%------------------------------------------------------------------------------
% File : CSI_E---1.1
% Problem : LCL888+1 : TPTP v9.3.1. Released v5.5.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar mcs_scs.jar %d %s
% Computer : n009.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 11:21:53 AM UTC 2026
% Result : Theorem 24.97s 4.07s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL888+1 : TPTP v9.3.1. Released v5.5.0.
% 0.00/0.03 % Command : java -jar mcs_scs.jar %d %s
% 0.08/0.35 % Computer : n009.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 : Sat Sep 5 20:48:52 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.25/0.47 start to proof:theBenchmark.p
% 24.97/4.07 % Version : CSI_E---1.1
% 24.97/4.07 % Problem : theBenchmark.p
% 24.97/4.07 % Proof found!
% 24.97/4.07 % SZS status Theorem for theBenchmark.p
% 24.97/4.07 % SZS output start Proof
% 24.97/4.07 fof(sos_06, axiom, ![X7, X8]:((('>='(X7,X8)&'>='(X8,X7))=>X7=X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', sos_06)).
% 24.97/4.07 fof(sos_08, axiom, ![X1]:('>='(X1,'0')), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', sos_08)).
% 24.97/4.07 fof(goals_13, conjecture, ![X21, X22, X23]:(((X21='==>'(X21,X22)&X23='==>'(X23,X22))=>X21=X23)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', goals_13)).
% 24.97/4.07 fof(sos_03, axiom, ![X1]:('+'(X1,'0')=X1), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', sos_03)).
% 24.97/4.07 fof(sos_02, axiom, ![X1, X2]:('+'(X1,X2)='+'(X2,X1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', sos_02)).
% 24.97/4.07 fof(sos_07, axiom, ![X9, X10, X11]:(('>='('+'(X9,X10),X11)<=>'>='(X10,'==>'(X9,X11)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', sos_07)).
% 24.97/4.07 fof(sos_09, axiom, ![X12, X13, X14]:(('>='(X12,X13)=>'>='('+'(X12,X14),'+'(X13,X14)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', sos_09)).
% 24.97/4.07 fof(sos_04, axiom, ![X1]:('>='(X1,X1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', sos_04)).
% 24.97/4.07 fof(sos_12, axiom, ![X1, X2]:('+'(X1,'==>'(X1,X2))='+'(X2,'==>'(X2,X1))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', sos_12)).
% 24.97/4.07 fof(sos_11, axiom, ![X18, X19, X20]:(('>='(X18,X19)=>'>='('==>'(X20,X18),'==>'(X20,X19)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', sos_11)).
% 24.97/4.07 fof(sos_01, axiom, ![X1, X2, X3]:('+'('+'(X1,X2),X3)='+'(X1,'+'(X2,X3))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', sos_01)).
% 24.97/4.07 fof(sos_05, axiom, ![X4, X5, X6]:((('>='(X4,X5)&'>='(X5,X6))=>'>='(X4,X6))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', sos_05)).
% 24.97/4.07 fof(sos_10, axiom, ![X15, X16, X17]:(('>='(X15,X16)=>'>='('==>'(X16,X17),'==>'(X15,X17)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', sos_10)).
% 24.97/4.07 fof(c_0_13, plain, ![X34, X35]:((~'>='(X34,X35)|~'>='(X35,X34)|X34=X35)), inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos_06])])])).
% 24.97/4.07 fof(c_0_14, plain, ![X39]:('>='(X39,'0')), inference(variable_rename,[status(thm)],[sos_08])).
% 24.97/4.07 fof(c_0_15, negated_conjecture, ~(![X21, X22, X23]:(((X21='==>'(X21,X22)&X23='==>'(X23,X22))=>X21=X23))), inference(assume_negation,[status(cth)],[goals_13])).
% 24.97/4.07 fof(c_0_16, plain, ![X29]:('+'(X29,'0')=X29), inference(variable_rename,[status(thm)],[sos_03])).
% 24.97/4.07 fof(c_0_17, plain, ![X27, X28]:('+'(X27,X28)='+'(X28,X27)), inference(variable_rename,[status(thm)],[sos_02])).
% 24.97/4.07 cnf(c_0_18, plain, (X1=X2|~'>='(X1,X2)|~'>='(X2,X1)), inference(split_conjunct,[status(thm)],[c_0_13])).
% 24.97/4.07 cnf(c_0_19, plain, ('>='(X1,'0')), inference(split_conjunct,[status(thm)],[c_0_14])).
% 24.97/4.07 fof(c_0_20, plain, ![X36, X37, X38]:(((~'>='('+'(X36,X37),X38)|'>='(X37,'==>'(X36,X38)))&(~'>='(X37,'==>'(X36,X38))|'>='('+'(X36,X37),X38)))), inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos_07])])])).
