TSTP Solution File: GRP123-1.003 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : GRP123-1.003 : TPTP v8.2.0. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : do_cvc5 %s %d
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed May 29 16:53:04 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
% 0.07/0.12 % Problem : GRP123-1.003 : TPTP v8.2.0. Released v1.2.0.
% 0.07/0.14 % Command : do_cvc5 %s %d
% 0.14/0.34 % Computer : n014.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Sun May 26 17:24:24 EDT 2024
% 0.14/0.34 % CPUTime :
% 0.20/0.48 %----Proving TF0_NAR, FOF, or CNF
% 0.20/0.49 --- 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/sandbox2/tmp/tmp.q6TbueFETy/cvc5---1.0.5_11886.smt2
% 0.20/0.53 % SZS output start Proof for /export/starexec/sandbox2/tmp/tmp.q6TbueFETy/cvc5---1.0.5_11886.smt2
% 0.20/0.53 (assume a0 (tptp.group_element tptp.e_1))
% 0.20/0.53 (assume a1 (tptp.group_element tptp.e_2))
% 0.20/0.53 (assume a2 (tptp.group_element tptp.e_3))
% 0.20/0.53 (assume a3 (not (tptp.equalish tptp.e_1 tptp.e_2)))
% 0.20/0.53 (assume a4 (not (tptp.equalish tptp.e_1 tptp.e_3)))
% 0.20/0.53 (assume a5 (not (tptp.equalish tptp.e_2 tptp.e_1)))
% 0.20/0.53 (assume a6 (not (tptp.equalish tptp.e_2 tptp.e_3)))
% 0.20/0.53 (assume a7 (not (tptp.equalish tptp.e_3 tptp.e_1)))
% 0.20/0.53 (assume a8 (not (tptp.equalish tptp.e_3 tptp.e_2)))
% 0.20/0.53 (assume a9 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.group_element X)) (not (tptp.group_element Y)) (tptp.product X Y tptp.e_1) (tptp.product X Y tptp.e_2) (tptp.product X Y tptp.e_3))))
% 0.20/0.53 (assume a10 (forall ((X $$unsorted) (Y $$unsorted) (W $$unsorted) (Z $$unsorted)) (or (not (tptp.product X Y W)) (not (tptp.product X Y Z)) (tptp.equalish W Z))))
% 0.20/0.53 (assume a11 (forall ((X $$unsorted) (W $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.product X W Y)) (not (tptp.product X Z Y)) (tptp.equalish W Z))))
% 0.20/0.53 (assume a12 (forall ((W $$unsorted) (Y $$unsorted) (X $$unsorted) (Z $$unsorted)) (or (not (tptp.product W Y X)) (not (tptp.product Z Y X)) (tptp.equalish W Z))))
% 0.20/0.53 (assume a13 (forall ((X $$unsorted)) (tptp.product X X X)))
% 0.20/0.53 (assume a14 (forall ((X1 $$unsorted) (Y1 $$unsorted) (Z1 $$unsorted) (X2 $$unsorted) (Y2 $$unsorted) (Z2 $$unsorted)) (or (not (tptp.product X1 Y1 Z1)) (not (tptp.product X2 Y2 Z1)) (not (tptp.product Z2 Y1 X1)) (not (tptp.product Z2 Y2 X2)) (tptp.equalish X1 X2))))
% 0.20/0.53 (assume a15 (forall ((X1 $$unsorted) (Y1 $$unsorted) (Z1 $$unsorted) (X2 $$unsorted) (Y2 $$unsorted) (Z2 $$unsorted)) (or (not (tptp.product X1 Y1 Z1)) (not (tptp.product X2 Y2 Z1)) (not (tptp.product Z2 Y1 X1)) (not (tptp.product Z2 Y2 X2)) (tptp.equalish Y1 Y2))))
% 0.20/0.53 (step t1 (cl (=> (forall ((X $$unsorted) (W $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.product X W Y)) (not (tptp.product X Z Y)) (tptp.equalish W Z))) (or (not (tptp.product tptp.e_2 tptp.e_1 tptp.e_2)) (not (tptp.product tptp.e_2 tptp.e_2 tptp.e_2)) (tptp.equalish tptp.e_1 tptp.e_2))) (forall ((X $$unsorted) (W $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.product X W Y)) (not (tptp.product X Z Y)) (tptp.equalish W Z)))) :rule implies_neg1)
% 0.20/0.53 (anchor :step t2)
% 0.20/0.53 (assume t2.a0 (forall ((X $$unsorted) (W $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.product X W Y)) (not (tptp.product X Z Y)) (tptp.equalish W Z))))
% 0.20/0.53 (step t2.t1 (cl (or (not (forall ((X $$unsorted) (W $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.product X W Y)) (not (tptp.product X Z Y)) (tptp.equalish W Z)))) (or (not (tptp.product tptp.e_2 tptp.e_1 tptp.e_2)) (not (tptp.product tptp.e_2 tptp.e_2 tptp.e_2)) (tptp.equalish tptp.e_1 tptp.e_2)))) :rule forall_inst :args ((:= X tptp.e_2) (:= W tptp.e_1) (:= Y tptp.e_2) (:= Z tptp.e_2)))
% 0.20/0.53 (step t2.t2 (cl (not (forall ((X $$unsorted) (W $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.product X W Y)) (not (tptp.product X Z Y)) (tptp.equalish W Z)))) (or (not (tptp.product tptp.e_2 tptp.e_1 tptp.e_2)) (not (tptp.product tptp.e_2 tptp.e_2 tptp.e_2)) (tptp.equalish tptp.e_1 tptp.e_2))) :rule or :premises (t2.t1))
% 0.20/0.53 (step t2.t3 (cl (or (not (tptp.product tptp.e_2 tptp.e_1 tptp.e_2)) (not (tptp.product tptp.e_2 tptp.e_2 tptp.e_2)) (tptp.equalish tptp.e_1 tptp.e_2))) :rule resolution :premises (t2.t2 t2.a0))
% 0.20/0.53 (step t2 (cl (not (forall ((X $$unsorted) (W $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.product X W Y)) (not (tptp.product X Z Y)) (tptp.equalish W Z)))) (or (not (tptp.product tptp.e_2 tptp.e_1 tptp.e_2)) (not (tptp.product tptp.e_2 tptp.e_2 tptp.e_2)) (tptp.equalish tptp.e_1 tptp.e_2))) :rule subproof :discharge (t2.a0))
% 0.20/0.53 (step t3 (cl (=> (forall ((X $$unsorted) (W $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.product X W Y)) (not (tptp.product X Z Y)) (tptp.equalish W Z))) (or (not (tptp.product tptp.e_2 tptp.e_1 tptp.e_2)) (not (tptp.product tptp.e_2 tptp.e_2 tptp.e_2)) (tptp.equalish tptp.e_1 tptp.e_2))) (or (not (tptp.product tptp.e_2 tptp.e_1 tptp.e_2)) (not (tptp.product tptp.e_2 tptp.e_2 tptp.e_2)) (tptp.equalish tptp.e_1 tptp.e_2))) :rule resolution :premises (t1 t2))
% 0.20/0.53 (step t4 (cl (=> (forall ((X $$unsorted) (W $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.product X W Y)) (not (tptp.product X Z Y)) (tptp.equalish W Z))) (or (not (tptp.product tptp.e_2 tptp.e_1 tptp.e_2)) (not (tptp.product tptp.e_2 tptp.e_2 tptp.e_2)) (tptp.equalish tptp.e_1 tptp.e_2))) (not (or (not (tptp.product tptp.e_2 tptp.e_1 tptp.e_2)) (not (tptp.product tptp.e_2 tptp.e_2 tptp.e_2)) (tptp.equalish tptp.e_1 tptp.e_2)))) :rule implies_neg2)
% 0.20/0.53 (step t5 (cl (=> (forall ((X $$unsorted) (W $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.product X W Y)) (not (tptp.product X Z Y)) (tptp.equalish W Z))) (or (not (tptp.product tptp.e_2 tptp.e_1 tptp.e_2)) (not (tptp.product tptp.e_2 tptp.e_2 tptp.e_2)) (tptp.equalish tptp.e_1 tptp.e_2))) (=> (forall ((X $$unsorted) (W $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.product X W Y)) (not (tptp.product X Z Y)) (tptp.equalish W Z))) (or (not (tptp.product tptp.e_2 tptp.e_1 tptp.e_2)) (not (tptp.product tptp.e_2 tptp.e_2 tptp.e_2)) (tptp.equalish tptp.e_1 tptp.e_2)))) :rule resolution :premises (t3 t4))
