> (and (not (tptp.c_in (tptp.c_Pair (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.v_x tptp.t_a tptp.t_a) tptp.v_r (tptp.tc_prod tptp.t_a tptp.t_a))) (= tptp.v_r (tptp.c_Tarski_Opotype_Oorder tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit))) (not (tptp.c_in (tptp.c_Pair (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.v_x tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a)))) (not (not (tptp.c_in (tptp.c_Pair (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.v_x tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a))))) :rule implies_neg2)
% 0.20/0.54 (step t100 (cl (=> (and (not (tptp.c_in (tptp.c_Pair (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.v_x tptp.t_a tptp.t_a) tptp.v_r (tptp.tc_prod tptp.t_a tptp.t_a))) (= tptp.v_r (tptp.c_Tarski_Opotype_Oorder tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit))) (not (tptp.c_in (tptp.c_Pair (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.v_x tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a)))) (=> (and (not (tptp.c_in (tptp.c_Pair (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.v_x tptp.t_a tptp.t_a) tptp.v_r (tptp.tc_prod tptp.t_a tptp.t_a))) (= tptp.v_r (tptp.c_Tarski_Opotype_Oorder tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit))) (not (tptp.c_in (tptp.c_Pair (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.v_x tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a))))) :rule resolution :premises (t98 t99))
% 0.20/0.54 (step t101 (cl (=> (and (not (tptp.c_in (tptp.c_Pair (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.v_x tptp.t_a tptp.t_a) tptp.v_r (tptp.tc_prod tptp.t_a tptp.t_a))) (= tptp.v_r (tptp.c_Tarski_Opotype_Oorder tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit))) (not (tptp.c_in (tptp.c_Pair (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.v_x tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a))))) :rule contraction :premises (t100))
% 0.20/0.54 (step t102 (cl (not (and (not (tptp.c_in (tptp.c_Pair (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.v_x tptp.t_a tptp.t_a) tptp.v_r (tptp.tc_prod tptp.t_a tptp.t_a))) (= tptp.v_r (tptp.c_Tarski_Opotype_Oorder tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit)))) (not (tptp.c_in (tptp.c_Pair (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.v_x tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a)))) :rule implies :premises (t101))
% 0.20/0.54 (step t103 (cl (not (not (tptp.c_in (tptp.c_Pair (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.v_x tptp.t_a tptp.t_a) tptp.v_r (tptp.tc_prod tptp.t_a tptp.t_a)))) (not (= tptp.v_r (tptp.c_Tarski_Opotype_Oorder tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit))) (not (tptp.c_in (tptp.c_Pair (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.v_x tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a)))) :rule resolution :premises (t90 t102))
% 0.20/0.54 (step t104 (cl (or (not (not (tptp.c_in (tptp.c_Pair (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.v_x tptp.t_a tptp.t_a) tptp.v_r (tptp.tc_prod tptp.t_a tptp.t_a)))) (not (= tptp.v_r (tptp.c_Tarski_Opotype_Oorder tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit))) (not (tptp.c_in (tptp.c_Pair (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.v_x tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a)))) (not (not (not (tptp.c_in (tptp.c_Pair (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.v_x tptp.t_a tptp.t_a) tptp.v_r (tptp.tc_prod tptp.t_a tptp.t_a)))))) :rule or_neg)
% 0.20/0.54 (step t105 (cl (or (not (not (tptp.c_in (tptp.c_Pair (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.v_x tptp.t_a tptp.t_a) tptp.v_r (tptp.tc_prod tptp.t_a tptp.t_a)))) (not (= tptp.v_r (tptp.c_Tarski_Opotype_Oorder tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit))) (not (tptp.c_in (tptp.c_Pair (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.v_x tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a)))) (not (not (= tptp.v_r (tptp.c_Tarski_Opotype_Oorder tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit))))) :rule or_neg)
% 0.20/0.54 (step t106 (cl (or (not (not (tptp.c_in (tptp.c_Pair (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.v_x tptp.t_a tptp.t_a) tptp.v_r (tptp.tc_prod tptp.t_a tptp.t_a)))) (not (= tptp.v_r (tptp.c_Tarski_Opotype_Oorder tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit))) (not (tptp.c_in (tptp.c_Pair (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.v_x tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a)))) (not (not (tptp.c_in (tptp.c_Pair (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.v_x tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a))))) :rule or_neg)
