%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : LCL433-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n007.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 11:49:51 AM UTC 2026
% Result : Unsatisfiable 0.09s 0.45s
% Output : Proof 0.09s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL433-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n007.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 27 15:40:55 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.45 Command-line arguments: --no-flatten-goal
% 0.09/0.45
% 0.09/0.45 % SZS status Unsatisfiable
% 0.09/0.45
% 0.09/0.46 % SZS output start Proof
% 0.09/0.46 Axiom 1 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 0.09/0.46 Axiom 2 (cls_conjecture_2): c_PropLog_Osat(c_insert(v_x, v_F, tc_PropLog_Opl(t_a)), v_xa, t_a) = true.
% 0.09/0.46 Axiom 3 (cls_Set_OinsertCI_1): c_in(X, c_insert(X, Y, Z), Z) = true.
% 0.09/0.46 Axiom 4 (cls_conjecture_4): ifeq(c_PropLog_Osat(v_F, X, t_a), true, c_in(X, c_PropLog_Othms(v_F, t_a), tc_PropLog_Opl(t_a)), true) = true.
% 0.09/0.46 Axiom 5 (cls_PropLog_Othms_OH_0): ifeq(c_in(X, Y, tc_PropLog_Opl(Z)), true, c_in(X, c_PropLog_Othms(Y, Z), tc_PropLog_Opl(Z)), true) = true.
% 0.09/0.46 Axiom 6 (cls_PropLog_Osat__imp_0): ifeq(c_PropLog_Osat(c_insert(X, Y, tc_PropLog_Opl(Z)), W, Z), true, c_PropLog_Osat(Y, c_PropLog_Opl_Oop_A_N_62(X, W, Z), Z), true) = true.
% 0.09/0.46 Axiom 7 (cls_PropLog_Oweaken__left__insert_0): ifeq(c_in(X, c_PropLog_Othms(Y, Z), tc_PropLog_Opl(Z)), true, c_in(X, c_PropLog_Othms(c_insert(W, Y, tc_PropLog_Opl(Z)), Z), tc_PropLog_Opl(Z)), true) = true.
% 0.09/0.46 Axiom 8 (cls_PropLog_Othms_OMP_0): ifeq(c_in(c_PropLog_Opl_Oop_A_N_62(X, Y, Z), c_PropLog_Othms(W, Z), tc_PropLog_Opl(Z)), true, ifeq(c_in(X, c_PropLog_Othms(W, Z), tc_PropLog_Opl(Z)), true, c_in(Y, c_PropLog_Othms(W, Z), tc_PropLog_Opl(Z)), true), true) = true.
% 0.09/0.46
% 0.09/0.46 Goal 1 (cls_conjecture_3): c_in(v_xa, c_PropLog_Othms(c_insert(v_x, v_F, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)) = true.
% 0.09/0.46 Proof:
% 0.09/0.46 c_in(v_xa, c_PropLog_Othms(c_insert(v_x, v_F, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a))
% 0.09/0.46 = { by axiom 1 (ifeq_axiom) R->L }
% 0.09/0.46 ifeq(true, true, c_in(v_xa, c_PropLog_Othms(c_insert(v_x, v_F, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)), true)
% 0.09/0.46 = { by axiom 5 (cls_PropLog_Othms_OH_0) R->L }
% 0.09/0.46 ifeq(ifeq(c_in(v_x, c_insert(v_x, v_F, tc_PropLog_Opl(t_a)), tc_PropLog_Opl(t_a)), true, c_in(v_x, c_PropLog_Othms(c_insert(v_x, v_F, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)), true), true, c_in(v_xa, c_PropLog_Othms(c_insert(v_x, v_F, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)), true)
% 0.09/0.46 = { by axiom 3 (cls_Set_OinsertCI_1) }
% 0.09/0.46 ifeq(ifeq(true, true, c_in(v_x, c_PropLog_Othms(c_insert(v_x, v_F, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)), true), true, c_in(v_xa, c_PropLog_Othms(c_insert(v_x, v_F, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)), true)
% 0.09/0.46 = { by axiom 1 (ifeq_axiom) }
% 0.09/0.46 ifeq(c_in(v_x, c_PropLog_Othms(c_insert(v_x, v_F, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)), true, c_in(v_xa, c_PropLog_Othms(c_insert(v_x, v_F, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)), true)
% 0.09/0.46 = { by axiom 1 (ifeq_axiom) R->L }
% 0.09/0.46 ifeq(true, true, ifeq(c_in(v_x, c_PropLog_Othms(c_insert(v_x, v_F, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)), true, c_in(v_xa, c_PropLog_Othms(c_insert(v_x, v_F, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)), true), true)
% 0.09/0.46 = { by axiom 7 (cls_PropLog_Oweaken__left__insert_0) R->L }
