TSTP Solution File: GRP123-7.003 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : GRP123-7.003 : TPTP v8.2.0. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : do_cvc5 %s %d
% Computer : n027.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 16:53:10 EDT 2024
% Result : Unsatisfiable 0.34s 0.57s
% Output : Proof 0.34s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.14 % Problem : GRP123-7.003 : TPTP v8.2.0. Released v1.2.0.
% 0.07/0.16 % Command : do_cvc5 %s %d
% 0.15/0.38 % Computer : n027.cluster.edu
% 0.15/0.38 % Model : x86_64 x86_64
% 0.15/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.38 % Memory : 8042.1875MB
% 0.15/0.38 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.38 % CPULimit : 300
% 0.15/0.38 % WCLimit : 300
% 0.15/0.38 % DateTime : Sun May 26 18:10:39 EDT 2024
% 0.15/0.38 % CPUTime :
% 0.22/0.51 %----Proving TF0_NAR, FOF, or CNF
% 0.22/0.51 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.34/0.57 % SZS status Unsatisfiable for /export/starexec/sandbox2/tmp/tmp.LsbbrUa3xC/cvc5---1.0.5_14373.smt2
% 0.34/0.57 % SZS output start Proof for /export/starexec/sandbox2/tmp/tmp.LsbbrUa3xC/cvc5---1.0.5_14373.smt2
% 0.34/0.58 (assume a0 (tptp.next tptp.e_1 tptp.e_2))
% 0.34/0.58 (assume a1 (tptp.next tptp.e_2 tptp.e_3))
% 0.34/0.58 (assume a2 (tptp.greater tptp.e_2 tptp.e_1))
% 0.34/0.58 (assume a3 (tptp.greater tptp.e_3 tptp.e_1))
% 0.34/0.58 (assume a4 (tptp.greater tptp.e_3 tptp.e_2))
% 0.34/0.58 (assume a5 (forall ((X $$unsorted) (Y $$unsorted) (X1 $$unsorted)) (or (not (tptp.product X tptp.e_1 Y)) (not (tptp.next X X1)) (not (tptp.greater Y X1)))))
% 0.34/0.58 (assume a6 (tptp.group_element tptp.e_1))
% 0.34/0.58 (assume a7 (tptp.group_element tptp.e_2))
% 0.34/0.58 (assume a8 (tptp.group_element tptp.e_3))
% 0.34/0.58 (assume a9 (not (tptp.equalish tptp.e_1 tptp.e_2)))
% 0.34/0.58 (assume a10 (not (tptp.equalish tptp.e_1 tptp.e_3)))
% 0.34/0.58 (assume a11 (not (tptp.equalish tptp.e_2 tptp.e_1)))
% 0.34/0.58 (assume a12 (not (tptp.equalish tptp.e_2 tptp.e_3)))
% 0.34/0.58 (assume a13 (not (tptp.equalish tptp.e_3 tptp.e_1)))
% 0.34/0.58 (assume a14 (not (tptp.equalish tptp.e_3 tptp.e_2)))
% 0.34/0.58 (assume a15 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.group_element X)) (not (tptp.group_element Y)) (tptp.product1 X Y tptp.e_1) (tptp.product1 X Y tptp.e_2) (tptp.product1 X Y tptp.e_3))))
% 0.34/0.58 (assume a16 (forall ((X $$unsorted) (Y $$unsorted) (W $$unsorted) (Z $$unsorted)) (or (not (tptp.product1 X Y W)) (not (tptp.product1 X Y Z)) (tptp.equalish W Z))))
% 0.34/0.58 (assume a17 (forall ((X $$unsorted) (W $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.product1 X W Y)) (not (tptp.product1 X Z Y)) (tptp.equalish W Z))))
% 0.34/0.58 (assume a18 (forall ((W $$unsorted) (Y $$unsorted) (X $$unsorted) (Z $$unsorted)) (or (not (tptp.product1 W Y X)) (not (tptp.product1 Z Y X)) (tptp.equalish W Z))))
% 0.34/0.58 (assume a19 (forall ((X $$unsorted)) (tptp.product1 X X X)))
% 0.34/0.58 (assume a20 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.group_element X)) (not (tptp.group_element Y)) (tptp.product2 X Y tptp.e_1) (tptp.product2 X Y tptp.e_2) (tptp.product2 X Y tptp.e_3))))
% 0.34/0.58 (assume a21 (forall ((X $$unsorted) (Y $$unsorted) (W $$unsorted) (Z $$unsorted)) (or (not (tptp.product2 X Y W)) (not (tptp.product2 X Y Z)) (tptp.equalish W Z))))
% 0.34/0.58 (assume a22 (forall ((X $$unsorted) (W $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.product2 X W Y)) (not (tptp.product2 X Z Y)) (tptp.equalish W Z))))
% 0.34/0.58 (assume a23 (forall ((W $$unsorted) (Y $$unsorted) (X $$unsorted) (Z $$unsorted)) (or (not (tptp.product2 W Y X)) (not (tptp.product2 Z Y X)) (tptp.equalish W Z))))
% 0.34/0.58 (assume a24 (forall ((X $$unsorted)) (tptp.product2 X X X)))
% 0.34/0.58 (assume a25 (forall ((X $$unsorted) (Y $$unsorted) (Z1 $$unsorted) (Z2 $$unsorted)) (or (not (tptp.product1 X Y Z1)) (not (tptp.product1 Z1 Y Z2)) (tptp.product2 Z2 X Y))))
% 0.34/0.58 (step t1 (cl (=> (forall ((W $$unsorted) (Y $$unsorted) (X $$unsorted) (Z $$unsorted)) (or (not (tptp.product1 W Y X)) (not (tptp.product1 Z Y X)) (tptp.equalish W Z))) (or (not (tptp.product1 tptp.e_1 tptp.e_2 tptp.e_3)) (not (tptp.product1 tptp.e_3 tptp.e_2 tptp.e_3)) (tptp.equalish tptp.e_1 tptp.e_3))) (forall ((W $$unsorted) (Y $$unsorted) (X $$unsorted) (Z $$unsorted)) (or (not (tptp.product1 W Y X)) (not (tptp.product1 Z Y X)) (tptp.equalish W Z)))) :rule implies_neg1)
% 0.34/0.58 (anchor :step t2)
% 0.34/0.58 (assume t2.a0 (forall ((W $$unsorted) (Y $$unsorted) (X $$unsorted) (Z $$unsorted)) (or (not (tptp.product1 W Y X)) (not (tptp.product1 Z Y X)) (tptp.equalish W Z))))
% 0.34/0.58 (step t2.t1 (cl (or (not (forall ((W $$unsorted) (Y $$unsorted) (X $$unsorted) (Z $$unsorted)) (or (not (tptp.product1 W Y X)) (not (tptp.product1 Z Y X)) (tptp.equalish W Z)))) (or (not (tptp.product1 tptp.e_1 tptp.e_2 tptp.e_3)) (not (tptp.product1 tptp.e_3 tptp.e_2 tptp.e_3)) (tptp.equalish tptp.e_1 tptp.e_3)))) :rule forall_inst :args ((:= W tptp.e_1) (:= Y tptp.e_2) (:= X tptp.e_3) (:= Z tptp.e_3)))
% 0.34/0.58 (step t2.t2 (cl (not (forall ((W $$unsorted) (Y $$unsorted) (X $$unsorted) (Z $$unsorted)) (or (not (tptp.product1 W Y X)) (not (tptp.product1 Z Y X)) (tptp.equalish W Z)))) (or (not (tptp.product1 tptp.e_1 tptp.e_2 tptp.e_3)) (not (tptp.product1 tptp.e_3 tptp.e_2 tptp.e_3)) (tptp.equalish tptp.e_1 tptp.e_3))) :rule or :premises (t2.t1))
% 0.34/0.58 (step t2.t3 (cl (or (not (tptp.product1 tptp.e_1 tptp.e_2 tptp.e_3)) (not (tptp.product1 tptp.e_3 tptp.e_2 tptp.e_3)) (tptp.equalish tptp.e_1 tptp.e_3))) :rule resolution :premises (t2.t2 t2.a0))
% 0.34/0.58 (step t2 (cl (not (forall ((W $$unsorted) (Y $$unsorted) (X $$unsorted) (Z $$unsorted)) (or (not (tptp.product1 W Y X)) (not (tptp.product1 Z Y X)) (tptp.equalish W Z)))) (or (not (tptp.product1 tptp.e_1 tptp.e_2 tptp.e_3)) (not (tptp.product1 tptp.e_3 tptp.e_2 tptp.e_3)) (tptp.equalish tptp.e_1 tptp.e_3))) :rule subproof :discharge (t2.a0))
% 0.34/0.58 (step t3 (cl (=> (forall ((W $$unsorted) (Y $$unsorted) (X $$unsorted) (Z $$unsorted)) (or (not (tptp.product1 W Y X)) (not (tptp.product1 Z Y X)) (tptp.equalish W Z))) (or (not (tptp.product1 tptp.e_1 tptp.e_2 tptp.e_3)) (not (tptp.product1 tptp.e_3 tptp.e_2 tptp.e_3)) (tptp.equalish tptp.e_1 tptp.e_3))) (or (not (tptp.product1 tptp.e_1 tptp.e_2 tptp.e_3)) (not (tptp.product1 tptp.e_3 tptp.e_2 tptp.e_3)) (tptp.equalish tptp.e_1 tptp.e_3))) :rule resolution :premises (t1 t2))
% 0.34/0.58 (step t4 (cl (=> (forall ((W $$unsorted) (Y $$unsorted) (X $$unsorted) (Z $$unsorted)) (or (not (tptp.product1 W Y X)) (not (tptp.product1 Z Y X)) (tptp.equalish W Z))) (or (not (tptp.product1 tptp.e_1 tptp.e_2 tptp.e_3)) (not (tptp.product1 tptp.e_3 tptp.e_2 tptp.e_3)) (tptp.equalish tptp.e_1 tptp.e_3))) (not (or (not (tptp.product1 tptp.e_1 tptp.e_2 tptp.e_3)) (not (tptp.product1 tptp.e_3 tptp.e_2 tptp.e_3)) (tptp.equalish tptp.e_1 tptp.e_3)))) :rule implies_neg2)