% 0.20/0.53 (step t6 (cl (=> (forall ((X $$unsorted) (W $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.product X W Y)) (not (tptp.product X Z Y)) (tptp.equalish W Z))) (or (not (tptp.product tptp.e_2 tptp.e_1 tptp.e_2)) (not (tptp.product tptp.e_2 tptp.e_2 tptp.e_2)) (tptp.equalish tptp.e_1 tptp.e_2)))) :rule contraction :premises (t5))
% 0.20/0.53 (step t7 (cl (not (forall ((X $$unsorted) (W $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.product X W Y)) (not (tptp.product X Z Y)) (tptp.equalish W Z)))) (or (not (tptp.product tptp.e_2 tptp.e_1 tptp.e_2)) (not (tptp.product tptp.e_2 tptp.e_2 tptp.e_2)) (tptp.equalish tptp.e_1 tptp.e_2))) :rule implies :premises (t6))
% 0.20/0.53 (step t8 (cl (not (or (not (tptp.product tptp.e_2 tptp.e_1 tptp.e_2)) (not (tptp.product tptp.e_2 tptp.e_2 tptp.e_2)) (tptp.equalish tptp.e_1 tptp.e_2))) (not (tptp.product tptp.e_2 tptp.e_1 tptp.e_2)) (not (tptp.product tptp.e_2 tptp.e_2 tptp.e_2)) (tptp.equalish tptp.e_1 tptp.e_2)) :rule or_pos)
% 0.20/0.53 (step t9 (cl (tptp.equalish tptp.e_1 tptp.e_2) (not (tptp.product tptp.e_2 tptp.e_2 tptp.e_2)) (not (tptp.product tptp.e_2 tptp.e_1 tptp.e_2)) (not (or (not (tptp.product tptp.e_2 tptp.e_1 tptp.e_2)) (not (tptp.product tptp.e_2 tptp.e_2 tptp.e_2)) (tptp.equalish tptp.e_1 tptp.e_2)))) :rule reordering :premises (t8))
% 0.20/0.53 (step t10 (cl (=> (forall ((X $$unsorted)) (tptp.product X X X)) (tptp.product tptp.e_2 tptp.e_2 tptp.e_2)) (forall ((X $$unsorted)) (tptp.product X X X))) :rule implies_neg1)
% 0.20/0.53 (anchor :step t11)
% 0.20/0.53 (assume t11.a0 (forall ((X $$unsorted)) (tptp.product X X X)))
% 0.20/0.53 (step t11.t1 (cl (or (not (forall ((X $$unsorted)) (tptp.product X X X))) (tptp.product tptp.e_2 tptp.e_2 tptp.e_2))) :rule forall_inst :args ((:= X tptp.e_2)))
% 0.20/0.53 (step t11.t2 (cl (not (forall ((X $$unsorted)) (tptp.product X X X))) (tptp.product tptp.e_2 tptp.e_2 tptp.e_2)) :rule or :premises (t11.t1))
% 0.20/0.53 (step t11.t3 (cl (tptp.product tptp.e_2 tptp.e_2 tptp.e_2)) :rule resolution :premises (t11.t2 t11.a0))
% 0.20/0.53 (step t11 (cl (not (forall ((X $$unsorted)) (tptp.product X X X))) (tptp.product tptp.e_2 tptp.e_2 tptp.e_2)) :rule subproof :discharge (t11.a0))
% 0.20/0.53 (step t12 (cl (=> (forall ((X $$unsorted)) (tptp.product X X X)) (tptp.product tptp.e_2 tptp.e_2 tptp.e_2)) (tptp.product tptp.e_2 tptp.e_2 tptp.e_2)) :rule resolution :premises (t10 t11))
% 0.20/0.53 (step t13 (cl (=> (forall ((X $$unsorted)) (tptp.product X X X)) (tptp.product tptp.e_2 tptp.e_2 tptp.e_2)) (not (tptp.product tptp.e_2 tptp.e_2 tptp.e_2))) :rule implies_neg2)
% 0.20/0.53 (step t14 (cl (=> (forall ((X $$unsorted)) (tptp.product X X X)) (tptp.product tptp.e_2 tptp.e_2 tptp.e_2)) (=> (forall ((X $$unsorted)) (tptp.product X X X)) (tptp.product tptp.e_2 tptp.e_2 tptp.e_2))) :rule resolution :premises (t12 t13))
% 0.20/0.53 (step t15 (cl (=> (forall ((X $$unsorted)) (tptp.product X X X)) (tptp.product tptp.e_2 tptp.e_2 tptp.e_2))) :rule contraction :premises (t14))
% 0.20/0.53 (step t16 (cl (not (forall ((X $$unsorted)) (tptp.product X X X))) (tptp.product tptp.e_2 tptp.e_2 tptp.e_2)) :rule implies :premises (t15))
% 0.20/0.53 (step t17 (cl (tptp.product tptp.e_2 tptp.e_2 tptp.e_2)) :rule resolution :premises (t16 a13))
% 0.20/0.53 (step t18 (cl (not (or (not (tptp.group_element tptp.e_2)) (not (tptp.group_element tptp.e_1)) (tptp.product tptp.e_2 tptp.e_1 tptp.e_1) (tptp.product tptp.e_2 tptp.e_1 tptp.e_2) (tptp.product tptp.e_2 tptp.e_1 tptp.e_3))) (not (tptp.group_element tptp.e_2)) (not (tptp.group_element tptp.e_1)) (tptp.product tptp.e_2 tptp.e_1 tptp.e_1) (tptp.product tptp.e_2 tptp.e_1 tptp.e_2) (tptp.product tptp.e_2 tptp.e_1 tptp.e_3)) :rule or_pos)
% 0.20/0.53 (step t19 (cl (not (tptp.group_element tptp.e_1)) (not (tptp.group_element tptp.e_2)) (tptp.product tptp.e_2 tptp.e_1 tptp.e_1) (tptp.product tptp.e_2 tptp.e_1 tptp.e_2) (tptp.product tptp.e_2 tptp.e_1 tptp.e_3) (not (or (not (tptp.group_element tptp.e_2)) (not (tptp.group_element tptp.e_1)) (tptp.product tptp.e_2 tptp.e_1 tptp.e_1) (tptp.product tptp.e_2 tptp.e_1 tptp.e_2) (tptp.product tptp.e_2 tptp.e_1 tptp.e_3)))) :rule reordering :premises (t18))
% 0.20/0.53 (step t20 (cl (not (or (not (tptp.product tptp.e_1 tptp.e_1 tptp.e_1)) (not (tptp.product tptp.e_2 tptp.e_1 tptp.e_1)) (tptp.equalish tptp.e_1 tptp.e_2))) (not (tptp.product tptp.e_1 tptp.e_1 tptp.e_1)) (not (tptp.product tptp.e_2 tptp.e_1 tptp.e_1)) (tptp.equalish tptp.e_1 tptp.e_2)) :rule or_pos)
% 0.20/0.53 (step t21 (cl (tptp.equalish tptp.e_1 tptp.e_2) (not (tptp.product tptp.e_1 tptp.e_1 tptp.e_1)) (not (tptp.product tptp.e_2 tptp.e_1 tptp.e_1)) (not (or (not (tptp.product tptp.e_1 tptp.e_1 tptp.e_1)) (not (tptp.product tptp.e_2 tptp.e_1 tptp.e_1)) (tptp.equalish tptp.e_1 tptp.e_2)))) :rule reordering :premises (t20))
% 0.20/0.53 (step t22 (cl (=> (forall ((X $$unsorted)) (tptp.product X X X)) (tptp.product tptp.e_1 tptp.e_1 tptp.e_1)) (forall ((X $$unsorted)) (tptp.product X X X))) :rule implies_neg1)
% 0.20/0.53 (anchor :step t23)
% 0.20/0.53 (assume t23.a0 (forall ((X $$unsorted)) (tptp.product X X X)))
% 0.20/0.53 (step t23.t1 (cl (or (not (forall ((X $$unsorted)) (tptp.product X X X))) (tptp.product tptp.e_1 tptp.e_1 tptp.e_1))) :rule forall_inst :args ((:= X tptp.e_1)))
% 0.20/0.53 (step t23.t2 (cl (not (forall ((X $$unsorted)) (tptp.product X X X))) (tptp.product tptp.e_1 tptp.e_1 tptp.e_1)) :rule or :premises (t23.t1))
% 0.20/0.53 (step t23.t3 (cl (tptp.product tptp.e_1 tptp.e_1 tptp.e_1)) :rule resolution :premises (t23.t2 t23.a0))
% 0.20/0.53 (step t23 (cl (not (forall ((X $$unsorted)) (tptp.product X X X))) (tptp.product tptp.e_1 tptp.e_1 tptp.e_1)) :rule subproof :discharge (t23.a0))
% 0.20/0.53 (step t24 (cl (=> (forall ((X $$unsorted)) (tptp.product X X X)) (tptp.product tptp.e_1 tptp.e_1 tptp.e_1)) (tptp.product tptp.e_1 tptp.e_1 tptp.e_1)) :rule resolution :premises (t22 t23))
% 0.20/0.53 (step t25 (cl (=> (forall ((X $$unsorted)) (tptp.product X X X)) (tptp.product tptp.e_1 tptp.e_1 tptp.e_1)) (not (tptp.product tptp.e_1 tptp.e_1 tptp.e_1))) :rule implies_neg2)
% 0.20/0.53 (step t26 (cl (=> (forall ((X $$unsorted)) (tptp.product X X X)) (tptp.product tptp.e_1 tptp.e_1 tptp.e_1)) (=> (forall ((X $$unsorted)) (tptp.product X X X)) (tptp.product tptp.e_1 tptp.e_1 tptp.e_1))) :rule resolution :premises (t24 t25))
