%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : GRP125-1.003 : TPTP v8.2.0. Released v1.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : do_cvc5 %s %d

% Computer : n007.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 16:53:13 EDT 2024

% Result   : Unsatisfiable 0.20s 0.55s
% Output   : Proof 0.20s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13  % Problem    : GRP125-1.003 : TPTP v8.2.0. Released v1.2.0.
% 0.11/0.14  % Command    : do_cvc5 %s %d
% 0.14/0.35  % Computer : n007.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit   : 300
% 0.14/0.35  % WCLimit    : 300
% 0.14/0.35  % DateTime   : Sun May 26 19:15:09 EDT 2024
% 0.14/0.35  % CPUTime    : 
% 0.20/0.51  %----Proving TF0_NAR, FOF, or CNF
% 0.20/0.51  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.20/0.55  % SZS status Unsatisfiable for /export/starexec/sandbox2/tmp/tmp.VE1T6tqt5t/cvc5---1.0.5_16361.smt2
% 0.20/0.55  % SZS output start Proof for /export/starexec/sandbox2/tmp/tmp.VE1T6tqt5t/cvc5---1.0.5_16361.smt2
% 0.20/0.57  (assume a0 (tptp.group_element tptp.e_1))
% 0.20/0.57  (assume a1 (tptp.group_element tptp.e_2))
% 0.20/0.57  (assume a2 (tptp.group_element tptp.e_3))
% 0.20/0.57  (assume a3 (not (tptp.equalish tptp.e_1 tptp.e_2)))
% 0.20/0.57  (assume a4 (not (tptp.equalish tptp.e_1 tptp.e_3)))
% 0.20/0.57  (assume a5 (not (tptp.equalish tptp.e_2 tptp.e_1)))
% 0.20/0.57  (assume a6 (not (tptp.equalish tptp.e_2 tptp.e_3)))
% 0.20/0.57  (assume a7 (not (tptp.equalish tptp.e_3 tptp.e_1)))
% 0.20/0.57  (assume a8 (not (tptp.equalish tptp.e_3 tptp.e_2)))
% 0.20/0.57  (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))))
% 0.20/0.57  (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))))
% 0.20/0.57  (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))))
% 0.20/0.57  (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))))
% 0.20/0.57  (assume a13 (forall ((X $$unsorted)) (tptp.product X X X)))
% 0.20/0.57  (assume a14 (forall ((X $$unsorted) (Y $$unsorted) (Z1 $$unsorted) (Z2 $$unsorted)) (or (not (tptp.product X Y Z1)) (not (tptp.product Y X Z2)) (tptp.product Z1 Z2 X))))
% 0.20/0.57  (step t1 (cl (=> (forall ((X $$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 $$unsorted)) (or (not (tptp.product X W Y)) (not (tptp.product X Z Y)) (tptp.equalish W Z)))) :rule implies_neg1)
% 0.20/0.57  (anchor :step t2)
% 0.20/0.57  (assume t2.a0 (forall ((X $$unsorted) (W $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.product X W Y)) (not (tptp.product X Z Y)) (tptp.equalish W Z))))
% 0.20/0.57  (step t2.t1 (cl (or (not (forall ((X $$unsorted) (W $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.product X W Y)) (not (tptp.product X Z Y)) (tptp.equalish W Z)))) (or (not (tptp.product tptp.e_2 tptp.e_1 tptp.e_2)) (not (tptp.product tptp.e_2 tptp.e_2 tptp.e_2)) (tptp.equalish tptp.e_1 tptp.e_2)))) :rule forall_inst :args ((:= X tptp.e_2) (:= W tptp.e_1) (:= Y tptp.e_2) (:= Z tptp.e_2)))
% 0.20/0.57  (step t2.t2 (cl (not (forall ((X $$unsorted) (W $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.product X W Y)) (not (tptp.product X Z Y)) (tptp.equalish W Z)))) (or (not (tptp.product tptp.e_2 tptp.e_1 tptp.e_2)) (not (tptp.product tptp.e_2 tptp.e_2 tptp.e_2)) (tptp.equalish tptp.e_1 tptp.e_2))) :rule or :premises (t2.t1))
% 0.20/0.57  (step t2.t3 (cl (or (not (tptp.product tptp.e_2 tptp.e_1 tptp.e_2)) (not (tptp.product tptp.e_2 tptp.e_2 tptp.e_2)) (tptp.equalish tptp.e_1 tptp.e_2))) :rule resolution :premises (t2.t2 t2.a0))
% 0.20/0.57  (step t2 (cl (not (forall ((X $$unsorted) (W $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.product X W Y)) (not (tptp.product X Z Y)) (tptp.equalish W Z)))) (or (not (tptp.product tptp.e_2 tptp.e_1 tptp.e_2)) (not (tptp.product tptp.e_2 tptp.e_2 tptp.e_2)) (tptp.equalish tptp.e_1 tptp.e_2))) :rule subproof :discharge (t2.a0))
% 0.20/0.57  (step t3 (cl (=> (forall ((X $$unsorted) (W $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.product X W Y)) (not (tptp.product X Z Y)) (tptp.equalish W Z))) (or (not (tptp.product tptp.e_2 tptp.e_1 tptp.e_2)) (not (tptp.product tptp.e_2 tptp.e_2 tptp.e_2)) (tptp.equalish tptp.e_1 tptp.e_2))) (or (not (tptp.product tptp.e_2 tptp.e_1 tptp.e_2)) (not (tptp.product tptp.e_2 tptp.e_2 tptp.e_2)) (tptp.equalish tptp.e_1 tptp.e_2))) :rule resolution :premises (t1 t2))
% 0.20/0.57  (step t4 (cl (=> (forall ((X $$unsorted) (W $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.product X W Y)) (not (tptp.product X Z Y)) (tptp.equalish W Z))) (or (not (tptp.product tptp.e_2 tptp.e_1 tptp.e_2)) (not (tptp.product tptp.e_2 tptp.e_2 tptp.e_2)) (tptp.equalish tptp.e_1 tptp.e_2))) (not (or (not (tptp.product tptp.e_2 tptp.e_1 tptp.e_2)) (not (tptp.product tptp.e_2 tptp.e_2 tptp.e_2)) (tptp.equalish tptp.e_1 tptp.e_2)))) :rule implies_neg2)
% 0.20/0.57  (step t5 (cl (=> (forall ((X $$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 $$unsorted)) (or (not (tptp.product X W Y)) (not (tptp.product X Z Y)) (tptp.equalish W Z))) (or (not (tptp.product tptp.e_2 tptp.e_1 tptp.e_2)) (not (tptp.product tptp.e_2 tptp.e_2 tptp.e_2)) (tptp.equalish tptp.e_1 tptp.e_2)))) :rule resolution :premises (t3 t4))
% 0.20/0.57  (step t6 (cl (=> (forall ((X $$unsorted) (W $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.product X W Y)) (not (tptp.product X Z Y)) (tptp.equalish W Z))) (or (not (tptp.product tptp.e_2 tptp.e_1 tptp.e_2)) (not (tptp.product tptp.e_2 tptp.e_2 tptp.e_2)) (tptp.equalish tptp.e_1 tptp.e_2)))) :rule contraction :premises (t5))
% 0.20/0.57  (step t7 (cl (not (forall ((X $$unsorted) (W $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.product X W Y)) (not (tptp.product X Z Y)) (tptp.equalish W Z)))) (or (not (tptp.product tptp.e_2 tptp.e_1 tptp.e_2)) (not (tptp.product tptp.e_2 tptp.e_2 tptp.e_2)) (tptp.equalish tptp.e_1 tptp.e_2))) :rule implies :premises (t6))
% 0.20/0.57  (step t8 (cl (not (or (not (tptp.product tptp.e_2 tptp.e_1 tptp.e_2)) (not (tptp.product tptp.e_2 tptp.e_2 tptp.e_2)) (tptp.equalish tptp.e_1 tptp.e_2))) (not (tptp.product tptp.e_2 tptp.e_1 tptp.e_2)) (not (tptp.product tptp.e_2 tptp.e_2 tptp.e_2)) (tptp.equalish tptp.e_1 tptp.e_2)) :rule or_pos)
% 0.20/0.57  (step t9 (cl (tptp.equalish tptp.e_1 tptp.e_2) (not (tptp.product tptp.e_2 tptp.e_2 tptp.e_2)) (not (tptp.product tptp.e_2 tptp.e_1 tptp.e_2)) (not (or (not (tptp.product tptp.e_2 tptp.e_1 tptp.e_2)) (not (tptp.product tptp.e_2 tptp.e_2 tptp.e_2)) (tptp.equalish tptp.e_1 tptp.e_2)))) :rule reordering :premises (t8))
% 0.20/0.57  (step t10 (cl (=> (forall ((X $$unsorted)) (tptp.product X X X)) (tptp.product tptp.e_2 tptp.e_2 tptp.e_2)) (forall ((X $$unsorted)) (tptp.product X X X))) :rule implies_neg1)
% 0.20/0.57  (anchor :step t11)
% 0.20/0.57  (assume t11.a0 (forall ((X $$unsorted)) (tptp.product X X X)))
% 0.20/0.57  (step t11.t1 (cl (or (not (forall ((X $$unsorted)) (tptp.product X X X))) (tptp.product tptp.e_2 tptp.e_2 tptp.e_2))) :rule forall_inst :args ((:= X tptp.e_2)))
% 0.20/0.57  (step t11.t2 (cl (not (forall ((X $$unsorted)) (tptp.product X X X))) (tptp.product tptp.e_2 tptp.e_2 tptp.e_2)) :rule or :premises (t11.t1))
% 0.20/0.57  (step t11.t3 (cl (tptp.product tptp.e_2 tptp.e_2 tptp.e_2)) :rule resolution :premises (t11.t2 t11.a0))
% 0.20/0.57  (step t11 (cl (not (forall ((X $$unsorted)) (tptp.product X X X))) (tptp.product tptp.e_2 tptp.e_2 tptp.e_2)) :rule subproof :discharge (t11.a0))
% 0.20/0.57  (step t12 (cl (=> (forall ((X $$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))
% 0.20/0.57  (step t13 (cl (=> (forall ((X $$unsorted)) (tptp.product X X X)) (tptp.product tptp.e_2 tptp.e_2 tptp.e_2)) (not (tptp.product tptp.e_2 tptp.e_2 tptp.e_2))) :rule implies_neg2)
% 0.20/0.57  (step t14 (cl (=> (forall ((X $$unsorted)) (tptp.product X X X)) (tptp.product tptp.e_2 tptp.e_2 tptp.e_2)) (=> (forall ((X $$unsorted)) (tptp.product X X X)) (tptp.product tptp.e_2 tptp.e_2 tptp.e_2))) :rule resolution :premises (t12 t13))
% 0.20/0.57  (step t15 (cl (=> (forall ((X $$unsorted)) (tptp.product X X X)) (tptp.product tptp.e_2 tptp.e_2 tptp.e_2))) :rule contraction :premises (t14))
% 0.20/0.57  (step t16 (cl (not (forall ((X $$unsorted)) (tptp.product X X X))) (tptp.product tptp.e_2 tptp.e_2 tptp.e_2)) :rule implies :premises (t15))
% 0.20/0.57  (step t17 (cl (tptp.product tptp.e_2 tptp.e_2 tptp.e_2)) :rule resolution :premises (t16 a13))
% 0.20/0.57  (step t18 (cl (not (or (not (tptp.group_element tptp.e_2)) (not (tptp.group_element tptp.e_1)) (tptp.product tptp.e_2 tptp.e_1 tptp.e_1) (tptp.product tptp.e_2 tptp.e_1 tptp.e_2) (tptp.product tptp.e_2 tptp.e_1 tptp.e_3))) (not (tptp.group_element tptp.e_2)) (not (tptp.group_element tptp.e_1)) (tptp.product tptp.e_2 tptp.e_1 tptp.e_1) (tptp.product tptp.e_2 tptp.e_1 tptp.e_2) (tptp.product tptp.e_2 tptp.e_1 tptp.e_3)) :rule or_pos)
% 0.20/0.57  (step t19 (cl (not (tptp.group_element tptp.e_1)) (not (tptp.group_element tptp.e_2)) (tptp.product tptp.e_2 tptp.e_1 tptp.e_1) (tptp.product tptp.e_2 tptp.e_1 tptp.e_2) (tptp.product tptp.e_2 tptp.e_1 tptp.e_3) (not (or (not (tptp.group_element tptp.e_2)) (not (tptp.group_element tptp.e_1)) (tptp.product tptp.e_2 tptp.e_1 tptp.e_1) (tptp.product tptp.e_2 tptp.e_1 tptp.e_2) (tptp.product tptp.e_2 tptp.e_1 tptp.e_3)))) :rule reordering :premises (t18))
% 0.20/0.57  (step t20 (cl (not (or (not (tptp.product tptp.e_1 tptp.e_1 tptp.e_1)) (not (tptp.product tptp.e_2 tptp.e_1 tptp.e_1)) (tptp.equalish tptp.e_1 tptp.e_2))) (not (tptp.product tptp.e_1 tptp.e_1 tptp.e_1)) (not (tptp.product tptp.e_2 tptp.e_1 tptp.e_1)) (tptp.equalish tptp.e_1 tptp.e_2)) :rule or_pos)
% 0.20/0.57  (step t21 (cl (tptp.equalish tptp.e_1 tptp.e_2) (not (tptp.product tptp.e_1 tptp.e_1 tptp.e_1)) (not (tptp.product tptp.e_2 tptp.e_1 tptp.e_1)) (not (or (not (tptp.product tptp.e_1 tptp.e_1 tptp.e_1)) (not (tptp.product tptp.e_2 tptp.e_1 tptp.e_1)) (tptp.equalish tptp.e_1 tptp.e_2)))) :rule reordering :premises (t20))
% 0.20/0.57  (step t22 (cl (=> (forall ((X $$unsorted)) (tptp.product X X X)) (tptp.product tptp.e_1 tptp.e_1 tptp.e_1)) (forall ((X $$unsorted)) (tptp.product X X X))) :rule implies_neg1)