% 0.34/0.58 (step t5 (cl (=> (forall ((W $$unsorted) (Y $$unsorted) (X $$unsorted) (Z $$unsorted)) (or (not (tptp.product1 W Y X)) (not (tptp.product1 Z Y X)) (tptp.equalish W Z))) (or (not (tptp.product1 tptp.e_1 tptp.e_2 tptp.e_3)) (not (tptp.product1 tptp.e_3 tptp.e_2 tptp.e_3)) (tptp.equalish tptp.e_1 tptp.e_3))) (=> (forall ((W $$unsorted) (Y $$unsorted) (X $$unsorted) (Z $$unsorted)) (or (not (tptp.product1 W Y X)) (not (tptp.product1 Z Y X)) (tptp.equalish W Z))) (or (not (tptp.product1 tptp.e_1 tptp.e_2 tptp.e_3)) (not (tptp.product1 tptp.e_3 tptp.e_2 tptp.e_3)) (tptp.equalish tptp.e_1 tptp.e_3)))) :rule resolution :premises (t3 t4))
% 0.34/0.58 (step t6 (cl (=> (forall ((W $$unsorted) (Y $$unsorted) (X $$unsorted) (Z $$unsorted)) (or (not (tptp.product1 W Y X)) (not (tptp.product1 Z Y X)) (tptp.equalish W Z))) (or (not (tptp.product1 tptp.e_1 tptp.e_2 tptp.e_3)) (not (tptp.product1 tptp.e_3 tptp.e_2 tptp.e_3)) (tptp.equalish tptp.e_1 tptp.e_3)))) :rule contraction :premises (t5))
% 0.34/0.58 (step t7 (cl (not (forall ((W $$unsorted) (Y $$unsorted) (X $$unsorted) (Z $$unsorted)) (or (not (tptp.product1 W Y X)) (not (tptp.product1 Z Y X)) (tptp.equalish W Z)))) (or (not (tptp.product1 tptp.e_1 tptp.e_2 tptp.e_3)) (not (tptp.product1 tptp.e_3 tptp.e_2 tptp.e_3)) (tptp.equalish tptp.e_1 tptp.e_3))) :rule implies :premises (t6))
% 0.34/0.58 (step t8 (cl (not (or (not (tptp.product1 tptp.e_1 tptp.e_2 tptp.e_3)) (not (tptp.product1 tptp.e_3 tptp.e_2 tptp.e_3)) (tptp.equalish tptp.e_1 tptp.e_3))) (not (tptp.product1 tptp.e_1 tptp.e_2 tptp.e_3)) (not (tptp.product1 tptp.e_3 tptp.e_2 tptp.e_3)) (tptp.equalish tptp.e_1 tptp.e_3)) :rule or_pos)
% 0.34/0.58 (step t9 (cl (tptp.equalish tptp.e_1 tptp.e_3) (not (tptp.product1 tptp.e_1 tptp.e_2 tptp.e_3)) (not (tptp.product1 tptp.e_3 tptp.e_2 tptp.e_3)) (not (or (not (tptp.product1 tptp.e_1 tptp.e_2 tptp.e_3)) (not (tptp.product1 tptp.e_3 tptp.e_2 tptp.e_3)) (tptp.equalish tptp.e_1 tptp.e_3)))) :rule reordering :premises (t8))
% 0.34/0.58 (step t10 (cl (not (or (not (tptp.group_element tptp.e_1)) (not (tptp.group_element tptp.e_2)) (tptp.product1 tptp.e_1 tptp.e_2 tptp.e_1) (tptp.product1 tptp.e_1 tptp.e_2 tptp.e_2) (tptp.product1 tptp.e_1 tptp.e_2 tptp.e_3))) (not (tptp.group_element tptp.e_1)) (not (tptp.group_element tptp.e_2)) (tptp.product1 tptp.e_1 tptp.e_2 tptp.e_1) (tptp.product1 tptp.e_1 tptp.e_2 tptp.e_2) (tptp.product1 tptp.e_1 tptp.e_2 tptp.e_3)) :rule or_pos)
% 0.34/0.58 (step t11 (cl (not (tptp.group_element tptp.e_1)) (not (tptp.group_element tptp.e_2)) (tptp.product1 tptp.e_1 tptp.e_2 tptp.e_1) (tptp.product1 tptp.e_1 tptp.e_2 tptp.e_2) (tptp.product1 tptp.e_1 tptp.e_2 tptp.e_3) (not (or (not (tptp.group_element tptp.e_1)) (not (tptp.group_element tptp.e_2)) (tptp.product1 tptp.e_1 tptp.e_2 tptp.e_1) (tptp.product1 tptp.e_1 tptp.e_2 tptp.e_2) (tptp.product1 tptp.e_1 tptp.e_2 tptp.e_3)))) :rule reordering :premises (t10))
% 0.34/0.58 (step t12 (cl (not (or (not (tptp.product1 tptp.e_1 tptp.e_1 tptp.e_1)) (not (tptp.product1 tptp.e_1 tptp.e_2 tptp.e_1)) (tptp.equalish tptp.e_1 tptp.e_2))) (not (tptp.product1 tptp.e_1 tptp.e_1 tptp.e_1)) (not (tptp.product1 tptp.e_1 tptp.e_2 tptp.e_1)) (tptp.equalish tptp.e_1 tptp.e_2)) :rule or_pos)
% 0.34/0.58 (step t13 (cl (tptp.equalish tptp.e_1 tptp.e_2) (not (tptp.product1 tptp.e_1 tptp.e_1 tptp.e_1)) (not (tptp.product1 tptp.e_1 tptp.e_2 tptp.e_1)) (not (or (not (tptp.product1 tptp.e_1 tptp.e_1 tptp.e_1)) (not (tptp.product1 tptp.e_1 tptp.e_2 tptp.e_1)) (tptp.equalish tptp.e_1 tptp.e_2)))) :rule reordering :premises (t12))
% 0.34/0.58 (step t14 (cl (=> (forall ((X $$unsorted)) (tptp.product1 X X X)) (tptp.product1 tptp.e_1 tptp.e_1 tptp.e_1)) (forall ((X $$unsorted)) (tptp.product1 X X X))) :rule implies_neg1)
% 0.34/0.58 (anchor :step t15)
% 0.34/0.58 (assume t15.a0 (forall ((X $$unsorted)) (tptp.product1 X X X)))
% 0.34/0.58 (step t15.t1 (cl (or (not (forall ((X $$unsorted)) (tptp.product1 X X X))) (tptp.product1 tptp.e_1 tptp.e_1 tptp.e_1))) :rule forall_inst :args ((:= X tptp.e_1)))
% 0.34/0.58 (step t15.t2 (cl (not (forall ((X $$unsorted)) (tptp.product1 X X X))) (tptp.product1 tptp.e_1 tptp.e_1 tptp.e_1)) :rule or :premises (t15.t1))
% 0.34/0.58 (step t15.t3 (cl (tptp.product1 tptp.e_1 tptp.e_1 tptp.e_1)) :rule resolution :premises (t15.t2 t15.a0))
% 0.34/0.58 (step t15 (cl (not (forall ((X $$unsorted)) (tptp.product1 X X X))) (tptp.product1 tptp.e_1 tptp.e_1 tptp.e_1)) :rule subproof :discharge (t15.a0))
% 0.34/0.58 (step t16 (cl (=> (forall ((X $$unsorted)) (tptp.product1 X X X)) (tptp.product1 tptp.e_1 tptp.e_1 tptp.e_1)) (tptp.product1 tptp.e_1 tptp.e_1 tptp.e_1)) :rule resolution :premises (t14 t15))
% 0.34/0.58 (step t17 (cl (=> (forall ((X $$unsorted)) (tptp.product1 X X X)) (tptp.product1 tptp.e_1 tptp.e_1 tptp.e_1)) (not (tptp.product1 tptp.e_1 tptp.e_1 tptp.e_1))) :rule implies_neg2)
% 0.34/0.58 (step t18 (cl (=> (forall ((X $$unsorted)) (tptp.product1 X X X)) (tptp.product1 tptp.e_1 tptp.e_1 tptp.e_1)) (=> (forall ((X $$unsorted)) (tptp.product1 X X X)) (tptp.product1 tptp.e_1 tptp.e_1 tptp.e_1))) :rule resolution :premises (t16 t17))
% 0.34/0.58 (step t19 (cl (=> (forall ((X $$unsorted)) (tptp.product1 X X X)) (tptp.product1 tptp.e_1 tptp.e_1 tptp.e_1))) :rule contraction :premises (t18))
% 0.34/0.58 (step t20 (cl (not (forall ((X $$unsorted)) (tptp.product1 X X X))) (tptp.product1 tptp.e_1 tptp.e_1 tptp.e_1)) :rule implies :premises (t19))
% 0.34/0.58 (step t21 (cl (tptp.product1 tptp.e_1 tptp.e_1 tptp.e_1)) :rule resolution :premises (t20 a19))
% 0.34/0.58 (step t22 (cl (=> (forall ((X $$unsorted) (W $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.product1 X W Y)) (not (tptp.product1 X Z Y)) (tptp.equalish W Z))) (or (not (tptp.product1 tptp.e_1 tptp.e_1 tptp.e_1)) (not (tptp.product1 tptp.e_1 tptp.e_2 tptp.e_1)) (tptp.equalish tptp.e_1 tptp.e_2))) (forall ((X $$unsorted) (W $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.product1 X W Y)) (not (tptp.product1 X Z Y)) (tptp.equalish W Z)))) :rule implies_neg1)
% 0.34/0.58 (anchor :step t23)
% 0.34/0.58 (assume t23.a0 (forall ((X $$unsorted) (W $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.product1 X W Y)) (not (tptp.product1 X Z Y)) (tptp.equalish W Z))))
% 0.34/0.58 (step t23.t1 (cl (or (not (forall ((X $$unsorted) (W $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.product1 X W Y)) (not (tptp.product1 X Z Y)) (tptp.equalish W Z)))) (or (not (tptp.product1 tptp.e_1 tptp.e_1 tptp.e_1)) (not (tptp.product1 tptp.e_1 tptp.e_2 tptp.e_1)) (tptp.equalish tptp.e_1 tptp.e_2)))) :rule forall_inst :args ((:= X tptp.e_1) (:= W tptp.e_1) (:= Y tptp.e_1) (:= Z tptp.e_2)))
% 0.34/0.58 (step t23.t2 (cl (not (forall ((X $$unsorted) (W $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.product1 X W Y)) (not (tptp.product1 X Z Y)) (tptp.equalish W Z)))) (or (not (tptp.product1 tptp.e_1 tptp.e_1 tptp.e_1)) (not (tptp.product1 tptp.e_1 tptp.e_2 tptp.e_1)) (tptp.equalish tptp.e_1 tptp.e_2))) :rule or :premises (t23.t1))
