%------------------------------------------------------------------------------
% File : CSI_E---1.1
% Problem : LCL901+1 : TPTP v9.3.1. Released v5.5.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar mcs_scs.jar %d %s
% Computer : n016.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 11:21:54 AM UTC 2026
% Result : Theorem 0.76s 0.58s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL901+1 : TPTP v9.3.1. Released v5.5.0.
% 0.00/0.03 % Command : java -jar mcs_scs.jar %d %s
% 0.09/0.36 % Computer : n016.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 : Sat Sep 5 10:27:29 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.25/0.48 start to proof:theBenchmark.p
% 0.76/0.58 % Version : CSI_E---1.1
% 0.76/0.58 % Problem : theBenchmark.p
% 0.76/0.58 % Proof found!
% 0.76/0.58 % SZS status Theorem for theBenchmark.p
% 0.76/0.58 % SZS output start Proof
% 0.76/0.58 fof(sos_03, axiom, ![X1]:('+'(X1,'0')=X1), file('/export/starexec/sandbox/benchmark/theBenchmark.p', sos_03)).
% 0.76/0.58 fof(sos_02, axiom, ![X1, X2]:('+'(X1,X2)='+'(X2,X1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', sos_02)).
% 0.76/0.58 fof(sos_07, axiom, ![X9, X10, X11]:(('>='('+'(X9,X10),X11)<=>'>='(X10,'==>'(X9,X11)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', sos_07)).
% 0.76/0.58 fof(sos_09, axiom, ![X12, X13, X14]:(('>='(X12,X13)=>'>='('+'(X12,X14),'+'(X13,X14)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', sos_09)).
% 0.76/0.58 fof(sos_08, axiom, ![X1]:('>='(X1,'0')), file('/export/starexec/sandbox/benchmark/theBenchmark.p', sos_08)).
% 0.76/0.58 fof(sos_04, axiom, ![X1]:('>='(X1,X1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', sos_04)).
% 0.76/0.58 fof(sos_06, axiom, ![X7, X8]:((('>='(X7,X8)&'>='(X8,X7))=>X7=X8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', sos_06)).
% 0.76/0.58 fof(sos_05, axiom, ![X4, X5, X6]:((('>='(X4,X5)&'>='(X5,X6))=>'>='(X4,X6))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', sos_05)).
% 0.76/0.58 fof(sos_13, axiom, ![X1, X2]:('==>'('==>'(X1,X2),X2)='==>'('==>'(X2,X1),X1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', sos_13)).
% 0.76/0.58 fof(sos_14, axiom, ![X1]:('+'(X1,X1)=X1), file('/export/starexec/sandbox/benchmark/theBenchmark.p', sos_14)).
% 0.76/0.58 fof(sos_12, axiom, ![X1]:('+'(X1,'1')='1'), file('/export/starexec/sandbox/benchmark/theBenchmark.p', sos_12)).
% 0.76/0.58 fof(sos_01, axiom, ![X1, X2, X3]:('+'('+'(X1,X2),X3)='+'(X1,'+'(X2,X3))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', sos_01)).
% 0.76/0.58 fof(sos_11, axiom, ![X18, X19, X20]:(('>='(X18,X19)=>'>='('==>'(X20,X18),'==>'(X20,X19)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', sos_11)).
% 0.76/0.58 fof(goals_15, conjecture, ![X21]:('==>'('==>'('==>'(X21,'1'),X21),X21)='0'), file('/export/starexec/sandbox/benchmark/theBenchmark.p', goals_15)).
% 0.76/0.58 fof(c_0_14, plain, ![X27]:('+'(X27,'0')=X27), inference(variable_rename,[status(thm)],[sos_03])).
% 0.76/0.58 fof(c_0_15, plain, ![X25, X26]:('+'(X25,X26)='+'(X26,X25)), inference(variable_rename,[status(thm)],[sos_02])).
% 0.76/0.58 fof(c_0_16, plain, ![X34, X35, X36]:(((~'>='('+'(X34,X35),X36)|'>='(X35,'==>'(X34,X36)))&(~'>='(X35,'==>'(X34,X36))|'>='('+'(X34,X35),X36)))), inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos_07])])])).