% 0.20/0.57  (anchor :step t23)
% 0.20/0.57  (assume t23.a0 (forall ((X $$unsorted)) (tptp.product X X X)))
% 0.20/0.57  (step t23.t1 (cl (or (not (forall ((X $$unsorted)) (tptp.product X X X))) (tptp.product tptp.e_1 tptp.e_1 tptp.e_1))) :rule forall_inst :args ((:= X tptp.e_1)))
% 0.20/0.57  (step t23.t2 (cl (not (forall ((X $$unsorted)) (tptp.product X X X))) (tptp.product tptp.e_1 tptp.e_1 tptp.e_1)) :rule or :premises (t23.t1))
% 0.20/0.57  (step t23.t3 (cl (tptp.product tptp.e_1 tptp.e_1 tptp.e_1)) :rule resolution :premises (t23.t2 t23.a0))
% 0.20/0.57  (step t23 (cl (not (forall ((X $$unsorted)) (tptp.product X X X))) (tptp.product tptp.e_1 tptp.e_1 tptp.e_1)) :rule subproof :discharge (t23.a0))
% 0.20/0.57  (step t24 (cl (=> (forall ((X $$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))
% 0.20/0.57  (step t25 (cl (=> (forall ((X $$unsorted)) (tptp.product X X X)) (tptp.product tptp.e_1 tptp.e_1 tptp.e_1)) (not (tptp.product tptp.e_1 tptp.e_1 tptp.e_1))) :rule implies_neg2)
% 0.20/0.57  (step t26 (cl (=> (forall ((X $$unsorted)) (tptp.product X X X)) (tptp.product tptp.e_1 tptp.e_1 tptp.e_1)) (=> (forall ((X $$unsorted)) (tptp.product X X X)) (tptp.product tptp.e_1 tptp.e_1 tptp.e_1))) :rule resolution :premises (t24 t25))
% 0.20/0.57  (step t27 (cl (=> (forall ((X $$unsorted)) (tptp.product X X X)) (tptp.product tptp.e_1 tptp.e_1 tptp.e_1))) :rule contraction :premises (t26))
% 0.20/0.57  (step t28 (cl (not (forall ((X $$unsorted)) (tptp.product X X X))) (tptp.product tptp.e_1 tptp.e_1 tptp.e_1)) :rule implies :premises (t27))
% 0.20/0.57  (step t29 (cl (tptp.product tptp.e_1 tptp.e_1 tptp.e_1)) :rule resolution :premises (t28 a13))
% 0.20/0.57  (step t30 (cl (=> (forall ((W $$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 $$unsorted)) (or (not (tptp.product W Y X)) (not (tptp.product Z Y X)) (tptp.equalish W Z)))) :rule implies_neg1)
% 0.20/0.57  (anchor :step t31)
% 0.20/0.57  (assume t31.a0 (forall ((W $$unsorted) (Y $$unsorted) (X $$unsorted) (Z $$unsorted)) (or (not (tptp.product W Y X)) (not (tptp.product Z Y X)) (tptp.equalish W Z))))
% 0.20/0.57  (step t31.t1 (cl (or (not (forall ((W $$unsorted) (Y $$unsorted) (X $$unsorted) (Z $$unsorted)) (or (not (tptp.product W Y X)) (not (tptp.product Z Y X)) (tptp.equalish W Z)))) (or (not (tptp.product tptp.e_1 tptp.e_1 tptp.e_1)) (not (tptp.product tptp.e_2 tptp.e_1 tptp.e_1)) (tptp.equalish tptp.e_1 tptp.e_2)))) :rule forall_inst :args ((:= W tptp.e_1) (:= Y tptp.e_1) (:= X tptp.e_1) (:= Z tptp.e_2)))
% 0.20/0.57  (step t31.t2 (cl (not (forall ((W $$unsorted) (Y $$unsorted) (X $$unsorted) (Z $$unsorted)) (or (not (tptp.product W Y X)) (not (tptp.product Z Y X)) (tptp.equalish W Z)))) (or (not (tptp.product tptp.e_1 tptp.e_1 tptp.e_1)) (not (tptp.product tptp.e_2 tptp.e_1 tptp.e_1)) (tptp.equalish tptp.e_1 tptp.e_2))) :rule or :premises (t31.t1))
% 0.20/0.57  (step t31.t3 (cl (or (not (tptp.product tptp.e_1 tptp.e_1 tptp.e_1)) (not (tptp.product tptp.e_2 tptp.e_1 tptp.e_1)) (tptp.equalish tptp.e_1 tptp.e_2))) :rule resolution :premises (t31.t2 t31.a0))
% 0.20/0.57  (step t31 (cl (not (forall ((W $$unsorted) (Y $$unsorted) (X $$unsorted) (Z $$unsorted)) (or (not (tptp.product W Y X)) (not (tptp.product Z Y X)) (tptp.equalish W Z)))) (or (not (tptp.product tptp.e_1 tptp.e_1 tptp.e_1)) (not (tptp.product tptp.e_2 tptp.e_1 tptp.e_1)) (tptp.equalish tptp.e_1 tptp.e_2))) :rule subproof :discharge (t31.a0))
% 0.20/0.57  (step t32 (cl (=> (forall ((W $$unsorted) (Y $$unsorted) (X $$unsorted) (Z $$unsorted)) (or (not (tptp.product W Y X)) (not (tptp.product Z Y X)) (tptp.equalish W Z))) (or (not (tptp.product tptp.e_1 tptp.e_1 tptp.e_1)) (not (tptp.product tptp.e_2 tptp.e_1 tptp.e_1)) (tptp.equalish tptp.e_1 tptp.e_2))) (or (not (tptp.product tptp.e_1 tptp.e_1 tptp.e_1)) (not (tptp.product tptp.e_2 tptp.e_1 tptp.e_1)) (tptp.equalish tptp.e_1 tptp.e_2))) :rule resolution :premises (t30 t31))
% 0.20/0.57  (step t33 (cl (=> (forall ((W $$unsorted) (Y $$unsorted) (X $$unsorted) (Z $$unsorted)) (or (not (tptp.product W Y X)) (not (tptp.product Z Y X)) (tptp.equalish W Z))) (or (not (tptp.product tptp.e_1 tptp.e_1 tptp.e_1)) (not (tptp.product tptp.e_2 tptp.e_1 tptp.e_1)) (tptp.equalish tptp.e_1 tptp.e_2))) (not (or (not (tptp.product tptp.e_1 tptp.e_1 tptp.e_1)) (not (tptp.product tptp.e_2 tptp.e_1 tptp.e_1)) (tptp.equalish tptp.e_1 tptp.e_2)))) :rule implies_neg2)
% 0.20/0.57  (step t34 (cl (=> (forall ((W $$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 $$unsorted)) (or (not (tptp.product W Y X)) (not (tptp.product Z Y X)) (tptp.equalish W Z))) (or (not (tptp.product tptp.e_1 tptp.e_1 tptp.e_1)) (not (tptp.product tptp.e_2 tptp.e_1 tptp.e_1)) (tptp.equalish tptp.e_1 tptp.e_2)))) :rule resolution :premises (t32 t33))
% 0.20/0.57  (step t35 (cl (=> (forall ((W $$unsorted) (Y $$unsorted) (X $$unsorted) (Z $$unsorted)) (or (not (tptp.product W Y X)) (not (tptp.product Z Y X)) (tptp.equalish W Z))) (or (not (tptp.product tptp.e_1 tptp.e_1 tptp.e_1)) (not (tptp.product tptp.e_2 tptp.e_1 tptp.e_1)) (tptp.equalish tptp.e_1 tptp.e_2)))) :rule contraction :premises (t34))
% 0.20/0.57  (step t36 (cl (not (forall ((W $$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))
% 0.20/0.57  (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))
% 0.20/0.57  (step t38 (cl (not (tptp.product tptp.e_2 tptp.e_1 tptp.e_1))) :rule resolution :premises (t21 a3 t29 t37))
% 0.20/0.57  (step t39 (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)
% 0.20/0.57  (step t40 (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 (t39))
% 0.20/0.57  (step t41 (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)
% 0.20/0.57  (step t42 (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 (t41))
% 0.20/0.57  (step t43 (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)
% 0.20/0.57  (step t44 (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 (t43))
% 0.20/0.57  (step t45 (cl (=> (forall ((W $$unsorted) (Y $$unsorted) (X $$unsorted) (Z $$unsorted)) (or (not (tptp.product W Y X)) (not (tptp.product Z Y X)) (tptp.equalish W Z))) (or (not (tptp.product tptp.e_1 tptp.e_1 tptp.e_1)) (not (tptp.product tptp.e_3 tptp.e_1 tptp.e_1)) (tptp.equalish tptp.e_1 tptp.e_3))) (forall ((W $$unsorted) (Y $$unsorted) (X $$unsorted) (Z $$unsorted)) (or (not (tptp.product W Y X)) (not (tptp.product Z Y X)) (tptp.equalish W Z)))) :rule implies_neg1)
% 0.20/0.57  (anchor :step t46)
% 0.20/0.57  (assume t46.a0 (forall ((W $$unsorted) (Y $$unsorted) (X $$unsorted) (Z $$unsorted)) (or (not (tptp.product W Y X)) (not (tptp.product Z Y X)) (tptp.equalish W Z))))
% 0.20/0.57  (step t46.t1 (cl (or (not (forall ((W $$unsorted) (Y $$unsorted) (X $$unsorted) (Z $$unsorted)) (or (not (tptp.product W Y X)) (not (tptp.product Z Y X)) (tptp.equalish W Z)))) (or (not (tptp.product tptp.e_1 tptp.e_1 tptp.e_1)) (not (tptp.product tptp.e_3 tptp.e_1 tptp.e_1)) (tptp.equalish tptp.e_1 tptp.e_3)))) :rule forall_inst :args ((:= W tptp.e_1) (:= Y tptp.e_1) (:= X tptp.e_1) (:= Z tptp.e_3)))
% 0.20/0.57  (step t46.t2 (cl (not (forall ((W $$unsorted) (Y $$unsorted) (X $$unsorted) (Z $$unsorted)) (or (not (tptp.product W Y X)) (not (tptp.product Z Y X)) (tptp.equalish W Z)))) (or (not (tptp.product tptp.e_1 tptp.e_1 tptp.e_1)) (not (tptp.product tptp.e_3 tptp.e_1 tptp.e_1)) (tptp.equalish tptp.e_1 tptp.e_3))) :rule or :premises (t46.t1))
% 0.20/0.57  (step t46.t3 (cl (or (not (tptp.product tptp.e_1 tptp.e_1 tptp.e_1)) (not (tptp.product tptp.e_3 tptp.e_1 tptp.e_1)) (tptp.equalish tptp.e_1 tptp.e_3))) :rule resolution :premises (t46.t2 t46.a0))
% 0.20/0.57  (step t46 (cl (not (forall ((W $$unsorted) (Y $$unsorted) (X $$unsorted) (Z $$unsorted)) (or (not (tptp.product W Y X)) (not (tptp.product Z Y X)) (tptp.equalish W Z)))) (or (not (tptp.product tptp.e_1 tptp.e_1 tptp.e_1)) (not (tptp.product tptp.e_3 tptp.e_1 tptp.e_1)) (tptp.equalish tptp.e_1 tptp.e_3))) :rule subproof :discharge (t46.a0))
% 0.20/0.57  (step t47 (cl (=> (forall ((W $$unsorted) (Y $$unsorted) (X $$unsorted) (Z $$unsorted)) (or (not (tptp.product W Y X)) (not (tptp.product Z Y X)) (tptp.equalish W Z))) (or (not (tptp.product tptp.e_1 tptp.e_1 tptp.e_1)) (not (tptp.product tptp.e_3 tptp.e_1 tptp.e_1)) (tptp.equalish tptp.e_1 tptp.e_3))) (or (not (tptp.product tptp.e_1 tptp.e_1 tptp.e_1)) (not (tptp.product tptp.e_3 tptp.e_1 tptp.e_1)) (tptp.equalish tptp.e_1 tptp.e_3))) :rule resolution :premises (t45 t46))
% 0.20/0.57  (step t48 (cl (=> (forall ((W $$unsorted) (Y $$unsorted) (X $$unsorted) (Z $$unsorted)) (or (not (tptp.product W Y X)) (not (tptp.product Z Y X)) (tptp.equalish W Z))) (or (not (tptp.product tptp.e_1 tptp.e_1 tptp.e_1)) (not (tptp.product tptp.e_3 tptp.e_1 tptp.e_1)) (tptp.equalish tptp.e_1 tptp.e_3))) (not (or (not (tptp.product tptp.e_1 tptp.e_1 tptp.e_1)) (not (tptp.product tptp.e_3 tptp.e_1 tptp.e_1)) (tptp.equalish tptp.e_1 tptp.e_3)))) :rule implies_neg2)
% 0.20/0.57  (step t49 (cl (=> (forall ((W $$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 $$unsorted)) (or (not (tptp.product W Y X)) (not (tptp.product Z Y X)) (tptp.equalish W Z))) (or (not (tptp.product tptp.e_1 tptp.e_1 tptp.e_1)) (not (tptp.product tptp.e_3 tptp.e_1 tptp.e_1)) (tptp.equalish tptp.e_1 tptp.e_3)))) :rule resolution :premises (t47 t48))
% 0.20/0.57  (step t50 (cl (=> (forall ((W $$unsorted) (Y $$unsorted) (X $$unsorted) (Z $$unsorted)) (or (not (tptp.product W Y X)) (not (tptp.product Z Y X)) (tptp.equalish W Z))) (or (not (tptp.product tptp.e_1 tptp.e_1 tptp.e_1)) (not (tptp.product tptp.e_3 tptp.e_1 tptp.e_1)) (tptp.equalish tptp.e_1 tptp.e_3)))) :rule contraction :premises (t49))
% 0.20/0.57  (step t51 (cl (not (forall ((W $$unsorted) (Y $$unsorted) (X $$unsorted) (Z $$unsorted)) (or (not (tptp.product W Y X)) (not (tptp.product Z Y X)) (tptp.equalish W Z)))) (or (not (tptp.product tptp.e_1 tptp.e_1 tptp.e_1)) (not (tptp.product tptp.e_3 tptp.e_1 tptp.e_1)) (tptp.equalish tptp.e_1 tptp.e_3))) :rule implies :premises (t50))