% 0.34/0.58 (step t23.t3 (cl (or (not (tptp.product1 tptp.e_1 tptp.e_1 tptp.e_1)) (not (tptp.product1 tptp.e_1 tptp.e_2 tptp.e_1)) (tptp.equalish tptp.e_1 tptp.e_2))) :rule resolution :premises (t23.t2 t23.a0))
% 0.34/0.58 (step t23 (cl (not (forall ((X $$unsorted) (W $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.product1 X W Y)) (not (tptp.product1 X Z Y)) (tptp.equalish W Z)))) (or (not (tptp.product1 tptp.e_1 tptp.e_1 tptp.e_1)) (not (tptp.product1 tptp.e_1 tptp.e_2 tptp.e_1)) (tptp.equalish tptp.e_1 tptp.e_2))) :rule subproof :discharge (t23.a0))
% 0.34/0.58 (step t24 (cl (=> (forall ((X $$unsorted) (W $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.product1 X W Y)) (not (tptp.product1 X Z Y)) (tptp.equalish W Z))) (or (not (tptp.product1 tptp.e_1 tptp.e_1 tptp.e_1)) (not (tptp.product1 tptp.e_1 tptp.e_2 tptp.e_1)) (tptp.equalish tptp.e_1 tptp.e_2))) (or (not (tptp.product1 tptp.e_1 tptp.e_1 tptp.e_1)) (not (tptp.product1 tptp.e_1 tptp.e_2 tptp.e_1)) (tptp.equalish tptp.e_1 tptp.e_2))) :rule resolution :premises (t22 t23))
% 0.34/0.58 (step t25 (cl (=> (forall ((X $$unsorted) (W $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.product1 X W Y)) (not (tptp.product1 X Z Y)) (tptp.equalish W Z))) (or (not (tptp.product1 tptp.e_1 tptp.e_1 tptp.e_1)) (not (tptp.product1 tptp.e_1 tptp.e_2 tptp.e_1)) (tptp.equalish tptp.e_1 tptp.e_2))) (not (or (not (tptp.product1 tptp.e_1 tptp.e_1 tptp.e_1)) (not (tptp.product1 tptp.e_1 tptp.e_2 tptp.e_1)) (tptp.equalish tptp.e_1 tptp.e_2)))) :rule implies_neg2)
% 0.34/0.58 (step t26 (cl (=> (forall ((X $$unsorted) (W $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.product1 X W Y)) (not (tptp.product1 X Z Y)) (tptp.equalish W Z))) (or (not (tptp.product1 tptp.e_1 tptp.e_1 tptp.e_1)) (not (tptp.product1 tptp.e_1 tptp.e_2 tptp.e_1)) (tptp.equalish tptp.e_1 tptp.e_2))) (=> (forall ((X $$unsorted) (W $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.product1 X W Y)) (not (tptp.product1 X Z Y)) (tptp.equalish W Z))) (or (not (tptp.product1 tptp.e_1 tptp.e_1 tptp.e_1)) (not (tptp.product1 tptp.e_1 tptp.e_2 tptp.e_1)) (tptp.equalish tptp.e_1 tptp.e_2)))) :rule resolution :premises (t24 t25))
% 0.34/0.58 (step t27 (cl (=> (forall ((X $$unsorted) (W $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.product1 X W Y)) (not (tptp.product1 X Z Y)) (tptp.equalish W Z))) (or (not (tptp.product1 tptp.e_1 tptp.e_1 tptp.e_1)) (not (tptp.product1 tptp.e_1 tptp.e_2 tptp.e_1)) (tptp.equalish tptp.e_1 tptp.e_2)))) :rule contraction :premises (t26))
% 0.34/0.58 (step t28 (cl (not (forall ((X $$unsorted) (W $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.product1 X W Y)) (not (tptp.product1 X Z Y)) (tptp.equalish W Z)))) (or (not (tptp.product1 tptp.e_1 tptp.e_1 tptp.e_1)) (not (tptp.product1 tptp.e_1 tptp.e_2 tptp.e_1)) (tptp.equalish tptp.e_1 tptp.e_2))) :rule implies :premises (t27))
% 0.34/0.58 (step t29 (cl (or (not (tptp.product1 tptp.e_1 tptp.e_1 tptp.e_1)) (not (tptp.product1 tptp.e_1 tptp.e_2 tptp.e_1)) (tptp.equalish tptp.e_1 tptp.e_2))) :rule resolution :premises (t28 a17))
% 0.34/0.58 (step t30 (cl (not (tptp.product1 tptp.e_1 tptp.e_2 tptp.e_1))) :rule resolution :premises (t13 a9 t21 t29))
% 0.34/0.58 (step t31 (cl (not (or (not (tptp.product1 tptp.e_2 tptp.e_2 tptp.e_2)) (not (tptp.product1 tptp.e_1 tptp.e_2 tptp.e_2)) (tptp.equalish tptp.e_2 tptp.e_1))) (not (tptp.product1 tptp.e_2 tptp.e_2 tptp.e_2)) (not (tptp.product1 tptp.e_1 tptp.e_2 tptp.e_2)) (tptp.equalish tptp.e_2 tptp.e_1)) :rule or_pos)
% 0.34/0.58 (step t32 (cl (tptp.equalish tptp.e_2 tptp.e_1) (not (tptp.product1 tptp.e_1 tptp.e_2 tptp.e_2)) (not (tptp.product1 tptp.e_2 tptp.e_2 tptp.e_2)) (not (or (not (tptp.product1 tptp.e_2 tptp.e_2 tptp.e_2)) (not (tptp.product1 tptp.e_1 tptp.e_2 tptp.e_2)) (tptp.equalish tptp.e_2 tptp.e_1)))) :rule reordering :premises (t31))
% 0.34/0.58 (step t33 (cl (=> (forall ((X $$unsorted)) (tptp.product1 X X X)) (tptp.product1 tptp.e_2 tptp.e_2 tptp.e_2)) (forall ((X $$unsorted)) (tptp.product1 X X X))) :rule implies_neg1)
% 0.34/0.58 (anchor :step t34)
% 0.34/0.58 (assume t34.a0 (forall ((X $$unsorted)) (tptp.product1 X X X)))
% 0.34/0.58 (step t34.t1 (cl (or (not (forall ((X $$unsorted)) (tptp.product1 X X X))) (tptp.product1 tptp.e_2 tptp.e_2 tptp.e_2))) :rule forall_inst :args ((:= X tptp.e_2)))
% 0.34/0.58 (step t34.t2 (cl (not (forall ((X $$unsorted)) (tptp.product1 X X X))) (tptp.product1 tptp.e_2 tptp.e_2 tptp.e_2)) :rule or :premises (t34.t1))
% 0.34/0.58 (step t34.t3 (cl (tptp.product1 tptp.e_2 tptp.e_2 tptp.e_2)) :rule resolution :premises (t34.t2 t34.a0))
% 0.34/0.58 (step t34 (cl (not (forall ((X $$unsorted)) (tptp.product1 X X X))) (tptp.product1 tptp.e_2 tptp.e_2 tptp.e_2)) :rule subproof :discharge (t34.a0))
% 0.34/0.58 (step t35 (cl (=> (forall ((X $$unsorted)) (tptp.product1 X X X)) (tptp.product1 tptp.e_2 tptp.e_2 tptp.e_2)) (tptp.product1 tptp.e_2 tptp.e_2 tptp.e_2)) :rule resolution :premises (t33 t34))
% 0.34/0.58 (step t36 (cl (=> (forall ((X $$unsorted)) (tptp.product1 X X X)) (tptp.product1 tptp.e_2 tptp.e_2 tptp.e_2)) (not (tptp.product1 tptp.e_2 tptp.e_2 tptp.e_2))) :rule implies_neg2)
% 0.34/0.58 (step t37 (cl (=> (forall ((X $$unsorted)) (tptp.product1 X X X)) (tptp.product1 tptp.e_2 tptp.e_2 tptp.e_2)) (=> (forall ((X $$unsorted)) (tptp.product1 X X X)) (tptp.product1 tptp.e_2 tptp.e_2 tptp.e_2))) :rule resolution :premises (t35 t36))
% 0.34/0.58 (step t38 (cl (=> (forall ((X $$unsorted)) (tptp.product1 X X X)) (tptp.product1 tptp.e_2 tptp.e_2 tptp.e_2))) :rule contraction :premises (t37))
% 0.34/0.58 (step t39 (cl (not (forall ((X $$unsorted)) (tptp.product1 X X X))) (tptp.product1 tptp.e_2 tptp.e_2 tptp.e_2)) :rule implies :premises (t38))
% 0.34/0.58 (step t40 (cl (tptp.product1 tptp.e_2 tptp.e_2 tptp.e_2)) :rule resolution :premises (t39 a19))
% 0.34/0.58 (step t41 (cl (=> (forall ((W $$unsorted) (Y $$unsorted) (X $$unsorted) (Z $$unsorted)) (or (not (tptp.product1 W Y X)) (not (tptp.product1 Z Y X)) (tptp.equalish W Z))) (or (not (tptp.product1 tptp.e_2 tptp.e_2 tptp.e_2)) (not (tptp.product1 tptp.e_1 tptp.e_2 tptp.e_2)) (tptp.equalish tptp.e_2 tptp.e_1))) (forall ((W $$unsorted) (Y $$unsorted) (X $$unsorted) (Z $$unsorted)) (or (not (tptp.product1 W Y X)) (not (tptp.product1 Z Y X)) (tptp.equalish W Z)))) :rule implies_neg1)
% 0.34/0.58 (anchor :step t42)
% 0.34/0.58 (assume t42.a0 (forall ((W $$unsorted) (Y $$unsorted) (X $$unsorted) (Z $$unsorted)) (or (not (tptp.product1 W Y X)) (not (tptp.product1 Z Y X)) (tptp.equalish W Z))))
% 0.34/0.58 (step t42.t1 (cl (or (not (forall ((W $$unsorted) (Y $$unsorted) (X $$unsorted) (Z $$unsorted)) (or (not (tptp.product1 W Y X)) (not (tptp.product1 Z Y X)) (tptp.equalish W Z)))) (or (not (tptp.product1 tptp.e_2 tptp.e_2 tptp.e_2)) (not (tptp.product1 tptp.e_1 tptp.e_2 tptp.e_2)) (tptp.equalish tptp.e_2 tptp.e_1)))) :rule forall_inst :args ((:= W tptp.e_2) (:= Y tptp.e_2) (:= X tptp.e_2) (:= Z tptp.e_1)))
% 0.34/0.58 (step t42.t2 (cl (not (forall ((W $$unsorted) (Y $$unsorted) (X $$unsorted) (Z $$unsorted)) (or (not (tptp.product1 W Y X)) (not (tptp.product1 Z Y X)) (tptp.equalish W Z)))) (or (not (tptp.product1 tptp.e_2 tptp.e_2 tptp.e_2)) (not (tptp.product1 tptp.e_1 tptp.e_2 tptp.e_2)) (tptp.equalish tptp.e_2 tptp.e_1))) :rule or :premises (t42.t1))
