%------------------------------------------------------------------------------
% File : CSI_E---1.1
% Problem : LCL894+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 0.98s 0.65s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL894+1 : TPTP v9.3.1. Released v5.5.0.
% 0.00/0.02 % Command : java -jar mcs_scs.jar %d %s
% 0.09/0.35 % Computer : n009.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sat Sep 5 21:09:06 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.23/0.47 start to proof:theBenchmark.p
% 0.98/0.65 % Version : CSI_E---1.1
% 0.98/0.65 % Problem : theBenchmark.p
% 0.98/0.65 % Proof found!
% 0.98/0.65 % SZS status Theorem for theBenchmark.p
% 0.98/0.65 % SZS output start Proof
% 0.98/0.65 fof(sos_03, axiom, ![X1]:('+'(X1,'0')=X1), file('/export/starexec/sandbox/benchmark/theBenchmark.p', sos_03)).
% 0.98/0.65 fof(sos_02, axiom, ![X1, X2]:('+'(X1,X2)='+'(X2,X1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', sos_02)).
% 0.98/0.65 fof(sos_09, axiom, ![X12, X13, X14]:(('>='(X12,X13)=>'>='('+'(X12,X14),'+'(X13,X14)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', sos_09)).
% 0.98/0.65 fof(sos_08, axiom, ![X1]:('>='(X1,'0')), file('/export/starexec/sandbox/benchmark/theBenchmark.p', sos_08)).
% 0.98/0.65 fof(sos_05, axiom, ![X4, X5, X6]:((('>='(X4,X5)&'>='(X5,X6))=>'>='(X4,X6))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', sos_05)).
% 0.98/0.65 fof(goals_13, conjecture, (('>='(c,a)&'>='(c,b))<=>'>='(c,'+'(a,'==>'(a,b)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', goals_13)).
% 0.98/0.65 fof(sos_07, axiom, ![X9, X10, X11]:(('>='('+'(X9,X10),X11)<=>'>='(X10,'==>'(X9,X11)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', sos_07)).
% 0.98/0.65 fof(sos_04, axiom, ![X1]:('>='(X1,X1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', sos_04)).
% 0.98/0.65 fof(sos_06, axiom, ![X7, X8]:((('>='(X7,X8)&'>='(X8,X7))=>X7=X8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', sos_06)).
% 0.98/0.65 fof(sos_10, axiom, ![X15, X16, X17]:(('>='(X15,X16)=>'>='('==>'(X16,X17),'==>'(X15,X17)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', sos_10)).
% 0.98/0.65 fof(sos_12, axiom, ![X1, X2]:('+'(X1,'==>'(X1,X2))='+'(X2,'==>'(X2,X1))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', sos_12)).
% 0.98/0.65 fof(sos_11, axiom, ![X18, X19, X20]:(('>='(X18,X19)=>'>='('==>'(X20,X18),'==>'(X20,X19)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', sos_11)).
% 0.98/0.65 fof(c_0_12, plain, ![X26]:('+'(X26,'0')=X26), inference(variable_rename,[status(thm)],[sos_03])).
% 0.98/0.65 fof(c_0_13, plain, ![X24, X25]:('+'(X24,X25)='+'(X25,X24)), inference(variable_rename,[status(thm)],[sos_02])).
% 0.98/0.65 fof(c_0_14, plain, ![X37, X38, X39]:((~'>='(X37,X38)|'>='('+'(X37,X39),'+'(X38,X39)))), inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos_09])])])).
% 0.98/0.65 cnf(c_0_15, plain, ('+'(X1,'0')=X1), inference(split_conjunct,[status(thm)],[c_0_12])).
% 0.98/0.65 cnf(c_0_16, plain, ('+'(X1,X2)='+'(X2,X1)), inference(split_conjunct,[status(thm)],[c_0_13])).
% 0.98/0.65 fof(c_0_17, plain, ![X36]:('>='(X36,'0')), inference(variable_rename,[status(thm)],[sos_08])).
% 0.98/0.65 fof(c_0_18, plain, ![X28, X29, X30]:((~'>='(X28,X29)|~'>='(X29,X30)|'>='(X28,X30))), inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos_05])])])).
% 0.98/0.65 cnf(c_0_19, plain, ('>='('+'(X1,X3),'+'(X2,X3))|~'>='(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_14])).
% 0.98/0.65 cnf(c_0_20, plain, ('+'('0',X1)=X1), inference(spm,[status(thm)],[c_0_15, c_0_16])).