% 0.20/0.53 (step t27 (cl (=> (forall ((X $$unsorted)) (tptp.product X X X)) (tptp.product tptp.e_1 tptp.e_1 tptp.e_1))) :rule contraction :premises (t26))
% 0.20/0.53 (step t28 (cl (not (forall ((X $$unsorted)) (tptp.product X X X))) (tptp.product tptp.e_1 tptp.e_1 tptp.e_1)) :rule implies :premises (t27))
% 0.20/0.53 (step t29 (cl (tptp.product tptp.e_1 tptp.e_1 tptp.e_1)) :rule resolution :premises (t28 a13))
% 0.20/0.53 (step t30 (cl (=> (forall ((W $$unsorted) (Y $$unsorted) (X $$unsorted) (Z $$unsorted)) (or (not (tptp.product W Y X)) (not (tptp.product Z Y X)) (tptp.equalish W Z))) (or (not (tptp.product tptp.e_1 tptp.e_1 tptp.e_1)) (not (tptp.product tptp.e_2 tptp.e_1 tptp.e_1)) (tptp.equalish tptp.e_1 tptp.e_2))) (forall ((W $$unsorted) (Y $$unsorted) (X $$unsorted) (Z $$unsorted)) (or (not (tptp.product W Y X)) (not (tptp.product Z Y X)) (tptp.equalish W Z)))) :rule implies_neg1)
% 0.20/0.53 (anchor :step t31)
% 0.20/0.53 (assume t31.a0 (forall ((W $$unsorted) (Y $$unsorted) (X $$unsorted) (Z $$unsorted)) (or (not (tptp.product W Y X)) (not (tptp.product Z Y X)) (tptp.equalish W Z))))
% 0.20/0.53 (step t31.t1 (cl (or (not (forall ((W $$unsorted) (Y $$unsorted) (X $$unsorted) (Z $$unsorted)) (or (not (tptp.product W Y X)) (not (tptp.product Z Y X)) (tptp.equalish W Z)))) (or (not (tptp.product tptp.e_1 tptp.e_1 tptp.e_1)) (not (tptp.product tptp.e_2 tptp.e_1 tptp.e_1)) (tptp.equalish tptp.e_1 tptp.e_2)))) :rule forall_inst :args ((:= W tptp.e_1) (:= Y tptp.e_1) (:= X tptp.e_1) (:= Z tptp.e_2)))
% 0.20/0.53 (step t31.t2 (cl (not (forall ((W $$unsorted) (Y $$unsorted) (X $$unsorted) (Z $$unsorted)) (or (not (tptp.product W Y X)) (not (tptp.product Z Y X)) (tptp.equalish W Z)))) (or (not (tptp.product tptp.e_1 tptp.e_1 tptp.e_1)) (not (tptp.product tptp.e_2 tptp.e_1 tptp.e_1)) (tptp.equalish tptp.e_1 tptp.e_2))) :rule or :premises (t31.t1))
% 0.20/0.53 (step t31.t3 (cl (or (not (tptp.product tptp.e_1 tptp.e_1 tptp.e_1)) (not (tptp.product tptp.e_2 tptp.e_1 tptp.e_1)) (tptp.equalish tptp.e_1 tptp.e_2))) :rule resolution :premises (t31.t2 t31.a0))
% 0.20/0.53 (step t31 (cl (not (forall ((W $$unsorted) (Y $$unsorted) (X $$unsorted) (Z $$unsorted)) (or (not (tptp.product W Y X)) (not (tptp.product Z Y X)) (tptp.equalish W Z)))) (or (not (tptp.product tptp.e_1 tptp.e_1 tptp.e_1)) (not (tptp.product tptp.e_2 tptp.e_1 tptp.e_1)) (tptp.equalish tptp.e_1 tptp.e_2))) :rule subproof :discharge (t31.a0))
% 0.20/0.53 (step t32 (cl (=> (forall ((W $$unsorted) (Y $$unsorted) (X $$unsorted) (Z $$unsorted)) (or (not (tptp.product W Y X)) (not (tptp.product Z Y X)) (tptp.equalish W Z))) (or (not (tptp.product tptp.e_1 tptp.e_1 tptp.e_1)) (not (tptp.product tptp.e_2 tptp.e_1 tptp.e_1)) (tptp.equalish tptp.e_1 tptp.e_2))) (or (not (tptp.product tptp.e_1 tptp.e_1 tptp.e_1)) (not (tptp.product tptp.e_2 tptp.e_1 tptp.e_1)) (tptp.equalish tptp.e_1 tptp.e_2))) :rule resolution :premises (t30 t31))
% 0.20/0.53 (step t33 (cl (=> (forall ((W $$unsorted) (Y $$unsorted) (X $$unsorted) (Z $$unsorted)) (or (not (tptp.product W Y X)) (not (tptp.product Z Y X)) (tptp.equalish W Z))) (or (not (tptp.product tptp.e_1 tptp.e_1 tptp.e_1)) (not (tptp.product tptp.e_2 tptp.e_1 tptp.e_1)) (tptp.equalish tptp.e_1 tptp.e_2))) (not (or (not (tptp.product tptp.e_1 tptp.e_1 tptp.e_1)) (not (tptp.product tptp.e_2 tptp.e_1 tptp.e_1)) (tptp.equalish tptp.e_1 tptp.e_2)))) :rule implies_neg2)
% 0.20/0.53 (step t34 (cl (=> (forall ((W $$unsorted) (Y $$unsorted) (X $$unsorted) (Z $$unsorted)) (or (not (tptp.product W Y X)) (not (tptp.product Z Y X)) (tptp.equalish W Z))) (or (not (tptp.product tptp.e_1 tptp.e_1 tptp.e_1)) (not (tptp.product tptp.e_2 tptp.e_1 tptp.e_1)) (tptp.equalish tptp.e_1 tptp.e_2))) (=> (forall ((W $$unsorted) (Y $$unsorted) (X $$unsorted) (Z $$unsorted)) (or (not (tptp.product W Y X)) (not (tptp.product Z Y X)) (tptp.equalish W Z))) (or (not (tptp.product tptp.e_1 tptp.e_1 tptp.e_1)) (not (tptp.product tptp.e_2 tptp.e_1 tptp.e_1)) (tptp.equalish tptp.e_1 tptp.e_2)))) :rule resolution :premises (t32 t33))
% 0.20/0.53 (step t35 (cl (=> (forall ((W $$unsorted) (Y $$unsorted) (X $$unsorted) (Z $$unsorted)) (or (not (tptp.product W Y X)) (not (tptp.product Z Y X)) (tptp.equalish W Z))) (or (not (tptp.product tptp.e_1 tptp.e_1 tptp.e_1)) (not (tptp.product tptp.e_2 tptp.e_1 tptp.e_1)) (tptp.equalish tptp.e_1 tptp.e_2)))) :rule contraction :premises (t34))
% 0.20/0.53 (step t36 (cl (not (forall ((W $$unsorted) (Y $$unsorted) (X $$unsorted) (Z $$unsorted)) (or (not (tptp.product W Y X)) (not (tptp.product Z Y X)) (tptp.equalish W Z)))) (or (not (tptp.product tptp.e_1 tptp.e_1 tptp.e_1)) (not (tptp.product tptp.e_2 tptp.e_1 tptp.e_1)) (tptp.equalish tptp.e_1 tptp.e_2))) :rule implies :premises (t35))
% 0.20/0.53 (step t37 (cl (or (not (tptp.product tptp.e_1 tptp.e_1 tptp.e_1)) (not (tptp.product tptp.e_2 tptp.e_1 tptp.e_1)) (tptp.equalish tptp.e_1 tptp.e_2))) :rule resolution :premises (t36 a12))
% 0.20/0.53 (step t38 (cl (not (tptp.product tptp.e_2 tptp.e_1 tptp.e_1))) :rule resolution :premises (t21 a3 t29 t37))
% 0.20/0.53 (step t39 (cl (not (or (not (tptp.group_element tptp.e_3)) (not (tptp.group_element tptp.e_1)) (tptp.product tptp.e_3 tptp.e_1 tptp.e_1) (tptp.product tptp.e_3 tptp.e_1 tptp.e_2) (tptp.product tptp.e_3 tptp.e_1 tptp.e_3))) (not (tptp.group_element tptp.e_3)) (not (tptp.group_element tptp.e_1)) (tptp.product tptp.e_3 tptp.e_1 tptp.e_1) (tptp.product tptp.e_3 tptp.e_1 tptp.e_2) (tptp.product tptp.e_3 tptp.e_1 tptp.e_3)) :rule or_pos)
% 0.20/0.53 (step t40 (cl (not (tptp.group_element tptp.e_1)) (not (tptp.group_element tptp.e_3)) (tptp.product tptp.e_3 tptp.e_1 tptp.e_1) (tptp.product tptp.e_3 tptp.e_1 tptp.e_2) (tptp.product tptp.e_3 tptp.e_1 tptp.e_3) (not (or (not (tptp.group_element tptp.e_3)) (not (tptp.group_element tptp.e_1)) (tptp.product tptp.e_3 tptp.e_1 tptp.e_1) (tptp.product tptp.e_3 tptp.e_1 tptp.e_2) (tptp.product tptp.e_3 tptp.e_1 tptp.e_3)))) :rule reordering :premises (t39))
% 0.20/0.53 (step t41 (cl (not (or (not (tptp.product tptp.e_1 tptp.e_1 tptp.e_1)) (not (tptp.product tptp.e_3 tptp.e_1 tptp.e_1)) (tptp.equalish tptp.e_1 tptp.e_3))) (not (tptp.product tptp.e_1 tptp.e_1 tptp.e_1)) (not (tptp.product tptp.e_3 tptp.e_1 tptp.e_1)) (tptp.equalish tptp.e_1 tptp.e_3)) :rule or_pos)
