%------------------------------------------------------------------------------
% File : CSI_E---1.1
% Problem : LCL837-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar mcs_scs.jar %d %s
% Computer : n029.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 11:21:49 AM UTC 2026
% Result : Unsatisfiable 1.01s 0.65s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL837-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.02 % Command : java -jar mcs_scs.jar %d %s
% 0.07/0.34 % Computer : n029.cluster.edu
% 0.07/0.34 % Model : x86_64 x86_64
% 0.07/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.34 % Memory : 8046.5625MB
% 0.07/0.34 % OS : Linux 6.8.0-71-generic
% 0.07/0.35 % CPULimit : 300
% 0.07/0.35 % WCLimit : 300
% 0.07/0.35 % DateTime : Sat Sep 5 09:30:55 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.12/0.44 start to proof:theBenchmark.p
% 1.01/0.65 % Version : CSI_E---1.1
% 1.01/0.65 % Problem : theBenchmark.p
% 1.01/0.65 % Proof found!
% 1.01/0.65 # SZS status Unsatisfiable
% 1.01/0.65 % SZS output start Proof
% 1.01/0.65 cnf(cls_subst__subst_0, axiom, (hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),hAPP(hAPP(c_Lambda_Olift,X2),X3)),c_Suc(X4))),hAPP(hAPP(hAPP(c_Lambda_Osubst,X5),X2),X4)),X3)=hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X5),X3)),X2),X4)|~c_HOL_Oord__class_Oless(X3,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X4),c_HOL_Oone__class_Oone(tc_nat)),tc_nat)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', cls_subst__subst_0)).
% 1.01/0.65 cnf(cls_Suc__eq__plus1_0, axiom, (c_Suc(X1)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', cls_Suc__eq__plus1_0)).
% 1.01/0.65 cnf(cls_One__nat__def_0, axiom, (c_HOL_Oone__class_Oone(tc_nat)=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', cls_One__nat__def_0)).
% 1.01/0.65 cnf(cls_conjecture_0, negated_conjecture, (~hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),hAPP(hAPP(c_Lambda_Olift,v_u____),c_HOL_Ozero__class_Ozero(tc_nat))),c_Suc(v_i____))),hAPP(hAPP(hAPP(c_Lambda_Osubst,v_a____),v_u____),v_i____)),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,v_u____,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_i____,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', cls_conjecture_0)).
% 1.01/0.65 cnf(cls_subst__map_0, axiom, (hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,X1,X2,tc_Lambda_OdB,tc_Lambda_OdB)),X3),X4)=c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X3),X4),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,X3,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),X4,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),X2,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', cls_subst__map_0)).
% 1.01/0.65 cnf(cls_CHAINED_0, axiom, (hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB)),v_u____),v_i____)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', cls_CHAINED_0)).
% 1.01/0.65 cnf(cls_zero__less__Suc_0, axiom, (c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(X1),tc_nat)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', cls_zero__less__Suc_0)).
% 1.01/0.65 cnf(c_0_7, plain, (hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),hAPP(hAPP(c_Lambda_Olift,X2),X3)),c_Suc(X4))),hAPP(hAPP(hAPP(c_Lambda_Osubst,X5),X2),X4)),X3)=hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X5),X3)),X2),X4)|~c_HOL_Oord__class_Oless(X3,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X4),c_HOL_Oone__class_Oone(tc_nat)),tc_nat)), inference(fof_simplification,[status(thm)],[cls_subst__subst_0])).
% 1.01/0.65 cnf(c_0_8, axiom, (c_Suc(X1)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat))), cls_Suc__eq__plus1_0).
% 1.01/0.65 cnf(c_0_9, axiom, (c_HOL_Oone__class_Oone(tc_nat)=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))), cls_One__nat__def_0).
% 1.01/0.65 cnf(c_0_10, negated_conjecture, (~hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),hAPP(hAPP(c_Lambda_Olift,v_u____),c_HOL_Ozero__class_Ozero(tc_nat))),c_Suc(v_i____))),hAPP(hAPP(hAPP(c_Lambda_Osubst,v_a____),v_u____),v_i____)),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,v_u____,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_i____,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB)))), inference(fof_simplification,[status(thm)],[cls_conjecture_0])).
% 1.01/0.65 cnf(c_0_11, plain, (hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),hAPP(hAPP(c_Lambda_Olift,X2),X3)),c_Suc(X4))),hAPP(hAPP(hAPP(c_Lambda_Osubst,X5),X2),X4)),X3)=hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X5),X3)),X2),X4)|~c_HOL_Oord__class_Oless(X3,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X4),c_HOL_Oone__class_Oone(tc_nat)),tc_nat)), c_0_7).
% 1.01/0.65 cnf(c_0_12, plain, (hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)))=c_Suc(X1)), inference(rw,[status(thm)],[c_0_8, c_0_9])).
% 1.01/0.65 cnf(c_0_13, negated_conjecture, (~hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),hAPP(hAPP(c_Lambda_Olift,v_u____),c_HOL_Ozero__class_Ozero(tc_nat))),c_Suc(v_i____))),hAPP(hAPP(hAPP(c_Lambda_Osubst,v_a____),v_u____),v_i____)),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,v_u____,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_i____,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB)))), c_0_10).
% 1.01/0.65 cnf(c_0_14, plain, (hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),hAPP(hAPP(c_Lambda_Olift,X2),X3)),c_Suc(X4))),hAPP(hAPP(hAPP(c_Lambda_Osubst,X5),X2),X4)),X3)=hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X5),X3)),X2),X4)|~c_HOL_Oord__class_Oless(X3,c_Suc(X4),tc_nat)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_11, c_0_9]), c_0_12])).
% 1.01/0.65 cnf(c_0_15, axiom, (hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,X1,X2,tc_Lambda_OdB,tc_Lambda_OdB)),X3),X4)=c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X3),X4),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,X3,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),X4,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),X2,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB)), cls_subst__map_0).
% 1.01/0.65 cnf(c_0_16, axiom, (hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB)),v_u____),v_i____)))), cls_CHAINED_0).
% 1.01/0.65 cnf(c_0_17, axiom, (c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(X1),tc_nat)), cls_zero__less__Suc_0).
% 1.01/0.65 cnf(c_0_18, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13, c_0_14]), c_0_15]), c_0_16]), c_0_17])]), ['proof']).
% 1.01/0.65 % SZS output end Proof
% 1.01/0.65 % User time : 0.121 s
% 1.01/0.65 % System time : 0.027 s
% 1.01/0.65 % Total time : 0.148 s
% 1.01/0.65 % User time : 0.140 s
% 1.01/0.65 % System time : 0.030 s
% 1.01/0.65 % Total time : 0.170 s
% 1.01/0.65
%------------------------------------------------------------------------------