% 0.20/0.54 (step t107 (cl (or (not (not (tptp.c_in (tptp.c_Pair (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.v_x tptp.t_a tptp.t_a) tptp.v_r (tptp.tc_prod tptp.t_a tptp.t_a)))) (not (= tptp.v_r (tptp.c_Tarski_Opotype_Oorder tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit))) (not (tptp.c_in (tptp.c_Pair (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.v_x tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a)))) (or (not (not (tptp.c_in (tptp.c_Pair (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.v_x tptp.t_a tptp.t_a) tptp.v_r (tptp.tc_prod tptp.t_a tptp.t_a)))) (not (= tptp.v_r (tptp.c_Tarski_Opotype_Oorder tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit))) (not (tptp.c_in (tptp.c_Pair (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.v_x tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a)))) (or (not (not (tptp.c_in (tptp.c_Pair (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.v_x tptp.t_a tptp.t_a) tptp.v_r (tptp.tc_prod tptp.t_a tptp.t_a)))) (not (= tptp.v_r (tptp.c_Tarski_Opotype_Oorder tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit))) (not (tptp.c_in (tptp.c_Pair (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.v_x tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a))))) :rule resolution :premises (t103 t104 t105 t106))
% 0.20/0.54 (step t108 (cl (or (not (not (tptp.c_in (tptp.c_Pair (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.v_x tptp.t_a tptp.t_a) tptp.v_r (tptp.tc_prod tptp.t_a tptp.t_a)))) (not (= tptp.v_r (tptp.c_Tarski_Opotype_Oorder tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit))) (not (tptp.c_in (tptp.c_Pair (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.v_x tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a))))) :rule contraction :premises (t107))
% 0.20/0.54 (step t109 (cl (or (tptp.c_in (tptp.c_Pair (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.v_x tptp.t_a tptp.t_a) tptp.v_r (tptp.tc_prod tptp.t_a tptp.t_a)) (not (= tptp.v_r (tptp.c_Tarski_Opotype_Oorder tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit))) (not (tptp.c_in (tptp.c_Pair (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.v_x tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a))))) :rule resolution :premises (t76 t89 t108))
% 0.20/0.54 (step t110 (cl (tptp.c_in (tptp.c_Pair (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.v_x tptp.t_a tptp.t_a) tptp.v_r (tptp.tc_prod tptp.t_a tptp.t_a)) (not (= tptp.v_r (tptp.c_Tarski_Opotype_Oorder tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit))) (not (tptp.c_in (tptp.c_Pair (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.v_x tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a)))) :rule or :premises (t109))
% 0.20/0.54 (step t111 (cl (not (tptp.c_in (tptp.c_Pair (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.v_x tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a)))) :rule resolution :premises (t110 a2 a10))
% 0.20/0.54 (step t112 (cl (=> (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted) (V_cl $$unsorted)) (or (not (tptp.c_in (tptp.c_Pair V_x V_y T_a T_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual V_cl T_a) T_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod T_a T_a))) (tptp.c_in (tptp.c_Pair V_y V_x T_a T_a) (tptp.c_Tarski_Opotype_Oorder V_cl T_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod T_a T_a)))) (or (not (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a))) (tptp.c_in (tptp.c_Pair (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.v_x tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a)))) (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted) (V_cl $$unsorted)) (or (not (tptp.c_in (tptp.c_Pair V_x V_y T_a T_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual V_cl T_a) T_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod T_a T_a))) (tptp.c_in (tptp.c_Pair V_y V_x T_a T_a) (tptp.c_Tarski_Opotype_Oorder V_cl T_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod T_a T_a))))) :rule implies_neg1)
% 0.20/0.54 (anchor :step t113)
% 0.20/0.54 (assume t113.a0 (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted) (V_cl $$unsorted)) (or (not (tptp.c_in (tptp.c_Pair V_x V_y T_a T_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual V_cl T_a) T_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod T_a T_a))) (tptp.c_in (tptp.c_Pair V_y V_x T_a T_a) (tptp.c_Tarski_Opotype_Oorder V_cl T_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod T_a T_a)))))