% 0.76/0.58 fof(c_0_17, plain, ![X38, X39, X40]:((~'>='(X38,X39)|'>='('+'(X38,X40),'+'(X39,X40)))), inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos_09])])])).
% 0.76/0.58 fof(c_0_18, plain, ![X37]:('>='(X37,'0')), inference(variable_rename,[status(thm)],[sos_08])).
% 0.76/0.58 cnf(c_0_19, plain, ('+'(X1,'0')=X1), inference(split_conjunct,[status(thm)],[c_0_14])).
% 0.76/0.58 cnf(c_0_20, plain, ('+'(X1,X2)='+'(X2,X1)), inference(split_conjunct,[status(thm)],[c_0_15])).
% 0.76/0.58 cnf(c_0_21, plain, ('>='(X2,'==>'(X1,X3))|~'>='('+'(X1,X2),X3)), inference(split_conjunct,[status(thm)],[c_0_16])).
% 0.76/0.58 fof(c_0_22, plain, ![X28]:('>='(X28,X28)), inference(variable_rename,[status(thm)],[sos_04])).
% 0.76/0.58 cnf(c_0_23, plain, ('>='('+'(X1,X3),'+'(X2,X3))|~'>='(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_17])).
% 0.76/0.58 cnf(c_0_24, plain, ('>='(X1,'0')), inference(split_conjunct,[status(thm)],[c_0_18])).
% 0.76/0.58 cnf(c_0_25, plain, ('+'('0',X1)=X1), inference(spm,[status(thm)],[c_0_19, c_0_20])).
% 0.76/0.58 fof(c_0_26, plain, ![X32, X33]:((~'>='(X32,X33)|~'>='(X33,X32)|X32=X33)), inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos_06])])])).
% 0.76/0.58 cnf(c_0_27, plain, ('>='('0','==>'(X1,X2))|~'>='(X1,X2)), inference(spm,[status(thm)],[c_0_21, c_0_19])).
% 0.76/0.58 fof(c_0_28, plain, ![X29, X30, X31]:((~'>='(X29,X30)|~'>='(X30,X31)|'>='(X29,X31))), inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos_05])])])).
% 0.76/0.58 cnf(c_0_29, plain, ('>='(X1,X1)), inference(split_conjunct,[status(thm)],[c_0_22])).
% 0.76/0.58 cnf(c_0_30, plain, ('>='('+'(X1,X2),X2)), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23, c_0_24]), c_0_25])).
% 0.76/0.58 fof(c_0_31, plain, ![X48, X49]:('==>'('==>'(X48,X49),X49)='==>'('==>'(X49,X48),X48)), inference(variable_rename,[status(thm)],[sos_13])).
% 0.76/0.58 cnf(c_0_32, plain, (X1=X2|~'>='(X1,X2)|~'>='(X2,X1)), inference(split_conjunct,[status(thm)],[c_0_26])).
% 0.76/0.58 cnf(c_0_33, plain, ('>='('0','==>'(X1,'0'))), inference(spm,[status(thm)],[c_0_27, c_0_24])).
% 0.76/0.58 cnf(c_0_34, plain, ('>='(X1,X3)|~'>='(X1,X2)|~'>='(X2,X3)), inference(split_conjunct,[status(thm)],[c_0_28])).
% 0.76/0.58 cnf(c_0_35, plain, ('>='('0','==>'(X1,X1))), inference(spm,[status(thm)],[c_0_27, c_0_29])).
% 0.76/0.58 cnf(c_0_36, plain, ('>='(X1,'==>'(X2,X1))), inference(spm,[status(thm)],[c_0_21, c_0_30])).
% 0.76/0.58 fof(c_0_37, plain, ![X50]:('+'(X50,X50)=X50), inference(variable_rename,[status(thm)],[sos_14])).
% 0.76/0.58 cnf(c_0_38, plain, ('==>'('==>'(X1,X2),X2)='==>'('==>'(X2,X1),X1)), inference(split_conjunct,[status(thm)],[c_0_31])).