% 0.20/0.53 (step t42 (cl (tptp.equalish tptp.e_1 tptp.e_3) (not (tptp.product tptp.e_1 tptp.e_1 tptp.e_1)) (not (tptp.product tptp.e_3 tptp.e_1 tptp.e_1)) (not (or (not (tptp.product tptp.e_1 tptp.e_1 tptp.e_1)) (not (tptp.product tptp.e_3 tptp.e_1 tptp.e_1)) (tptp.equalish tptp.e_1 tptp.e_3)))) :rule reordering :premises (t41))
% 0.20/0.53 (step t43 (cl (=> (forall ((W $$unsorted) (Y $$unsorted) (X $$unsorted) (Z $$unsorted)) (or (not (tptp.product W Y X)) (not (tptp.product Z Y X)) (tptp.equalish W Z))) (or (not (tptp.product tptp.e_1 tptp.e_1 tptp.e_1)) (not (tptp.product tptp.e_3 tptp.e_1 tptp.e_1)) (tptp.equalish tptp.e_1 tptp.e_3))) (forall ((W $$unsorted) (Y $$unsorted) (X $$unsorted) (Z $$unsorted)) (or (not (tptp.product W Y X)) (not (tptp.product Z Y X)) (tptp.equalish W Z)))) :rule implies_neg1)
% 0.20/0.53 (anchor :step t44)
% 0.20/0.53 (assume t44.a0 (forall ((W $$unsorted) (Y $$unsorted) (X $$unsorted) (Z $$unsorted)) (or (not (tptp.product W Y X)) (not (tptp.product Z Y X)) (tptp.equalish W Z))))
% 0.20/0.53 (step t44.t1 (cl (or (not (forall ((W $$unsorted) (Y $$unsorted) (X $$unsorted) (Z $$unsorted)) (or (not (tptp.product W Y X)) (not (tptp.product Z Y X)) (tptp.equalish W Z)))) (or (not (tptp.product tptp.e_1 tptp.e_1 tptp.e_1)) (not (tptp.product tptp.e_3 tptp.e_1 tptp.e_1)) (tptp.equalish tptp.e_1 tptp.e_3)))) :rule forall_inst :args ((:= W tptp.e_1) (:= Y tptp.e_1) (:= X tptp.e_1) (:= Z tptp.e_3)))
% 0.20/0.53 (step t44.t2 (cl (not (forall ((W $$unsorted) (Y $$unsorted) (X $$unsorted) (Z $$unsorted)) (or (not (tptp.product W Y X)) (not (tptp.product Z Y X)) (tptp.equalish W Z)))) (or (not (tptp.product tptp.e_1 tptp.e_1 tptp.e_1)) (not (tptp.product tptp.e_3 tptp.e_1 tptp.e_1)) (tptp.equalish tptp.e_1 tptp.e_3))) :rule or :premises (t44.t1))
% 0.20/0.53 (step t44.t3 (cl (or (not (tptp.product tptp.e_1 tptp.e_1 tptp.e_1)) (not (tptp.product tptp.e_3 tptp.e_1 tptp.e_1)) (tptp.equalish tptp.e_1 tptp.e_3))) :rule resolution :premises (t44.t2 t44.a0))
% 0.20/0.53 (step t44 (cl (not (forall ((W $$unsorted) (Y $$unsorted) (X $$unsorted) (Z $$unsorted)) (or (not (tptp.product W Y X)) (not (tptp.product Z Y X)) (tptp.equalish W Z)))) (or (not (tptp.product tptp.e_1 tptp.e_1 tptp.e_1)) (not (tptp.product tptp.e_3 tptp.e_1 tptp.e_1)) (tptp.equalish tptp.e_1 tptp.e_3))) :rule subproof :discharge (t44.a0))
% 0.20/0.53 (step t45 (cl (=> (forall ((W $$unsorted) (Y $$unsorted) (X $$unsorted) (Z $$unsorted)) (or (not (tptp.product W Y X)) (not (tptp.product Z Y X)) (tptp.equalish W Z))) (or (not (tptp.product tptp.e_1 tptp.e_1 tptp.e_1)) (not (tptp.product tptp.e_3 tptp.e_1 tptp.e_1)) (tptp.equalish tptp.e_1 tptp.e_3))) (or (not (tptp.product tptp.e_1 tptp.e_1 tptp.e_1)) (not (tptp.product tptp.e_3 tptp.e_1 tptp.e_1)) (tptp.equalish tptp.e_1 tptp.e_3))) :rule resolution :premises (t43 t44))
% 0.20/0.53 (step t46 (cl (=> (forall ((W $$unsorted) (Y $$unsorted) (X $$unsorted) (Z $$unsorted)) (or (not (tptp.product W Y X)) (not (tptp.product Z Y X)) (tptp.equalish W Z))) (or (not (tptp.product tptp.e_1 tptp.e_1 tptp.e_1)) (not (tptp.product tptp.e_3 tptp.e_1 tptp.e_1)) (tptp.equalish tptp.e_1 tptp.e_3))) (not (or (not (tptp.product tptp.e_1 tptp.e_1 tptp.e_1)) (not (tptp.product tptp.e_3 tptp.e_1 tptp.e_1)) (tptp.equalish tptp.e_1 tptp.e_3)))) :rule implies_neg2)
% 0.20/0.53 (step t47 (cl (=> (forall ((W $$unsorted) (Y $$unsorted) (X $$unsorted) (Z $$unsorted)) (or (not (tptp.product W Y X)) (not (tptp.product Z Y X)) (tptp.equalish W Z))) (or (not (tptp.product tptp.e_1 tptp.e_1 tptp.e_1)) (not (tptp.product tptp.e_3 tptp.e_1 tptp.e_1)) (tptp.equalish tptp.e_1 tptp.e_3))) (=> (forall ((W $$unsorted) (Y $$unsorted) (X $$unsorted) (Z $$unsorted)) (or (not (tptp.product W Y X)) (not (tptp.product Z Y X)) (tptp.equalish W Z))) (or (not (tptp.product tptp.e_1 tptp.e_1 tptp.e_1)) (not (tptp.product tptp.e_3 tptp.e_1 tptp.e_1)) (tptp.equalish tptp.e_1 tptp.e_3)))) :rule resolution :premises (t45 t46))
% 0.20/0.53 (step t48 (cl (=> (forall ((W $$unsorted) (Y $$unsorted) (X $$unsorted) (Z $$unsorted)) (or (not (tptp.product W Y X)) (not (tptp.product Z Y X)) (tptp.equalish W Z))) (or (not (tptp.product tptp.e_1 tptp.e_1 tptp.e_1)) (not (tptp.product tptp.e_3 tptp.e_1 tptp.e_1)) (tptp.equalish tptp.e_1 tptp.e_3)))) :rule contraction :premises (t47))
% 0.20/0.53 (step t49 (cl (not (forall ((W $$unsorted) (Y $$unsorted) (X $$unsorted) (Z $$unsorted)) (or (not (tptp.product W Y X)) (not (tptp.product Z Y X)) (tptp.equalish W Z)))) (or (not (tptp.product tptp.e_1 tptp.e_1 tptp.e_1)) (not (tptp.product tptp.e_3 tptp.e_1 tptp.e_1)) (tptp.equalish tptp.e_1 tptp.e_3))) :rule implies :premises (t48))
% 0.20/0.53 (step t50 (cl (or (not (tptp.product tptp.e_1 tptp.e_1 tptp.e_1)) (not (tptp.product tptp.e_3 tptp.e_1 tptp.e_1)) (tptp.equalish tptp.e_1 tptp.e_3))) :rule resolution :premises (t49 a12))
% 0.20/0.53 (step t51 (cl (not (tptp.product tptp.e_3 tptp.e_1 tptp.e_1))) :rule resolution :premises (t42 a4 t29 t50))
% 0.20/0.53 (step t52 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.group_element X)) (not (tptp.group_element Y)) (tptp.product X Y tptp.e_1) (tptp.product X Y tptp.e_2) (tptp.product X Y tptp.e_3))) (or (not (tptp.group_element tptp.e_3)) (not (tptp.group_element tptp.e_1)) (tptp.product tptp.e_3 tptp.e_1 tptp.e_1) (tptp.product tptp.e_3 tptp.e_1 tptp.e_2) (tptp.product tptp.e_3 tptp.e_1 tptp.e_3))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.group_element X)) (not (tptp.group_element Y)) (tptp.product X Y tptp.e_1) (tptp.product X Y tptp.e_2) (tptp.product X Y tptp.e_3)))) :rule implies_neg1)
% 0.20/0.53 (anchor :step t53)
% 0.20/0.53 (assume t53.a0 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.group_element X)) (not (tptp.group_element Y)) (tptp.product X Y tptp.e_1) (tptp.product X Y tptp.e_2) (tptp.product X Y tptp.e_3))))
% 0.20/0.53 (step t53.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.group_element X)) (not (tptp.group_element Y)) (tptp.product X Y tptp.e_1) (tptp.product X Y tptp.e_2) (tptp.product X Y tptp.e_3)))) (or (not (tptp.group_element tptp.e_3)) (not (tptp.group_element tptp.e_1)) (tptp.product tptp.e_3 tptp.e_1 tptp.e_1) (tptp.product tptp.e_3 tptp.e_1 tptp.e_2) (tptp.product tptp.e_3 tptp.e_1 tptp.e_3)))) :rule forall_inst :args ((:= X tptp.e_3) (:= Y tptp.e_1)))