% 0.20/0.54 (step t113.t1 (cl (or (not (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted) (V_cl $$unsorted)) (or (not (tptp.c_in (tptp.c_Pair V_x V_y T_a T_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual V_cl T_a) T_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod T_a T_a))) (tptp.c_in (tptp.c_Pair V_y V_x T_a T_a) (tptp.c_Tarski_Opotype_Oorder V_cl T_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod T_a T_a))))) (or (not (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a))) (tptp.c_in (tptp.c_Pair (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.v_x tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a))))) :rule forall_inst :args ((:= V_x tptp.v_x) (:= V_y (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a)) (:= T_a tptp.t_a) (:= V_cl tptp.v_cl)))
% 0.20/0.54 (step t113.t2 (cl (not (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted) (V_cl $$unsorted)) (or (not (tptp.c_in (tptp.c_Pair V_x V_y T_a T_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual V_cl T_a) T_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod T_a T_a))) (tptp.c_in (tptp.c_Pair V_y V_x T_a T_a) (tptp.c_Tarski_Opotype_Oorder V_cl T_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod T_a T_a))))) (or (not (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a))) (tptp.c_in (tptp.c_Pair (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.v_x tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a)))) :rule or :premises (t113.t1))
% 0.20/0.54 (step t113.t3 (cl (or (not (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a))) (tptp.c_in (tptp.c_Pair (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.v_x tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a)))) :rule resolution :premises (t113.t2 t113.a0))
% 0.20/0.54 (step t113 (cl (not (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted) (V_cl $$unsorted)) (or (not (tptp.c_in (tptp.c_Pair V_x V_y T_a T_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual V_cl T_a) T_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod T_a T_a))) (tptp.c_in (tptp.c_Pair V_y V_x T_a T_a) (tptp.c_Tarski_Opotype_Oorder V_cl T_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod T_a T_a))))) (or (not (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a))) (tptp.c_in (tptp.c_Pair (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.v_x tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a)))) :rule subproof :discharge (t113.a0))
% 0.20/0.54 (step t114 (cl (=> (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted) (V_cl $$unsorted)) (or (not (tptp.c_in (tptp.c_Pair V_x V_y T_a T_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual V_cl T_a) T_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod T_a T_a))) (tptp.c_in (tptp.c_Pair V_y V_x T_a T_a) (tptp.c_Tarski_Opotype_Oorder V_cl T_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod T_a T_a)))) (or (not (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a))) (tptp.c_in (tptp.c_Pair (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.v_x tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a)))) (or (not (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a))) (tptp.c_in (tptp.c_Pair (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.v_x tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a)))) :rule resolution :premises (t112 t113))
% 0.20/0.54 (step t115 (cl (=> (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted) (V_cl $$unsorted)) (or (not (tptp.c_in (tptp.c_Pair V_x V_y T_a T_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual V_cl T_a) T_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod T_a T_a))) (tptp.c_in (tptp.c_Pair V_y V_x T_a T_a) (tptp.c_Tarski_Opotype_Oorder V_cl T_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod T_a T_a)))) (or (not (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a))) (tptp.c_in (tptp.c_Pair (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.v_x tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a)))) (not (or (not (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a))) (tptp.c_in (tptp.c_Pair (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.v_x tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a))))) :rule implies_neg2)