% 24.97/4.07 fof(c_0_21, negated_conjecture, ((esk1_0='==>'(esk1_0,esk2_0)&esk3_0='==>'(esk3_0,esk2_0))&esk1_0!=esk3_0), inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_15])])])])).
% 24.97/4.07 fof(c_0_22, plain, ![X40, X41, X42]:((~'>='(X40,X41)|'>='('+'(X40,X42),'+'(X41,X42)))), inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos_09])])])).
% 24.97/4.07 cnf(c_0_23, plain, ('+'(X1,'0')=X1), inference(split_conjunct,[status(thm)],[c_0_16])).
% 24.97/4.07 cnf(c_0_24, plain, ('+'(X1,X2)='+'(X2,X1)), inference(split_conjunct,[status(thm)],[c_0_17])).
% 24.97/4.07 fof(c_0_25, plain, ![X30]:('>='(X30,X30)), inference(variable_rename,[status(thm)],[sos_04])).
% 24.97/4.07 fof(c_0_26, plain, ![X49, X50]:('+'(X49,'==>'(X49,X50))='+'(X50,'==>'(X50,X49))), inference(variable_rename,[status(thm)],[sos_12])).
% 24.97/4.07 cnf(c_0_27, plain, ('0'=X1|~'>='('0',X1)), inference(spm,[status(thm)],[c_0_18, c_0_19])).
% 24.97/4.07 cnf(c_0_28, plain, ('>='(X2,'==>'(X1,X3))|~'>='('+'(X1,X2),X3)), inference(split_conjunct,[status(thm)],[c_0_20])).
% 24.97/4.07 cnf(c_0_29, negated_conjecture, (esk1_0='==>'(esk1_0,esk2_0)), inference(split_conjunct,[status(thm)],[c_0_21])).
% 24.97/4.07 cnf(c_0_30, plain, ('>='('+'(X1,X3),'+'(X2,X3))|~'>='(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_22])).
% 24.97/4.07 cnf(c_0_31, plain, ('+'('0',X1)=X1), inference(spm,[status(thm)],[c_0_23, c_0_24])).
% 24.97/4.07 cnf(c_0_32, plain, ('>='('+'(X2,X1),X3)|~'>='(X1,'==>'(X2,X3))), inference(split_conjunct,[status(thm)],[c_0_20])).
% 24.97/4.07 cnf(c_0_33, plain, ('>='(X1,X1)), inference(split_conjunct,[status(thm)],[c_0_25])).
% 24.97/4.07 fof(c_0_34, plain, ![X46, X47, X48]:((~'>='(X46,X47)|'>='('==>'(X48,X46),'==>'(X48,X47)))), inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos_11])])])).
% 24.97/4.07 fof(c_0_35, plain, ![X24, X25, X26]:('+'('+'(X24,X25),X26)='+'(X24,'+'(X25,X26))), inference(variable_rename,[status(thm)],[sos_01])).
% 24.97/4.07 cnf(c_0_36, plain, ('+'(X1,'==>'(X1,X2))='+'(X2,'==>'(X2,X1))), inference(split_conjunct,[status(thm)],[c_0_26])).
% 24.97/4.07 cnf(c_0_37, plain, ('==>'(X1,X2)='0'|~'>='(X1,X2)), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27, c_0_28]), c_0_23])).
% 24.97/4.07 cnf(c_0_38, negated_conjecture, ('>='(X1,esk1_0)|~'>='('+'(esk1_0,X1),esk2_0)), inference(spm,[status(thm)],[c_0_28, c_0_29])).
% 24.97/4.07 cnf(c_0_39, plain, ('>='('+'(X1,X2),X2)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30, c_0_31]), c_0_19])])).
% 24.97/4.07 cnf(c_0_40, negated_conjecture, (esk3_0='==>'(esk3_0,esk2_0)), inference(split_conjunct,[status(thm)],[c_0_21])).
% 24.97/4.07 cnf(c_0_41, plain, ('>='('+'(X1,'==>'(X1,X2)),X2)), inference(spm,[status(thm)],[c_0_32, c_0_33])).
% 24.97/4.07 cnf(c_0_42, plain, ('>='('==>'(X3,X1),'==>'(X3,X2))|~'>='(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_34])).
% 24.97/4.07 cnf(c_0_43, plain, ('+'('+'(X1,X2),X3)='+'(X1,'+'(X2,X3))), inference(split_conjunct,[status(thm)],[c_0_35])).
% 24.97/4.07 cnf(c_0_44, plain, ('+'(X1,'==>'(X1,X2))=X2|~'>='(X2,X1)), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36, c_0_37]), c_0_23])).
% 24.97/4.07 cnf(c_0_45, negated_conjecture, ('>='(esk2_0,esk1_0)), inference(spm,[status(thm)],[c_0_38, c_0_39])).