% 0.34/0.58 (step t42.t3 (cl (or (not (tptp.product1 tptp.e_2 tptp.e_2 tptp.e_2)) (not (tptp.product1 tptp.e_1 tptp.e_2 tptp.e_2)) (tptp.equalish tptp.e_2 tptp.e_1))) :rule resolution :premises (t42.t2 t42.a0))
% 0.34/0.58 (step t42 (cl (not (forall ((W $$unsorted) (Y $$unsorted) (X $$unsorted) (Z $$unsorted)) (or (not (tptp.product1 W Y X)) (not (tptp.product1 Z Y X)) (tptp.equalish W Z)))) (or (not (tptp.product1 tptp.e_2 tptp.e_2 tptp.e_2)) (not (tptp.product1 tptp.e_1 tptp.e_2 tptp.e_2)) (tptp.equalish tptp.e_2 tptp.e_1))) :rule subproof :discharge (t42.a0))
% 0.34/0.58 (step t43 (cl (=> (forall ((W $$unsorted) (Y $$unsorted) (X $$unsorted) (Z $$unsorted)) (or (not (tptp.product1 W Y X)) (not (tptp.product1 Z Y X)) (tptp.equalish W Z))) (or (not (tptp.product1 tptp.e_2 tptp.e_2 tptp.e_2)) (not (tptp.product1 tptp.e_1 tptp.e_2 tptp.e_2)) (tptp.equalish tptp.e_2 tptp.e_1))) (or (not (tptp.product1 tptp.e_2 tptp.e_2 tptp.e_2)) (not (tptp.product1 tptp.e_1 tptp.e_2 tptp.e_2)) (tptp.equalish tptp.e_2 tptp.e_1))) :rule resolution :premises (t41 t42))
% 0.34/0.58 (step t44 (cl (=> (forall ((W $$unsorted) (Y $$unsorted) (X $$unsorted) (Z $$unsorted)) (or (not (tptp.product1 W Y X)) (not (tptp.product1 Z Y X)) (tptp.equalish W Z))) (or (not (tptp.product1 tptp.e_2 tptp.e_2 tptp.e_2)) (not (tptp.product1 tptp.e_1 tptp.e_2 tptp.e_2)) (tptp.equalish tptp.e_2 tptp.e_1))) (not (or (not (tptp.product1 tptp.e_2 tptp.e_2 tptp.e_2)) (not (tptp.product1 tptp.e_1 tptp.e_2 tptp.e_2)) (tptp.equalish tptp.e_2 tptp.e_1)))) :rule implies_neg2)
% 0.34/0.58 (step t45 (cl (=> (forall ((W $$unsorted) (Y $$unsorted) (X $$unsorted) (Z $$unsorted)) (or (not (tptp.product1 W Y X)) (not (tptp.product1 Z Y X)) (tptp.equalish W Z))) (or (not (tptp.product1 tptp.e_2 tptp.e_2 tptp.e_2)) (not (tptp.product1 tptp.e_1 tptp.e_2 tptp.e_2)) (tptp.equalish tptp.e_2 tptp.e_1))) (=> (forall ((W $$unsorted) (Y $$unsorted) (X $$unsorted) (Z $$unsorted)) (or (not (tptp.product1 W Y X)) (not (tptp.product1 Z Y X)) (tptp.equalish W Z))) (or (not (tptp.product1 tptp.e_2 tptp.e_2 tptp.e_2)) (not (tptp.product1 tptp.e_1 tptp.e_2 tptp.e_2)) (tptp.equalish tptp.e_2 tptp.e_1)))) :rule resolution :premises (t43 t44))
% 0.34/0.58 (step t46 (cl (=> (forall ((W $$unsorted) (Y $$unsorted) (X $$unsorted) (Z $$unsorted)) (or (not (tptp.product1 W Y X)) (not (tptp.product1 Z Y X)) (tptp.equalish W Z))) (or (not (tptp.product1 tptp.e_2 tptp.e_2 tptp.e_2)) (not (tptp.product1 tptp.e_1 tptp.e_2 tptp.e_2)) (tptp.equalish tptp.e_2 tptp.e_1)))) :rule contraction :premises (t45))
% 0.34/0.58 (step t47 (cl (not (forall ((W $$unsorted) (Y $$unsorted) (X $$unsorted) (Z $$unsorted)) (or (not (tptp.product1 W Y X)) (not (tptp.product1 Z Y X)) (tptp.equalish W Z)))) (or (not (tptp.product1 tptp.e_2 tptp.e_2 tptp.e_2)) (not (tptp.product1 tptp.e_1 tptp.e_2 tptp.e_2)) (tptp.equalish tptp.e_2 tptp.e_1))) :rule implies :premises (t46))
% 0.34/0.58 (step t48 (cl (or (not (tptp.product1 tptp.e_2 tptp.e_2 tptp.e_2)) (not (tptp.product1 tptp.e_1 tptp.e_2 tptp.e_2)) (tptp.equalish tptp.e_2 tptp.e_1))) :rule resolution :premises (t47 a18))
% 0.34/0.58 (step t49 (cl (not (tptp.product1 tptp.e_1 tptp.e_2 tptp.e_2))) :rule resolution :premises (t32 a11 t40 t48))
% 0.34/0.58 (step t50 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.group_element X)) (not (tptp.group_element Y)) (tptp.product1 X Y tptp.e_1) (tptp.product1 X Y tptp.e_2) (tptp.product1 X Y tptp.e_3))) (or (not (tptp.group_element tptp.e_1)) (not (tptp.group_element tptp.e_2)) (tptp.product1 tptp.e_1 tptp.e_2 tptp.e_1) (tptp.product1 tptp.e_1 tptp.e_2 tptp.e_2) (tptp.product1 tptp.e_1 tptp.e_2 tptp.e_3))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.group_element X)) (not (tptp.group_element Y)) (tptp.product1 X Y tptp.e_1) (tptp.product1 X Y tptp.e_2) (tptp.product1 X Y tptp.e_3)))) :rule implies_neg1)
% 0.34/0.58 (anchor :step t51)
% 0.34/0.58 (assume t51.a0 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.group_element X)) (not (tptp.group_element Y)) (tptp.product1 X Y tptp.e_1) (tptp.product1 X Y tptp.e_2) (tptp.product1 X Y tptp.e_3))))
% 0.34/0.58 (step t51.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.group_element X)) (not (tptp.group_element Y)) (tptp.product1 X Y tptp.e_1) (tptp.product1 X Y tptp.e_2) (tptp.product1 X Y tptp.e_3)))) (or (not (tptp.group_element tptp.e_1)) (not (tptp.group_element tptp.e_2)) (tptp.product1 tptp.e_1 tptp.e_2 tptp.e_1) (tptp.product1 tptp.e_1 tptp.e_2 tptp.e_2) (tptp.product1 tptp.e_1 tptp.e_2 tptp.e_3)))) :rule forall_inst :args ((:= X tptp.e_1) (:= Y tptp.e_2)))
% 0.34/0.58 (step t51.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.group_element X)) (not (tptp.group_element Y)) (tptp.product1 X Y tptp.e_1) (tptp.product1 X Y tptp.e_2) (tptp.product1 X Y tptp.e_3)))) (or (not (tptp.group_element tptp.e_1)) (not (tptp.group_element tptp.e_2)) (tptp.product1 tptp.e_1 tptp.e_2 tptp.e_1) (tptp.product1 tptp.e_1 tptp.e_2 tptp.e_2) (tptp.product1 tptp.e_1 tptp.e_2 tptp.e_3))) :rule or :premises (t51.t1))
% 0.34/0.58 (step t51.t3 (cl (or (not (tptp.group_element tptp.e_1)) (not (tptp.group_element tptp.e_2)) (tptp.product1 tptp.e_1 tptp.e_2 tptp.e_1) (tptp.product1 tptp.e_1 tptp.e_2 tptp.e_2) (tptp.product1 tptp.e_1 tptp.e_2 tptp.e_3))) :rule resolution :premises (t51.t2 t51.a0))
% 0.34/0.58 (step t51 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.group_element X)) (not (tptp.group_element Y)) (tptp.product1 X Y tptp.e_1) (tptp.product1 X Y tptp.e_2) (tptp.product1 X Y tptp.e_3)))) (or (not (tptp.group_element tptp.e_1)) (not (tptp.group_element tptp.e_2)) (tptp.product1 tptp.e_1 tptp.e_2 tptp.e_1) (tptp.product1 tptp.e_1 tptp.e_2 tptp.e_2) (tptp.product1 tptp.e_1 tptp.e_2 tptp.e_3))) :rule subproof :discharge (t51.a0))
% 0.34/0.58 (step t52 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.group_element X)) (not (tptp.group_element Y)) (tptp.product1 X Y tptp.e_1) (tptp.product1 X Y tptp.e_2) (tptp.product1 X Y tptp.e_3))) (or (not (tptp.group_element tptp.e_1)) (not (tptp.group_element tptp.e_2)) (tptp.product1 tptp.e_1 tptp.e_2 tptp.e_1) (tptp.product1 tptp.e_1 tptp.e_2 tptp.e_2) (tptp.product1 tptp.e_1 tptp.e_2 tptp.e_3))) (or (not (tptp.group_element tptp.e_1)) (not (tptp.group_element tptp.e_2)) (tptp.product1 tptp.e_1 tptp.e_2 tptp.e_1) (tptp.product1 tptp.e_1 tptp.e_2 tptp.e_2) (tptp.product1 tptp.e_1 tptp.e_2 tptp.e_3))) :rule resolution :premises (t50 t51))
% 0.34/0.58 (step t53 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.group_element X)) (not (tptp.group_element Y)) (tptp.product1 X Y tptp.e_1) (tptp.product1 X Y tptp.e_2) (tptp.product1 X Y tptp.e_3))) (or (not (tptp.group_element tptp.e_1)) (not (tptp.group_element tptp.e_2)) (tptp.product1 tptp.e_1 tptp.e_2 tptp.e_1) (tptp.product1 tptp.e_1 tptp.e_2 tptp.e_2) (tptp.product1 tptp.e_1 tptp.e_2 tptp.e_3))) (not (or (not (tptp.group_element tptp.e_1)) (not (tptp.group_element tptp.e_2)) (tptp.product1 tptp.e_1 tptp.e_2 tptp.e_1) (tptp.product1 tptp.e_1 tptp.e_2 tptp.e_2) (tptp.product1 tptp.e_1 tptp.e_2 tptp.e_3)))) :rule implies_neg2)