% 0.20/0.57  (step t52 (cl (or (not (tptp.product tptp.e_1 tptp.e_1 tptp.e_1)) (not (tptp.product tptp.e_3 tptp.e_1 tptp.e_1)) (tptp.equalish tptp.e_1 tptp.e_3))) :rule resolution :premises (t51 a12))
% 0.20/0.57  (step t53 (cl (not (tptp.product tptp.e_3 tptp.e_1 tptp.e_1))) :rule resolution :premises (t44 a4 t29 t52))
% 0.20/0.57  (step t54 (cl (not (or (not (tptp.product tptp.e_1 tptp.e_3 tptp.e_2)) (not (tptp.product tptp.e_3 tptp.e_1 tptp.e_2)) (tptp.product tptp.e_2 tptp.e_2 tptp.e_1))) (not (tptp.product tptp.e_1 tptp.e_3 tptp.e_2)) (not (tptp.product tptp.e_3 tptp.e_1 tptp.e_2)) (tptp.product tptp.e_2 tptp.e_2 tptp.e_1)) :rule or_pos)
% 0.20/0.57  (step t55 (cl (tptp.product tptp.e_2 tptp.e_2 tptp.e_1) (not (tptp.product tptp.e_1 tptp.e_3 tptp.e_2)) (not (tptp.product tptp.e_3 tptp.e_1 tptp.e_2)) (not (or (not (tptp.product tptp.e_1 tptp.e_3 tptp.e_2)) (not (tptp.product tptp.e_3 tptp.e_1 tptp.e_2)) (tptp.product tptp.e_2 tptp.e_2 tptp.e_1)))) :rule reordering :premises (t54))
% 0.20/0.57  (step t56 (cl (not (or (not (tptp.product tptp.e_2 tptp.e_2 tptp.e_1)) (not (tptp.product tptp.e_2 tptp.e_2 tptp.e_2)) (tptp.equalish tptp.e_1 tptp.e_2))) (not (tptp.product tptp.e_2 tptp.e_2 tptp.e_1)) (not (tptp.product tptp.e_2 tptp.e_2 tptp.e_2)) (tptp.equalish tptp.e_1 tptp.e_2)) :rule or_pos)
% 0.20/0.57  (step t57 (cl (tptp.equalish tptp.e_1 tptp.e_2) (not (tptp.product tptp.e_2 tptp.e_2 tptp.e_2)) (not (tptp.product tptp.e_2 tptp.e_2 tptp.e_1)) (not (or (not (tptp.product tptp.e_2 tptp.e_2 tptp.e_1)) (not (tptp.product tptp.e_2 tptp.e_2 tptp.e_2)) (tptp.equalish tptp.e_1 tptp.e_2)))) :rule reordering :premises (t56))
% 0.20/0.57  (step t58 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (W $$unsorted) (Z $$unsorted)) (or (not (tptp.product X Y W)) (not (tptp.product X Y Z)) (tptp.equalish W Z))) (or (not (tptp.product tptp.e_2 tptp.e_2 tptp.e_1)) (not (tptp.product tptp.e_2 tptp.e_2 tptp.e_2)) (tptp.equalish tptp.e_1 tptp.e_2))) (forall ((X $$unsorted) (Y $$unsorted) (W $$unsorted) (Z $$unsorted)) (or (not (tptp.product X Y W)) (not (tptp.product X Y Z)) (tptp.equalish W Z)))) :rule implies_neg1)
% 0.20/0.57  (anchor :step t59)
% 0.20/0.57  (assume t59.a0 (forall ((X $$unsorted) (Y $$unsorted) (W $$unsorted) (Z $$unsorted)) (or (not (tptp.product X Y W)) (not (tptp.product X Y Z)) (tptp.equalish W Z))))
% 0.20/0.57  (step t59.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted) (W $$unsorted) (Z $$unsorted)) (or (not (tptp.product X Y W)) (not (tptp.product X Y Z)) (tptp.equalish W Z)))) (or (not (tptp.product tptp.e_2 tptp.e_2 tptp.e_1)) (not (tptp.product tptp.e_2 tptp.e_2 tptp.e_2)) (tptp.equalish tptp.e_1 tptp.e_2)))) :rule forall_inst :args ((:= X tptp.e_2) (:= Y tptp.e_2) (:= W tptp.e_1) (:= Z tptp.e_2)))
% 0.20/0.57  (step t59.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (W $$unsorted) (Z $$unsorted)) (or (not (tptp.product X Y W)) (not (tptp.product X Y Z)) (tptp.equalish W Z)))) (or (not (tptp.product tptp.e_2 tptp.e_2 tptp.e_1)) (not (tptp.product tptp.e_2 tptp.e_2 tptp.e_2)) (tptp.equalish tptp.e_1 tptp.e_2))) :rule or :premises (t59.t1))
% 0.20/0.57  (step t59.t3 (cl (or (not (tptp.product tptp.e_2 tptp.e_2 tptp.e_1)) (not (tptp.product tptp.e_2 tptp.e_2 tptp.e_2)) (tptp.equalish tptp.e_1 tptp.e_2))) :rule resolution :premises (t59.t2 t59.a0))
% 0.20/0.57  (step t59 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (W $$unsorted) (Z $$unsorted)) (or (not (tptp.product X Y W)) (not (tptp.product X Y Z)) (tptp.equalish W Z)))) (or (not (tptp.product tptp.e_2 tptp.e_2 tptp.e_1)) (not (tptp.product tptp.e_2 tptp.e_2 tptp.e_2)) (tptp.equalish tptp.e_1 tptp.e_2))) :rule subproof :discharge (t59.a0))
% 0.20/0.57  (step t60 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (W $$unsorted) (Z $$unsorted)) (or (not (tptp.product X Y W)) (not (tptp.product X Y Z)) (tptp.equalish W Z))) (or (not (tptp.product tptp.e_2 tptp.e_2 tptp.e_1)) (not (tptp.product tptp.e_2 tptp.e_2 tptp.e_2)) (tptp.equalish tptp.e_1 tptp.e_2))) (or (not (tptp.product tptp.e_2 tptp.e_2 tptp.e_1)) (not (tptp.product tptp.e_2 tptp.e_2 tptp.e_2)) (tptp.equalish tptp.e_1 tptp.e_2))) :rule resolution :premises (t58 t59))
% 0.20/0.57  (step t61 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (W $$unsorted) (Z $$unsorted)) (or (not (tptp.product X Y W)) (not (tptp.product X Y Z)) (tptp.equalish W Z))) (or (not (tptp.product tptp.e_2 tptp.e_2 tptp.e_1)) (not (tptp.product tptp.e_2 tptp.e_2 tptp.e_2)) (tptp.equalish tptp.e_1 tptp.e_2))) (not (or (not (tptp.product tptp.e_2 tptp.e_2 tptp.e_1)) (not (tptp.product tptp.e_2 tptp.e_2 tptp.e_2)) (tptp.equalish tptp.e_1 tptp.e_2)))) :rule implies_neg2)
% 0.20/0.57  (step t62 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (W $$unsorted) (Z $$unsorted)) (or (not (tptp.product X Y W)) (not (tptp.product X Y Z)) (tptp.equalish W Z))) (or (not (tptp.product tptp.e_2 tptp.e_2 tptp.e_1)) (not (tptp.product tptp.e_2 tptp.e_2 tptp.e_2)) (tptp.equalish tptp.e_1 tptp.e_2))) (=> (forall ((X $$unsorted) (Y $$unsorted) (W $$unsorted) (Z $$unsorted)) (or (not (tptp.product X Y W)) (not (tptp.product X Y Z)) (tptp.equalish W Z))) (or (not (tptp.product tptp.e_2 tptp.e_2 tptp.e_1)) (not (tptp.product tptp.e_2 tptp.e_2 tptp.e_2)) (tptp.equalish tptp.e_1 tptp.e_2)))) :rule resolution :premises (t60 t61))
% 0.20/0.57  (step t63 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (W $$unsorted) (Z $$unsorted)) (or (not (tptp.product X Y W)) (not (tptp.product X Y Z)) (tptp.equalish W Z))) (or (not (tptp.product tptp.e_2 tptp.e_2 tptp.e_1)) (not (tptp.product tptp.e_2 tptp.e_2 tptp.e_2)) (tptp.equalish tptp.e_1 tptp.e_2)))) :rule contraction :premises (t62))
% 0.20/0.57  (step t64 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (W $$unsorted) (Z $$unsorted)) (or (not (tptp.product X Y W)) (not (tptp.product X Y Z)) (tptp.equalish W Z)))) (or (not (tptp.product tptp.e_2 tptp.e_2 tptp.e_1)) (not (tptp.product tptp.e_2 tptp.e_2 tptp.e_2)) (tptp.equalish tptp.e_1 tptp.e_2))) :rule implies :premises (t63))
% 0.20/0.57  (step t65 (cl (or (not (tptp.product tptp.e_2 tptp.e_2 tptp.e_1)) (not (tptp.product tptp.e_2 tptp.e_2 tptp.e_2)) (tptp.equalish tptp.e_1 tptp.e_2))) :rule resolution :premises (t64 a10))
% 0.20/0.57  (step t66 (cl (not (tptp.product tptp.e_2 tptp.e_2 tptp.e_1))) :rule resolution :premises (t57 a3 t17 t65))
% 0.20/0.57  (step t67 (cl (not (or (not (tptp.group_element tptp.e_1)) (not (tptp.group_element tptp.e_3)) (tptp.product tptp.e_1 tptp.e_3 tptp.e_1) (tptp.product tptp.e_1 tptp.e_3 tptp.e_2) (tptp.product tptp.e_1 tptp.e_3 tptp.e_3))) (not (tptp.group_element tptp.e_1)) (not (tptp.group_element tptp.e_3)) (tptp.product tptp.e_1 tptp.e_3 tptp.e_1) (tptp.product tptp.e_1 tptp.e_3 tptp.e_2) (tptp.product tptp.e_1 tptp.e_3 tptp.e_3)) :rule or_pos)
% 0.20/0.57  (step t68 (cl (not (tptp.group_element tptp.e_1)) (not (tptp.group_element tptp.e_3)) (tptp.product tptp.e_1 tptp.e_3 tptp.e_1) (tptp.product tptp.e_1 tptp.e_3 tptp.e_2) (tptp.product tptp.e_1 tptp.e_3 tptp.e_3) (not (or (not (tptp.group_element tptp.e_1)) (not (tptp.group_element tptp.e_3)) (tptp.product tptp.e_1 tptp.e_3 tptp.e_1) (tptp.product tptp.e_1 tptp.e_3 tptp.e_2) (tptp.product tptp.e_1 tptp.e_3 tptp.e_3)))) :rule reordering :premises (t67))
% 0.20/0.57  (step t69 (cl (not (or (not (tptp.product tptp.e_1 tptp.e_3 tptp.e_1)) (not (tptp.product tptp.e_1 tptp.e_1 tptp.e_1)) (tptp.equalish tptp.e_3 tptp.e_1))) (not (tptp.product tptp.e_1 tptp.e_3 tptp.e_1)) (not (tptp.product tptp.e_1 tptp.e_1 tptp.e_1)) (tptp.equalish tptp.e_3 tptp.e_1)) :rule or_pos)
% 0.20/0.57  (step t70 (cl (tptp.equalish tptp.e_3 tptp.e_1) (not (tptp.product tptp.e_1 tptp.e_1 tptp.e_1)) (not (tptp.product tptp.e_1 tptp.e_3 tptp.e_1)) (not (or (not (tptp.product tptp.e_1 tptp.e_3 tptp.e_1)) (not (tptp.product tptp.e_1 tptp.e_1 tptp.e_1)) (tptp.equalish tptp.e_3 tptp.e_1)))) :rule reordering :premises (t69))
% 0.20/0.57  (step t71 (cl (=> (forall ((X $$unsorted) (W $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.product X W Y)) (not (tptp.product X Z Y)) (tptp.equalish W Z))) (or (not (tptp.product tptp.e_1 tptp.e_3 tptp.e_1)) (not (tptp.product tptp.e_1 tptp.e_1 tptp.e_1)) (tptp.equalish tptp.e_3 tptp.e_1))) (forall ((X $$unsorted) (W $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.product X W Y)) (not (tptp.product X Z Y)) (tptp.equalish W Z)))) :rule implies_neg1)
% 0.20/0.57  (anchor :step t72)
% 0.20/0.57  (assume t72.a0 (forall ((X $$unsorted) (W $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.product X W Y)) (not (tptp.product X Z Y)) (tptp.equalish W Z))))
% 0.20/0.57  (step t72.t1 (cl (or (not (forall ((X $$unsorted) (W $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.product X W Y)) (not (tptp.product X Z Y)) (tptp.equalish W Z)))) (or (not (tptp.product tptp.e_1 tptp.e_3 tptp.e_1)) (not (tptp.product tptp.e_1 tptp.e_1 tptp.e_1)) (tptp.equalish tptp.e_3 tptp.e_1)))) :rule forall_inst :args ((:= X tptp.e_1) (:= W tptp.e_3) (:= Y tptp.e_1) (:= Z tptp.e_1)))
% 0.20/0.57  (step t72.t2 (cl (not (forall ((X $$unsorted) (W $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.product X W Y)) (not (tptp.product X Z Y)) (tptp.equalish W Z)))) (or (not (tptp.product tptp.e_1 tptp.e_3 tptp.e_1)) (not (tptp.product tptp.e_1 tptp.e_1 tptp.e_1)) (tptp.equalish tptp.e_3 tptp.e_1))) :rule or :premises (t72.t1))
% 0.20/0.57  (step t72.t3 (cl (or (not (tptp.product tptp.e_1 tptp.e_3 tptp.e_1)) (not (tptp.product tptp.e_1 tptp.e_1 tptp.e_1)) (tptp.equalish tptp.e_3 tptp.e_1))) :rule resolution :premises (t72.t2 t72.a0))
% 0.20/0.57  (step t72 (cl (not (forall ((X $$unsorted) (W $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.product X W Y)) (not (tptp.product X Z Y)) (tptp.equalish W Z)))) (or (not (tptp.product tptp.e_1 tptp.e_3 tptp.e_1)) (not (tptp.product tptp.e_1 tptp.e_1 tptp.e_1)) (tptp.equalish tptp.e_3 tptp.e_1))) :rule subproof :discharge (t72.a0))