% 24.97/4.07 cnf(c_0_46, negated_conjecture, ('>='(X1,esk3_0)|~'>='('+'(esk3_0,X1),esk2_0)), inference(spm,[status(thm)],[c_0_28, c_0_40])).
% 24.97/4.07 fof(c_0_47, plain, ![X31, X32, X33]:((~'>='(X31,X32)|~'>='(X32,X33)|'>='(X31,X33))), inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos_05])])])).
% 24.97/4.07 fof(c_0_48, plain, ![X43, X44, X45]:((~'>='(X43,X44)|'>='('==>'(X44,X45),'==>'(X43,X45)))), inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos_10])])])).
% 24.97/4.07 cnf(c_0_49, plain, ('==>'(X1,X2)=X3|~'>='('==>'(X1,X2),X3)|~'>='('+'(X1,X3),X2)), inference(spm,[status(thm)],[c_0_18, c_0_28])).
% 24.97/4.07 cnf(c_0_50, plain, ('>='('==>'('0',X1),X1)), inference(spm,[status(thm)],[c_0_41, c_0_31])).
% 24.97/4.07 cnf(c_0_51, negated_conjecture, ('>='('==>'(esk3_0,X1),esk3_0)|~'>='(X1,esk2_0)), inference(spm,[status(thm)],[c_0_42, c_0_40])).
% 24.97/4.07 cnf(c_0_52, plain, ('+'(X1,'+'('==>'(X1,X2),X3))='+'(X2,'+'('==>'(X2,X1),X3))), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43, c_0_36]), c_0_43])).
% 24.97/4.07 cnf(c_0_53, plain, ('+'(X1,'+'(X2,X3))='+'(X3,'+'(X1,X2))), inference(spm,[status(thm)],[c_0_24, c_0_43])).
% 24.97/4.07 cnf(c_0_54, negated_conjecture, ('+'(esk1_0,esk1_0)=esk2_0), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44, c_0_29]), c_0_45])])).
% 24.97/4.07 cnf(c_0_55, negated_conjecture, ('>='(esk2_0,esk3_0)), inference(spm,[status(thm)],[c_0_46, c_0_39])).
% 24.97/4.07 cnf(c_0_56, plain, ('>='(X1,X3)|~'>='(X1,X2)|~'>='(X2,X3)), inference(split_conjunct,[status(thm)],[c_0_47])).
% 24.97/4.07 cnf(c_0_57, plain, ('>='('==>'(X2,X3),'==>'(X1,X3))|~'>='(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_48])).
% 24.97/4.07 cnf(c_0_58, plain, ('==>'('0',X1)=X1), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49, c_0_50]), c_0_31]), c_0_33])])).
% 24.97/4.07 cnf(c_0_59, negated_conjecture, ('==>'(esk3_0,X1)=esk3_0|~'>='(esk3_0,'==>'(esk3_0,X1))|~'>='(X1,esk2_0)), inference(spm,[status(thm)],[c_0_18, c_0_51])).
% 24.97/4.07 cnf(c_0_60, negated_conjecture, ('>='(esk3_0,'==>'(esk3_0,X1))|~'>='(esk2_0,X1)), inference(spm,[status(thm)],[c_0_42, c_0_40])).
% 24.97/4.07 cnf(c_0_61, negated_conjecture, ('>='('+'('==>'(esk3_0,X1),X2),esk3_0)|~'>='('+'(X1,'+'('==>'(X1,esk3_0),X2)),esk2_0)), inference(spm,[status(thm)],[c_0_46, c_0_52])).
% 24.97/4.07 cnf(c_0_62, negated_conjecture, ('+'(esk1_0,'+'(X1,esk1_0))='+'(X1,esk2_0)), inference(spm,[status(thm)],[c_0_53, c_0_54])).
% 24.97/4.07 cnf(c_0_63, negated_conjecture, ('+'(esk3_0,esk3_0)=esk2_0), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44, c_0_40]), c_0_55])])).
% 24.97/4.07 cnf(c_0_64, plain, ('>='(X1,'==>'(X2,X3))|~'>='('+'(X2,X4),X3)|~'>='(X1,X4)), inference(spm,[status(thm)],[c_0_56, c_0_28])).
% 24.97/4.07 cnf(c_0_65, plain, ('>='(X1,'==>'(X2,X1))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57, c_0_58]), c_0_19])])).
% 24.97/4.07 cnf(c_0_66, negated_conjecture, ('>='('==>'(X1,esk2_0),esk1_0)|~'>='(esk1_0,X1)), inference(spm,[status(thm)],[c_0_57, c_0_29])).
% 24.97/4.07 cnf(c_0_67, negated_conjecture, ('==>'(esk3_0,X1)=esk3_0|~'>='(X1,esk2_0)|~'>='(esk2_0,X1)), inference(spm,[status(thm)],[c_0_59, c_0_60])).