% 0.34/0.58 (step t54 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.group_element X)) (not (tptp.group_element Y)) (tptp.product1 X Y tptp.e_1) (tptp.product1 X Y tptp.e_2) (tptp.product1 X Y tptp.e_3))) (or (not (tptp.group_element tptp.e_1)) (not (tptp.group_element tptp.e_2)) (tptp.product1 tptp.e_1 tptp.e_2 tptp.e_1) (tptp.product1 tptp.e_1 tptp.e_2 tptp.e_2) (tptp.product1 tptp.e_1 tptp.e_2 tptp.e_3))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.group_element X)) (not (tptp.group_element Y)) (tptp.product1 X Y tptp.e_1) (tptp.product1 X Y tptp.e_2) (tptp.product1 X Y tptp.e_3))) (or (not (tptp.group_element tptp.e_1)) (not (tptp.group_element tptp.e_2)) (tptp.product1 tptp.e_1 tptp.e_2 tptp.e_1) (tptp.product1 tptp.e_1 tptp.e_2 tptp.e_2) (tptp.product1 tptp.e_1 tptp.e_2 tptp.e_3)))) :rule resolution :premises (t52 t53))
% 0.34/0.58 (step t55 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.group_element X)) (not (tptp.group_element Y)) (tptp.product1 X Y tptp.e_1) (tptp.product1 X Y tptp.e_2) (tptp.product1 X Y tptp.e_3))) (or (not (tptp.group_element tptp.e_1)) (not (tptp.group_element tptp.e_2)) (tptp.product1 tptp.e_1 tptp.e_2 tptp.e_1) (tptp.product1 tptp.e_1 tptp.e_2 tptp.e_2) (tptp.product1 tptp.e_1 tptp.e_2 tptp.e_3)))) :rule contraction :premises (t54))
% 0.34/0.58 (step t56 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.group_element X)) (not (tptp.group_element Y)) (tptp.product1 X Y tptp.e_1) (tptp.product1 X Y tptp.e_2) (tptp.product1 X Y tptp.e_3)))) (or (not (tptp.group_element tptp.e_1)) (not (tptp.group_element tptp.e_2)) (tptp.product1 tptp.e_1 tptp.e_2 tptp.e_1) (tptp.product1 tptp.e_1 tptp.e_2 tptp.e_2) (tptp.product1 tptp.e_1 tptp.e_2 tptp.e_3))) :rule implies :premises (t55))
% 0.34/0.58 (step t57 (cl (or (not (tptp.group_element tptp.e_1)) (not (tptp.group_element tptp.e_2)) (tptp.product1 tptp.e_1 tptp.e_2 tptp.e_1) (tptp.product1 tptp.e_1 tptp.e_2 tptp.e_2) (tptp.product1 tptp.e_1 tptp.e_2 tptp.e_3))) :rule resolution :premises (t56 a15))
% 0.34/0.58 (step t58 (cl (tptp.product1 tptp.e_1 tptp.e_2 tptp.e_3)) :rule resolution :premises (t11 a6 a7 t30 t49 t57))
% 0.34/0.58 (step t59 (cl (not (or (not (tptp.group_element tptp.e_3)) (not (tptp.group_element tptp.e_2)) (tptp.product1 tptp.e_3 tptp.e_2 tptp.e_1) (tptp.product1 tptp.e_3 tptp.e_2 tptp.e_2) (tptp.product1 tptp.e_3 tptp.e_2 tptp.e_3))) (not (tptp.group_element tptp.e_3)) (not (tptp.group_element tptp.e_2)) (tptp.product1 tptp.e_3 tptp.e_2 tptp.e_1) (tptp.product1 tptp.e_3 tptp.e_2 tptp.e_2) (tptp.product1 tptp.e_3 tptp.e_2 tptp.e_3)) :rule or_pos)
% 0.34/0.58 (step t60 (cl (not (tptp.group_element tptp.e_2)) (not (tptp.group_element tptp.e_3)) (tptp.product1 tptp.e_3 tptp.e_2 tptp.e_1) (tptp.product1 tptp.e_3 tptp.e_2 tptp.e_2) (tptp.product1 tptp.e_3 tptp.e_2 tptp.e_3) (not (or (not (tptp.group_element tptp.e_3)) (not (tptp.group_element tptp.e_2)) (tptp.product1 tptp.e_3 tptp.e_2 tptp.e_1) (tptp.product1 tptp.e_3 tptp.e_2 tptp.e_2) (tptp.product1 tptp.e_3 tptp.e_2 tptp.e_3)))) :rule reordering :premises (t59))
% 0.34/0.58 (step t61 (cl (not (or (not (tptp.product1 tptp.e_1 tptp.e_2 tptp.e_3)) (not (tptp.product1 tptp.e_3 tptp.e_2 tptp.e_1)) (tptp.product2 tptp.e_1 tptp.e_1 tptp.e_2))) (not (tptp.product1 tptp.e_1 tptp.e_2 tptp.e_3)) (not (tptp.product1 tptp.e_3 tptp.e_2 tptp.e_1)) (tptp.product2 tptp.e_1 tptp.e_1 tptp.e_2)) :rule or_pos)
% 0.34/0.58 (step t62 (cl (tptp.product2 tptp.e_1 tptp.e_1 tptp.e_2) (not (tptp.product1 tptp.e_1 tptp.e_2 tptp.e_3)) (not (tptp.product1 tptp.e_3 tptp.e_2 tptp.e_1)) (not (or (not (tptp.product1 tptp.e_1 tptp.e_2 tptp.e_3)) (not (tptp.product1 tptp.e_3 tptp.e_2 tptp.e_1)) (tptp.product2 tptp.e_1 tptp.e_1 tptp.e_2)))) :rule reordering :premises (t61))
% 0.34/0.58 (step t63 (cl (not (or (not (tptp.product2 tptp.e_1 tptp.e_1 tptp.e_1)) (not (tptp.product2 tptp.e_1 tptp.e_1 tptp.e_2)) (tptp.equalish tptp.e_1 tptp.e_2))) (not (tptp.product2 tptp.e_1 tptp.e_1 tptp.e_1)) (not (tptp.product2 tptp.e_1 tptp.e_1 tptp.e_2)) (tptp.equalish tptp.e_1 tptp.e_2)) :rule or_pos)
% 0.34/0.58 (step t64 (cl (tptp.equalish tptp.e_1 tptp.e_2) (not (tptp.product2 tptp.e_1 tptp.e_1 tptp.e_1)) (not (tptp.product2 tptp.e_1 tptp.e_1 tptp.e_2)) (not (or (not (tptp.product2 tptp.e_1 tptp.e_1 tptp.e_1)) (not (tptp.product2 tptp.e_1 tptp.e_1 tptp.e_2)) (tptp.equalish tptp.e_1 tptp.e_2)))) :rule reordering :premises (t63))
% 0.34/0.58 (step t65 (cl (=> (forall ((X $$unsorted)) (tptp.product2 X X X)) (tptp.product2 tptp.e_1 tptp.e_1 tptp.e_1)) (forall ((X $$unsorted)) (tptp.product2 X X X))) :rule implies_neg1)
% 0.34/0.58 (anchor :step t66)
% 0.34/0.58 (assume t66.a0 (forall ((X $$unsorted)) (tptp.product2 X X X)))
% 0.34/0.58 (step t66.t1 (cl (or (not (forall ((X $$unsorted)) (tptp.product2 X X X))) (tptp.product2 tptp.e_1 tptp.e_1 tptp.e_1))) :rule forall_inst :args ((:= X tptp.e_1)))
% 0.34/0.58 (step t66.t2 (cl (not (forall ((X $$unsorted)) (tptp.product2 X X X))) (tptp.product2 tptp.e_1 tptp.e_1 tptp.e_1)) :rule or :premises (t66.t1))
% 0.34/0.58 (step t66.t3 (cl (tptp.product2 tptp.e_1 tptp.e_1 tptp.e_1)) :rule resolution :premises (t66.t2 t66.a0))
% 0.34/0.58 (step t66 (cl (not (forall ((X $$unsorted)) (tptp.product2 X X X))) (tptp.product2 tptp.e_1 tptp.e_1 tptp.e_1)) :rule subproof :discharge (t66.a0))
% 0.34/0.58 (step t67 (cl (=> (forall ((X $$unsorted)) (tptp.product2 X X X)) (tptp.product2 tptp.e_1 tptp.e_1 tptp.e_1)) (tptp.product2 tptp.e_1 tptp.e_1 tptp.e_1)) :rule resolution :premises (t65 t66))
% 0.34/0.58 (step t68 (cl (=> (forall ((X $$unsorted)) (tptp.product2 X X X)) (tptp.product2 tptp.e_1 tptp.e_1 tptp.e_1)) (not (tptp.product2 tptp.e_1 tptp.e_1 tptp.e_1))) :rule implies_neg2)
% 0.34/0.58 (step t69 (cl (=> (forall ((X $$unsorted)) (tptp.product2 X X X)) (tptp.product2 tptp.e_1 tptp.e_1 tptp.e_1)) (=> (forall ((X $$unsorted)) (tptp.product2 X X X)) (tptp.product2 tptp.e_1 tptp.e_1 tptp.e_1))) :rule resolution :premises (t67 t68))
% 0.34/0.58 (step t70 (cl (=> (forall ((X $$unsorted)) (tptp.product2 X X X)) (tptp.product2 tptp.e_1 tptp.e_1 tptp.e_1))) :rule contraction :premises (t69))
% 0.34/0.58 (step t71 (cl (not (forall ((X $$unsorted)) (tptp.product2 X X X))) (tptp.product2 tptp.e_1 tptp.e_1 tptp.e_1)) :rule implies :premises (t70))
% 0.34/0.58 (step t72 (cl (tptp.product2 tptp.e_1 tptp.e_1 tptp.e_1)) :rule resolution :premises (t71 a24))
% 0.34/0.58 (step t73 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (W $$unsorted) (Z $$unsorted)) (or (not (tptp.product2 X Y W)) (not (tptp.product2 X Y Z)) (tptp.equalish W Z))) (or (not (tptp.product2 tptp.e_1 tptp.e_1 tptp.e_1)) (not (tptp.product2 tptp.e_1 tptp.e_1 tptp.e_2)) (tptp.equalish tptp.e_1 tptp.e_2))) (forall ((X $$unsorted) (Y $$unsorted) (W $$unsorted) (Z $$unsorted)) (or (not (tptp.product2 X Y W)) (not (tptp.product2 X Y Z)) (tptp.equalish W Z)))) :rule implies_neg1)