% 0.20/0.57  (step t73 (cl (=> (forall ((X $$unsorted) (W $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.product X W Y)) (not (tptp.product X Z Y)) (tptp.equalish W Z))) (or (not (tptp.product tptp.e_1 tptp.e_3 tptp.e_1)) (not (tptp.product tptp.e_1 tptp.e_1 tptp.e_1)) (tptp.equalish tptp.e_3 tptp.e_1))) (or (not (tptp.product tptp.e_1 tptp.e_3 tptp.e_1)) (not (tptp.product tptp.e_1 tptp.e_1 tptp.e_1)) (tptp.equalish tptp.e_3 tptp.e_1))) :rule resolution :premises (t71 t72))
% 0.20/0.57  (step t74 (cl (=> (forall ((X $$unsorted) (W $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.product X W Y)) (not (tptp.product X Z Y)) (tptp.equalish W Z))) (or (not (tptp.product tptp.e_1 tptp.e_3 tptp.e_1)) (not (tptp.product tptp.e_1 tptp.e_1 tptp.e_1)) (tptp.equalish tptp.e_3 tptp.e_1))) (not (or (not (tptp.product tptp.e_1 tptp.e_3 tptp.e_1)) (not (tptp.product tptp.e_1 tptp.e_1 tptp.e_1)) (tptp.equalish tptp.e_3 tptp.e_1)))) :rule implies_neg2)
% 0.20/0.57  (step t75 (cl (=> (forall ((X $$unsorted) (W $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.product X W Y)) (not (tptp.product X Z Y)) (tptp.equalish W Z))) (or (not (tptp.product tptp.e_1 tptp.e_3 tptp.e_1)) (not (tptp.product tptp.e_1 tptp.e_1 tptp.e_1)) (tptp.equalish tptp.e_3 tptp.e_1))) (=> (forall ((X $$unsorted) (W $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.product X W Y)) (not (tptp.product X Z Y)) (tptp.equalish W Z))) (or (not (tptp.product tptp.e_1 tptp.e_3 tptp.e_1)) (not (tptp.product tptp.e_1 tptp.e_1 tptp.e_1)) (tptp.equalish tptp.e_3 tptp.e_1)))) :rule resolution :premises (t73 t74))
% 0.20/0.57  (step t76 (cl (=> (forall ((X $$unsorted) (W $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.product X W Y)) (not (tptp.product X Z Y)) (tptp.equalish W Z))) (or (not (tptp.product tptp.e_1 tptp.e_3 tptp.e_1)) (not (tptp.product tptp.e_1 tptp.e_1 tptp.e_1)) (tptp.equalish tptp.e_3 tptp.e_1)))) :rule contraction :premises (t75))
% 0.20/0.57  (step t77 (cl (not (forall ((X $$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_1 tptp.e_3 tptp.e_1)) (not (tptp.product tptp.e_1 tptp.e_1 tptp.e_1)) (tptp.equalish tptp.e_3 tptp.e_1))) :rule implies :premises (t76))
% 0.20/0.57  (step t78 (cl (or (not (tptp.product tptp.e_1 tptp.e_3 tptp.e_1)) (not (tptp.product tptp.e_1 tptp.e_1 tptp.e_1)) (tptp.equalish tptp.e_3 tptp.e_1))) :rule resolution :premises (t77 a11))
% 0.20/0.57  (step t79 (cl (not (tptp.product tptp.e_1 tptp.e_3 tptp.e_1))) :rule resolution :premises (t70 a7 t29 t78))
% 0.20/0.57  (step t80 (cl (not (or (not (tptp.product tptp.e_1 tptp.e_3 tptp.e_3)) (not (tptp.product tptp.e_1 tptp.e_2 tptp.e_3)) (tptp.equalish tptp.e_3 tptp.e_2))) (not (tptp.product tptp.e_1 tptp.e_3 tptp.e_3)) (not (tptp.product tptp.e_1 tptp.e_2 tptp.e_3)) (tptp.equalish tptp.e_3 tptp.e_2)) :rule or_pos)
% 0.20/0.57  (step t81 (cl (tptp.equalish tptp.e_3 tptp.e_2) (not (tptp.product tptp.e_1 tptp.e_2 tptp.e_3)) (not (tptp.product tptp.e_1 tptp.e_3 tptp.e_3)) (not (or (not (tptp.product tptp.e_1 tptp.e_3 tptp.e_3)) (not (tptp.product tptp.e_1 tptp.e_2 tptp.e_3)) (tptp.equalish tptp.e_3 tptp.e_2)))) :rule reordering :premises (t80))
% 0.20/0.57  (step t82 (cl (not (or (not (tptp.group_element tptp.e_1)) (not (tptp.group_element tptp.e_2)) (tptp.product tptp.e_1 tptp.e_2 tptp.e_1) (tptp.product tptp.e_1 tptp.e_2 tptp.e_2) (tptp.product tptp.e_1 tptp.e_2 tptp.e_3))) (not (tptp.group_element tptp.e_1)) (not (tptp.group_element tptp.e_2)) (tptp.product tptp.e_1 tptp.e_2 tptp.e_1) (tptp.product tptp.e_1 tptp.e_2 tptp.e_2) (tptp.product tptp.e_1 tptp.e_2 tptp.e_3)) :rule or_pos)
% 0.20/0.57  (step t83 (cl (not (tptp.group_element tptp.e_1)) (not (tptp.group_element tptp.e_2)) (tptp.product tptp.e_1 tptp.e_2 tptp.e_1) (tptp.product tptp.e_1 tptp.e_2 tptp.e_2) (tptp.product 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.product tptp.e_1 tptp.e_2 tptp.e_1) (tptp.product tptp.e_1 tptp.e_2 tptp.e_2) (tptp.product tptp.e_1 tptp.e_2 tptp.e_3)))) :rule reordering :premises (t82))
% 0.20/0.57  (step t84 (cl (not (or (not (tptp.product tptp.e_1 tptp.e_1 tptp.e_1)) (not (tptp.product tptp.e_1 tptp.e_2 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_1 tptp.e_2 tptp.e_1)) (tptp.equalish tptp.e_1 tptp.e_2)) :rule or_pos)
% 0.20/0.57  (step t85 (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_1 tptp.e_2 tptp.e_1)) (not (or (not (tptp.product tptp.e_1 tptp.e_1 tptp.e_1)) (not (tptp.product tptp.e_1 tptp.e_2 tptp.e_1)) (tptp.equalish tptp.e_1 tptp.e_2)))) :rule reordering :premises (t84))
% 0.20/0.57  (step t86 (cl (=> (forall ((X $$unsorted) (W $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.product X W Y)) (not (tptp.product X Z Y)) (tptp.equalish W Z))) (or (not (tptp.product tptp.e_1 tptp.e_1 tptp.e_1)) (not (tptp.product tptp.e_1 tptp.e_2 tptp.e_1)) (tptp.equalish tptp.e_1 tptp.e_2))) (forall ((X $$unsorted) (W $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.product X W Y)) (not (tptp.product X Z Y)) (tptp.equalish W Z)))) :rule implies_neg1)
% 0.20/0.57  (anchor :step t87)
% 0.20/0.57  (assume t87.a0 (forall ((X $$unsorted) (W $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.product X W Y)) (not (tptp.product X Z Y)) (tptp.equalish W Z))))
% 0.20/0.57  (step t87.t1 (cl (or (not (forall ((X $$unsorted) (W $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.product X W Y)) (not (tptp.product X Z Y)) (tptp.equalish W Z)))) (or (not (tptp.product tptp.e_1 tptp.e_1 tptp.e_1)) (not (tptp.product tptp.e_1 tptp.e_2 tptp.e_1)) (tptp.equalish tptp.e_1 tptp.e_2)))) :rule forall_inst :args ((:= X tptp.e_1) (:= W tptp.e_1) (:= Y tptp.e_1) (:= Z tptp.e_2)))
% 0.20/0.57  (step t87.t2 (cl (not (forall ((X $$unsorted) (W $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.product X W Y)) (not (tptp.product X Z Y)) (tptp.equalish W Z)))) (or (not (tptp.product tptp.e_1 tptp.e_1 tptp.e_1)) (not (tptp.product tptp.e_1 tptp.e_2 tptp.e_1)) (tptp.equalish tptp.e_1 tptp.e_2))) :rule or :premises (t87.t1))
% 0.20/0.57  (step t87.t3 (cl (or (not (tptp.product tptp.e_1 tptp.e_1 tptp.e_1)) (not (tptp.product tptp.e_1 tptp.e_2 tptp.e_1)) (tptp.equalish tptp.e_1 tptp.e_2))) :rule resolution :premises (t87.t2 t87.a0))
% 0.20/0.57  (step t87 (cl (not (forall ((X $$unsorted) (W $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.product X W Y)) (not (tptp.product X Z Y)) (tptp.equalish W Z)))) (or (not (tptp.product tptp.e_1 tptp.e_1 tptp.e_1)) (not (tptp.product tptp.e_1 tptp.e_2 tptp.e_1)) (tptp.equalish tptp.e_1 tptp.e_2))) :rule subproof :discharge (t87.a0))
% 0.20/0.57  (step t88 (cl (=> (forall ((X $$unsorted) (W $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.product X W Y)) (not (tptp.product X Z Y)) (tptp.equalish W Z))) (or (not (tptp.product tptp.e_1 tptp.e_1 tptp.e_1)) (not (tptp.product tptp.e_1 tptp.e_2 tptp.e_1)) (tptp.equalish tptp.e_1 tptp.e_2))) (or (not (tptp.product tptp.e_1 tptp.e_1 tptp.e_1)) (not (tptp.product tptp.e_1 tptp.e_2 tptp.e_1)) (tptp.equalish tptp.e_1 tptp.e_2))) :rule resolution :premises (t86 t87))
% 0.20/0.57  (step t89 (cl (=> (forall ((X $$unsorted) (W $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.product X W Y)) (not (tptp.product X Z Y)) (tptp.equalish W Z))) (or (not (tptp.product tptp.e_1 tptp.e_1 tptp.e_1)) (not (tptp.product tptp.e_1 tptp.e_2 tptp.e_1)) (tptp.equalish tptp.e_1 tptp.e_2))) (not (or (not (tptp.product tptp.e_1 tptp.e_1 tptp.e_1)) (not (tptp.product tptp.e_1 tptp.e_2 tptp.e_1)) (tptp.equalish tptp.e_1 tptp.e_2)))) :rule implies_neg2)
% 0.20/0.57  (step t90 (cl (=> (forall ((X $$unsorted) (W $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.product X W Y)) (not (tptp.product X Z Y)) (tptp.equalish W Z))) (or (not (tptp.product tptp.e_1 tptp.e_1 tptp.e_1)) (not (tptp.product tptp.e_1 tptp.e_2 tptp.e_1)) (tptp.equalish tptp.e_1 tptp.e_2))) (=> (forall ((X $$unsorted) (W $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.product X W Y)) (not (tptp.product X Z Y)) (tptp.equalish W Z))) (or (not (tptp.product tptp.e_1 tptp.e_1 tptp.e_1)) (not (tptp.product tptp.e_1 tptp.e_2 tptp.e_1)) (tptp.equalish tptp.e_1 tptp.e_2)))) :rule resolution :premises (t88 t89))
% 0.20/0.57  (step t91 (cl (=> (forall ((X $$unsorted) (W $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.product X W Y)) (not (tptp.product X Z Y)) (tptp.equalish W Z))) (or (not (tptp.product tptp.e_1 tptp.e_1 tptp.e_1)) (not (tptp.product tptp.e_1 tptp.e_2 tptp.e_1)) (tptp.equalish tptp.e_1 tptp.e_2)))) :rule contraction :premises (t90))
% 0.20/0.57  (step t92 (cl (not (forall ((X $$unsorted) (W $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.product X W Y)) (not (tptp.product X Z Y)) (tptp.equalish W Z)))) (or (not (tptp.product tptp.e_1 tptp.e_1 tptp.e_1)) (not (tptp.product tptp.e_1 tptp.e_2 tptp.e_1)) (tptp.equalish tptp.e_1 tptp.e_2))) :rule implies :premises (t91))
% 0.20/0.57  (step t93 (cl (or (not (tptp.product tptp.e_1 tptp.e_1 tptp.e_1)) (not (tptp.product tptp.e_1 tptp.e_2 tptp.e_1)) (tptp.equalish tptp.e_1 tptp.e_2))) :rule resolution :premises (t92 a11))
% 0.20/0.57  (step t94 (cl (not (tptp.product tptp.e_1 tptp.e_2 tptp.e_1))) :rule resolution :premises (t85 a3 t29 t93))
% 0.20/0.57  (step t95 (cl (not (or (not (tptp.product tptp.e_2 tptp.e_2 tptp.e_2)) (not (tptp.product tptp.e_1 tptp.e_2 tptp.e_2)) (tptp.equalish tptp.e_2 tptp.e_1))) (not (tptp.product tptp.e_2 tptp.e_2 tptp.e_2)) (not (tptp.product tptp.e_1 tptp.e_2 tptp.e_2)) (tptp.equalish tptp.e_2 tptp.e_1)) :rule or_pos)
% 0.20/0.57  (step t96 (cl (tptp.equalish tptp.e_2 tptp.e_1) (not (tptp.product tptp.e_1 tptp.e_2 tptp.e_2)) (not (tptp.product tptp.e_2 tptp.e_2 tptp.e_2)) (not (or (not (tptp.product tptp.e_2 tptp.e_2 tptp.e_2)) (not (tptp.product tptp.e_1 tptp.e_2 tptp.e_2)) (tptp.equalish tptp.e_2 tptp.e_1)))) :rule reordering :premises (t95))
% 0.20/0.57  (step t97 (cl (=> (forall ((W $$unsorted) (Y $$unsorted) (X $$unsorted) (Z $$unsorted)) (or (not (tptp.product W Y X)) (not (tptp.product Z Y X)) (tptp.equalish W Z))) (or (not (tptp.product tptp.e_2 tptp.e_2 tptp.e_2)) (not (tptp.product tptp.e_1 tptp.e_2 tptp.e_2)) (tptp.equalish tptp.e_2 tptp.e_1))) (forall ((W $$unsorted) (Y $$unsorted) (X $$unsorted) (Z $$unsorted)) (or (not (tptp.product W Y X)) (not (tptp.product Z Y X)) (tptp.equalish W Z)))) :rule implies_neg1)