% 24.97/4.07 cnf(c_0_68, plain, ('==>'(X1,X2)='==>'(X3,X4)|~'>='('+'(X1,'==>'(X3,X4)),X2)|~'>='('+'(X3,'==>'(X1,X2)),X4)), inference(spm,[status(thm)],[c_0_49, c_0_28])).
% 24.97/4.07 cnf(c_0_69, negated_conjecture, ('>='('+'(esk1_0,'==>'(esk3_0,esk1_0)),esk3_0)), inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61, c_0_62]), c_0_39])]), c_0_24])).
% 24.97/4.07 cnf(c_0_70, negated_conjecture, ('>='('+'('==>'(esk1_0,X1),X2),esk1_0)|~'>='('+'(X1,'+'('==>'(X1,esk1_0),X2)),esk2_0)), inference(spm,[status(thm)],[c_0_38, c_0_52])).
% 24.97/4.07 cnf(c_0_71, negated_conjecture, ('+'(esk3_0,'+'(X1,esk3_0))='+'(X1,esk2_0)), inference(spm,[status(thm)],[c_0_53, c_0_63])).
% 24.97/4.07 cnf(c_0_72, plain, ('>='(X1,'==>'(X2,'==>'(X3,'+'(X2,X4))))|~'>='(X1,X4)), inference(spm,[status(thm)],[c_0_64, c_0_65])).
% 24.97/4.07 cnf(c_0_73, negated_conjecture, ('>='(esk3_0,esk1_0)|~'>='(esk1_0,esk3_0)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66, c_0_67]), c_0_33])])).
% 24.97/4.07 cnf(c_0_74, negated_conjecture, (esk1_0!=esk3_0), inference(split_conjunct,[status(thm)],[c_0_21])).
% 24.97/4.07 cnf(c_0_75, negated_conjecture, ('+'(esk3_0,'+'(esk3_0,X1))='+'(esk2_0,X1)), inference(spm,[status(thm)],[c_0_43, c_0_63])).
% 24.97/4.07 cnf(c_0_76, negated_conjecture, ('==>'(esk3_0,esk1_0)='==>'(esk1_0,esk3_0)|~'>='('+'(esk3_0,'==>'(esk1_0,esk3_0)),esk1_0)), inference(spm,[status(thm)],[c_0_68, c_0_69])).
% 24.97/4.07 cnf(c_0_77, negated_conjecture, ('>='('+'(esk3_0,'==>'(esk1_0,esk3_0)),esk1_0)), inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70, c_0_71]), c_0_39])]), c_0_24])).
% 24.97/4.07 cnf(c_0_78, plain, ('>='(X1,'==>'(X2,'==>'(X3,X2)))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72, c_0_23]), c_0_19])])).
% 24.97/4.07 cnf(c_0_79, negated_conjecture, ('>='(esk1_0,'==>'(X1,esk2_0))|~'>='(X1,esk1_0)), inference(spm,[status(thm)],[c_0_57, c_0_29])).
% 24.97/4.07 cnf(c_0_80, negated_conjecture, (~'>='(esk1_0,esk3_0)), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_18, c_0_73]), c_0_74])).
% 24.97/4.07 cnf(c_0_81, negated_conjecture, ('+'(esk3_0,'+'(X1,'==>'(X1,esk3_0)))='+'(esk2_0,'==>'(esk3_0,X1))), inference(spm,[status(thm)],[c_0_75, c_0_36])).
% 24.97/4.07 cnf(c_0_82, negated_conjecture, ('==>'(esk3_0,esk1_0)='==>'(esk1_0,esk3_0)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_76, c_0_77])])).
% 24.97/4.07 cnf(c_0_83, plain, ('==>'(X1,'==>'(X2,X1))='0'), inference(spm,[status(thm)],[c_0_27, c_0_78])).
% 24.97/4.07 cnf(c_0_84, negated_conjecture, (~'>='(esk3_0,esk1_0)), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79, c_0_67]), c_0_33])]), c_0_80])).
% 24.97/4.07 cnf(c_0_85, negated_conjecture, ($false), inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70, c_0_81]), c_0_82]), c_0_82]), c_0_83]), c_0_23]), c_0_33])]), c_0_36]), c_0_83]), c_0_23]), c_0_84]), ['proof']).
% 24.97/4.07 % SZS output end Proof
% 24.97/4.07 % User time : 3.351 s
% 24.97/4.07 % System time : 0.154 s
% 24.97/4.07 % Total time : 3.505 s
% 24.97/4.07 % User time : 17.162 s
% 24.97/4.07 % System time : 0.346 s
% 24.97/4.07 % Total time : 17.508 s
% 24.97/4.07
%------------------------------------------------------------------------------