% 0.76/0.58 cnf(c_0_39, plain, ('==>'(X1,'0')='0'), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32, c_0_33]), c_0_24])])).
% 0.76/0.58 cnf(c_0_40, plain, ('0'=X1|~'>='('0',X1)), inference(spm,[status(thm)],[c_0_32, c_0_24])).
% 0.76/0.58 cnf(c_0_41, plain, ('>='(X1,'==>'(X2,X2))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34, c_0_35]), c_0_24])])).
% 0.76/0.58 cnf(c_0_42, plain, ('>='('+'(X1,X2),'+'('==>'(X3,X1),X2))), inference(spm,[status(thm)],[c_0_23, c_0_36])).
% 0.76/0.58 cnf(c_0_43, plain, ('+'(X1,X1)=X1), inference(split_conjunct,[status(thm)],[c_0_37])).
% 0.76/0.58 cnf(c_0_44, plain, ('>='('+'(X2,X1),X3)|~'>='(X1,'==>'(X2,X3))), inference(split_conjunct,[status(thm)],[c_0_16])).
% 0.76/0.58 cnf(c_0_45, plain, ('==>'('==>'('0',X1),X1)='0'), inference(spm,[status(thm)],[c_0_38, c_0_39])).
% 0.76/0.58 cnf(c_0_46, plain, ('0'='==>'(X1,X1)), inference(spm,[status(thm)],[c_0_40, c_0_41])).
% 0.76/0.58 fof(c_0_47, plain, ![X47]:('+'(X47,'1')='1'), inference(variable_rename,[status(thm)],[sos_12])).
% 0.76/0.58 cnf(c_0_48, plain, ('>='(X1,'+'(X1,'==>'(X2,X1)))), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42, c_0_43]), c_0_20])).
% 0.76/0.58 cnf(c_0_49, plain, ('>='('+'(X1,X2),X1)), inference(spm,[status(thm)],[c_0_30, c_0_20])).
% 0.76/0.58 cnf(c_0_50, plain, ('>='('+'(X1,'==>'(X1,X2)),X2)), inference(spm,[status(thm)],[c_0_44, c_0_29])).
% 0.76/0.58 cnf(c_0_51, plain, ('>='('+'('==>'('0',X1),X2),X1)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44, c_0_45]), c_0_24])])).
% 0.76/0.58 cnf(c_0_52, plain, ('+'(X1,'==>'(X2,X2))=X1), inference(spm,[status(thm)],[c_0_19, c_0_46])).
% 0.76/0.58 cnf(c_0_53, plain, ('+'(X1,'1')='1'), inference(split_conjunct,[status(thm)],[c_0_47])).
% 0.76/0.58 cnf(c_0_54, plain, ('+'(X1,'==>'(X2,X1))=X1), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32, c_0_48]), c_0_49])])).
% 0.76/0.58 cnf(c_0_55, plain, ('>='('0','==>'('+'(X1,'==>'(X1,X2)),X2))), inference(spm,[status(thm)],[c_0_27, c_0_50])).
% 0.76/0.58 cnf(c_0_56, plain, ('>='('==>'('0',X1),X1)), inference(spm,[status(thm)],[c_0_51, c_0_52])).
% 0.76/0.58 fof(c_0_57, plain, ![X22, X23, X24]:('+'('+'(X22,X23),X24)='+'(X22,'+'(X23,X24))), inference(variable_rename,[status(thm)],[sos_01])).
% 0.76/0.58 fof(c_0_58, plain, ![X44, X45, X46]:((~'>='(X44,X45)|'>='('==>'(X46,X44),'==>'(X46,X45)))), inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos_11])])])).
% 0.76/0.58 cnf(c_0_59, plain, ('+'('1',X1)='1'), inference(spm,[status(thm)],[c_0_53, c_0_20])).
% 0.76/0.58 fof(c_0_60, negated_conjecture, ~(![X21]:('==>'('==>'('==>'(X21,'1'),X21),X21)='0')), inference(assume_negation,[status(cth)],[goals_15])).