% 0.20/0.53 (step t53.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.group_element X)) (not (tptp.group_element Y)) (tptp.product X Y tptp.e_1) (tptp.product X Y tptp.e_2) (tptp.product X Y tptp.e_3)))) (or (not (tptp.group_element tptp.e_3)) (not (tptp.group_element tptp.e_1)) (tptp.product tptp.e_3 tptp.e_1 tptp.e_1) (tptp.product tptp.e_3 tptp.e_1 tptp.e_2) (tptp.product tptp.e_3 tptp.e_1 tptp.e_3))) :rule or :premises (t53.t1))
% 0.20/0.53 (step t53.t3 (cl (or (not (tptp.group_element tptp.e_3)) (not (tptp.group_element tptp.e_1)) (tptp.product tptp.e_3 tptp.e_1 tptp.e_1) (tptp.product tptp.e_3 tptp.e_1 tptp.e_2) (tptp.product tptp.e_3 tptp.e_1 tptp.e_3))) :rule resolution :premises (t53.t2 t53.a0))
% 0.20/0.53 (step t53 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.group_element X)) (not (tptp.group_element Y)) (tptp.product X Y tptp.e_1) (tptp.product X Y tptp.e_2) (tptp.product X Y tptp.e_3)))) (or (not (tptp.group_element tptp.e_3)) (not (tptp.group_element tptp.e_1)) (tptp.product tptp.e_3 tptp.e_1 tptp.e_1) (tptp.product tptp.e_3 tptp.e_1 tptp.e_2) (tptp.product tptp.e_3 tptp.e_1 tptp.e_3))) :rule subproof :discharge (t53.a0))
% 0.20/0.53 (step t54 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.group_element X)) (not (tptp.group_element Y)) (tptp.product X Y tptp.e_1) (tptp.product X Y tptp.e_2) (tptp.product X Y tptp.e_3))) (or (not (tptp.group_element tptp.e_3)) (not (tptp.group_element tptp.e_1)) (tptp.product tptp.e_3 tptp.e_1 tptp.e_1) (tptp.product tptp.e_3 tptp.e_1 tptp.e_2) (tptp.product tptp.e_3 tptp.e_1 tptp.e_3))) (or (not (tptp.group_element tptp.e_3)) (not (tptp.group_element tptp.e_1)) (tptp.product tptp.e_3 tptp.e_1 tptp.e_1) (tptp.product tptp.e_3 tptp.e_1 tptp.e_2) (tptp.product tptp.e_3 tptp.e_1 tptp.e_3))) :rule resolution :premises (t52 t53))
% 0.20/0.53 (step t55 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.group_element X)) (not (tptp.group_element Y)) (tptp.product X Y tptp.e_1) (tptp.product X Y tptp.e_2) (tptp.product X Y tptp.e_3))) (or (not (tptp.group_element tptp.e_3)) (not (tptp.group_element tptp.e_1)) (tptp.product tptp.e_3 tptp.e_1 tptp.e_1) (tptp.product tptp.e_3 tptp.e_1 tptp.e_2) (tptp.product tptp.e_3 tptp.e_1 tptp.e_3))) (not (or (not (tptp.group_element tptp.e_3)) (not (tptp.group_element tptp.e_1)) (tptp.product tptp.e_3 tptp.e_1 tptp.e_1) (tptp.product tptp.e_3 tptp.e_1 tptp.e_2) (tptp.product tptp.e_3 tptp.e_1 tptp.e_3)))) :rule implies_neg2)
% 0.20/0.53 (step t56 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.group_element X)) (not (tptp.group_element Y)) (tptp.product X Y tptp.e_1) (tptp.product X Y tptp.e_2) (tptp.product X Y tptp.e_3))) (or (not (tptp.group_element tptp.e_3)) (not (tptp.group_element tptp.e_1)) (tptp.product tptp.e_3 tptp.e_1 tptp.e_1) (tptp.product tptp.e_3 tptp.e_1 tptp.e_2) (tptp.product tptp.e_3 tptp.e_1 tptp.e_3))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.group_element X)) (not (tptp.group_element Y)) (tptp.product X Y tptp.e_1) (tptp.product X Y tptp.e_2) (tptp.product X Y tptp.e_3))) (or (not (tptp.group_element tptp.e_3)) (not (tptp.group_element tptp.e_1)) (tptp.product tptp.e_3 tptp.e_1 tptp.e_1) (tptp.product tptp.e_3 tptp.e_1 tptp.e_2) (tptp.product tptp.e_3 tptp.e_1 tptp.e_3)))) :rule resolution :premises (t54 t55))
% 0.20/0.53 (step t57 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.group_element X)) (not (tptp.group_element Y)) (tptp.product X Y tptp.e_1) (tptp.product X Y tptp.e_2) (tptp.product X Y tptp.e_3))) (or (not (tptp.group_element tptp.e_3)) (not (tptp.group_element tptp.e_1)) (tptp.product tptp.e_3 tptp.e_1 tptp.e_1) (tptp.product tptp.e_3 tptp.e_1 tptp.e_2) (tptp.product tptp.e_3 tptp.e_1 tptp.e_3)))) :rule contraction :premises (t56))
% 0.20/0.53 (step t58 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.group_element X)) (not (tptp.group_element Y)) (tptp.product X Y tptp.e_1) (tptp.product X Y tptp.e_2) (tptp.product X Y tptp.e_3)))) (or (not (tptp.group_element tptp.e_3)) (not (tptp.group_element tptp.e_1)) (tptp.product tptp.e_3 tptp.e_1 tptp.e_1) (tptp.product tptp.e_3 tptp.e_1 tptp.e_2) (tptp.product tptp.e_3 tptp.e_1 tptp.e_3))) :rule implies :premises (t57))
% 0.20/0.53 (step t59 (cl (or (not (tptp.group_element tptp.e_3)) (not (tptp.group_element tptp.e_1)) (tptp.product tptp.e_3 tptp.e_1 tptp.e_1) (tptp.product tptp.e_3 tptp.e_1 tptp.e_2) (tptp.product tptp.e_3 tptp.e_1 tptp.e_3))) :rule resolution :premises (t58 a9))
% 0.20/0.53 (step t60 (cl (not (or (not (tptp.product tptp.e_2 tptp.e_2 tptp.e_2)) (not (tptp.product tptp.e_3 tptp.e_1 tptp.e_2)) (not (tptp.product tptp.e_2 tptp.e_2 tptp.e_2)) (not (tptp.product tptp.e_2 tptp.e_1 tptp.e_3)) (tptp.equalish tptp.e_2 tptp.e_3))) (not (tptp.product tptp.e_2 tptp.e_2 tptp.e_2)) (not (tptp.product tptp.e_3 tptp.e_1 tptp.e_2)) (not (tptp.product tptp.e_2 tptp.e_2 tptp.e_2)) (not (tptp.product tptp.e_2 tptp.e_1 tptp.e_3)) (tptp.equalish tptp.e_2 tptp.e_3)) :rule or_pos)
% 0.20/0.53 (step t61 (cl (not (or (not (tptp.product tptp.e_2 tptp.e_2 tptp.e_2)) (not (tptp.product tptp.e_3 tptp.e_1 tptp.e_2)) (not (tptp.product tptp.e_2 tptp.e_2 tptp.e_2)) (not (tptp.product tptp.e_2 tptp.e_1 tptp.e_3)) (tptp.equalish tptp.e_2 tptp.e_3))) (not (tptp.product tptp.e_2 tptp.e_2 tptp.e_2)) (not (tptp.product tptp.e_3 tptp.e_1 tptp.e_2)) (not (tptp.product tptp.e_2 tptp.e_1 tptp.e_3)) (tptp.equalish tptp.e_2 tptp.e_3)) :rule contraction :premises (t60))
% 0.20/0.53 (step t62 (cl (tptp.equalish tptp.e_2 tptp.e_3) (not (tptp.product tptp.e_2 tptp.e_2 tptp.e_2)) (not (tptp.product tptp.e_2 tptp.e_1 tptp.e_3)) (not (tptp.product tptp.e_3 tptp.e_1 tptp.e_2)) (not (or (not (tptp.product tptp.e_2 tptp.e_2 tptp.e_2)) (not (tptp.product tptp.e_3 tptp.e_1 tptp.e_2)) (not (tptp.product tptp.e_2 tptp.e_2 tptp.e_2)) (not (tptp.product tptp.e_2 tptp.e_1 tptp.e_3)) (tptp.equalish tptp.e_2 tptp.e_3)))) :rule reordering :premises (t61))
