%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : LCL445-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n010.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 11:49:53 AM UTC 2026
% Result : Unsatisfiable 0.19s 0.46s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL445-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n010.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sun Sep 27 15:44:03 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.46 Command-line arguments: --flatten-regeneralise
% 0.19/0.46
% 0.19/0.46 % SZS status Unsatisfiable
% 0.19/0.46
% 0.19/0.46 % SZS output start Proof
% 0.19/0.46 Axiom 1 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 0.19/0.46 Axiom 2 (cls_conjecture_0): c_in(v_q, c_PropLog_Othms(c_insert(v_p, v_H, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)) = true.
% 0.19/0.46 Axiom 3 (cls_conjecture_1): c_in(v_q, c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p, c_PropLog_Opl_Ofalse, t_a), v_H, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)) = true.
% 0.19/0.46 Axiom 4 (cls_PropLog_Odeduction_0): ifeq(c_in(X, c_PropLog_Othms(c_insert(Y, Z, tc_PropLog_Opl(W)), W), tc_PropLog_Opl(W)), true, c_in(c_PropLog_Opl_Oop_A_N_62(Y, X, W), c_PropLog_Othms(Z, W), tc_PropLog_Opl(W)), true) = true.
% 0.19/0.46 Axiom 5 (cls_PropLog_Othms__excluded__middle_0): c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(X, Y, Z), c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(X, c_PropLog_Opl_Ofalse, Z), Y, Z), Y, Z), Z), c_PropLog_Othms(W, Z), tc_PropLog_Opl(Z)) = true.
% 0.19/0.46 Axiom 6 (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.
% 0.19/0.46
% 0.19/0.46 Goal 1 (cls_conjecture_2): c_in(v_q, c_PropLog_Othms(v_H, t_a), tc_PropLog_Opl(t_a)) = true.
% 0.19/0.46 Proof:
% 0.19/0.46 c_in(v_q, c_PropLog_Othms(v_H, t_a), tc_PropLog_Opl(t_a))
% 0.19/0.46 = { by axiom 1 (ifeq_axiom) R->L }
% 0.19/0.46 ifeq(true, true, c_in(v_q, c_PropLog_Othms(v_H, t_a), tc_PropLog_Opl(t_a)), true)
% 0.19/0.46 = { by axiom 4 (cls_PropLog_Odeduction_0) R->L }
% 0.19/0.46 ifeq(ifeq(c_in(v_q, c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p, c_PropLog_Opl_Ofalse, t_a), v_H, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)), true, c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_p, c_PropLog_Opl_Ofalse, t_a), v_q, t_a), c_PropLog_Othms(v_H, t_a), tc_PropLog_Opl(t_a)), true), true, c_in(v_q, c_PropLog_Othms(v_H, t_a), tc_PropLog_Opl(t_a)), true)
% 0.19/0.46 = { by axiom 3 (cls_conjecture_1) }
% 0.19/0.46 ifeq(ifeq(true, true, c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_p, c_PropLog_Opl_Ofalse, t_a), v_q, t_a), c_PropLog_Othms(v_H, t_a), tc_PropLog_Opl(t_a)), true), true, c_in(v_q, c_PropLog_Othms(v_H, t_a), tc_PropLog_Opl(t_a)), true)
% 0.19/0.46 = { by axiom 1 (ifeq_axiom) }
% 0.19/0.47 ifeq(c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_p, c_PropLog_Opl_Ofalse, t_a), v_q, t_a), c_PropLog_Othms(v_H, t_a), tc_PropLog_Opl(t_a)), true, c_in(v_q, c_PropLog_Othms(v_H, t_a), tc_PropLog_Opl(t_a)), true)
% 0.19/0.47 = { by axiom 1 (ifeq_axiom) R->L }
% 0.19/0.47 ifeq(true, true, ifeq(c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_p, c_PropLog_Opl_Ofalse, t_a), v_q, t_a), c_PropLog_Othms(v_H, t_a), tc_PropLog_Opl(t_a)), true, c_in(v_q, c_PropLog_Othms(v_H, t_a), tc_PropLog_Opl(t_a)), true), true)
% 0.19/0.47 = { by axiom 6 (cls_PropLog_Othms_OMP_0) R->L }
% 0.19/0.47 ifeq(ifeq(c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_p, v_q, t_a), c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_p, c_PropLog_Opl_Ofalse, t_a), v_q, t_a), v_q, t_a), t_a), c_PropLog_Othms(v_H, t_a), tc_PropLog_Opl(t_a)), true, ifeq(c_in(c_PropLog_Opl_Oop_A_N_62(v_p, v_q, t_a), c_PropLog_Othms(v_H, t_a), tc_PropLog_Opl(t_a)), true, c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_p, c_PropLog_Opl_Ofalse, t_a), v_q, t_a), v_q, t_a), c_PropLog_Othms(v_H, t_a), tc_PropLog_Opl(t_a)), true), true), true, ifeq(c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_p, c_PropLog_Opl_Ofalse, t_a), v_q, t_a), c_PropLog_Othms(v_H, t_a), tc_PropLog_Opl(t_a)), true, c_in(v_q, c_PropLog_Othms(v_H, t_a), tc_PropLog_Opl(t_a)), true), true)
% 0.19/0.47 = { by axiom 1 (ifeq_axiom) R->L }
