%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : ANA035-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 09:30:39 AM UTC 2026
% Result : Unsatisfiable 0.11s 0.26s
% Output : Proof 0.11s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ANA035-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.16 % Computer : n016.cluster.edu
% 0.11/0.16 % Model : x86_64 x86_64
% 0.11/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.16 % Memory : 8046.5625MB
% 0.11/0.16 % OS : Linux 6.8.0-71-generic
% 0.11/0.16 % CPULimit : 300
% 0.11/0.16 % WCLimit : 300
% 0.11/0.16 % DateTime : Mon Sep 28 20:38:18 UTC 2026
% 0.11/0.17 % CPUTime :
% 0.11/0.17 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.26 Command-line arguments: --no-flatten-goal
% 0.11/0.26
% 0.11/0.26 % SZS status Unsatisfiable
% 0.11/0.26
% 0.11/0.26 % SZS output start Proof
% 0.11/0.26 Axiom 1 (tfree_tcs): class_Ring__and__Field_Oordered__idom(t_b) = true.
% 0.11/0.26 Axiom 2 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 0.11/0.26 Axiom 3 (ifeq_axiom): ifeq2(X, X, Y, Z) = Y.
% 0.11/0.26 Axiom 4 (clsrel_Ring__and__Field_Oordered__idom_17): ifeq(class_Ring__and__Field_Oordered__idom(X), true, class_OrderedGroup_Oab__semigroup__mult(X), true) = true.
% 0.11/0.26 Axiom 5 (cls_OrderedGroup_Omult__ac__2_0): ifeq2(class_OrderedGroup_Oab__semigroup__mult(X), true, c_times(Y, Z, X), c_times(Z, Y, X)) = c_times(Z, Y, X).
% 0.11/0.26 Axiom 6 (cls_OrderedGroup_Omult__ac__3_0): ifeq2(class_OrderedGroup_Oab__semigroup__mult(X), true, c_times(Y, c_times(Z, W, X), X), c_times(Z, c_times(Y, W, X), X)) = c_times(Z, c_times(Y, W, X), X).
% 0.11/0.26 Axiom 7 (cls_Ring__and__Field_Oabs__mult_0): ifeq2(class_Ring__and__Field_Oordered__idom(X), true, c_times(c_HOL_Oabs(Y, X), c_HOL_Oabs(Z, X), X), c_HOL_Oabs(c_times(Y, Z, X), X)) = c_HOL_Oabs(c_times(Y, Z, X), X).
% 0.11/0.26
% 0.11/0.26 Lemma 8: c_times(X, Y, t_b) = c_times(Y, X, t_b).
% 0.11/0.26 Proof:
% 0.11/0.26 c_times(X, Y, t_b)
% 0.11/0.26 = { by axiom 5 (cls_OrderedGroup_Omult__ac__2_0) R->L }
% 0.11/0.26 ifeq2(class_OrderedGroup_Oab__semigroup__mult(t_b), true, c_times(Y, X, t_b), c_times(X, Y, t_b))
% 0.11/0.26 = { by axiom 2 (ifeq_axiom) R->L }
% 0.11/0.26 ifeq2(ifeq(true, true, class_OrderedGroup_Oab__semigroup__mult(t_b), true), true, c_times(Y, X, t_b), c_times(X, Y, t_b))
% 0.11/0.26 = { by axiom 1 (tfree_tcs) R->L }
% 0.11/0.26 ifeq2(ifeq(class_Ring__and__Field_Oordered__idom(t_b), true, class_OrderedGroup_Oab__semigroup__mult(t_b), true), true, c_times(Y, X, t_b), c_times(X, Y, t_b))
% 0.11/0.26 = { by axiom 4 (clsrel_Ring__and__Field_Oordered__idom_17) }
% 0.11/0.26 ifeq2(true, true, c_times(Y, X, t_b), c_times(X, Y, t_b))
% 0.11/0.26 = { by axiom 3 (ifeq_axiom) }
% 0.11/0.26 c_times(Y, X, t_b)
% 0.11/0.26
% 0.11/0.26 Lemma 9: c_times(X, c_times(Y, Z, t_b), t_b) = c_times(Y, c_times(X, Z, t_b), t_b).