% 0.20/0.53 (step t63 (cl (=> (forall ((X1 $$unsorted) (Y1 $$unsorted) (Z1 $$unsorted) (X2 $$unsorted) (Y2 $$unsorted) (Z2 $$unsorted)) (or (not (tptp.product X1 Y1 Z1)) (not (tptp.product X2 Y2 Z1)) (not (tptp.product Z2 Y1 X1)) (not (tptp.product Z2 Y2 X2)) (tptp.equalish X1 X2))) (or (not (tptp.product tptp.e_2 tptp.e_2 tptp.e_2)) (not (tptp.product tptp.e_3 tptp.e_1 tptp.e_2)) (not (tptp.product tptp.e_2 tptp.e_2 tptp.e_2)) (not (tptp.product tptp.e_2 tptp.e_1 tptp.e_3)) (tptp.equalish tptp.e_2 tptp.e_3))) (forall ((X1 $$unsorted) (Y1 $$unsorted) (Z1 $$unsorted) (X2 $$unsorted) (Y2 $$unsorted) (Z2 $$unsorted)) (or (not (tptp.product X1 Y1 Z1)) (not (tptp.product X2 Y2 Z1)) (not (tptp.product Z2 Y1 X1)) (not (tptp.product Z2 Y2 X2)) (tptp.equalish X1 X2)))) :rule implies_neg1)
% 0.20/0.53 (anchor :step t64)
% 0.20/0.53 (assume t64.a0 (forall ((X1 $$unsorted) (Y1 $$unsorted) (Z1 $$unsorted) (X2 $$unsorted) (Y2 $$unsorted) (Z2 $$unsorted)) (or (not (tptp.product X1 Y1 Z1)) (not (tptp.product X2 Y2 Z1)) (not (tptp.product Z2 Y1 X1)) (not (tptp.product Z2 Y2 X2)) (tptp.equalish X1 X2))))
% 0.20/0.53 (step t64.t1 (cl (or (not (forall ((X1 $$unsorted) (Y1 $$unsorted) (Z1 $$unsorted) (X2 $$unsorted) (Y2 $$unsorted) (Z2 $$unsorted)) (or (not (tptp.product X1 Y1 Z1)) (not (tptp.product X2 Y2 Z1)) (not (tptp.product Z2 Y1 X1)) (not (tptp.product Z2 Y2 X2)) (tptp.equalish X1 X2)))) (or (not (tptp.product tptp.e_2 tptp.e_2 tptp.e_2)) (not (tptp.product tptp.e_3 tptp.e_1 tptp.e_2)) (not (tptp.product tptp.e_2 tptp.e_2 tptp.e_2)) (not (tptp.product tptp.e_2 tptp.e_1 tptp.e_3)) (tptp.equalish tptp.e_2 tptp.e_3)))) :rule forall_inst :args ((:= X1 tptp.e_2) (:= Y1 tptp.e_2) (:= Z1 tptp.e_2) (:= X2 tptp.e_3) (:= Y2 tptp.e_1) (:= Z2 tptp.e_2)))
% 0.20/0.53 (step t64.t2 (cl (not (forall ((X1 $$unsorted) (Y1 $$unsorted) (Z1 $$unsorted) (X2 $$unsorted) (Y2 $$unsorted) (Z2 $$unsorted)) (or (not (tptp.product X1 Y1 Z1)) (not (tptp.product X2 Y2 Z1)) (not (tptp.product Z2 Y1 X1)) (not (tptp.product Z2 Y2 X2)) (tptp.equalish X1 X2)))) (or (not (tptp.product tptp.e_2 tptp.e_2 tptp.e_2)) (not (tptp.product tptp.e_3 tptp.e_1 tptp.e_2)) (not (tptp.product tptp.e_2 tptp.e_2 tptp.e_2)) (not (tptp.product tptp.e_2 tptp.e_1 tptp.e_3)) (tptp.equalish tptp.e_2 tptp.e_3))) :rule or :premises (t64.t1))
% 0.20/0.53 (step t64.t3 (cl (or (not (tptp.product tptp.e_2 tptp.e_2 tptp.e_2)) (not (tptp.product tptp.e_3 tptp.e_1 tptp.e_2)) (not (tptp.product tptp.e_2 tptp.e_2 tptp.e_2)) (not (tptp.product tptp.e_2 tptp.e_1 tptp.e_3)) (tptp.equalish tptp.e_2 tptp.e_3))) :rule resolution :premises (t64.t2 t64.a0))
% 0.20/0.53 (step t64 (cl (not (forall ((X1 $$unsorted) (Y1 $$unsorted) (Z1 $$unsorted) (X2 $$unsorted) (Y2 $$unsorted) (Z2 $$unsorted)) (or (not (tptp.product X1 Y1 Z1)) (not (tptp.product X2 Y2 Z1)) (not (tptp.product Z2 Y1 X1)) (not (tptp.product Z2 Y2 X2)) (tptp.equalish X1 X2)))) (or (not (tptp.product tptp.e_2 tptp.e_2 tptp.e_2)) (not (tptp.product tptp.e_3 tptp.e_1 tptp.e_2)) (not (tptp.product tptp.e_2 tptp.e_2 tptp.e_2)) (not (tptp.product tptp.e_2 tptp.e_1 tptp.e_3)) (tptp.equalish tptp.e_2 tptp.e_3))) :rule subproof :discharge (t64.a0))
% 0.20/0.53 (step t65 (cl (=> (forall ((X1 $$unsorted) (Y1 $$unsorted) (Z1 $$unsorted) (X2 $$unsorted) (Y2 $$unsorted) (Z2 $$unsorted)) (or (not (tptp.product X1 Y1 Z1)) (not (tptp.product X2 Y2 Z1)) (not (tptp.product Z2 Y1 X1)) (not (tptp.product Z2 Y2 X2)) (tptp.equalish X1 X2))) (or (not (tptp.product tptp.e_2 tptp.e_2 tptp.e_2)) (not (tptp.product tptp.e_3 tptp.e_1 tptp.e_2)) (not (tptp.product tptp.e_2 tptp.e_2 tptp.e_2)) (not (tptp.product tptp.e_2 tptp.e_1 tptp.e_3)) (tptp.equalish tptp.e_2 tptp.e_3))) (or (not (tptp.product tptp.e_2 tptp.e_2 tptp.e_2)) (not (tptp.product tptp.e_3 tptp.e_1 tptp.e_2)) (not (tptp.product tptp.e_2 tptp.e_2 tptp.e_2)) (not (tptp.product tptp.e_2 tptp.e_1 tptp.e_3)) (tptp.equalish tptp.e_2 tptp.e_3))) :rule resolution :premises (t63 t64))
% 0.20/0.53 (step t66 (cl (=> (forall ((X1 $$unsorted) (Y1 $$unsorted) (Z1 $$unsorted) (X2 $$unsorted) (Y2 $$unsorted) (Z2 $$unsorted)) (or (not (tptp.product X1 Y1 Z1)) (not (tptp.product X2 Y2 Z1)) (not (tptp.product Z2 Y1 X1)) (not (tptp.product Z2 Y2 X2)) (tptp.equalish X1 X2))) (or (not (tptp.product tptp.e_2 tptp.e_2 tptp.e_2)) (not (tptp.product tptp.e_3 tptp.e_1 tptp.e_2)) (not (tptp.product tptp.e_2 tptp.e_2 tptp.e_2)) (not (tptp.product tptp.e_2 tptp.e_1 tptp.e_3)) (tptp.equalish tptp.e_2 tptp.e_3))) (not (or (not (tptp.product tptp.e_2 tptp.e_2 tptp.e_2)) (not (tptp.product tptp.e_3 tptp.e_1 tptp.e_2)) (not (tptp.product tptp.e_2 tptp.e_2 tptp.e_2)) (not (tptp.product tptp.e_2 tptp.e_1 tptp.e_3)) (tptp.equalish tptp.e_2 tptp.e_3)))) :rule implies_neg2)
% 0.20/0.53 (step t67 (cl (=> (forall ((X1 $$unsorted) (Y1 $$unsorted) (Z1 $$unsorted) (X2 $$unsorted) (Y2 $$unsorted) (Z2 $$unsorted)) (or (not (tptp.product X1 Y1 Z1)) (not (tptp.product X2 Y2 Z1)) (not (tptp.product Z2 Y1 X1)) (not (tptp.product Z2 Y2 X2)) (tptp.equalish X1 X2))) (or (not (tptp.product tptp.e_2 tptp.e_2 tptp.e_2)) (not (tptp.product tptp.e_3 tptp.e_1 tptp.e_2)) (not (tptp.product tptp.e_2 tptp.e_2 tptp.e_2)) (not (tptp.product tptp.e_2 tptp.e_1 tptp.e_3)) (tptp.equalish tptp.e_2 tptp.e_3))) (=> (forall ((X1 $$unsorted) (Y1 $$unsorted) (Z1 $$unsorted) (X2 $$unsorted) (Y2 $$unsorted) (Z2 $$unsorted)) (or (not (tptp.product X1 Y1 Z1)) (not (tptp.product X2 Y2 Z1)) (not (tptp.product Z2 Y1 X1)) (not (tptp.product Z2 Y2 X2)) (tptp.equalish X1 X2))) (or (not (tptp.product tptp.e_2 tptp.e_2 tptp.e_2)) (not (tptp.product tptp.e_3 tptp.e_1 tptp.e_2)) (not (tptp.product tptp.e_2 tptp.e_2 tptp.e_2)) (not (tptp.product tptp.e_2 tptp.e_1 tptp.e_3)) (tptp.equalish tptp.e_2 tptp.e_3)))) :rule resolution :premises (t65 t66))
% 0.20/0.53 (step t68 (cl (=> (forall ((X1 $$unsorted) (Y1 $$unsorted) (Z1 $$unsorted) (X2 $$unsorted) (Y2 $$unsorted) (Z2 $$unsorted)) (or (not (tptp.product X1 Y1 Z1)) (not (tptp.product X2 Y2 Z1)) (not (tptp.product Z2 Y1 X1)) (not (tptp.product Z2 Y2 X2)) (tptp.equalish X1 X2))) (or (not (tptp.product tptp.e_2 tptp.e_2 tptp.e_2)) (not (tptp.product tptp.e_3 tptp.e_1 tptp.e_2)) (not (tptp.product tptp.e_2 tptp.e_2 tptp.e_2)) (not (tptp.product tptp.e_2 tptp.e_1 tptp.e_3)) (tptp.equalish tptp.e_2 tptp.e_3)))) :rule contraction :premises (t67))