% 0.20/0.57  (anchor :step t98)
% 0.20/0.57  (assume t98.a0 (forall ((W $$unsorted) (Y $$unsorted) (X $$unsorted) (Z $$unsorted)) (or (not (tptp.product W Y X)) (not (tptp.product Z Y X)) (tptp.equalish W Z))))
% 0.20/0.57  (step t98.t1 (cl (or (not (forall ((W $$unsorted) (Y $$unsorted) (X $$unsorted) (Z $$unsorted)) (or (not (tptp.product W Y X)) (not (tptp.product Z Y X)) (tptp.equalish W Z)))) (or (not (tptp.product tptp.e_2 tptp.e_2 tptp.e_2)) (not (tptp.product tptp.e_1 tptp.e_2 tptp.e_2)) (tptp.equalish tptp.e_2 tptp.e_1)))) :rule forall_inst :args ((:= W tptp.e_2) (:= Y tptp.e_2) (:= X tptp.e_2) (:= Z tptp.e_1)))
% 0.20/0.57  (step t98.t2 (cl (not (forall ((W $$unsorted) (Y $$unsorted) (X $$unsorted) (Z $$unsorted)) (or (not (tptp.product W Y X)) (not (tptp.product Z Y X)) (tptp.equalish W Z)))) (or (not (tptp.product tptp.e_2 tptp.e_2 tptp.e_2)) (not (tptp.product tptp.e_1 tptp.e_2 tptp.e_2)) (tptp.equalish tptp.e_2 tptp.e_1))) :rule or :premises (t98.t1))
% 0.20/0.57  (step t98.t3 (cl (or (not (tptp.product tptp.e_2 tptp.e_2 tptp.e_2)) (not (tptp.product tptp.e_1 tptp.e_2 tptp.e_2)) (tptp.equalish tptp.e_2 tptp.e_1))) :rule resolution :premises (t98.t2 t98.a0))
% 0.20/0.57  (step t98 (cl (not (forall ((W $$unsorted) (Y $$unsorted) (X $$unsorted) (Z $$unsorted)) (or (not (tptp.product W Y X)) (not (tptp.product Z Y X)) (tptp.equalish W Z)))) (or (not (tptp.product tptp.e_2 tptp.e_2 tptp.e_2)) (not (tptp.product tptp.e_1 tptp.e_2 tptp.e_2)) (tptp.equalish tptp.e_2 tptp.e_1))) :rule subproof :discharge (t98.a0))
% 0.20/0.57  (step t99 (cl (=> (forall ((W $$unsorted) (Y $$unsorted) (X $$unsorted) (Z $$unsorted)) (or (not (tptp.product W Y X)) (not (tptp.product Z Y X)) (tptp.equalish W Z))) (or (not (tptp.product tptp.e_2 tptp.e_2 tptp.e_2)) (not (tptp.product tptp.e_1 tptp.e_2 tptp.e_2)) (tptp.equalish tptp.e_2 tptp.e_1))) (or (not (tptp.product tptp.e_2 tptp.e_2 tptp.e_2)) (not (tptp.product tptp.e_1 tptp.e_2 tptp.e_2)) (tptp.equalish tptp.e_2 tptp.e_1))) :rule resolution :premises (t97 t98))
% 0.20/0.57  (step t100 (cl (=> (forall ((W $$unsorted) (Y $$unsorted) (X $$unsorted) (Z $$unsorted)) (or (not (tptp.product W Y X)) (not (tptp.product Z Y X)) (tptp.equalish W Z))) (or (not (tptp.product tptp.e_2 tptp.e_2 tptp.e_2)) (not (tptp.product tptp.e_1 tptp.e_2 tptp.e_2)) (tptp.equalish tptp.e_2 tptp.e_1))) (not (or (not (tptp.product tptp.e_2 tptp.e_2 tptp.e_2)) (not (tptp.product tptp.e_1 tptp.e_2 tptp.e_2)) (tptp.equalish tptp.e_2 tptp.e_1)))) :rule implies_neg2)
% 0.20/0.57  (step t101 (cl (=> (forall ((W $$unsorted) (Y $$unsorted) (X $$unsorted) (Z $$unsorted)) (or (not (tptp.product W Y X)) (not (tptp.product Z Y X)) (tptp.equalish W Z))) (or (not (tptp.product tptp.e_2 tptp.e_2 tptp.e_2)) (not (tptp.product tptp.e_1 tptp.e_2 tptp.e_2)) (tptp.equalish tptp.e_2 tptp.e_1))) (=> (forall ((W $$unsorted) (Y $$unsorted) (X $$unsorted) (Z $$unsorted)) (or (not (tptp.product W Y X)) (not (tptp.product Z Y X)) (tptp.equalish W Z))) (or (not (tptp.product tptp.e_2 tptp.e_2 tptp.e_2)) (not (tptp.product tptp.e_1 tptp.e_2 tptp.e_2)) (tptp.equalish tptp.e_2 tptp.e_1)))) :rule resolution :premises (t99 t100))
% 0.20/0.57  (step t102 (cl (=> (forall ((W $$unsorted) (Y $$unsorted) (X $$unsorted) (Z $$unsorted)) (or (not (tptp.product W Y X)) (not (tptp.product Z Y X)) (tptp.equalish W Z))) (or (not (tptp.product tptp.e_2 tptp.e_2 tptp.e_2)) (not (tptp.product tptp.e_1 tptp.e_2 tptp.e_2)) (tptp.equalish tptp.e_2 tptp.e_1)))) :rule contraction :premises (t101))
% 0.20/0.57  (step t103 (cl (not (forall ((W $$unsorted) (Y $$unsorted) (X $$unsorted) (Z $$unsorted)) (or (not (tptp.product W Y X)) (not (tptp.product Z Y X)) (tptp.equalish W Z)))) (or (not (tptp.product tptp.e_2 tptp.e_2 tptp.e_2)) (not (tptp.product tptp.e_1 tptp.e_2 tptp.e_2)) (tptp.equalish tptp.e_2 tptp.e_1))) :rule implies :premises (t102))
% 0.20/0.57  (step t104 (cl (or (not (tptp.product tptp.e_2 tptp.e_2 tptp.e_2)) (not (tptp.product tptp.e_1 tptp.e_2 tptp.e_2)) (tptp.equalish tptp.e_2 tptp.e_1))) :rule resolution :premises (t103 a12))
% 0.20/0.57  (step t105 (cl (not (tptp.product tptp.e_1 tptp.e_2 tptp.e_2))) :rule resolution :premises (t96 a5 t17 t104))
% 0.20/0.57  (step t106 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.group_element X)) (not (tptp.group_element Y)) (tptp.product X Y tptp.e_1) (tptp.product X Y tptp.e_2) (tptp.product X Y tptp.e_3))) (or (not (tptp.group_element tptp.e_1)) (not (tptp.group_element tptp.e_2)) (tptp.product tptp.e_1 tptp.e_2 tptp.e_1) (tptp.product tptp.e_1 tptp.e_2 tptp.e_2) (tptp.product tptp.e_1 tptp.e_2 tptp.e_3))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.group_element X)) (not (tptp.group_element Y)) (tptp.product X Y tptp.e_1) (tptp.product X Y tptp.e_2) (tptp.product X Y tptp.e_3)))) :rule implies_neg1)
% 0.20/0.57  (anchor :step t107)
% 0.20/0.57  (assume t107.a0 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.group_element X)) (not (tptp.group_element Y)) (tptp.product X Y tptp.e_1) (tptp.product X Y tptp.e_2) (tptp.product X Y tptp.e_3))))
% 0.20/0.57  (step t107.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.group_element X)) (not (tptp.group_element Y)) (tptp.product X Y tptp.e_1) (tptp.product X Y tptp.e_2) (tptp.product X Y tptp.e_3)))) (or (not (tptp.group_element tptp.e_1)) (not (tptp.group_element tptp.e_2)) (tptp.product tptp.e_1 tptp.e_2 tptp.e_1) (tptp.product tptp.e_1 tptp.e_2 tptp.e_2) (tptp.product tptp.e_1 tptp.e_2 tptp.e_3)))) :rule forall_inst :args ((:= X tptp.e_1) (:= Y tptp.e_2)))
% 0.20/0.57  (step t107.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.group_element X)) (not (tptp.group_element Y)) (tptp.product X Y tptp.e_1) (tptp.product X Y tptp.e_2) (tptp.product X Y tptp.e_3)))) (or (not (tptp.group_element tptp.e_1)) (not (tptp.group_element tptp.e_2)) (tptp.product tptp.e_1 tptp.e_2 tptp.e_1) (tptp.product tptp.e_1 tptp.e_2 tptp.e_2) (tptp.product tptp.e_1 tptp.e_2 tptp.e_3))) :rule or :premises (t107.t1))
% 0.20/0.57  (step t107.t3 (cl (or (not (tptp.group_element tptp.e_1)) (not (tptp.group_element tptp.e_2)) (tptp.product tptp.e_1 tptp.e_2 tptp.e_1) (tptp.product tptp.e_1 tptp.e_2 tptp.e_2) (tptp.product tptp.e_1 tptp.e_2 tptp.e_3))) :rule resolution :premises (t107.t2 t107.a0))
% 0.20/0.57  (step t107 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.group_element X)) (not (tptp.group_element Y)) (tptp.product X Y tptp.e_1) (tptp.product X Y tptp.e_2) (tptp.product X Y tptp.e_3)))) (or (not (tptp.group_element tptp.e_1)) (not (tptp.group_element tptp.e_2)) (tptp.product tptp.e_1 tptp.e_2 tptp.e_1) (tptp.product tptp.e_1 tptp.e_2 tptp.e_2) (tptp.product tptp.e_1 tptp.e_2 tptp.e_3))) :rule subproof :discharge (t107.a0))
% 0.20/0.57  (step t108 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.group_element X)) (not (tptp.group_element Y)) (tptp.product X Y tptp.e_1) (tptp.product X Y tptp.e_2) (tptp.product X Y tptp.e_3))) (or (not (tptp.group_element tptp.e_1)) (not (tptp.group_element tptp.e_2)) (tptp.product tptp.e_1 tptp.e_2 tptp.e_1) (tptp.product tptp.e_1 tptp.e_2 tptp.e_2) (tptp.product tptp.e_1 tptp.e_2 tptp.e_3))) (or (not (tptp.group_element tptp.e_1)) (not (tptp.group_element tptp.e_2)) (tptp.product tptp.e_1 tptp.e_2 tptp.e_1) (tptp.product tptp.e_1 tptp.e_2 tptp.e_2) (tptp.product tptp.e_1 tptp.e_2 tptp.e_3))) :rule resolution :premises (t106 t107))
% 0.20/0.57  (step t109 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.group_element X)) (not (tptp.group_element Y)) (tptp.product X Y tptp.e_1) (tptp.product X Y tptp.e_2) (tptp.product X Y tptp.e_3))) (or (not (tptp.group_element tptp.e_1)) (not (tptp.group_element tptp.e_2)) (tptp.product tptp.e_1 tptp.e_2 tptp.e_1) (tptp.product tptp.e_1 tptp.e_2 tptp.e_2) (tptp.product tptp.e_1 tptp.e_2 tptp.e_3))) (not (or (not (tptp.group_element tptp.e_1)) (not (tptp.group_element tptp.e_2)) (tptp.product tptp.e_1 tptp.e_2 tptp.e_1) (tptp.product tptp.e_1 tptp.e_2 tptp.e_2) (tptp.product tptp.e_1 tptp.e_2 tptp.e_3)))) :rule implies_neg2)
% 0.20/0.57  (step t110 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.group_element X)) (not (tptp.group_element Y)) (tptp.product X Y tptp.e_1) (tptp.product X Y tptp.e_2) (tptp.product X Y tptp.e_3))) (or (not (tptp.group_element tptp.e_1)) (not (tptp.group_element tptp.e_2)) (tptp.product tptp.e_1 tptp.e_2 tptp.e_1) (tptp.product tptp.e_1 tptp.e_2 tptp.e_2) (tptp.product tptp.e_1 tptp.e_2 tptp.e_3))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.group_element X)) (not (tptp.group_element Y)) (tptp.product X Y tptp.e_1) (tptp.product X Y tptp.e_2) (tptp.product X Y tptp.e_3))) (or (not (tptp.group_element tptp.e_1)) (not (tptp.group_element tptp.e_2)) (tptp.product tptp.e_1 tptp.e_2 tptp.e_1) (tptp.product tptp.e_1 tptp.e_2 tptp.e_2) (tptp.product tptp.e_1 tptp.e_2 tptp.e_3)))) :rule resolution :premises (t108 t109))
% 0.20/0.57  (step t111 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.group_element X)) (not (tptp.group_element Y)) (tptp.product X Y tptp.e_1) (tptp.product X Y tptp.e_2) (tptp.product X Y tptp.e_3))) (or (not (tptp.group_element tptp.e_1)) (not (tptp.group_element tptp.e_2)) (tptp.product tptp.e_1 tptp.e_2 tptp.e_1) (tptp.product tptp.e_1 tptp.e_2 tptp.e_2) (tptp.product tptp.e_1 tptp.e_2 tptp.e_3)))) :rule contraction :premises (t110))
% 0.20/0.57  (step t112 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.group_element X)) (not (tptp.group_element Y)) (tptp.product X Y tptp.e_1) (tptp.product X Y tptp.e_2) (tptp.product X Y tptp.e_3)))) (or (not (tptp.group_element tptp.e_1)) (not (tptp.group_element tptp.e_2)) (tptp.product tptp.e_1 tptp.e_2 tptp.e_1) (tptp.product tptp.e_1 tptp.e_2 tptp.e_2) (tptp.product tptp.e_1 tptp.e_2 tptp.e_3))) :rule implies :premises (t111))
% 0.20/0.57  (step t113 (cl (or (not (tptp.group_element tptp.e_1)) (not (tptp.group_element tptp.e_2)) (tptp.product tptp.e_1 tptp.e_2 tptp.e_1) (tptp.product tptp.e_1 tptp.e_2 tptp.e_2) (tptp.product tptp.e_1 tptp.e_2 tptp.e_3))) :rule resolution :premises (t112 a9))