% 0.98/0.65 cnf(c_0_21, plain, ('>='(X1,'0')), inference(split_conjunct,[status(thm)],[c_0_17])).
% 0.98/0.65 cnf(c_0_22, plain, ('>='(X1,X3)|~'>='(X1,X2)|~'>='(X2,X3)), inference(split_conjunct,[status(thm)],[c_0_18])).
% 0.98/0.65 cnf(c_0_23, plain, ('>='('+'(X1,X2),X2)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19, c_0_20]), c_0_21])])).
% 0.98/0.65 fof(c_0_24, negated_conjecture, ~((('>='(c,a)&'>='(c,b))<=>'>='(c,'+'(a,'==>'(a,b))))), inference(assume_negation,[status(cth)],[goals_13])).
% 0.98/0.65 cnf(c_0_25, plain, ('>='(X1,X2)|~'>='(X1,'+'(X3,X2))), inference(spm,[status(thm)],[c_0_22, c_0_23])).
% 0.98/0.65 fof(c_0_26, negated_conjecture, ((~'>='(c,a)|~'>='(c,b)|~'>='(c,'+'(a,'==>'(a,b))))&(('>='(c,a)|'>='(c,'+'(a,'==>'(a,b))))&('>='(c,b)|'>='(c,'+'(a,'==>'(a,b)))))), inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_24])])])).
% 0.98/0.65 fof(c_0_27, plain, ![X33, X34, X35]:(((~'>='('+'(X33,X34),X35)|'>='(X34,'==>'(X33,X35)))&(~'>='(X34,'==>'(X33,X35))|'>='('+'(X33,X34),X35)))), inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos_07])])])).
% 0.98/0.65 fof(c_0_28, plain, ![X27]:('>='(X27,X27)), inference(variable_rename,[status(thm)],[sos_04])).
% 0.98/0.65 cnf(c_0_29, plain, ('>='(X1,X2)|~'>='(X1,'+'(X2,X3))), inference(spm,[status(thm)],[c_0_25, c_0_16])).
% 0.98/0.65 cnf(c_0_30, negated_conjecture, ('>='(c,a)|'>='(c,'+'(a,'==>'(a,b)))), inference(split_conjunct,[status(thm)],[c_0_26])).
% 0.98/0.65 fof(c_0_31, plain, ![X31, X32]:((~'>='(X31,X32)|~'>='(X32,X31)|X31=X32)), inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos_06])])])).
% 0.98/0.65 cnf(c_0_32, plain, ('>='('+'(X2,X1),X3)|~'>='(X1,'==>'(X2,X3))), inference(split_conjunct,[status(thm)],[c_0_27])).
% 0.98/0.65 cnf(c_0_33, plain, ('>='(X1,X1)), inference(split_conjunct,[status(thm)],[c_0_28])).
% 0.98/0.65 cnf(c_0_34, negated_conjecture, ('>='(c,a)), inference(spm,[status(thm)],[c_0_29, c_0_30])).
% 0.98/0.65 cnf(c_0_35, plain, (X1=X2|~'>='(X1,X2)|~'>='(X2,X1)), inference(split_conjunct,[status(thm)],[c_0_31])).
% 0.98/0.65 cnf(c_0_36, plain, ('>='(X2,'==>'(X1,X3))|~'>='('+'(X1,X2),X3)), inference(split_conjunct,[status(thm)],[c_0_27])).
% 0.98/0.65 cnf(c_0_37, plain, ('>='('+'(X1,'==>'(X1,X2)),X2)), inference(spm,[status(thm)],[c_0_32, c_0_33])).
% 0.98/0.65 cnf(c_0_38, negated_conjecture, ('>='(X1,a)|~'>='(X1,c)), inference(spm,[status(thm)],[c_0_22, c_0_34])).
% 0.98/0.65 cnf(c_0_39, plain, ('>='('+'(X1,X2),X1)), inference(spm,[status(thm)],[c_0_23, c_0_16])).
% 0.98/0.65 fof(c_0_40, plain, ![X40, X41, X42]:((~'>='(X40,X41)|'>='('==>'(X41,X42),'==>'(X40,X42)))), inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos_10])])])).
% 0.98/0.65 cnf(c_0_41, plain, ('==>'(X1,X2)=X3|~'>='('==>'(X1,X2),X3)|~'>='('+'(X1,X3),X2)), inference(spm,[status(thm)],[c_0_35, c_0_36])).
% 0.98/0.65 cnf(c_0_42, plain, ('>='('==>'('0',X1),X1)), inference(spm,[status(thm)],[c_0_37, c_0_20])).