% 0.34/0.58 (anchor :step t74)
% 0.34/0.58 (assume t74.a0 (forall ((X $$unsorted) (Y $$unsorted) (W $$unsorted) (Z $$unsorted)) (or (not (tptp.product2 X Y W)) (not (tptp.product2 X Y Z)) (tptp.equalish W Z))))
% 0.34/0.58 (step t74.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted) (W $$unsorted) (Z $$unsorted)) (or (not (tptp.product2 X Y W)) (not (tptp.product2 X Y Z)) (tptp.equalish W Z)))) (or (not (tptp.product2 tptp.e_1 tptp.e_1 tptp.e_1)) (not (tptp.product2 tptp.e_1 tptp.e_1 tptp.e_2)) (tptp.equalish tptp.e_1 tptp.e_2)))) :rule forall_inst :args ((:= X tptp.e_1) (:= Y tptp.e_1) (:= W tptp.e_1) (:= Z tptp.e_2)))
% 0.34/0.58 (step t74.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (W $$unsorted) (Z $$unsorted)) (or (not (tptp.product2 X Y W)) (not (tptp.product2 X Y Z)) (tptp.equalish W Z)))) (or (not (tptp.product2 tptp.e_1 tptp.e_1 tptp.e_1)) (not (tptp.product2 tptp.e_1 tptp.e_1 tptp.e_2)) (tptp.equalish tptp.e_1 tptp.e_2))) :rule or :premises (t74.t1))
% 0.34/0.58 (step t74.t3 (cl (or (not (tptp.product2 tptp.e_1 tptp.e_1 tptp.e_1)) (not (tptp.product2 tptp.e_1 tptp.e_1 tptp.e_2)) (tptp.equalish tptp.e_1 tptp.e_2))) :rule resolution :premises (t74.t2 t74.a0))
% 0.34/0.58 (step t74 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (W $$unsorted) (Z $$unsorted)) (or (not (tptp.product2 X Y W)) (not (tptp.product2 X Y Z)) (tptp.equalish W Z)))) (or (not (tptp.product2 tptp.e_1 tptp.e_1 tptp.e_1)) (not (tptp.product2 tptp.e_1 tptp.e_1 tptp.e_2)) (tptp.equalish tptp.e_1 tptp.e_2))) :rule subproof :discharge (t74.a0))
% 0.34/0.58 (step t75 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (W $$unsorted) (Z $$unsorted)) (or (not (tptp.product2 X Y W)) (not (tptp.product2 X Y Z)) (tptp.equalish W Z))) (or (not (tptp.product2 tptp.e_1 tptp.e_1 tptp.e_1)) (not (tptp.product2 tptp.e_1 tptp.e_1 tptp.e_2)) (tptp.equalish tptp.e_1 tptp.e_2))) (or (not (tptp.product2 tptp.e_1 tptp.e_1 tptp.e_1)) (not (tptp.product2 tptp.e_1 tptp.e_1 tptp.e_2)) (tptp.equalish tptp.e_1 tptp.e_2))) :rule resolution :premises (t73 t74))
% 0.34/0.58 (step t76 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (W $$unsorted) (Z $$unsorted)) (or (not (tptp.product2 X Y W)) (not (tptp.product2 X Y Z)) (tptp.equalish W Z))) (or (not (tptp.product2 tptp.e_1 tptp.e_1 tptp.e_1)) (not (tptp.product2 tptp.e_1 tptp.e_1 tptp.e_2)) (tptp.equalish tptp.e_1 tptp.e_2))) (not (or (not (tptp.product2 tptp.e_1 tptp.e_1 tptp.e_1)) (not (tptp.product2 tptp.e_1 tptp.e_1 tptp.e_2)) (tptp.equalish tptp.e_1 tptp.e_2)))) :rule implies_neg2)
% 0.34/0.58 (step t77 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (W $$unsorted) (Z $$unsorted)) (or (not (tptp.product2 X Y W)) (not (tptp.product2 X Y Z)) (tptp.equalish W Z))) (or (not (tptp.product2 tptp.e_1 tptp.e_1 tptp.e_1)) (not (tptp.product2 tptp.e_1 tptp.e_1 tptp.e_2)) (tptp.equalish tptp.e_1 tptp.e_2))) (=> (forall ((X $$unsorted) (Y $$unsorted) (W $$unsorted) (Z $$unsorted)) (or (not (tptp.product2 X Y W)) (not (tptp.product2 X Y Z)) (tptp.equalish W Z))) (or (not (tptp.product2 tptp.e_1 tptp.e_1 tptp.e_1)) (not (tptp.product2 tptp.e_1 tptp.e_1 tptp.e_2)) (tptp.equalish tptp.e_1 tptp.e_2)))) :rule resolution :premises (t75 t76))
% 0.34/0.58 (step t78 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (W $$unsorted) (Z $$unsorted)) (or (not (tptp.product2 X Y W)) (not (tptp.product2 X Y Z)) (tptp.equalish W Z))) (or (not (tptp.product2 tptp.e_1 tptp.e_1 tptp.e_1)) (not (tptp.product2 tptp.e_1 tptp.e_1 tptp.e_2)) (tptp.equalish tptp.e_1 tptp.e_2)))) :rule contraction :premises (t77))
% 0.34/0.58 (step t79 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (W $$unsorted) (Z $$unsorted)) (or (not (tptp.product2 X Y W)) (not (tptp.product2 X Y Z)) (tptp.equalish W Z)))) (or (not (tptp.product2 tptp.e_1 tptp.e_1 tptp.e_1)) (not (tptp.product2 tptp.e_1 tptp.e_1 tptp.e_2)) (tptp.equalish tptp.e_1 tptp.e_2))) :rule implies :premises (t78))
% 0.34/0.58 (step t80 (cl (or (not (tptp.product2 tptp.e_1 tptp.e_1 tptp.e_1)) (not (tptp.product2 tptp.e_1 tptp.e_1 tptp.e_2)) (tptp.equalish tptp.e_1 tptp.e_2))) :rule resolution :premises (t79 a21))
% 0.34/0.58 (step t81 (cl (not (tptp.product2 tptp.e_1 tptp.e_1 tptp.e_2))) :rule resolution :premises (t64 a9 t72 t80))
% 0.34/0.58 (step t82 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z1 $$unsorted) (Z2 $$unsorted)) (or (not (tptp.product1 X Y Z1)) (not (tptp.product1 Z1 Y Z2)) (tptp.product2 Z2 X Y))) (or (not (tptp.product1 tptp.e_1 tptp.e_2 tptp.e_3)) (not (tptp.product1 tptp.e_3 tptp.e_2 tptp.e_1)) (tptp.product2 tptp.e_1 tptp.e_1 tptp.e_2))) (forall ((X $$unsorted) (Y $$unsorted) (Z1 $$unsorted) (Z2 $$unsorted)) (or (not (tptp.product1 X Y Z1)) (not (tptp.product1 Z1 Y Z2)) (tptp.product2 Z2 X Y)))) :rule implies_neg1)
% 0.34/0.58 (anchor :step t83)
% 0.34/0.58 (assume t83.a0 (forall ((X $$unsorted) (Y $$unsorted) (Z1 $$unsorted) (Z2 $$unsorted)) (or (not (tptp.product1 X Y Z1)) (not (tptp.product1 Z1 Y Z2)) (tptp.product2 Z2 X Y))))
% 0.34/0.58 (step t83.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted) (Z1 $$unsorted) (Z2 $$unsorted)) (or (not (tptp.product1 X Y Z1)) (not (tptp.product1 Z1 Y Z2)) (tptp.product2 Z2 X Y)))) (or (not (tptp.product1 tptp.e_1 tptp.e_2 tptp.e_3)) (not (tptp.product1 tptp.e_3 tptp.e_2 tptp.e_1)) (tptp.product2 tptp.e_1 tptp.e_1 tptp.e_2)))) :rule forall_inst :args ((:= X tptp.e_1) (:= Y tptp.e_2) (:= Z1 tptp.e_3) (:= Z2 tptp.e_1)))
% 0.34/0.58 (step t83.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z1 $$unsorted) (Z2 $$unsorted)) (or (not (tptp.product1 X Y Z1)) (not (tptp.product1 Z1 Y Z2)) (tptp.product2 Z2 X Y)))) (or (not (tptp.product1 tptp.e_1 tptp.e_2 tptp.e_3)) (not (tptp.product1 tptp.e_3 tptp.e_2 tptp.e_1)) (tptp.product2 tptp.e_1 tptp.e_1 tptp.e_2))) :rule or :premises (t83.t1))
% 0.34/0.58 (step t83.t3 (cl (or (not (tptp.product1 tptp.e_1 tptp.e_2 tptp.e_3)) (not (tptp.product1 tptp.e_3 tptp.e_2 tptp.e_1)) (tptp.product2 tptp.e_1 tptp.e_1 tptp.e_2))) :rule resolution :premises (t83.t2 t83.a0))
% 0.34/0.58 (step t83 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z1 $$unsorted) (Z2 $$unsorted)) (or (not (tptp.product1 X Y Z1)) (not (tptp.product1 Z1 Y Z2)) (tptp.product2 Z2 X Y)))) (or (not (tptp.product1 tptp.e_1 tptp.e_2 tptp.e_3)) (not (tptp.product1 tptp.e_3 tptp.e_2 tptp.e_1)) (tptp.product2 tptp.e_1 tptp.e_1 tptp.e_2))) :rule subproof :discharge (t83.a0))
% 0.34/0.58 (step t84 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z1 $$unsorted) (Z2 $$unsorted)) (or (not (tptp.product1 X Y Z1)) (not (tptp.product1 Z1 Y Z2)) (tptp.product2 Z2 X Y))) (or (not (tptp.product1 tptp.e_1 tptp.e_2 tptp.e_3)) (not (tptp.product1 tptp.e_3 tptp.e_2 tptp.e_1)) (tptp.product2 tptp.e_1 tptp.e_1 tptp.e_2))) (or (not (tptp.product1 tptp.e_1 tptp.e_2 tptp.e_3)) (not (tptp.product1 tptp.e_3 tptp.e_2 tptp.e_1)) (tptp.product2 tptp.e_1 tptp.e_1 tptp.e_2))) :rule resolution :premises (t82 t83))