% 0.20/0.57  (step t114 (cl (tptp.product tptp.e_1 tptp.e_2 tptp.e_3)) :rule resolution :premises (t83 a0 a1 t94 t105 t113))
% 0.20/0.57  (step t115 (cl (=> (forall ((X $$unsorted) (W $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.product X W Y)) (not (tptp.product X Z Y)) (tptp.equalish W Z))) (or (not (tptp.product tptp.e_1 tptp.e_3 tptp.e_3)) (not (tptp.product tptp.e_1 tptp.e_2 tptp.e_3)) (tptp.equalish tptp.e_3 tptp.e_2))) (forall ((X $$unsorted) (W $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.product X W Y)) (not (tptp.product X Z Y)) (tptp.equalish W Z)))) :rule implies_neg1)
% 0.20/0.57  (anchor :step t116)
% 0.20/0.57  (assume t116.a0 (forall ((X $$unsorted) (W $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.product X W Y)) (not (tptp.product X Z Y)) (tptp.equalish W Z))))
% 0.20/0.57  (step t116.t1 (cl (or (not (forall ((X $$unsorted) (W $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.product X W Y)) (not (tptp.product X Z Y)) (tptp.equalish W Z)))) (or (not (tptp.product tptp.e_1 tptp.e_3 tptp.e_3)) (not (tptp.product tptp.e_1 tptp.e_2 tptp.e_3)) (tptp.equalish tptp.e_3 tptp.e_2)))) :rule forall_inst :args ((:= X tptp.e_1) (:= W tptp.e_3) (:= Y tptp.e_3) (:= Z tptp.e_2)))
% 0.20/0.57  (step t116.t2 (cl (not (forall ((X $$unsorted) (W $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.product X W Y)) (not (tptp.product X Z Y)) (tptp.equalish W Z)))) (or (not (tptp.product tptp.e_1 tptp.e_3 tptp.e_3)) (not (tptp.product tptp.e_1 tptp.e_2 tptp.e_3)) (tptp.equalish tptp.e_3 tptp.e_2))) :rule or :premises (t116.t1))
% 0.20/0.57  (step t116.t3 (cl (or (not (tptp.product tptp.e_1 tptp.e_3 tptp.e_3)) (not (tptp.product tptp.e_1 tptp.e_2 tptp.e_3)) (tptp.equalish tptp.e_3 tptp.e_2))) :rule resolution :premises (t116.t2 t116.a0))
% 0.20/0.57  (step t116 (cl (not (forall ((X $$unsorted) (W $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.product X W Y)) (not (tptp.product X Z Y)) (tptp.equalish W Z)))) (or (not (tptp.product tptp.e_1 tptp.e_3 tptp.e_3)) (not (tptp.product tptp.e_1 tptp.e_2 tptp.e_3)) (tptp.equalish tptp.e_3 tptp.e_2))) :rule subproof :discharge (t116.a0))
% 0.20/0.57  (step t117 (cl (=> (forall ((X $$unsorted) (W $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.product X W Y)) (not (tptp.product X Z Y)) (tptp.equalish W Z))) (or (not (tptp.product tptp.e_1 tptp.e_3 tptp.e_3)) (not (tptp.product tptp.e_1 tptp.e_2 tptp.e_3)) (tptp.equalish tptp.e_3 tptp.e_2))) (or (not (tptp.product tptp.e_1 tptp.e_3 tptp.e_3)) (not (tptp.product tptp.e_1 tptp.e_2 tptp.e_3)) (tptp.equalish tptp.e_3 tptp.e_2))) :rule resolution :premises (t115 t116))
% 0.20/0.57  (step t118 (cl (=> (forall ((X $$unsorted) (W $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.product X W Y)) (not (tptp.product X Z Y)) (tptp.equalish W Z))) (or (not (tptp.product tptp.e_1 tptp.e_3 tptp.e_3)) (not (tptp.product tptp.e_1 tptp.e_2 tptp.e_3)) (tptp.equalish tptp.e_3 tptp.e_2))) (not (or (not (tptp.product tptp.e_1 tptp.e_3 tptp.e_3)) (not (tptp.product tptp.e_1 tptp.e_2 tptp.e_3)) (tptp.equalish tptp.e_3 tptp.e_2)))) :rule implies_neg2)
% 0.20/0.57  (step t119 (cl (=> (forall ((X $$unsorted) (W $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.product X W Y)) (not (tptp.product X Z Y)) (tptp.equalish W Z))) (or (not (tptp.product tptp.e_1 tptp.e_3 tptp.e_3)) (not (tptp.product tptp.e_1 tptp.e_2 tptp.e_3)) (tptp.equalish tptp.e_3 tptp.e_2))) (=> (forall ((X $$unsorted) (W $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.product X W Y)) (not (tptp.product X Z Y)) (tptp.equalish W Z))) (or (not (tptp.product tptp.e_1 tptp.e_3 tptp.e_3)) (not (tptp.product tptp.e_1 tptp.e_2 tptp.e_3)) (tptp.equalish tptp.e_3 tptp.e_2)))) :rule resolution :premises (t117 t118))
% 0.20/0.57  (step t120 (cl (=> (forall ((X $$unsorted) (W $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.product X W Y)) (not (tptp.product X Z Y)) (tptp.equalish W Z))) (or (not (tptp.product tptp.e_1 tptp.e_3 tptp.e_3)) (not (tptp.product tptp.e_1 tptp.e_2 tptp.e_3)) (tptp.equalish tptp.e_3 tptp.e_2)))) :rule contraction :premises (t119))
% 0.20/0.57  (step t121 (cl (not (forall ((X $$unsorted) (W $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.product X W Y)) (not (tptp.product X Z Y)) (tptp.equalish W Z)))) (or (not (tptp.product tptp.e_1 tptp.e_3 tptp.e_3)) (not (tptp.product tptp.e_1 tptp.e_2 tptp.e_3)) (tptp.equalish tptp.e_3 tptp.e_2))) :rule implies :premises (t120))
% 0.20/0.57  (step t122 (cl (or (not (tptp.product tptp.e_1 tptp.e_3 tptp.e_3)) (not (tptp.product tptp.e_1 tptp.e_2 tptp.e_3)) (tptp.equalish tptp.e_3 tptp.e_2))) :rule resolution :premises (t121 a11))
% 0.20/0.57  (step t123 (cl (not (tptp.product tptp.e_1 tptp.e_3 tptp.e_3))) :rule resolution :premises (t81 a8 t114 t122))
% 0.20/0.57  (step t124 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.group_element X)) (not (tptp.group_element Y)) (tptp.product X Y tptp.e_1) (tptp.product X Y tptp.e_2) (tptp.product X Y tptp.e_3))) (or (not (tptp.group_element tptp.e_1)) (not (tptp.group_element tptp.e_3)) (tptp.product tptp.e_1 tptp.e_3 tptp.e_1) (tptp.product tptp.e_1 tptp.e_3 tptp.e_2) (tptp.product tptp.e_1 tptp.e_3 tptp.e_3))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.group_element X)) (not (tptp.group_element Y)) (tptp.product X Y tptp.e_1) (tptp.product X Y tptp.e_2) (tptp.product X Y tptp.e_3)))) :rule implies_neg1)
% 0.20/0.57  (anchor :step t125)
% 0.20/0.57  (assume t125.a0 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.group_element X)) (not (tptp.group_element Y)) (tptp.product X Y tptp.e_1) (tptp.product X Y tptp.e_2) (tptp.product X Y tptp.e_3))))
% 0.20/0.57  (step t125.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.group_element X)) (not (tptp.group_element Y)) (tptp.product X Y tptp.e_1) (tptp.product X Y tptp.e_2) (tptp.product X Y tptp.e_3)))) (or (not (tptp.group_element tptp.e_1)) (not (tptp.group_element tptp.e_3)) (tptp.product tptp.e_1 tptp.e_3 tptp.e_1) (tptp.product tptp.e_1 tptp.e_3 tptp.e_2) (tptp.product tptp.e_1 tptp.e_3 tptp.e_3)))) :rule forall_inst :args ((:= X tptp.e_1) (:= Y tptp.e_3)))
% 0.20/0.57  (step t125.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.group_element X)) (not (tptp.group_element Y)) (tptp.product X Y tptp.e_1) (tptp.product X Y tptp.e_2) (tptp.product X Y tptp.e_3)))) (or (not (tptp.group_element tptp.e_1)) (not (tptp.group_element tptp.e_3)) (tptp.product tptp.e_1 tptp.e_3 tptp.e_1) (tptp.product tptp.e_1 tptp.e_3 tptp.e_2) (tptp.product tptp.e_1 tptp.e_3 tptp.e_3))) :rule or :premises (t125.t1))
% 0.20/0.57  (step t125.t3 (cl (or (not (tptp.group_element tptp.e_1)) (not (tptp.group_element tptp.e_3)) (tptp.product tptp.e_1 tptp.e_3 tptp.e_1) (tptp.product tptp.e_1 tptp.e_3 tptp.e_2) (tptp.product tptp.e_1 tptp.e_3 tptp.e_3))) :rule resolution :premises (t125.t2 t125.a0))
% 0.20/0.57  (step t125 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.group_element X)) (not (tptp.group_element Y)) (tptp.product X Y tptp.e_1) (tptp.product X Y tptp.e_2) (tptp.product X Y tptp.e_3)))) (or (not (tptp.group_element tptp.e_1)) (not (tptp.group_element tptp.e_3)) (tptp.product tptp.e_1 tptp.e_3 tptp.e_1) (tptp.product tptp.e_1 tptp.e_3 tptp.e_2) (tptp.product tptp.e_1 tptp.e_3 tptp.e_3))) :rule subproof :discharge (t125.a0))
% 0.20/0.57  (step t126 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.group_element X)) (not (tptp.group_element Y)) (tptp.product X Y tptp.e_1) (tptp.product X Y tptp.e_2) (tptp.product X Y tptp.e_3))) (or (not (tptp.group_element tptp.e_1)) (not (tptp.group_element tptp.e_3)) (tptp.product tptp.e_1 tptp.e_3 tptp.e_1) (tptp.product tptp.e_1 tptp.e_3 tptp.e_2) (tptp.product tptp.e_1 tptp.e_3 tptp.e_3))) (or (not (tptp.group_element tptp.e_1)) (not (tptp.group_element tptp.e_3)) (tptp.product tptp.e_1 tptp.e_3 tptp.e_1) (tptp.product tptp.e_1 tptp.e_3 tptp.e_2) (tptp.product tptp.e_1 tptp.e_3 tptp.e_3))) :rule resolution :premises (t124 t125))
% 0.20/0.57  (step t127 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.group_element X)) (not (tptp.group_element Y)) (tptp.product X Y tptp.e_1) (tptp.product X Y tptp.e_2) (tptp.product X Y tptp.e_3))) (or (not (tptp.group_element tptp.e_1)) (not (tptp.group_element tptp.e_3)) (tptp.product tptp.e_1 tptp.e_3 tptp.e_1) (tptp.product tptp.e_1 tptp.e_3 tptp.e_2) (tptp.product tptp.e_1 tptp.e_3 tptp.e_3))) (not (or (not (tptp.group_element tptp.e_1)) (not (tptp.group_element tptp.e_3)) (tptp.product tptp.e_1 tptp.e_3 tptp.e_1) (tptp.product tptp.e_1 tptp.e_3 tptp.e_2) (tptp.product tptp.e_1 tptp.e_3 tptp.e_3)))) :rule implies_neg2)
% 0.20/0.57  (step t128 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.group_element X)) (not (tptp.group_element Y)) (tptp.product X Y tptp.e_1) (tptp.product X Y tptp.e_2) (tptp.product X Y tptp.e_3))) (or (not (tptp.group_element tptp.e_1)) (not (tptp.group_element tptp.e_3)) (tptp.product tptp.e_1 tptp.e_3 tptp.e_1) (tptp.product tptp.e_1 tptp.e_3 tptp.e_2) (tptp.product tptp.e_1 tptp.e_3 tptp.e_3))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.group_element X)) (not (tptp.group_element Y)) (tptp.product X Y tptp.e_1) (tptp.product X Y tptp.e_2) (tptp.product X Y tptp.e_3))) (or (not (tptp.group_element tptp.e_1)) (not (tptp.group_element tptp.e_3)) (tptp.product tptp.e_1 tptp.e_3 tptp.e_1) (tptp.product tptp.e_1 tptp.e_3 tptp.e_2) (tptp.product tptp.e_1 tptp.e_3 tptp.e_3)))) :rule resolution :premises (t126 t127))
% 0.20/0.57  (step t129 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.group_element X)) (not (tptp.group_element Y)) (tptp.product X Y tptp.e_1) (tptp.product X Y tptp.e_2) (tptp.product X Y tptp.e_3))) (or (not (tptp.group_element tptp.e_1)) (not (tptp.group_element tptp.e_3)) (tptp.product tptp.e_1 tptp.e_3 tptp.e_1) (tptp.product tptp.e_1 tptp.e_3 tptp.e_2) (tptp.product tptp.e_1 tptp.e_3 tptp.e_3)))) :rule contraction :premises (t128))