% 0.20/0.53 (step t69 (cl (not (forall ((X1 $$unsorted) (Y1 $$unsorted) (Z1 $$unsorted) (X2 $$unsorted) (Y2 $$unsorted) (Z2 $$unsorted)) (or (not (tptp.product X1 Y1 Z1)) (not (tptp.product X2 Y2 Z1)) (not (tptp.product Z2 Y1 X1)) (not (tptp.product Z2 Y2 X2)) (tptp.equalish X1 X2)))) (or (not (tptp.product tptp.e_2 tptp.e_2 tptp.e_2)) (not (tptp.product tptp.e_3 tptp.e_1 tptp.e_2)) (not (tptp.product tptp.e_2 tptp.e_2 tptp.e_2)) (not (tptp.product tptp.e_2 tptp.e_1 tptp.e_3)) (tptp.equalish tptp.e_2 tptp.e_3))) :rule implies :premises (t68))
% 0.20/0.53 (step t70 (cl (or (not (tptp.product tptp.e_2 tptp.e_2 tptp.e_2)) (not (tptp.product tptp.e_3 tptp.e_1 tptp.e_2)) (not (tptp.product tptp.e_2 tptp.e_2 tptp.e_2)) (not (tptp.product tptp.e_2 tptp.e_1 tptp.e_3)) (tptp.equalish tptp.e_2 tptp.e_3))) :rule resolution :premises (t69 a14))
% 0.20/0.53 (step t71 (cl (not (or (not (tptp.product tptp.e_2 tptp.e_1 tptp.e_3)) (not (tptp.product tptp.e_3 tptp.e_1 tptp.e_3)) (tptp.equalish tptp.e_2 tptp.e_3))) (not (tptp.product tptp.e_2 tptp.e_1 tptp.e_3)) (not (tptp.product tptp.e_3 tptp.e_1 tptp.e_3)) (tptp.equalish tptp.e_2 tptp.e_3)) :rule or_pos)
% 0.20/0.53 (step t72 (cl (tptp.equalish tptp.e_2 tptp.e_3) (not (tptp.product tptp.e_2 tptp.e_1 tptp.e_3)) (not (tptp.product tptp.e_3 tptp.e_1 tptp.e_3)) (not (or (not (tptp.product tptp.e_2 tptp.e_1 tptp.e_3)) (not (tptp.product tptp.e_3 tptp.e_1 tptp.e_3)) (tptp.equalish tptp.e_2 tptp.e_3)))) :rule reordering :premises (t71))
% 0.20/0.53 (step t73 (cl (=> (forall ((W $$unsorted) (Y $$unsorted) (X $$unsorted) (Z $$unsorted)) (or (not (tptp.product W Y X)) (not (tptp.product Z Y X)) (tptp.equalish W Z))) (or (not (tptp.product tptp.e_2 tptp.e_1 tptp.e_3)) (not (tptp.product tptp.e_3 tptp.e_1 tptp.e_3)) (tptp.equalish tptp.e_2 tptp.e_3))) (forall ((W $$unsorted) (Y $$unsorted) (X $$unsorted) (Z $$unsorted)) (or (not (tptp.product W Y X)) (not (tptp.product Z Y X)) (tptp.equalish W Z)))) :rule implies_neg1)
% 0.20/0.53 (anchor :step t74)
% 0.20/0.53 (assume t74.a0 (forall ((W $$unsorted) (Y $$unsorted) (X $$unsorted) (Z $$unsorted)) (or (not (tptp.product W Y X)) (not (tptp.product Z Y X)) (tptp.equalish W Z))))
% 0.20/0.53 (step t74.t1 (cl (or (not (forall ((W $$unsorted) (Y $$unsorted) (X $$unsorted) (Z $$unsorted)) (or (not (tptp.product W Y X)) (not (tptp.product Z Y X)) (tptp.equalish W Z)))) (or (not (tptp.product tptp.e_2 tptp.e_1 tptp.e_3)) (not (tptp.product tptp.e_3 tptp.e_1 tptp.e_3)) (tptp.equalish tptp.e_2 tptp.e_3)))) :rule forall_inst :args ((:= W tptp.e_2) (:= Y tptp.e_1) (:= X tptp.e_3) (:= Z tptp.e_3)))
% 0.20/0.53 (step t74.t2 (cl (not (forall ((W $$unsorted) (Y $$unsorted) (X $$unsorted) (Z $$unsorted)) (or (not (tptp.product W Y X)) (not (tptp.product Z Y X)) (tptp.equalish W Z)))) (or (not (tptp.product tptp.e_2 tptp.e_1 tptp.e_3)) (not (tptp.product tptp.e_3 tptp.e_1 tptp.e_3)) (tptp.equalish tptp.e_2 tptp.e_3))) :rule or :premises (t74.t1))
% 0.20/0.53 (step t74.t3 (cl (or (not (tptp.product tptp.e_2 tptp.e_1 tptp.e_3)) (not (tptp.product tptp.e_3 tptp.e_1 tptp.e_3)) (tptp.equalish tptp.e_2 tptp.e_3))) :rule resolution :premises (t74.t2 t74.a0))
% 0.20/0.53 (step t74 (cl (not (forall ((W $$unsorted) (Y $$unsorted) (X $$unsorted) (Z $$unsorted)) (or (not (tptp.product W Y X)) (not (tptp.product Z Y X)) (tptp.equalish W Z)))) (or (not (tptp.product tptp.e_2 tptp.e_1 tptp.e_3)) (not (tptp.product tptp.e_3 tptp.e_1 tptp.e_3)) (tptp.equalish tptp.e_2 tptp.e_3))) :rule subproof :discharge (t74.a0))
% 0.20/0.53 (step t75 (cl (=> (forall ((W $$unsorted) (Y $$unsorted) (X $$unsorted) (Z $$unsorted)) (or (not (tptp.product W Y X)) (not (tptp.product Z Y X)) (tptp.equalish W Z))) (or (not (tptp.product tptp.e_2 tptp.e_1 tptp.e_3)) (not (tptp.product tptp.e_3 tptp.e_1 tptp.e_3)) (tptp.equalish tptp.e_2 tptp.e_3))) (or (not (tptp.product tptp.e_2 tptp.e_1 tptp.e_3)) (not (tptp.product tptp.e_3 tptp.e_1 tptp.e_3)) (tptp.equalish tptp.e_2 tptp.e_3))) :rule resolution :premises (t73 t74))
% 0.20/0.53 (step t76 (cl (=> (forall ((W $$unsorted) (Y $$unsorted) (X $$unsorted) (Z $$unsorted)) (or (not (tptp.product W Y X)) (not (tptp.product Z Y X)) (tptp.equalish W Z))) (or (not (tptp.product tptp.e_2 tptp.e_1 tptp.e_3)) (not (tptp.product tptp.e_3 tptp.e_1 tptp.e_3)) (tptp.equalish tptp.e_2 tptp.e_3))) (not (or (not (tptp.product tptp.e_2 tptp.e_1 tptp.e_3)) (not (tptp.product tptp.e_3 tptp.e_1 tptp.e_3)) (tptp.equalish tptp.e_2 tptp.e_3)))) :rule implies_neg2)
% 0.20/0.53 (step t77 (cl (=> (forall ((W $$unsorted) (Y $$unsorted) (X $$unsorted) (Z $$unsorted)) (or (not (tptp.product W Y X)) (not (tptp.product Z Y X)) (tptp.equalish W Z))) (or (not (tptp.product tptp.e_2 tptp.e_1 tptp.e_3)) (not (tptp.product tptp.e_3 tptp.e_1 tptp.e_3)) (tptp.equalish tptp.e_2 tptp.e_3))) (=> (forall ((W $$unsorted) (Y $$unsorted) (X $$unsorted) (Z $$unsorted)) (or (not (tptp.product W Y X)) (not (tptp.product Z Y X)) (tptp.equalish W Z))) (or (not (tptp.product tptp.e_2 tptp.e_1 tptp.e_3)) (not (tptp.product tptp.e_3 tptp.e_1 tptp.e_3)) (tptp.equalish tptp.e_2 tptp.e_3)))) :rule resolution :premises (t75 t76))
% 0.20/0.53 (step t78 (cl (=> (forall ((W $$unsorted) (Y $$unsorted) (X $$unsorted) (Z $$unsorted)) (or (not (tptp.product W Y X)) (not (tptp.product Z Y X)) (tptp.equalish W Z))) (or (not (tptp.product tptp.e_2 tptp.e_1 tptp.e_3)) (not (tptp.product tptp.e_3 tptp.e_1 tptp.e_3)) (tptp.equalish tptp.e_2 tptp.e_3)))) :rule contraction :premises (t77))
% 0.20/0.53 (step t79 (cl (not (forall ((W $$unsorted) (Y $$unsorted) (X $$unsorted) (Z $$unsorted)) (or (not (tptp.product W Y X)) (not (tptp.product Z Y X)) (tptp.equalish W Z)))) (or (not (tptp.product tptp.e_2 tptp.e_1 tptp.e_3)) (not (tptp.product tptp.e_3 tptp.e_1 tptp.e_3)) (tptp.equalish tptp.e_2 tptp.e_3))) :rule implies :premises (t78))
% 0.20/0.53 (step t80 (cl (or (not (tptp.product tptp.e_2 tptp.e_1 tptp.e_3)) (not (tptp.product tptp.e_3 tptp.e_1 tptp.e_3)) (tptp.equalish tptp.e_2 tptp.e_3))) :rule resolution :premises (t79 a12))
% 0.20/0.53 (step t81 (cl (not (tptp.product tptp.e_2 tptp.e_1 tptp.e_3)) (not (tptp.product tptp.e_2 tptp.e_1 tptp.e_3))) :rule resolution :premises (t40 t51 t59 a2 a0 t62 t70 t17 a6 t72 t80 a6))
% 0.20/0.53 (step t82 (cl (not (tptp.product tptp.e_2 tptp.e_1 tptp.e_3))) :rule contraction :premises (t81))