% 0.11/0.26 Proof:
% 0.11/0.26 c_times(X, c_times(Y, Z, t_b), t_b)
% 0.11/0.26 = { by axiom 6 (cls_OrderedGroup_Omult__ac__3_0) R->L }
% 0.11/0.26 ifeq2(class_OrderedGroup_Oab__semigroup__mult(t_b), true, c_times(Y, c_times(X, Z, t_b), t_b), c_times(X, c_times(Y, Z, t_b), t_b))
% 0.11/0.26 = { by axiom 2 (ifeq_axiom) R->L }
% 0.11/0.26 ifeq2(ifeq(true, true, class_OrderedGroup_Oab__semigroup__mult(t_b), true), true, c_times(Y, c_times(X, Z, t_b), t_b), c_times(X, c_times(Y, Z, t_b), t_b))
% 0.11/0.26 = { by axiom 1 (tfree_tcs) R->L }
% 0.11/0.26 ifeq2(ifeq(class_Ring__and__Field_Oordered__idom(t_b), true, class_OrderedGroup_Oab__semigroup__mult(t_b), true), true, c_times(Y, c_times(X, Z, t_b), t_b), c_times(X, c_times(Y, Z, t_b), t_b))
% 0.11/0.26 = { by axiom 4 (clsrel_Ring__and__Field_Oordered__idom_17) }
% 0.11/0.26 ifeq2(true, true, c_times(Y, c_times(X, Z, t_b), t_b), c_times(X, c_times(Y, Z, t_b), t_b))
% 0.11/0.26 = { by axiom 3 (ifeq_axiom) }
% 0.11/0.26 c_times(Y, c_times(X, Z, t_b), t_b)
% 0.11/0.26
% 0.11/0.26 Goal 1 (cls_conjecture_4): c_times(c_times(v_c, v_ca, t_b), c_HOL_Oabs(c_times(v_f(v_x), v_g(v_x), t_b), t_b), t_b) = c_times(c_times(v_c, c_HOL_Oabs(v_f(v_x), t_b), t_b), c_times(v_ca, c_HOL_Oabs(v_g(v_x), t_b), t_b), t_b).
% 0.11/0.26 Proof:
% 0.11/0.27 c_times(c_times(v_c, v_ca, t_b), c_HOL_Oabs(c_times(v_f(v_x), v_g(v_x), t_b), t_b), t_b)
% 0.11/0.27 = { by lemma 8 R->L }
% 0.11/0.27 c_times(c_HOL_Oabs(c_times(v_f(v_x), v_g(v_x), t_b), t_b), c_times(v_c, v_ca, t_b), t_b)
% 0.11/0.27 = { by lemma 9 }
% 0.11/0.27 c_times(v_c, c_times(c_HOL_Oabs(c_times(v_f(v_x), v_g(v_x), t_b), t_b), v_ca, t_b), t_b)
% 0.11/0.27 = { by lemma 8 }
% 0.11/0.27 c_times(v_c, c_times(v_ca, c_HOL_Oabs(c_times(v_f(v_x), v_g(v_x), t_b), t_b), t_b), t_b)
% 0.11/0.27 = { by lemma 8 R->L }
% 0.11/0.27 c_times(v_c, c_times(v_ca, c_HOL_Oabs(c_times(v_g(v_x), v_f(v_x), t_b), t_b), t_b), t_b)
% 0.11/0.27 = { by axiom 7 (cls_Ring__and__Field_Oabs__mult_0) R->L }
% 0.11/0.27 c_times(v_c, c_times(v_ca, ifeq2(class_Ring__and__Field_Oordered__idom(t_b), true, c_times(c_HOL_Oabs(v_g(v_x), t_b), c_HOL_Oabs(v_f(v_x), t_b), t_b), c_HOL_Oabs(c_times(v_g(v_x), v_f(v_x), t_b), t_b)), t_b), t_b)
% 0.11/0.27 = { by axiom 1 (tfree_tcs) }
% 0.11/0.27 c_times(v_c, c_times(v_ca, ifeq2(true, true, c_times(c_HOL_Oabs(v_g(v_x), t_b), c_HOL_Oabs(v_f(v_x), t_b), t_b), c_HOL_Oabs(c_times(v_g(v_x), v_f(v_x), t_b), t_b)), t_b), t_b)
% 0.11/0.27 = { by axiom 3 (ifeq_axiom) }
% 0.11/0.27 c_times(v_c, c_times(v_ca, c_times(c_HOL_Oabs(v_g(v_x), t_b), c_HOL_Oabs(v_f(v_x), t_b), t_b), t_b), t_b)
% 0.11/0.27 = { by lemma 9 R->L }
% 0.11/0.27 c_times(v_ca, c_times(v_c, c_times(c_HOL_Oabs(v_g(v_x), t_b), c_HOL_Oabs(v_f(v_x), t_b), t_b), t_b), t_b)
% 0.11/0.27 = { by lemma 9 R->L }
% 0.11/0.27 c_times(v_ca, c_times(c_HOL_Oabs(v_g(v_x), t_b), c_times(v_c, c_HOL_Oabs(v_f(v_x), t_b), t_b), t_b), t_b)
% 0.11/0.27 = { by lemma 8 R->L }
% 0.11/0.27 c_times(v_ca, c_times(c_times(v_c, c_HOL_Oabs(v_f(v_x), t_b), t_b), c_HOL_Oabs(v_g(v_x), t_b), t_b), t_b)
% 0.11/0.27 = { by lemma 9 R->L }
% 0.11/0.27 c_times(c_times(v_c, c_HOL_Oabs(v_f(v_x), t_b), t_b), c_times(v_ca, c_HOL_Oabs(v_g(v_x), t_b), t_b), t_b)
% 0.11/0.27 % SZS output end Proof
% 0.11/0.27
% 0.11/0.27 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------