% 0.20/0.57  (step t130 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.group_element X)) (not (tptp.group_element Y)) (tptp.product X Y tptp.e_1) (tptp.product X Y tptp.e_2) (tptp.product X Y tptp.e_3)))) (or (not (tptp.group_element tptp.e_1)) (not (tptp.group_element tptp.e_3)) (tptp.product tptp.e_1 tptp.e_3 tptp.e_1) (tptp.product tptp.e_1 tptp.e_3 tptp.e_2) (tptp.product tptp.e_1 tptp.e_3 tptp.e_3))) :rule implies :premises (t129))
% 0.20/0.57  (step t131 (cl (or (not (tptp.group_element tptp.e_1)) (not (tptp.group_element tptp.e_3)) (tptp.product tptp.e_1 tptp.e_3 tptp.e_1) (tptp.product tptp.e_1 tptp.e_3 tptp.e_2) (tptp.product tptp.e_1 tptp.e_3 tptp.e_3))) :rule resolution :premises (t130 a9))
% 0.20/0.57  (step t132 (cl (tptp.product tptp.e_1 tptp.e_3 tptp.e_2)) :rule resolution :premises (t68 a0 a2 t79 t123 t131))
% 0.20/0.57  (step t133 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z1 $$unsorted) (Z2 $$unsorted)) (or (not (tptp.product X Y Z1)) (not (tptp.product Y X Z2)) (tptp.product Z1 Z2 X))) (or (not (tptp.product tptp.e_1 tptp.e_3 tptp.e_2)) (not (tptp.product tptp.e_3 tptp.e_1 tptp.e_2)) (tptp.product tptp.e_2 tptp.e_2 tptp.e_1))) (forall ((X $$unsorted) (Y $$unsorted) (Z1 $$unsorted) (Z2 $$unsorted)) (or (not (tptp.product X Y Z1)) (not (tptp.product Y X Z2)) (tptp.product Z1 Z2 X)))) :rule implies_neg1)
% 0.20/0.57  (anchor :step t134)
% 0.20/0.57  (assume t134.a0 (forall ((X $$unsorted) (Y $$unsorted) (Z1 $$unsorted) (Z2 $$unsorted)) (or (not (tptp.product X Y Z1)) (not (tptp.product Y X Z2)) (tptp.product Z1 Z2 X))))
% 0.20/0.57  (step t134.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted) (Z1 $$unsorted) (Z2 $$unsorted)) (or (not (tptp.product X Y Z1)) (not (tptp.product Y X Z2)) (tptp.product Z1 Z2 X)))) (or (not (tptp.product tptp.e_1 tptp.e_3 tptp.e_2)) (not (tptp.product tptp.e_3 tptp.e_1 tptp.e_2)) (tptp.product tptp.e_2 tptp.e_2 tptp.e_1)))) :rule forall_inst :args ((:= X tptp.e_1) (:= Y tptp.e_3) (:= Z1 tptp.e_2) (:= Z2 tptp.e_2)))
% 0.20/0.57  (step t134.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z1 $$unsorted) (Z2 $$unsorted)) (or (not (tptp.product X Y Z1)) (not (tptp.product Y X Z2)) (tptp.product Z1 Z2 X)))) (or (not (tptp.product tptp.e_1 tptp.e_3 tptp.e_2)) (not (tptp.product tptp.e_3 tptp.e_1 tptp.e_2)) (tptp.product tptp.e_2 tptp.e_2 tptp.e_1))) :rule or :premises (t134.t1))
% 0.20/0.57  (step t134.t3 (cl (or (not (tptp.product tptp.e_1 tptp.e_3 tptp.e_2)) (not (tptp.product tptp.e_3 tptp.e_1 tptp.e_2)) (tptp.product tptp.e_2 tptp.e_2 tptp.e_1))) :rule resolution :premises (t134.t2 t134.a0))
% 0.20/0.57  (step t134 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z1 $$unsorted) (Z2 $$unsorted)) (or (not (tptp.product X Y Z1)) (not (tptp.product Y X Z2)) (tptp.product Z1 Z2 X)))) (or (not (tptp.product tptp.e_1 tptp.e_3 tptp.e_2)) (not (tptp.product tptp.e_3 tptp.e_1 tptp.e_2)) (tptp.product tptp.e_2 tptp.e_2 tptp.e_1))) :rule subproof :discharge (t134.a0))
% 0.20/0.57  (step t135 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z1 $$unsorted) (Z2 $$unsorted)) (or (not (tptp.product X Y Z1)) (not (tptp.product Y X Z2)) (tptp.product Z1 Z2 X))) (or (not (tptp.product tptp.e_1 tptp.e_3 tptp.e_2)) (not (tptp.product tptp.e_3 tptp.e_1 tptp.e_2)) (tptp.product tptp.e_2 tptp.e_2 tptp.e_1))) (or (not (tptp.product tptp.e_1 tptp.e_3 tptp.e_2)) (not (tptp.product tptp.e_3 tptp.e_1 tptp.e_2)) (tptp.product tptp.e_2 tptp.e_2 tptp.e_1))) :rule resolution :premises (t133 t134))
% 0.20/0.57  (step t136 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z1 $$unsorted) (Z2 $$unsorted)) (or (not (tptp.product X Y Z1)) (not (tptp.product Y X Z2)) (tptp.product Z1 Z2 X))) (or (not (tptp.product tptp.e_1 tptp.e_3 tptp.e_2)) (not (tptp.product tptp.e_3 tptp.e_1 tptp.e_2)) (tptp.product tptp.e_2 tptp.e_2 tptp.e_1))) (not (or (not (tptp.product tptp.e_1 tptp.e_3 tptp.e_2)) (not (tptp.product tptp.e_3 tptp.e_1 tptp.e_2)) (tptp.product tptp.e_2 tptp.e_2 tptp.e_1)))) :rule implies_neg2)
% 0.20/0.57  (step t137 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z1 $$unsorted) (Z2 $$unsorted)) (or (not (tptp.product X Y Z1)) (not (tptp.product Y X Z2)) (tptp.product Z1 Z2 X))) (or (not (tptp.product tptp.e_1 tptp.e_3 tptp.e_2)) (not (tptp.product tptp.e_3 tptp.e_1 tptp.e_2)) (tptp.product tptp.e_2 tptp.e_2 tptp.e_1))) (=> (forall ((X $$unsorted) (Y $$unsorted) (Z1 $$unsorted) (Z2 $$unsorted)) (or (not (tptp.product X Y Z1)) (not (tptp.product Y X Z2)) (tptp.product Z1 Z2 X))) (or (not (tptp.product tptp.e_1 tptp.e_3 tptp.e_2)) (not (tptp.product tptp.e_3 tptp.e_1 tptp.e_2)) (tptp.product tptp.e_2 tptp.e_2 tptp.e_1)))) :rule resolution :premises (t135 t136))
% 0.20/0.57  (step t138 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z1 $$unsorted) (Z2 $$unsorted)) (or (not (tptp.product X Y Z1)) (not (tptp.product Y X Z2)) (tptp.product Z1 Z2 X))) (or (not (tptp.product tptp.e_1 tptp.e_3 tptp.e_2)) (not (tptp.product tptp.e_3 tptp.e_1 tptp.e_2)) (tptp.product tptp.e_2 tptp.e_2 tptp.e_1)))) :rule contraction :premises (t137))
% 0.20/0.57  (step t139 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z1 $$unsorted) (Z2 $$unsorted)) (or (not (tptp.product X Y Z1)) (not (tptp.product Y X Z2)) (tptp.product Z1 Z2 X)))) (or (not (tptp.product tptp.e_1 tptp.e_3 tptp.e_2)) (not (tptp.product tptp.e_3 tptp.e_1 tptp.e_2)) (tptp.product tptp.e_2 tptp.e_2 tptp.e_1))) :rule implies :premises (t138))
% 0.20/0.57  (step t140 (cl (or (not (tptp.product tptp.e_1 tptp.e_3 tptp.e_2)) (not (tptp.product tptp.e_3 tptp.e_1 tptp.e_2)) (tptp.product tptp.e_2 tptp.e_2 tptp.e_1))) :rule resolution :premises (t139 a14))
% 0.20/0.57  (step t141 (cl (not (tptp.product tptp.e_3 tptp.e_1 tptp.e_2))) :rule resolution :premises (t55 t66 t132 t140))
% 0.20/0.57  (step t142 (cl (=> (forall ((X $$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 $$unsorted)) (or (not (tptp.group_element X)) (not (tptp.group_element Y)) (tptp.product X Y tptp.e_1) (tptp.product X Y tptp.e_2) (tptp.product X Y tptp.e_3)))) :rule implies_neg1)
% 0.20/0.57  (anchor :step t143)
% 0.20/0.57  (assume t143.a0 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.group_element X)) (not (tptp.group_element Y)) (tptp.product X Y tptp.e_1) (tptp.product X Y tptp.e_2) (tptp.product X Y tptp.e_3))))
% 0.20/0.57  (step t143.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.group_element X)) (not (tptp.group_element Y)) (tptp.product X Y tptp.e_1) (tptp.product X Y tptp.e_2) (tptp.product X Y tptp.e_3)))) (or (not (tptp.group_element tptp.e_3)) (not (tptp.group_element tptp.e_1)) (tptp.product tptp.e_3 tptp.e_1 tptp.e_1) (tptp.product tptp.e_3 tptp.e_1 tptp.e_2) (tptp.product tptp.e_3 tptp.e_1 tptp.e_3)))) :rule forall_inst :args ((:= X tptp.e_3) (:= Y tptp.e_1)))
% 0.20/0.57  (step t143.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.group_element X)) (not (tptp.group_element Y)) (tptp.product X Y tptp.e_1) (tptp.product X Y tptp.e_2) (tptp.product X Y tptp.e_3)))) (or (not (tptp.group_element tptp.e_3)) (not (tptp.group_element tptp.e_1)) (tptp.product tptp.e_3 tptp.e_1 tptp.e_1) (tptp.product tptp.e_3 tptp.e_1 tptp.e_2) (tptp.product tptp.e_3 tptp.e_1 tptp.e_3))) :rule or :premises (t143.t1))
% 0.20/0.57  (step t143.t3 (cl (or (not (tptp.group_element tptp.e_3)) (not (tptp.group_element tptp.e_1)) (tptp.product tptp.e_3 tptp.e_1 tptp.e_1) (tptp.product tptp.e_3 tptp.e_1 tptp.e_2) (tptp.product tptp.e_3 tptp.e_1 tptp.e_3))) :rule resolution :premises (t143.t2 t143.a0))
% 0.20/0.57  (step t143 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.group_element X)) (not (tptp.group_element Y)) (tptp.product X Y tptp.e_1) (tptp.product X Y tptp.e_2) (tptp.product X Y tptp.e_3)))) (or (not (tptp.group_element tptp.e_3)) (not (tptp.group_element tptp.e_1)) (tptp.product tptp.e_3 tptp.e_1 tptp.e_1) (tptp.product tptp.e_3 tptp.e_1 tptp.e_2) (tptp.product tptp.e_3 tptp.e_1 tptp.e_3))) :rule subproof :discharge (t143.a0))
% 0.20/0.57  (step t144 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.group_element X)) (not (tptp.group_element Y)) (tptp.product X Y tptp.e_1) (tptp.product X Y tptp.e_2) (tptp.product X Y tptp.e_3))) (or (not (tptp.group_element tptp.e_3)) (not (tptp.group_element tptp.e_1)) (tptp.product tptp.e_3 tptp.e_1 tptp.e_1) (tptp.product tptp.e_3 tptp.e_1 tptp.e_2) (tptp.product tptp.e_3 tptp.e_1 tptp.e_3))) (or (not (tptp.group_element tptp.e_3)) (not (tptp.group_element tptp.e_1)) (tptp.product tptp.e_3 tptp.e_1 tptp.e_1) (tptp.product tptp.e_3 tptp.e_1 tptp.e_2) (tptp.product tptp.e_3 tptp.e_1 tptp.e_3))) :rule resolution :premises (t142 t143))
% 0.20/0.57  (step t145 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.group_element X)) (not (tptp.group_element Y)) (tptp.product X Y tptp.e_1) (tptp.product X Y tptp.e_2) (tptp.product X Y tptp.e_3))) (or (not (tptp.group_element tptp.e_3)) (not (tptp.group_element tptp.e_1)) (tptp.product tptp.e_3 tptp.e_1 tptp.e_1) (tptp.product tptp.e_3 tptp.e_1 tptp.e_2) (tptp.product tptp.e_3 tptp.e_1 tptp.e_3))) (not (or (not (tptp.group_element tptp.e_3)) (not (tptp.group_element tptp.e_1)) (tptp.product tptp.e_3 tptp.e_1 tptp.e_1) (tptp.product tptp.e_3 tptp.e_1 tptp.e_2) (tptp.product tptp.e_3 tptp.e_1 tptp.e_3)))) :rule implies_neg2)
% 0.20/0.57  (step t146 (cl (=> (forall ((X $$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 $$unsorted)) (or (not (tptp.group_element X)) (not (tptp.group_element Y)) (tptp.product X Y tptp.e_1) (tptp.product X Y tptp.e_2) (tptp.product X Y tptp.e_3))) (or (not (tptp.group_element tptp.e_3)) (not (tptp.group_element tptp.e_1)) (tptp.product tptp.e_3 tptp.e_1 tptp.e_1) (tptp.product tptp.e_3 tptp.e_1 tptp.e_2) (tptp.product tptp.e_3 tptp.e_1 tptp.e_3)))) :rule resolution :premises (t144 t145))
% 0.20/0.57  (step t147 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.group_element X)) (not (tptp.group_element Y)) (tptp.product X Y tptp.e_1) (tptp.product X Y tptp.e_2) (tptp.product X Y tptp.e_3))) (or (not (tptp.group_element tptp.e_3)) (not (tptp.group_element tptp.e_1)) (tptp.product tptp.e_3 tptp.e_1 tptp.e_1) (tptp.product tptp.e_3 tptp.e_1 tptp.e_2) (tptp.product tptp.e_3 tptp.e_1 tptp.e_3)))) :rule contraction :premises (t146))