% 0.20/0.54 (step t116 (cl (=> (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted) (V_cl $$unsorted)) (or (not (tptp.c_in (tptp.c_Pair V_x V_y T_a T_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual V_cl T_a) T_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod T_a T_a))) (tptp.c_in (tptp.c_Pair V_y V_x T_a T_a) (tptp.c_Tarski_Opotype_Oorder V_cl T_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod T_a T_a)))) (or (not (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a))) (tptp.c_in (tptp.c_Pair (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.v_x tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a)))) (=> (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted) (V_cl $$unsorted)) (or (not (tptp.c_in (tptp.c_Pair V_x V_y T_a T_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual V_cl T_a) T_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod T_a T_a))) (tptp.c_in (tptp.c_Pair V_y V_x T_a T_a) (tptp.c_Tarski_Opotype_Oorder V_cl T_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod T_a T_a)))) (or (not (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a))) (tptp.c_in (tptp.c_Pair (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.v_x tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a))))) :rule resolution :premises (t114 t115))
% 0.20/0.54 (step t117 (cl (=> (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted) (V_cl $$unsorted)) (or (not (tptp.c_in (tptp.c_Pair V_x V_y T_a T_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual V_cl T_a) T_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod T_a T_a))) (tptp.c_in (tptp.c_Pair V_y V_x T_a T_a) (tptp.c_Tarski_Opotype_Oorder V_cl T_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod T_a T_a)))) (or (not (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a))) (tptp.c_in (tptp.c_Pair (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.v_x tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a))))) :rule contraction :premises (t116))
% 0.20/0.54 (step t118 (cl (not (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted) (V_cl $$unsorted)) (or (not (tptp.c_in (tptp.c_Pair V_x V_y T_a T_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual V_cl T_a) T_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod T_a T_a))) (tptp.c_in (tptp.c_Pair V_y V_x T_a T_a) (tptp.c_Tarski_Opotype_Oorder V_cl T_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod T_a T_a))))) (or (not (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a))) (tptp.c_in (tptp.c_Pair (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.v_x tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a)))) :rule implies :premises (t117))
% 0.20/0.54 (step t119 (cl (or (not (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a))) (tptp.c_in (tptp.c_Pair (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.v_x tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder tptp.v_cl tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a)))) :rule resolution :premises (t118 a5))
% 0.20/0.54 (step t120 (cl (not (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a)))) :rule resolution :premises (t75 t111 t119))
% 0.20/0.54 (step t121 (cl (=> (forall ((V_S $$unsorted) (V_cl $$unsorted) (T_a $$unsorted)) (= (tptp.c_Tarski_Oglb V_S V_cl T_a) (tptp.c_Tarski_Olub V_S (tptp.c_Tarski_Odual V_cl T_a) T_a))) (= (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) (tptp.c_Tarski_Olub tptp.v_S (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a))) (forall ((V_S $$unsorted) (V_cl $$unsorted) (T_a $$unsorted)) (= (tptp.c_Tarski_Oglb V_S V_cl T_a) (tptp.c_Tarski_Olub V_S (tptp.c_Tarski_Odual V_cl T_a) T_a)))) :rule implies_neg1)
% 0.20/0.54 (anchor :step t122)
% 0.20/0.54 (assume t122.a0 (forall ((V_S $$unsorted) (V_cl $$unsorted) (T_a $$unsorted)) (= (tptp.c_Tarski_Oglb V_S V_cl T_a) (tptp.c_Tarski_Olub V_S (tptp.c_Tarski_Odual V_cl T_a) T_a))))
% 0.20/0.54 (step t122.t1 (cl (or (not (forall ((V_S $$unsorted) (V_cl $$unsorted) (T_a $$unsorted)) (= (tptp.c_Tarski_Oglb V_S V_cl T_a) (tptp.c_Tarski_Olub V_S (tptp.c_Tarski_Odual V_cl T_a) T_a)))) (= (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) (tptp.c_Tarski_Olub tptp.v_S (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a)))) :rule forall_inst :args ((:= V_S tptp.v_S) (:= V_cl tptp.v_cl) (:= T_a tptp.t_a)))
% 0.20/0.54 (step t122.t2 (cl (not (forall ((V_S $$unsorted) (V_cl $$unsorted) (T_a $$unsorted)) (= (tptp.c_Tarski_Oglb V_S V_cl T_a) (tptp.c_Tarski_Olub V_S (tptp.c_Tarski_Odual V_cl T_a) T_a)))) (= (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) (tptp.c_Tarski_Olub tptp.v_S (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a))) :rule or :premises (t122.t1))
% 0.20/0.54 (step t122.t3 (cl (= (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) (tptp.c_Tarski_Olub tptp.v_S (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a))) :rule resolution :premises (t122.t2 t122.a0))