% 0.34/0.58 (step t85 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z1 $$unsorted) (Z2 $$unsorted)) (or (not (tptp.product1 X Y Z1)) (not (tptp.product1 Z1 Y Z2)) (tptp.product2 Z2 X Y))) (or (not (tptp.product1 tptp.e_1 tptp.e_2 tptp.e_3)) (not (tptp.product1 tptp.e_3 tptp.e_2 tptp.e_1)) (tptp.product2 tptp.e_1 tptp.e_1 tptp.e_2))) (not (or (not (tptp.product1 tptp.e_1 tptp.e_2 tptp.e_3)) (not (tptp.product1 tptp.e_3 tptp.e_2 tptp.e_1)) (tptp.product2 tptp.e_1 tptp.e_1 tptp.e_2)))) :rule implies_neg2)
% 0.34/0.58 (step t86 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z1 $$unsorted) (Z2 $$unsorted)) (or (not (tptp.product1 X Y Z1)) (not (tptp.product1 Z1 Y Z2)) (tptp.product2 Z2 X Y))) (or (not (tptp.product1 tptp.e_1 tptp.e_2 tptp.e_3)) (not (tptp.product1 tptp.e_3 tptp.e_2 tptp.e_1)) (tptp.product2 tptp.e_1 tptp.e_1 tptp.e_2))) (=> (forall ((X $$unsorted) (Y $$unsorted) (Z1 $$unsorted) (Z2 $$unsorted)) (or (not (tptp.product1 X Y Z1)) (not (tptp.product1 Z1 Y Z2)) (tptp.product2 Z2 X Y))) (or (not (tptp.product1 tptp.e_1 tptp.e_2 tptp.e_3)) (not (tptp.product1 tptp.e_3 tptp.e_2 tptp.e_1)) (tptp.product2 tptp.e_1 tptp.e_1 tptp.e_2)))) :rule resolution :premises (t84 t85))
% 0.34/0.58 (step t87 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z1 $$unsorted) (Z2 $$unsorted)) (or (not (tptp.product1 X Y Z1)) (not (tptp.product1 Z1 Y Z2)) (tptp.product2 Z2 X Y))) (or (not (tptp.product1 tptp.e_1 tptp.e_2 tptp.e_3)) (not (tptp.product1 tptp.e_3 tptp.e_2 tptp.e_1)) (tptp.product2 tptp.e_1 tptp.e_1 tptp.e_2)))) :rule contraction :premises (t86))
% 0.34/0.58 (step t88 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z1 $$unsorted) (Z2 $$unsorted)) (or (not (tptp.product1 X Y Z1)) (not (tptp.product1 Z1 Y Z2)) (tptp.product2 Z2 X Y)))) (or (not (tptp.product1 tptp.e_1 tptp.e_2 tptp.e_3)) (not (tptp.product1 tptp.e_3 tptp.e_2 tptp.e_1)) (tptp.product2 tptp.e_1 tptp.e_1 tptp.e_2))) :rule implies :premises (t87))
% 0.34/0.58 (step t89 (cl (or (not (tptp.product1 tptp.e_1 tptp.e_2 tptp.e_3)) (not (tptp.product1 tptp.e_3 tptp.e_2 tptp.e_1)) (tptp.product2 tptp.e_1 tptp.e_1 tptp.e_2))) :rule resolution :premises (t88 a25))
% 0.34/0.58 (step t90 (cl (not (tptp.product1 tptp.e_3 tptp.e_2 tptp.e_1))) :rule resolution :premises (t62 t81 t58 t89))
% 0.34/0.58 (step t91 (cl (not (or (not (tptp.product1 tptp.e_2 tptp.e_2 tptp.e_2)) (not (tptp.product1 tptp.e_3 tptp.e_2 tptp.e_2)) (tptp.equalish tptp.e_2 tptp.e_3))) (not (tptp.product1 tptp.e_2 tptp.e_2 tptp.e_2)) (not (tptp.product1 tptp.e_3 tptp.e_2 tptp.e_2)) (tptp.equalish tptp.e_2 tptp.e_3)) :rule or_pos)
% 0.34/0.58 (step t92 (cl (tptp.equalish tptp.e_2 tptp.e_3) (not (tptp.product1 tptp.e_2 tptp.e_2 tptp.e_2)) (not (tptp.product1 tptp.e_3 tptp.e_2 tptp.e_2)) (not (or (not (tptp.product1 tptp.e_2 tptp.e_2 tptp.e_2)) (not (tptp.product1 tptp.e_3 tptp.e_2 tptp.e_2)) (tptp.equalish tptp.e_2 tptp.e_3)))) :rule reordering :premises (t91))
% 0.34/0.58 (step t93 (cl (=> (forall ((W $$unsorted) (Y $$unsorted) (X $$unsorted) (Z $$unsorted)) (or (not (tptp.product1 W Y X)) (not (tptp.product1 Z Y X)) (tptp.equalish W Z))) (or (not (tptp.product1 tptp.e_2 tptp.e_2 tptp.e_2)) (not (tptp.product1 tptp.e_3 tptp.e_2 tptp.e_2)) (tptp.equalish tptp.e_2 tptp.e_3))) (forall ((W $$unsorted) (Y $$unsorted) (X $$unsorted) (Z $$unsorted)) (or (not (tptp.product1 W Y X)) (not (tptp.product1 Z Y X)) (tptp.equalish W Z)))) :rule implies_neg1)
% 0.34/0.58 (anchor :step t94)
% 0.34/0.58 (assume t94.a0 (forall ((W $$unsorted) (Y $$unsorted) (X $$unsorted) (Z $$unsorted)) (or (not (tptp.product1 W Y X)) (not (tptp.product1 Z Y X)) (tptp.equalish W Z))))
% 0.34/0.58 (step t94.t1 (cl (or (not (forall ((W $$unsorted) (Y $$unsorted) (X $$unsorted) (Z $$unsorted)) (or (not (tptp.product1 W Y X)) (not (tptp.product1 Z Y X)) (tptp.equalish W Z)))) (or (not (tptp.product1 tptp.e_2 tptp.e_2 tptp.e_2)) (not (tptp.product1 tptp.e_3 tptp.e_2 tptp.e_2)) (tptp.equalish tptp.e_2 tptp.e_3)))) :rule forall_inst :args ((:= W tptp.e_2) (:= Y tptp.e_2) (:= X tptp.e_2) (:= Z tptp.e_3)))
% 0.34/0.58 (step t94.t2 (cl (not (forall ((W $$unsorted) (Y $$unsorted) (X $$unsorted) (Z $$unsorted)) (or (not (tptp.product1 W Y X)) (not (tptp.product1 Z Y X)) (tptp.equalish W Z)))) (or (not (tptp.product1 tptp.e_2 tptp.e_2 tptp.e_2)) (not (tptp.product1 tptp.e_3 tptp.e_2 tptp.e_2)) (tptp.equalish tptp.e_2 tptp.e_3))) :rule or :premises (t94.t1))
% 0.34/0.58 (step t94.t3 (cl (or (not (tptp.product1 tptp.e_2 tptp.e_2 tptp.e_2)) (not (tptp.product1 tptp.e_3 tptp.e_2 tptp.e_2)) (tptp.equalish tptp.e_2 tptp.e_3))) :rule resolution :premises (t94.t2 t94.a0))
% 0.34/0.58 (step t94 (cl (not (forall ((W $$unsorted) (Y $$unsorted) (X $$unsorted) (Z $$unsorted)) (or (not (tptp.product1 W Y X)) (not (tptp.product1 Z Y X)) (tptp.equalish W Z)))) (or (not (tptp.product1 tptp.e_2 tptp.e_2 tptp.e_2)) (not (tptp.product1 tptp.e_3 tptp.e_2 tptp.e_2)) (tptp.equalish tptp.e_2 tptp.e_3))) :rule subproof :discharge (t94.a0))
% 0.34/0.58 (step t95 (cl (=> (forall ((W $$unsorted) (Y $$unsorted) (X $$unsorted) (Z $$unsorted)) (or (not (tptp.product1 W Y X)) (not (tptp.product1 Z Y X)) (tptp.equalish W Z))) (or (not (tptp.product1 tptp.e_2 tptp.e_2 tptp.e_2)) (not (tptp.product1 tptp.e_3 tptp.e_2 tptp.e_2)) (tptp.equalish tptp.e_2 tptp.e_3))) (or (not (tptp.product1 tptp.e_2 tptp.e_2 tptp.e_2)) (not (tptp.product1 tptp.e_3 tptp.e_2 tptp.e_2)) (tptp.equalish tptp.e_2 tptp.e_3))) :rule resolution :premises (t93 t94))
% 0.34/0.58 (step t96 (cl (=> (forall ((W $$unsorted) (Y $$unsorted) (X $$unsorted) (Z $$unsorted)) (or (not (tptp.product1 W Y X)) (not (tptp.product1 Z Y X)) (tptp.equalish W Z))) (or (not (tptp.product1 tptp.e_2 tptp.e_2 tptp.e_2)) (not (tptp.product1 tptp.e_3 tptp.e_2 tptp.e_2)) (tptp.equalish tptp.e_2 tptp.e_3))) (not (or (not (tptp.product1 tptp.e_2 tptp.e_2 tptp.e_2)) (not (tptp.product1 tptp.e_3 tptp.e_2 tptp.e_2)) (tptp.equalish tptp.e_2 tptp.e_3)))) :rule implies_neg2)
% 0.34/0.58 (step t97 (cl (=> (forall ((W $$unsorted) (Y $$unsorted) (X $$unsorted) (Z $$unsorted)) (or (not (tptp.product1 W Y X)) (not (tptp.product1 Z Y X)) (tptp.equalish W Z))) (or (not (tptp.product1 tptp.e_2 tptp.e_2 tptp.e_2)) (not (tptp.product1 tptp.e_3 tptp.e_2 tptp.e_2)) (tptp.equalish tptp.e_2 tptp.e_3))) (=> (forall ((W $$unsorted) (Y $$unsorted) (X $$unsorted) (Z $$unsorted)) (or (not (tptp.product1 W Y X)) (not (tptp.product1 Z Y X)) (tptp.equalish W Z))) (or (not (tptp.product1 tptp.e_2 tptp.e_2 tptp.e_2)) (not (tptp.product1 tptp.e_3 tptp.e_2 tptp.e_2)) (tptp.equalish tptp.e_2 tptp.e_3)))) :rule resolution :premises (t95 t96))
% 0.34/0.58 (step t98 (cl (=> (forall ((W $$unsorted) (Y $$unsorted) (X $$unsorted) (Z $$unsorted)) (or (not (tptp.product1 W Y X)) (not (tptp.product1 Z Y X)) (tptp.equalish W Z))) (or (not (tptp.product1 tptp.e_2 tptp.e_2 tptp.e_2)) (not (tptp.product1 tptp.e_3 tptp.e_2 tptp.e_2)) (tptp.equalish tptp.e_2 tptp.e_3)))) :rule contraction :premises (t97))