% 0.76/0.58 cnf(c_0_61, plain, ('>='(X1,'==>'(X2,'+'(X2,X1)))), inference(spm,[status(thm)],[c_0_21, c_0_29])).
% 0.76/0.58 cnf(c_0_62, plain, ('+'(X1,'==>'('==>'(X1,X2),X2))=X1), inference(spm,[status(thm)],[c_0_54, c_0_38])).
% 0.76/0.58 cnf(c_0_63, plain, ('==>'('+'(X1,'==>'(X1,X2)),X2)='0'), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32, c_0_55]), c_0_24])])).
% 0.76/0.58 cnf(c_0_64, plain, ('==>'('0',X1)=X1), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32, c_0_56]), c_0_36])])).
% 0.76/0.58 cnf(c_0_65, plain, ('+'('+'(X1,X2),X3)='+'(X1,'+'(X2,X3))), inference(split_conjunct,[status(thm)],[c_0_57])).
% 0.76/0.58 cnf(c_0_66, plain, ('>='('==>'(X3,X1),'==>'(X3,X2))|~'>='(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_58])).
% 0.76/0.58 cnf(c_0_67, plain, ('>='('1',X1)), inference(spm,[status(thm)],[c_0_30, c_0_59])).
% 0.76/0.58 fof(c_0_68, negated_conjecture, '==>'('==>'('==>'(esk1_0,'1'),esk1_0),esk1_0)!='0', inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_60])])])])).
% 0.76/0.58 cnf(c_0_69, plain, ('==>'(X1,'+'(X1,X2))=X2|~'>='('==>'(X1,'+'(X1,X2)),X2)), inference(spm,[status(thm)],[c_0_32, c_0_61])).
% 0.76/0.58 cnf(c_0_70, plain, ('+'(X1,'==>'(X1,X2))='+'(X1,X2)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62, c_0_63]), c_0_64]), c_0_65]), c_0_20]), c_0_54])).
% 0.76/0.58 cnf(c_0_71, plain, ('>='('==>'(X1,'+'(X2,X3)),'==>'(X1,X3))), inference(spm,[status(thm)],[c_0_66, c_0_30])).
% 0.76/0.58 cnf(c_0_72, plain, ('>='('==>'(X1,'1'),'==>'(X1,X2))), inference(spm,[status(thm)],[c_0_66, c_0_67])).
% 0.76/0.58 cnf(c_0_73, negated_conjecture, ('==>'('==>'('==>'(esk1_0,'1'),esk1_0),esk1_0)!='0'), inference(split_conjunct,[status(thm)],[c_0_68])).
% 0.76/0.58 cnf(c_0_74, plain, ('==>'(X1,'+'(X1,X2))='==>'(X1,X2)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69, c_0_70]), c_0_71])])).
% 0.76/0.58 cnf(c_0_75, plain, ('>='('0','==>'('==>'(X1,'1'),'==>'(X1,X2)))), inference(spm,[status(thm)],[c_0_27, c_0_72])).
% 0.76/0.58 cnf(c_0_76, negated_conjecture, ('==>'('==>'(esk1_0,'==>'(esk1_0,'1')),'==>'(esk1_0,'1'))!='0'), inference(rw,[status(thm)],[c_0_73, c_0_38])).
% 0.76/0.58 cnf(c_0_77, plain, ('==>'(X1,'==>'(X1,X2))='==>'(X1,X2)), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74, c_0_70]), c_0_74])).
% 0.76/0.58 cnf(c_0_78, plain, ('==>'('==>'(X1,'1'),'==>'(X1,X2))='0'), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32, c_0_75]), c_0_24])])).
% 0.76/0.58 cnf(c_0_79, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_76, c_0_77]), c_0_78])]), ['proof']).
% 0.76/0.58 % SZS output end Proof
% 0.76/0.58 % User time : 0.047 s
% 0.76/0.58 % System time : 0.009 s
% 0.76/0.58 % Total time : 0.055 s
% 0.76/0.58 % User time : 0.195 s
% 0.76/0.58 % System time : 0.023 s
% 0.76/0.58 % Total time : 0.219 s
% 0.76/0.58
%------------------------------------------------------------------------------