% 0.20/0.57  (step t148 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.group_element X)) (not (tptp.group_element Y)) (tptp.product X Y tptp.e_1) (tptp.product X Y tptp.e_2) (tptp.product X Y tptp.e_3)))) (or (not (tptp.group_element tptp.e_3)) (not (tptp.group_element tptp.e_1)) (tptp.product tptp.e_3 tptp.e_1 tptp.e_1) (tptp.product tptp.e_3 tptp.e_1 tptp.e_2) (tptp.product tptp.e_3 tptp.e_1 tptp.e_3))) :rule implies :premises (t147))
% 0.20/0.57  (step t149 (cl (or (not (tptp.group_element tptp.e_3)) (not (tptp.group_element tptp.e_1)) (tptp.product tptp.e_3 tptp.e_1 tptp.e_1) (tptp.product tptp.e_3 tptp.e_1 tptp.e_2) (tptp.product tptp.e_3 tptp.e_1 tptp.e_3))) :rule resolution :premises (t148 a9))
% 0.20/0.57  (step t150 (cl (tptp.product tptp.e_3 tptp.e_1 tptp.e_3)) :rule resolution :premises (t42 a0 a2 t53 t141 t149))
% 0.20/0.57  (step t151 (cl (=> (forall ((W $$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 $$unsorted)) (or (not (tptp.product W Y X)) (not (tptp.product Z Y X)) (tptp.equalish W Z)))) :rule implies_neg1)
% 0.20/0.57  (anchor :step t152)
% 0.20/0.57  (assume t152.a0 (forall ((W $$unsorted) (Y $$unsorted) (X $$unsorted) (Z $$unsorted)) (or (not (tptp.product W Y X)) (not (tptp.product Z Y X)) (tptp.equalish W Z))))
% 0.20/0.57  (step t152.t1 (cl (or (not (forall ((W $$unsorted) (Y $$unsorted) (X $$unsorted) (Z $$unsorted)) (or (not (tptp.product W Y X)) (not (tptp.product Z Y X)) (tptp.equalish W Z)))) (or (not (tptp.product tptp.e_2 tptp.e_1 tptp.e_3)) (not (tptp.product tptp.e_3 tptp.e_1 tptp.e_3)) (tptp.equalish tptp.e_2 tptp.e_3)))) :rule forall_inst :args ((:= W tptp.e_2) (:= Y tptp.e_1) (:= X tptp.e_3) (:= Z tptp.e_3)))
% 0.20/0.57  (step t152.t2 (cl (not (forall ((W $$unsorted) (Y $$unsorted) (X $$unsorted) (Z $$unsorted)) (or (not (tptp.product W Y X)) (not (tptp.product Z Y X)) (tptp.equalish W Z)))) (or (not (tptp.product tptp.e_2 tptp.e_1 tptp.e_3)) (not (tptp.product tptp.e_3 tptp.e_1 tptp.e_3)) (tptp.equalish tptp.e_2 tptp.e_3))) :rule or :premises (t152.t1))
% 0.20/0.57  (step t152.t3 (cl (or (not (tptp.product tptp.e_2 tptp.e_1 tptp.e_3)) (not (tptp.product tptp.e_3 tptp.e_1 tptp.e_3)) (tptp.equalish tptp.e_2 tptp.e_3))) :rule resolution :premises (t152.t2 t152.a0))
% 0.20/0.57  (step t152 (cl (not (forall ((W $$unsorted) (Y $$unsorted) (X $$unsorted) (Z $$unsorted)) (or (not (tptp.product W Y X)) (not (tptp.product Z Y X)) (tptp.equalish W Z)))) (or (not (tptp.product tptp.e_2 tptp.e_1 tptp.e_3)) (not (tptp.product tptp.e_3 tptp.e_1 tptp.e_3)) (tptp.equalish tptp.e_2 tptp.e_3))) :rule subproof :discharge (t152.a0))
% 0.20/0.57  (step t153 (cl (=> (forall ((W $$unsorted) (Y $$unsorted) (X $$unsorted) (Z $$unsorted)) (or (not (tptp.product W Y X)) (not (tptp.product Z Y X)) (tptp.equalish W Z))) (or (not (tptp.product tptp.e_2 tptp.e_1 tptp.e_3)) (not (tptp.product tptp.e_3 tptp.e_1 tptp.e_3)) (tptp.equalish tptp.e_2 tptp.e_3))) (or (not (tptp.product tptp.e_2 tptp.e_1 tptp.e_3)) (not (tptp.product tptp.e_3 tptp.e_1 tptp.e_3)) (tptp.equalish tptp.e_2 tptp.e_3))) :rule resolution :premises (t151 t152))
% 0.20/0.57  (step t154 (cl (=> (forall ((W $$unsorted) (Y $$unsorted) (X $$unsorted) (Z $$unsorted)) (or (not (tptp.product W Y X)) (not (tptp.product Z Y X)) (tptp.equalish W Z))) (or (not (tptp.product tptp.e_2 tptp.e_1 tptp.e_3)) (not (tptp.product tptp.e_3 tptp.e_1 tptp.e_3)) (tptp.equalish tptp.e_2 tptp.e_3))) (not (or (not (tptp.product tptp.e_2 tptp.e_1 tptp.e_3)) (not (tptp.product tptp.e_3 tptp.e_1 tptp.e_3)) (tptp.equalish tptp.e_2 tptp.e_3)))) :rule implies_neg2)
% 0.20/0.57  (step t155 (cl (=> (forall ((W $$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 $$unsorted)) (or (not (tptp.product W Y X)) (not (tptp.product Z Y X)) (tptp.equalish W Z))) (or (not (tptp.product tptp.e_2 tptp.e_1 tptp.e_3)) (not (tptp.product tptp.e_3 tptp.e_1 tptp.e_3)) (tptp.equalish tptp.e_2 tptp.e_3)))) :rule resolution :premises (t153 t154))
% 0.20/0.57  (step t156 (cl (=> (forall ((W $$unsorted) (Y $$unsorted) (X $$unsorted) (Z $$unsorted)) (or (not (tptp.product W Y X)) (not (tptp.product Z Y X)) (tptp.equalish W Z))) (or (not (tptp.product tptp.e_2 tptp.e_1 tptp.e_3)) (not (tptp.product tptp.e_3 tptp.e_1 tptp.e_3)) (tptp.equalish tptp.e_2 tptp.e_3)))) :rule contraction :premises (t155))
% 0.20/0.57  (step t157 (cl (not (forall ((W $$unsorted) (Y $$unsorted) (X $$unsorted) (Z $$unsorted)) (or (not (tptp.product W Y X)) (not (tptp.product Z Y X)) (tptp.equalish W Z)))) (or (not (tptp.product tptp.e_2 tptp.e_1 tptp.e_3)) (not (tptp.product tptp.e_3 tptp.e_1 tptp.e_3)) (tptp.equalish tptp.e_2 tptp.e_3))) :rule implies :premises (t156))
% 0.20/0.57  (step t158 (cl (or (not (tptp.product tptp.e_2 tptp.e_1 tptp.e_3)) (not (tptp.product tptp.e_3 tptp.e_1 tptp.e_3)) (tptp.equalish tptp.e_2 tptp.e_3))) :rule resolution :premises (t157 a12))
% 0.20/0.57  (step t159 (cl (not (tptp.product tptp.e_2 tptp.e_1 tptp.e_3))) :rule resolution :premises (t40 a6 t150 t158))
% 0.20/0.57  (step t160 (cl (=> (forall ((X $$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 $$unsorted)) (or (not (tptp.group_element X)) (not (tptp.group_element Y)) (tptp.product X Y tptp.e_1) (tptp.product X Y tptp.e_2) (tptp.product X Y tptp.e_3)))) :rule implies_neg1)
% 0.20/0.57  (anchor :step t161)
% 0.20/0.57  (assume t161.a0 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.group_element X)) (not (tptp.group_element Y)) (tptp.product X Y tptp.e_1) (tptp.product X Y tptp.e_2) (tptp.product X Y tptp.e_3))))
% 0.20/0.57  (step t161.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.group_element X)) (not (tptp.group_element Y)) (tptp.product X Y tptp.e_1) (tptp.product X Y tptp.e_2) (tptp.product X Y tptp.e_3)))) (or (not (tptp.group_element tptp.e_2)) (not (tptp.group_element tptp.e_1)) (tptp.product tptp.e_2 tptp.e_1 tptp.e_1) (tptp.product tptp.e_2 tptp.e_1 tptp.e_2) (tptp.product tptp.e_2 tptp.e_1 tptp.e_3)))) :rule forall_inst :args ((:= X tptp.e_2) (:= Y tptp.e_1)))
% 0.20/0.57  (step t161.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.group_element X)) (not (tptp.group_element Y)) (tptp.product X Y tptp.e_1) (tptp.product X Y tptp.e_2) (tptp.product X Y tptp.e_3)))) (or (not (tptp.group_element tptp.e_2)) (not (tptp.group_element tptp.e_1)) (tptp.product tptp.e_2 tptp.e_1 tptp.e_1) (tptp.product tptp.e_2 tptp.e_1 tptp.e_2) (tptp.product tptp.e_2 tptp.e_1 tptp.e_3))) :rule or :premises (t161.t1))
% 0.20/0.57  (step t161.t3 (cl (or (not (tptp.group_element tptp.e_2)) (not (tptp.group_element tptp.e_1)) (tptp.product tptp.e_2 tptp.e_1 tptp.e_1) (tptp.product tptp.e_2 tptp.e_1 tptp.e_2) (tptp.product tptp.e_2 tptp.e_1 tptp.e_3))) :rule resolution :premises (t161.t2 t161.a0))
% 0.20/0.57  (step t161 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.group_element X)) (not (tptp.group_element Y)) (tptp.product X Y tptp.e_1) (tptp.product X Y tptp.e_2) (tptp.product X Y tptp.e_3)))) (or (not (tptp.group_element tptp.e_2)) (not (tptp.group_element tptp.e_1)) (tptp.product tptp.e_2 tptp.e_1 tptp.e_1) (tptp.product tptp.e_2 tptp.e_1 tptp.e_2) (tptp.product tptp.e_2 tptp.e_1 tptp.e_3))) :rule subproof :discharge (t161.a0))
% 0.20/0.57  (step t162 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.group_element X)) (not (tptp.group_element Y)) (tptp.product X Y tptp.e_1) (tptp.product X Y tptp.e_2) (tptp.product X Y tptp.e_3))) (or (not (tptp.group_element tptp.e_2)) (not (tptp.group_element tptp.e_1)) (tptp.product tptp.e_2 tptp.e_1 tptp.e_1) (tptp.product tptp.e_2 tptp.e_1 tptp.e_2) (tptp.product tptp.e_2 tptp.e_1 tptp.e_3))) (or (not (tptp.group_element tptp.e_2)) (not (tptp.group_element tptp.e_1)) (tptp.product tptp.e_2 tptp.e_1 tptp.e_1) (tptp.product tptp.e_2 tptp.e_1 tptp.e_2) (tptp.product tptp.e_2 tptp.e_1 tptp.e_3))) :rule resolution :premises (t160 t161))
% 0.20/0.57  (step t163 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.group_element X)) (not (tptp.group_element Y)) (tptp.product X Y tptp.e_1) (tptp.product X Y tptp.e_2) (tptp.product X Y tptp.e_3))) (or (not (tptp.group_element tptp.e_2)) (not (tptp.group_element tptp.e_1)) (tptp.product tptp.e_2 tptp.e_1 tptp.e_1) (tptp.product tptp.e_2 tptp.e_1 tptp.e_2) (tptp.product tptp.e_2 tptp.e_1 tptp.e_3))) (not (or (not (tptp.group_element tptp.e_2)) (not (tptp.group_element tptp.e_1)) (tptp.product tptp.e_2 tptp.e_1 tptp.e_1) (tptp.product tptp.e_2 tptp.e_1 tptp.e_2) (tptp.product tptp.e_2 tptp.e_1 tptp.e_3)))) :rule implies_neg2)
% 0.20/0.57  (step t164 (cl (=> (forall ((X $$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 $$unsorted)) (or (not (tptp.group_element X)) (not (tptp.group_element Y)) (tptp.product X Y tptp.e_1) (tptp.product X Y tptp.e_2) (tptp.product X Y tptp.e_3))) (or (not (tptp.group_element tptp.e_2)) (not (tptp.group_element tptp.e_1)) (tptp.product tptp.e_2 tptp.e_1 tptp.e_1) (tptp.product tptp.e_2 tptp.e_1 tptp.e_2) (tptp.product tptp.e_2 tptp.e_1 tptp.e_3)))) :rule resolution :premises (t162 t163))
% 0.20/0.57  (step t165 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.group_element X)) (not (tptp.group_element Y)) (tptp.product X Y tptp.e_1) (tptp.product X Y tptp.e_2) (tptp.product X Y tptp.e_3))) (or (not (tptp.group_element tptp.e_2)) (not (tptp.group_element tptp.e_1)) (tptp.product tptp.e_2 tptp.e_1 tptp.e_1) (tptp.product tptp.e_2 tptp.e_1 tptp.e_2) (tptp.product tptp.e_2 tptp.e_1 tptp.e_3)))) :rule contraction :premises (t164))
% 0.20/0.57  (step t166 (cl (not (forall ((X $$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 (t165))
% 0.20/0.57  (step t167 (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 (t166 a9))
% 0.20/0.57  (step t168 (cl (tptp.product tptp.e_2 tptp.e_1 tptp.e_2)) :rule resolution :premises (t19 a0 a1 t38 t159 t167))
% 0.20/0.57  (step t169 (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 t168))
% 0.20/0.57  (step t170 (cl) :rule resolution :premises (t7 t169 a11))
% 0.20/0.57  
% 0.20/0.57  % SZS output end Proof for /export/starexec/sandbox2/tmp/tmp.VE1T6tqt5t/cvc5---1.0.5_16361.smt2
% 0.20/0.57  % cvc5---1.0.5 exiting
% 0.20/0.58  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------