%------------------------------------------------------------------------------
% File : CSI_E---1.1
% Problem : LCL754-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar mcs_scs.jar %d %s
% Computer : n011.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 : Mon Sep 7 11:21:37 AM UTC 2026
% Result : Unsatisfiable 0.67s 0.88s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL754-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.03 % Command : java -jar mcs_scs.jar %d %s
% 0.08/0.35 % Computer : n011.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Fri Sep 4 15:40:13 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.24/0.47 start to proof:theBenchmark.p
% 0.67/0.88 % Version : CSI_E---1.1
% 0.67/0.88 % Problem : theBenchmark.p
% 0.67/0.88 % Proof found!
% 0.67/0.88 # SZS status Unsatisfiable
% 0.67/0.88 % SZS output start Proof
% 0.67/0.88 cnf(cls_Lambda_0, axiom, (c_InductTermi_OIT(c_Lambda_OdB_OAbs(X1))|~c_InductTermi_OIT(X1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', cls_Lambda_0)).
% 0.67/0.88 cnf(cls_subst__Abs_0, axiom, (c_Lambda_Osubst(c_Lambda_OdB_OAbs(X1),X2,X3)=c_Lambda_OdB_OAbs(c_Lambda_Osubst(X1,c_Lambda_Olift(X2,c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', cls_subst__Abs_0)).
% 0.67/0.88 cnf(cls_Suc__eq__plus1_0, axiom, (c_Suc(X1)=c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', cls_Suc__eq__plus1_0)).
% 0.67/0.88 cnf(cls_lift_Osimps_I1_J_1, axiom, (c_Lambda_Olift(c_Lambda_OdB_OVar(X1),X2)=c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat))|c_HOL_Oord__class_Oless(X1,X2,tc_nat)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', cls_lift_Osimps_I1_J_1)).
% 0.67/0.88 cnf(cls_gr__implies__not0_0, axiom, (~c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', cls_gr__implies__not0_0)).
% 0.67/0.88 cnf(cls_conjecture_2, negated_conjecture, (~c_InductTermi_OIT(c_Lambda_Osubst(c_Lambda_OdB_OAbs(v_ra),c_Lambda_OdB_OVar(v_ia),v_ja))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', cls_conjecture_2)).
% 0.67/0.88 cnf(cls_conjecture_1, negated_conjecture, (c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_OdB_OVar(X1),X2))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', cls_conjecture_1)).
% 0.67/0.88 cnf(c_0_7, plain, (c_InductTermi_OIT(c_Lambda_OdB_OAbs(X1))|~c_InductTermi_OIT(X1)), inference(fof_simplification,[status(thm)],[cls_Lambda_0])).
% 0.67/0.88 cnf(c_0_8, axiom, (c_Lambda_Osubst(c_Lambda_OdB_OAbs(X1),X2,X3)=c_Lambda_OdB_OAbs(c_Lambda_Osubst(X1,c_Lambda_Olift(X2,c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat)))), cls_subst__Abs_0).
% 0.67/0.88 cnf(c_0_9, axiom, (c_Suc(X1)=c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat)), cls_Suc__eq__plus1_0).
% 0.67/0.88 cnf(c_0_10, plain, (c_InductTermi_OIT(c_Lambda_OdB_OAbs(X1))|~c_InductTermi_OIT(X1)), c_0_7).
% 0.67/0.88 cnf(c_0_11, plain, (c_Lambda_OdB_OAbs(c_Lambda_Osubst(X1,c_Lambda_Olift(X2,c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(X3)))=c_Lambda_Osubst(c_Lambda_OdB_OAbs(X1),X2,X3)), inference(rw,[status(thm)],[c_0_8, c_0_9])).
% 0.67/0.88 cnf(c_0_12, axiom, (c_Lambda_Olift(c_Lambda_OdB_OVar(X1),X2)=c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat))|c_HOL_Oord__class_Oless(X1,X2,tc_nat)), cls_lift_Osimps_I1_J_1).
% 0.67/0.88 cnf(c_0_13, plain, (~c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)), inference(fof_simplification,[status(thm)],[cls_gr__implies__not0_0])).
% 0.67/0.88 cnf(c_0_14, plain, (c_InductTermi_OIT(c_Lambda_Osubst(c_Lambda_OdB_OAbs(X1),X2,X3))|~c_InductTermi_OIT(c_Lambda_Osubst(X1,c_Lambda_Olift(X2,c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(X3)))), inference(spm,[status(thm)],[c_0_10, c_0_11])).
% 0.67/0.88 cnf(c_0_15, plain, (c_Lambda_Olift(c_Lambda_OdB_OVar(X1),X2)=c_Lambda_OdB_OVar(c_Suc(X1))|c_HOL_Oord__class_Oless(X1,X2,tc_nat)), inference(rw,[status(thm)],[c_0_12, c_0_9])).
% 0.67/0.88 cnf(c_0_16, plain, (~c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)), c_0_13).
% 0.67/0.88 cnf(c_0_17, negated_conjecture, (~c_InductTermi_OIT(c_Lambda_Osubst(c_Lambda_OdB_OAbs(v_ra),c_Lambda_OdB_OVar(v_ia),v_ja))), inference(fof_simplification,[status(thm)],[cls_conjecture_2])).
% 0.67/0.88 cnf(c_0_18, plain, (c_InductTermi_OIT(c_Lambda_Osubst(c_Lambda_OdB_OAbs(X1),c_Lambda_OdB_OVar(X2),X3))|~c_InductTermi_OIT(c_Lambda_Osubst(X1,c_Lambda_OdB_OVar(c_Suc(X2)),c_Suc(X3)))), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_14, c_0_15]), c_0_16])).
% 0.67/0.88 cnf(c_0_19, negated_conjecture, (c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_OdB_OVar(X1),X2))), cls_conjecture_1).
% 0.67/0.88 cnf(c_0_20, negated_conjecture, (~c_InductTermi_OIT(c_Lambda_Osubst(c_Lambda_OdB_OAbs(v_ra),c_Lambda_OdB_OVar(v_ia),v_ja))), c_0_17).
% 0.67/0.88 cnf(c_0_21, negated_conjecture, (c_InductTermi_OIT(c_Lambda_Osubst(c_Lambda_OdB_OAbs(v_ra),c_Lambda_OdB_OVar(X1),X2))), inference(spm,[status(thm)],[c_0_18, c_0_19])).
% 0.67/0.88 cnf(c_0_22, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_20, c_0_21])]), ['proof']).
% 0.67/0.88 % SZS output end Proof
% 0.67/0.88 % User time : 0.324 s
% 0.67/0.88 % System time : 0.010 s
% 0.67/0.88 % Total time : 0.333 s
% 0.67/0.88 % User time : 0.334 s
% 0.67/0.88 % System time : 0.012 s
% 0.67/0.88 % Total time : 0.346 s
% 0.67/0.88
%------------------------------------------------------------------------------