% 0.19/0.47 ifeq(ifeq(c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_p, v_q, t_a), c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_p, c_PropLog_Opl_Ofalse, t_a), v_q, t_a), v_q, t_a), t_a), c_PropLog_Othms(v_H, t_a), tc_PropLog_Opl(t_a)), true, ifeq(ifeq(true, true, c_in(c_PropLog_Opl_Oop_A_N_62(v_p, v_q, t_a), c_PropLog_Othms(v_H, t_a), tc_PropLog_Opl(t_a)), true), true, c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_p, c_PropLog_Opl_Ofalse, t_a), v_q, t_a), v_q, t_a), c_PropLog_Othms(v_H, t_a), tc_PropLog_Opl(t_a)), true), true), true, ifeq(c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_p, c_PropLog_Opl_Ofalse, t_a), v_q, t_a), c_PropLog_Othms(v_H, t_a), tc_PropLog_Opl(t_a)), true, c_in(v_q, c_PropLog_Othms(v_H, t_a), tc_PropLog_Opl(t_a)), true), true)
% 0.19/0.47 = { by axiom 2 (cls_conjecture_0) R->L }
% 0.19/0.47 ifeq(ifeq(c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_p, v_q, t_a), c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_p, c_PropLog_Opl_Ofalse, t_a), v_q, t_a), v_q, t_a), t_a), c_PropLog_Othms(v_H, t_a), tc_PropLog_Opl(t_a)), true, ifeq(ifeq(c_in(v_q, c_PropLog_Othms(c_insert(v_p, v_H, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)), true, c_in(c_PropLog_Opl_Oop_A_N_62(v_p, v_q, t_a), c_PropLog_Othms(v_H, t_a), tc_PropLog_Opl(t_a)), true), true, c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_p, c_PropLog_Opl_Ofalse, t_a), v_q, t_a), v_q, t_a), c_PropLog_Othms(v_H, t_a), tc_PropLog_Opl(t_a)), true), true), true, ifeq(c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_p, c_PropLog_Opl_Ofalse, t_a), v_q, t_a), c_PropLog_Othms(v_H, t_a), tc_PropLog_Opl(t_a)), true, c_in(v_q, c_PropLog_Othms(v_H, t_a), tc_PropLog_Opl(t_a)), true), true)
% 0.19/0.47 = { by axiom 4 (cls_PropLog_Odeduction_0) }
% 0.19/0.47 ifeq(ifeq(c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_p, v_q, t_a), c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_p, c_PropLog_Opl_Ofalse, t_a), v_q, t_a), v_q, t_a), t_a), c_PropLog_Othms(v_H, t_a), tc_PropLog_Opl(t_a)), true, ifeq(true, true, c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_p, c_PropLog_Opl_Ofalse, t_a), v_q, t_a), v_q, t_a), c_PropLog_Othms(v_H, t_a), tc_PropLog_Opl(t_a)), true), true), true, ifeq(c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_p, c_PropLog_Opl_Ofalse, t_a), v_q, t_a), c_PropLog_Othms(v_H, t_a), tc_PropLog_Opl(t_a)), true, c_in(v_q, c_PropLog_Othms(v_H, t_a), tc_PropLog_Opl(t_a)), true), true)
% 0.19/0.47 = { by axiom 1 (ifeq_axiom) }
% 0.19/0.47 ifeq(ifeq(c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_p, v_q, t_a), c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_p, c_PropLog_Opl_Ofalse, t_a), v_q, t_a), v_q, t_a), t_a), c_PropLog_Othms(v_H, t_a), tc_PropLog_Opl(t_a)), true, c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_p, c_PropLog_Opl_Ofalse, t_a), v_q, t_a), v_q, t_a), c_PropLog_Othms(v_H, t_a), tc_PropLog_Opl(t_a)), true), true, ifeq(c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_p, c_PropLog_Opl_Ofalse, t_a), v_q, t_a), c_PropLog_Othms(v_H, t_a), tc_PropLog_Opl(t_a)), true, c_in(v_q, c_PropLog_Othms(v_H, t_a), tc_PropLog_Opl(t_a)), true), true)
% 0.19/0.47 = { by axiom 5 (cls_PropLog_Othms__excluded__middle_0) }
% 0.19/0.47 ifeq(ifeq(true, true, c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_p, c_PropLog_Opl_Ofalse, t_a), v_q, t_a), v_q, t_a), c_PropLog_Othms(v_H, t_a), tc_PropLog_Opl(t_a)), true), true, ifeq(c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_p, c_PropLog_Opl_Ofalse, t_a), v_q, t_a), c_PropLog_Othms(v_H, t_a), tc_PropLog_Opl(t_a)), true, c_in(v_q, c_PropLog_Othms(v_H, t_a), tc_PropLog_Opl(t_a)), true), true)
% 0.19/0.47 = { by axiom 1 (ifeq_axiom) }
% 0.19/0.47 ifeq(c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_p, c_PropLog_Opl_Ofalse, t_a), v_q, t_a), v_q, t_a), c_PropLog_Othms(v_H, t_a), tc_PropLog_Opl(t_a)), true, ifeq(c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_p, c_PropLog_Opl_Ofalse, t_a), v_q, t_a), c_PropLog_Othms(v_H, t_a), tc_PropLog_Opl(t_a)), true, c_in(v_q, c_PropLog_Othms(v_H, t_a), tc_PropLog_Opl(t_a)), true), true)
% 0.19/0.47 = { by axiom 6 (cls_PropLog_Othms_OMP_0) }
% 0.19/0.47 true
% 0.19/0.47 % SZS output end Proof
% 0.19/0.47
% 0.19/0.47 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------