% 0.09/0.46 ifeq(ifeq(c_in(c_PropLog_Opl_Oop_A_N_62(v_x, v_xa, t_a), c_PropLog_Othms(v_F, t_a), tc_PropLog_Opl(t_a)), true, c_in(c_PropLog_Opl_Oop_A_N_62(v_x, v_xa, t_a), c_PropLog_Othms(c_insert(v_x, v_F, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)), true), true, ifeq(c_in(v_x, c_PropLog_Othms(c_insert(v_x, v_F, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)), true, c_in(v_xa, c_PropLog_Othms(c_insert(v_x, v_F, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)), true), true)
% 0.09/0.46 = { by axiom 1 (ifeq_axiom) R->L }
% 0.09/0.46 ifeq(ifeq(ifeq(true, true, c_in(c_PropLog_Opl_Oop_A_N_62(v_x, v_xa, t_a), c_PropLog_Othms(v_F, t_a), tc_PropLog_Opl(t_a)), true), true, c_in(c_PropLog_Opl_Oop_A_N_62(v_x, v_xa, t_a), c_PropLog_Othms(c_insert(v_x, v_F, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)), true), true, ifeq(c_in(v_x, c_PropLog_Othms(c_insert(v_x, v_F, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)), true, c_in(v_xa, c_PropLog_Othms(c_insert(v_x, v_F, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)), true), true)
% 0.09/0.46 = { by axiom 6 (cls_PropLog_Osat__imp_0) R->L }
% 0.09/0.46 ifeq(ifeq(ifeq(ifeq(c_PropLog_Osat(c_insert(v_x, v_F, tc_PropLog_Opl(t_a)), v_xa, t_a), true, c_PropLog_Osat(v_F, c_PropLog_Opl_Oop_A_N_62(v_x, v_xa, t_a), t_a), true), true, c_in(c_PropLog_Opl_Oop_A_N_62(v_x, v_xa, t_a), c_PropLog_Othms(v_F, t_a), tc_PropLog_Opl(t_a)), true), true, c_in(c_PropLog_Opl_Oop_A_N_62(v_x, v_xa, t_a), c_PropLog_Othms(c_insert(v_x, v_F, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)), true), true, ifeq(c_in(v_x, c_PropLog_Othms(c_insert(v_x, v_F, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)), true, c_in(v_xa, c_PropLog_Othms(c_insert(v_x, v_F, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)), true), true)
% 0.09/0.46 = { by axiom 2 (cls_conjecture_2) }
% 0.09/0.46 ifeq(ifeq(ifeq(ifeq(true, true, c_PropLog_Osat(v_F, c_PropLog_Opl_Oop_A_N_62(v_x, v_xa, t_a), t_a), true), true, c_in(c_PropLog_Opl_Oop_A_N_62(v_x, v_xa, t_a), c_PropLog_Othms(v_F, t_a), tc_PropLog_Opl(t_a)), true), true, c_in(c_PropLog_Opl_Oop_A_N_62(v_x, v_xa, t_a), c_PropLog_Othms(c_insert(v_x, v_F, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)), true), true, ifeq(c_in(v_x, c_PropLog_Othms(c_insert(v_x, v_F, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)), true, c_in(v_xa, c_PropLog_Othms(c_insert(v_x, v_F, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)), true), true)
% 0.09/0.46 = { by axiom 1 (ifeq_axiom) }
% 0.09/0.46 ifeq(ifeq(ifeq(c_PropLog_Osat(v_F, c_PropLog_Opl_Oop_A_N_62(v_x, v_xa, t_a), t_a), true, c_in(c_PropLog_Opl_Oop_A_N_62(v_x, v_xa, t_a), c_PropLog_Othms(v_F, t_a), tc_PropLog_Opl(t_a)), true), true, c_in(c_PropLog_Opl_Oop_A_N_62(v_x, v_xa, t_a), c_PropLog_Othms(c_insert(v_x, v_F, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)), true), true, ifeq(c_in(v_x, c_PropLog_Othms(c_insert(v_x, v_F, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)), true, c_in(v_xa, c_PropLog_Othms(c_insert(v_x, v_F, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)), true), true)
% 0.09/0.46 = { by axiom 4 (cls_conjecture_4) }
% 0.09/0.46 ifeq(ifeq(true, true, c_in(c_PropLog_Opl_Oop_A_N_62(v_x, v_xa, t_a), c_PropLog_Othms(c_insert(v_x, v_F, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)), true), true, ifeq(c_in(v_x, c_PropLog_Othms(c_insert(v_x, v_F, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)), true, c_in(v_xa, c_PropLog_Othms(c_insert(v_x, v_F, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)), true), true)
% 0.09/0.46 = { by axiom 1 (ifeq_axiom) }
% 0.09/0.46 ifeq(c_in(c_PropLog_Opl_Oop_A_N_62(v_x, v_xa, t_a), c_PropLog_Othms(c_insert(v_x, v_F, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)), true, ifeq(c_in(v_x, c_PropLog_Othms(c_insert(v_x, v_F, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)), true, c_in(v_xa, c_PropLog_Othms(c_insert(v_x, v_F, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)), true), true)
% 0.09/0.46 = { by axiom 8 (cls_PropLog_Othms_OMP_0) }
% 0.09/0.46 true
% 0.09/0.46 % SZS output end Proof
% 0.09/0.46
% 0.09/0.46 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------