% 0.34/0.58 (step t99 (cl (not (forall ((W $$unsorted) (Y $$unsorted) (X $$unsorted) (Z $$unsorted)) (or (not (tptp.product1 W Y X)) (not (tptp.product1 Z Y X)) (tptp.equalish W Z)))) (or (not (tptp.product1 tptp.e_2 tptp.e_2 tptp.e_2)) (not (tptp.product1 tptp.e_3 tptp.e_2 tptp.e_2)) (tptp.equalish tptp.e_2 tptp.e_3))) :rule implies :premises (t98))
% 0.34/0.58 (step t100 (cl (or (not (tptp.product1 tptp.e_2 tptp.e_2 tptp.e_2)) (not (tptp.product1 tptp.e_3 tptp.e_2 tptp.e_2)) (tptp.equalish tptp.e_2 tptp.e_3))) :rule resolution :premises (t99 a18))
% 0.34/0.58 (step t101 (cl (not (tptp.product1 tptp.e_3 tptp.e_2 tptp.e_2))) :rule resolution :premises (t92 a12 t40 t100))
% 0.34/0.58 (step t102 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.group_element X)) (not (tptp.group_element Y)) (tptp.product1 X Y tptp.e_1) (tptp.product1 X Y tptp.e_2) (tptp.product1 X Y tptp.e_3))) (or (not (tptp.group_element tptp.e_3)) (not (tptp.group_element tptp.e_2)) (tptp.product1 tptp.e_3 tptp.e_2 tptp.e_1) (tptp.product1 tptp.e_3 tptp.e_2 tptp.e_2) (tptp.product1 tptp.e_3 tptp.e_2 tptp.e_3))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.group_element X)) (not (tptp.group_element Y)) (tptp.product1 X Y tptp.e_1) (tptp.product1 X Y tptp.e_2) (tptp.product1 X Y tptp.e_3)))) :rule implies_neg1)
% 0.34/0.58 (anchor :step t103)
% 0.34/0.58 (assume t103.a0 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.group_element X)) (not (tptp.group_element Y)) (tptp.product1 X Y tptp.e_1) (tptp.product1 X Y tptp.e_2) (tptp.product1 X Y tptp.e_3))))
% 0.34/0.58 (step t103.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.group_element X)) (not (tptp.group_element Y)) (tptp.product1 X Y tptp.e_1) (tptp.product1 X Y tptp.e_2) (tptp.product1 X Y tptp.e_3)))) (or (not (tptp.group_element tptp.e_3)) (not (tptp.group_element tptp.e_2)) (tptp.product1 tptp.e_3 tptp.e_2 tptp.e_1) (tptp.product1 tptp.e_3 tptp.e_2 tptp.e_2) (tptp.product1 tptp.e_3 tptp.e_2 tptp.e_3)))) :rule forall_inst :args ((:= X tptp.e_3) (:= Y tptp.e_2)))
% 0.34/0.58 (step t103.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.group_element X)) (not (tptp.group_element Y)) (tptp.product1 X Y tptp.e_1) (tptp.product1 X Y tptp.e_2) (tptp.product1 X Y tptp.e_3)))) (or (not (tptp.group_element tptp.e_3)) (not (tptp.group_element tptp.e_2)) (tptp.product1 tptp.e_3 tptp.e_2 tptp.e_1) (tptp.product1 tptp.e_3 tptp.e_2 tptp.e_2) (tptp.product1 tptp.e_3 tptp.e_2 tptp.e_3))) :rule or :premises (t103.t1))
% 0.34/0.58 (step t103.t3 (cl (or (not (tptp.group_element tptp.e_3)) (not (tptp.group_element tptp.e_2)) (tptp.product1 tptp.e_3 tptp.e_2 tptp.e_1) (tptp.product1 tptp.e_3 tptp.e_2 tptp.e_2) (tptp.product1 tptp.e_3 tptp.e_2 tptp.e_3))) :rule resolution :premises (t103.t2 t103.a0))
% 0.34/0.58 (step t103 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.group_element X)) (not (tptp.group_element Y)) (tptp.product1 X Y tptp.e_1) (tptp.product1 X Y tptp.e_2) (tptp.product1 X Y tptp.e_3)))) (or (not (tptp.group_element tptp.e_3)) (not (tptp.group_element tptp.e_2)) (tptp.product1 tptp.e_3 tptp.e_2 tptp.e_1) (tptp.product1 tptp.e_3 tptp.e_2 tptp.e_2) (tptp.product1 tptp.e_3 tptp.e_2 tptp.e_3))) :rule subproof :discharge (t103.a0))
% 0.34/0.58 (step t104 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.group_element X)) (not (tptp.group_element Y)) (tptp.product1 X Y tptp.e_1) (tptp.product1 X Y tptp.e_2) (tptp.product1 X Y tptp.e_3))) (or (not (tptp.group_element tptp.e_3)) (not (tptp.group_element tptp.e_2)) (tptp.product1 tptp.e_3 tptp.e_2 tptp.e_1) (tptp.product1 tptp.e_3 tptp.e_2 tptp.e_2) (tptp.product1 tptp.e_3 tptp.e_2 tptp.e_3))) (or (not (tptp.group_element tptp.e_3)) (not (tptp.group_element tptp.e_2)) (tptp.product1 tptp.e_3 tptp.e_2 tptp.e_1) (tptp.product1 tptp.e_3 tptp.e_2 tptp.e_2) (tptp.product1 tptp.e_3 tptp.e_2 tptp.e_3))) :rule resolution :premises (t102 t103))
% 0.34/0.58 (step t105 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.group_element X)) (not (tptp.group_element Y)) (tptp.product1 X Y tptp.e_1) (tptp.product1 X Y tptp.e_2) (tptp.product1 X Y tptp.e_3))) (or (not (tptp.group_element tptp.e_3)) (not (tptp.group_element tptp.e_2)) (tptp.product1 tptp.e_3 tptp.e_2 tptp.e_1) (tptp.product1 tptp.e_3 tptp.e_2 tptp.e_2) (tptp.product1 tptp.e_3 tptp.e_2 tptp.e_3))) (not (or (not (tptp.group_element tptp.e_3)) (not (tptp.group_element tptp.e_2)) (tptp.product1 tptp.e_3 tptp.e_2 tptp.e_1) (tptp.product1 tptp.e_3 tptp.e_2 tptp.e_2) (tptp.product1 tptp.e_3 tptp.e_2 tptp.e_3)))) :rule implies_neg2)
% 0.34/0.58 (step t106 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.group_element X)) (not (tptp.group_element Y)) (tptp.product1 X Y tptp.e_1) (tptp.product1 X Y tptp.e_2) (tptp.product1 X Y tptp.e_3))) (or (not (tptp.group_element tptp.e_3)) (not (tptp.group_element tptp.e_2)) (tptp.product1 tptp.e_3 tptp.e_2 tptp.e_1) (tptp.product1 tptp.e_3 tptp.e_2 tptp.e_2) (tptp.product1 tptp.e_3 tptp.e_2 tptp.e_3))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.group_element X)) (not (tptp.group_element Y)) (tptp.product1 X Y tptp.e_1) (tptp.product1 X Y tptp.e_2) (tptp.product1 X Y tptp.e_3))) (or (not (tptp.group_element tptp.e_3)) (not (tptp.group_element tptp.e_2)) (tptp.product1 tptp.e_3 tptp.e_2 tptp.e_1) (tptp.product1 tptp.e_3 tptp.e_2 tptp.e_2) (tptp.product1 tptp.e_3 tptp.e_2 tptp.e_3)))) :rule resolution :premises (t104 t105))
% 0.34/0.58 (step t107 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.group_element X)) (not (tptp.group_element Y)) (tptp.product1 X Y tptp.e_1) (tptp.product1 X Y tptp.e_2) (tptp.product1 X Y tptp.e_3))) (or (not (tptp.group_element tptp.e_3)) (not (tptp.group_element tptp.e_2)) (tptp.product1 tptp.e_3 tptp.e_2 tptp.e_1) (tptp.product1 tptp.e_3 tptp.e_2 tptp.e_2) (tptp.product1 tptp.e_3 tptp.e_2 tptp.e_3)))) :rule contraction :premises (t106))
% 0.34/0.58 (step t108 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.group_element X)) (not (tptp.group_element Y)) (tptp.product1 X Y tptp.e_1) (tptp.product1 X Y tptp.e_2) (tptp.product1 X Y tptp.e_3)))) (or (not (tptp.group_element tptp.e_3)) (not (tptp.group_element tptp.e_2)) (tptp.product1 tptp.e_3 tptp.e_2 tptp.e_1) (tptp.product1 tptp.e_3 tptp.e_2 tptp.e_2) (tptp.product1 tptp.e_3 tptp.e_2 tptp.e_3))) :rule implies :premises (t107))
% 0.34/0.58 (step t109 (cl (or (not (tptp.group_element tptp.e_3)) (not (tptp.group_element tptp.e_2)) (tptp.product1 tptp.e_3 tptp.e_2 tptp.e_1) (tptp.product1 tptp.e_3 tptp.e_2 tptp.e_2) (tptp.product1 tptp.e_3 tptp.e_2 tptp.e_3))) :rule resolution :premises (t108 a15))
% 0.34/0.58 (step t110 (cl (tptp.product1 tptp.e_3 tptp.e_2 tptp.e_3)) :rule resolution :premises (t60 a7 a8 t90 t101 t109))
% 0.34/0.58 (step t111 (cl (not (or (not (tptp.product1 tptp.e_1 tptp.e_2 tptp.e_3)) (not (tptp.product1 tptp.e_3 tptp.e_2 tptp.e_3)) (tptp.equalish tptp.e_1 tptp.e_3)))) :rule resolution :premises (t9 a10 t58 t110))
% 0.34/0.58 (step t112 (cl) :rule resolution :premises (t7 t111 a18))
% 0.34/0.58
% 0.34/0.58 % SZS output end Proof for /export/starexec/sandbox2/tmp/tmp.LsbbrUa3xC/cvc5---1.0.5_14373.smt2
% 0.34/0.59 % cvc5---1.0.5 exiting
% 0.34/0.59 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------