% 0.20/0.54 (step t122 (cl (not (forall ((V_S $$unsorted) (V_cl $$unsorted) (T_a $$unsorted)) (= (tptp.c_Tarski_Oglb V_S V_cl T_a) (tptp.c_Tarski_Olub V_S (tptp.c_Tarski_Odual V_cl T_a) T_a)))) (= (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) (tptp.c_Tarski_Olub tptp.v_S (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a))) :rule subproof :discharge (t122.a0))
% 0.20/0.54 (step t123 (cl (=> (forall ((V_S $$unsorted) (V_cl $$unsorted) (T_a $$unsorted)) (= (tptp.c_Tarski_Oglb V_S V_cl T_a) (tptp.c_Tarski_Olub V_S (tptp.c_Tarski_Odual V_cl T_a) T_a))) (= (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) (tptp.c_Tarski_Olub tptp.v_S (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a))) (= (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) (tptp.c_Tarski_Olub tptp.v_S (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a))) :rule resolution :premises (t121 t122))
% 0.20/0.54 (step t124 (cl (=> (forall ((V_S $$unsorted) (V_cl $$unsorted) (T_a $$unsorted)) (= (tptp.c_Tarski_Oglb V_S V_cl T_a) (tptp.c_Tarski_Olub V_S (tptp.c_Tarski_Odual V_cl T_a) T_a))) (= (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) (tptp.c_Tarski_Olub tptp.v_S (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a))) (not (= (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) (tptp.c_Tarski_Olub tptp.v_S (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a)))) :rule implies_neg2)
% 0.20/0.54 (step t125 (cl (=> (forall ((V_S $$unsorted) (V_cl $$unsorted) (T_a $$unsorted)) (= (tptp.c_Tarski_Oglb V_S V_cl T_a) (tptp.c_Tarski_Olub V_S (tptp.c_Tarski_Odual V_cl T_a) T_a))) (= (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) (tptp.c_Tarski_Olub tptp.v_S (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a))) (=> (forall ((V_S $$unsorted) (V_cl $$unsorted) (T_a $$unsorted)) (= (tptp.c_Tarski_Oglb V_S V_cl T_a) (tptp.c_Tarski_Olub V_S (tptp.c_Tarski_Odual V_cl T_a) T_a))) (= (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) (tptp.c_Tarski_Olub tptp.v_S (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a)))) :rule resolution :premises (t123 t124))
% 0.20/0.54 (step t126 (cl (=> (forall ((V_S $$unsorted) (V_cl $$unsorted) (T_a $$unsorted)) (= (tptp.c_Tarski_Oglb V_S V_cl T_a) (tptp.c_Tarski_Olub V_S (tptp.c_Tarski_Odual V_cl T_a) T_a))) (= (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) (tptp.c_Tarski_Olub tptp.v_S (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a)))) :rule contraction :premises (t125))
% 0.20/0.54 (step t127 (cl (not (forall ((V_S $$unsorted) (V_cl $$unsorted) (T_a $$unsorted)) (= (tptp.c_Tarski_Oglb V_S V_cl T_a) (tptp.c_Tarski_Olub V_S (tptp.c_Tarski_Odual V_cl T_a) T_a)))) (= (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) (tptp.c_Tarski_Olub tptp.v_S (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a))) :rule implies :premises (t126))
% 0.20/0.54 (step t128 (cl (= (tptp.c_Tarski_Oglb tptp.v_S tptp.v_cl tptp.t_a) (tptp.c_Tarski_Olub tptp.v_S (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a))) :rule resolution :premises (t127 a8))
% 0.20/0.54 (step t129 (cl (not (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Olub tptp.v_S (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a)))) :rule resolution :premises (t73 t120 t128))
% 0.20/0.54 (step t130 (cl (not (or (not (tptp.c_in tptp.v_x tptp.v_S tptp.t_a)) (not (tptp.c_in (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.c_Tarski_OCompleteLattice (tptp.tc_Tarski_Opotype_Opotype__ext__type tptp.t_a tptp.tc_Product__Type_Ounit))) (not (tptp.c_in (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.c_Tarski_OPartialOrder (tptp.tc_Tarski_Opotype_Opotype__ext__type tptp.t_a tptp.tc_Product__Type_Ounit))) (not (tptp.c_lessequals tptp.v_S (tptp.c_Tarski_Opotype_Opset (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_set tptp.t_a))) (tptp.c_in (tptp.c_Pair tptp.v_x (tptp.c_Tarski_Olub tptp.v_S (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a) tptp.t_a tptp.t_a) (tptp.c_Tarski_Opotype_Oorder (tptp.c_Tarski_Odual tptp.v_cl tptp.t_a) tptp.t_a tptp.tc_Product__Type_Ounit) (tptp.tc_prod tptp.t_a tptp.t_a))))) :rule resolution :premises (t9 a1 a6 a7 t38 t129))
% 0.20/0.54 (step t131 (cl) :rule resolution :premises (t7 t130 a4))
% 0.20/0.54
% 0.20/0.54 % SZS output end Proof for /export/starexec/sandbox/tmp/tmp.wtFAa4pIGx/cvc5---1.0.5_27261.smt2
% 0.20/0.55 % cvc5---1.0.5 exiting
% 0.20/0.55 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------