% 0.20/0.53 (step t83 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.group_element X)) (not (tptp.group_element Y)) (tptp.product X Y tptp.e_1) (tptp.product X Y tptp.e_2) (tptp.product X Y tptp.e_3))) (or (not (tptp.group_element tptp.e_2)) (not (tptp.group_element tptp.e_1)) (tptp.product tptp.e_2 tptp.e_1 tptp.e_1) (tptp.product tptp.e_2 tptp.e_1 tptp.e_2) (tptp.product tptp.e_2 tptp.e_1 tptp.e_3))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.group_element X)) (not (tptp.group_element Y)) (tptp.product X Y tptp.e_1) (tptp.product X Y tptp.e_2) (tptp.product X Y tptp.e_3)))) :rule implies_neg1)
% 0.20/0.53 (anchor :step t84)
% 0.20/0.53 (assume t84.a0 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.group_element X)) (not (tptp.group_element Y)) (tptp.product X Y tptp.e_1) (tptp.product X Y tptp.e_2) (tptp.product X Y tptp.e_3))))
% 0.20/0.53 (step t84.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.group_element X)) (not (tptp.group_element Y)) (tptp.product X Y tptp.e_1) (tptp.product X Y tptp.e_2) (tptp.product X Y tptp.e_3)))) (or (not (tptp.group_element tptp.e_2)) (not (tptp.group_element tptp.e_1)) (tptp.product tptp.e_2 tptp.e_1 tptp.e_1) (tptp.product tptp.e_2 tptp.e_1 tptp.e_2) (tptp.product tptp.e_2 tptp.e_1 tptp.e_3)))) :rule forall_inst :args ((:= X tptp.e_2) (:= Y tptp.e_1)))
% 0.20/0.53 (step t84.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.group_element X)) (not (tptp.group_element Y)) (tptp.product X Y tptp.e_1) (tptp.product X Y tptp.e_2) (tptp.product X Y tptp.e_3)))) (or (not (tptp.group_element tptp.e_2)) (not (tptp.group_element tptp.e_1)) (tptp.product tptp.e_2 tptp.e_1 tptp.e_1) (tptp.product tptp.e_2 tptp.e_1 tptp.e_2) (tptp.product tptp.e_2 tptp.e_1 tptp.e_3))) :rule or :premises (t84.t1))
% 0.20/0.53 (step t84.t3 (cl (or (not (tptp.group_element tptp.e_2)) (not (tptp.group_element tptp.e_1)) (tptp.product tptp.e_2 tptp.e_1 tptp.e_1) (tptp.product tptp.e_2 tptp.e_1 tptp.e_2) (tptp.product tptp.e_2 tptp.e_1 tptp.e_3))) :rule resolution :premises (t84.t2 t84.a0))
% 0.20/0.53 (step t84 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.group_element X)) (not (tptp.group_element Y)) (tptp.product X Y tptp.e_1) (tptp.product X Y tptp.e_2) (tptp.product X Y tptp.e_3)))) (or (not (tptp.group_element tptp.e_2)) (not (tptp.group_element tptp.e_1)) (tptp.product tptp.e_2 tptp.e_1 tptp.e_1) (tptp.product tptp.e_2 tptp.e_1 tptp.e_2) (tptp.product tptp.e_2 tptp.e_1 tptp.e_3))) :rule subproof :discharge (t84.a0))
% 0.20/0.53 (step t85 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.group_element X)) (not (tptp.group_element Y)) (tptp.product X Y tptp.e_1) (tptp.product X Y tptp.e_2) (tptp.product X Y tptp.e_3))) (or (not (tptp.group_element tptp.e_2)) (not (tptp.group_element tptp.e_1)) (tptp.product tptp.e_2 tptp.e_1 tptp.e_1) (tptp.product tptp.e_2 tptp.e_1 tptp.e_2) (tptp.product tptp.e_2 tptp.e_1 tptp.e_3))) (or (not (tptp.group_element tptp.e_2)) (not (tptp.group_element tptp.e_1)) (tptp.product tptp.e_2 tptp.e_1 tptp.e_1) (tptp.product tptp.e_2 tptp.e_1 tptp.e_2) (tptp.product tptp.e_2 tptp.e_1 tptp.e_3))) :rule resolution :premises (t83 t84))
% 0.20/0.53 (step t86 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.group_element X)) (not (tptp.group_element Y)) (tptp.product X Y tptp.e_1) (tptp.product X Y tptp.e_2) (tptp.product X Y tptp.e_3))) (or (not (tptp.group_element tptp.e_2)) (not (tptp.group_element tptp.e_1)) (tptp.product tptp.e_2 tptp.e_1 tptp.e_1) (tptp.product tptp.e_2 tptp.e_1 tptp.e_2) (tptp.product tptp.e_2 tptp.e_1 tptp.e_3))) (not (or (not (tptp.group_element tptp.e_2)) (not (tptp.group_element tptp.e_1)) (tptp.product tptp.e_2 tptp.e_1 tptp.e_1) (tptp.product tptp.e_2 tptp.e_1 tptp.e_2) (tptp.product tptp.e_2 tptp.e_1 tptp.e_3)))) :rule implies_neg2)
% 0.20/0.53 (step t87 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.group_element X)) (not (tptp.group_element Y)) (tptp.product X Y tptp.e_1) (tptp.product X Y tptp.e_2) (tptp.product X Y tptp.e_3))) (or (not (tptp.group_element tptp.e_2)) (not (tptp.group_element tptp.e_1)) (tptp.product tptp.e_2 tptp.e_1 tptp.e_1) (tptp.product tptp.e_2 tptp.e_1 tptp.e_2) (tptp.product tptp.e_2 tptp.e_1 tptp.e_3))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.group_element X)) (not (tptp.group_element Y)) (tptp.product X Y tptp.e_1) (tptp.product X Y tptp.e_2) (tptp.product X Y tptp.e_3))) (or (not (tptp.group_element tptp.e_2)) (not (tptp.group_element tptp.e_1)) (tptp.product tptp.e_2 tptp.e_1 tptp.e_1) (tptp.product tptp.e_2 tptp.e_1 tptp.e_2) (tptp.product tptp.e_2 tptp.e_1 tptp.e_3)))) :rule resolution :premises (t85 t86))
% 0.20/0.53 (step t88 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.group_element X)) (not (tptp.group_element Y)) (tptp.product X Y tptp.e_1) (tptp.product X Y tptp.e_2) (tptp.product X Y tptp.e_3))) (or (not (tptp.group_element tptp.e_2)) (not (tptp.group_element tptp.e_1)) (tptp.product tptp.e_2 tptp.e_1 tptp.e_1) (tptp.product tptp.e_2 tptp.e_1 tptp.e_2) (tptp.product tptp.e_2 tptp.e_1 tptp.e_3)))) :rule contraction :premises (t87))
% 0.20/0.53 (step t89 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.group_element X)) (not (tptp.group_element Y)) (tptp.product X Y tptp.e_1) (tptp.product X Y tptp.e_2) (tptp.product X Y tptp.e_3)))) (or (not (tptp.group_element tptp.e_2)) (not (tptp.group_element tptp.e_1)) (tptp.product tptp.e_2 tptp.e_1 tptp.e_1) (tptp.product tptp.e_2 tptp.e_1 tptp.e_2) (tptp.product tptp.e_2 tptp.e_1 tptp.e_3))) :rule implies :premises (t88))
% 0.20/0.53 (step t90 (cl (or (not (tptp.group_element tptp.e_2)) (not (tptp.group_element tptp.e_1)) (tptp.product tptp.e_2 tptp.e_1 tptp.e_1) (tptp.product tptp.e_2 tptp.e_1 tptp.e_2) (tptp.product tptp.e_2 tptp.e_1 tptp.e_3))) :rule resolution :premises (t89 a9))
% 0.20/0.53 (step t91 (cl (tptp.product tptp.e_2 tptp.e_1 tptp.e_2)) :rule resolution :premises (t19 a0 a1 t38 t82 t90))
% 0.20/0.53 (step t92 (cl (not (or (not (tptp.product tptp.e_2 tptp.e_1 tptp.e_2)) (not (tptp.product tptp.e_2 tptp.e_2 tptp.e_2)) (tptp.equalish tptp.e_1 tptp.e_2)))) :rule resolution :premises (t9 a3 t17 t91))
% 0.20/0.53 (step t93 (cl) :rule resolution :premises (t7 t92 a11))
% 0.20/0.53
% 0.20/0.53 % SZS output end Proof for /export/starexec/sandbox2/tmp/tmp.q6TbueFETy/cvc5---1.0.5_11886.smt2
% 0.36/0.54 % cvc5---1.0.5 exiting
% 0.36/0.54 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------