% 0.98/0.65 cnf(c_0_43, plain, ('>='(X1,'==>'(X2,X3))|~'>='('+'(X2,X4),X3)|~'>='(X1,X4)), inference(spm,[status(thm)],[c_0_22, c_0_36])).
% 0.98/0.65 cnf(c_0_44, negated_conjecture, ('>='('+'(c,X1),a)), inference(spm,[status(thm)],[c_0_38, c_0_39])).
% 0.98/0.65 cnf(c_0_45, plain, ('>='('==>'(X2,X3),'==>'(X1,X3))|~'>='(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_40])).
% 0.98/0.65 cnf(c_0_46, plain, ('==>'('0',X1)=X1), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41, c_0_42]), c_0_20]), c_0_33])])).
% 0.98/0.65 cnf(c_0_47, negated_conjecture, ('>='(X1,'==>'(c,a))|~'>='(X1,X2)), inference(spm,[status(thm)],[c_0_43, c_0_44])).
% 0.98/0.65 cnf(c_0_48, plain, ('>='(X1,'==>'(X2,X1))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45, c_0_46]), c_0_21])])).
% 0.98/0.65 fof(c_0_49, plain, ![X46, X47]:('+'(X46,'==>'(X46,X47))='+'(X47,'==>'(X47,X46))), inference(variable_rename,[status(thm)],[sos_12])).
% 0.98/0.65 cnf(c_0_50, plain, ('0'=X1|~'>='('0',X1)), inference(spm,[status(thm)],[c_0_35, c_0_21])).
% 0.98/0.65 cnf(c_0_51, negated_conjecture, ('>='(X1,'==>'(c,a))), inference(spm,[status(thm)],[c_0_47, c_0_48])).
% 0.98/0.65 cnf(c_0_52, plain, ('+'(X1,'==>'(X1,X2))='+'(X2,'==>'(X2,X1))), inference(split_conjunct,[status(thm)],[c_0_49])).
% 0.98/0.65 cnf(c_0_53, negated_conjecture, ('==>'(c,a)='0'), inference(spm,[status(thm)],[c_0_50, c_0_51])).
% 0.98/0.65 cnf(c_0_54, negated_conjecture, (~'>='(c,a)|~'>='(c,b)|~'>='(c,'+'(a,'==>'(a,b)))), inference(split_conjunct,[status(thm)],[c_0_26])).
% 0.98/0.65 cnf(c_0_55, plain, ('>='(X1,X2)|~'>='(X1,'+'(X3,'==>'(X3,X2)))), inference(spm,[status(thm)],[c_0_29, c_0_52])).
% 0.98/0.65 cnf(c_0_56, negated_conjecture, ('>='(c,b)|'>='(c,'+'(a,'==>'(a,b)))), inference(split_conjunct,[status(thm)],[c_0_26])).
% 0.98/0.65 cnf(c_0_57, plain, ('>='('+'(X1,X2),'+'(X3,X1))|~'>='(X2,X3)), inference(spm,[status(thm)],[c_0_19, c_0_16])).
% 0.98/0.65 cnf(c_0_58, negated_conjecture, ('+'(a,'==>'(a,c))=c), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52, c_0_53]), c_0_15])).
% 0.98/0.65 fof(c_0_59, plain, ![X43, X44, X45]:((~'>='(X43,X44)|'>='('==>'(X45,X43),'==>'(X45,X44)))), inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos_11])])])).
% 0.98/0.65 cnf(c_0_60, negated_conjecture, (~'>='(c,'+'(a,'==>'(a,b)))|~'>='(c,b)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_54, c_0_34])])).
% 0.98/0.65 cnf(c_0_61, negated_conjecture, ('>='(c,b)), inference(spm,[status(thm)],[c_0_55, c_0_56])).
% 0.98/0.65 cnf(c_0_62, negated_conjecture, ('>='(c,'+'(X1,a))|~'>='('==>'(a,c),X1)), inference(spm,[status(thm)],[c_0_57, c_0_58])).
% 0.98/0.65 cnf(c_0_63, plain, ('>='('==>'(X3,X1),'==>'(X3,X2))|~'>='(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_59])).
% 0.98/0.65 cnf(c_0_64, negated_conjecture, (~'>='(c,'+'(a,'==>'(a,b)))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_60, c_0_61])])).
% 0.98/0.65 cnf(c_0_65, negated_conjecture, ('>='(c,'+'(a,'==>'(a,X1)))|~'>='(c,X1)), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62, c_0_63]), c_0_16])).
% 0.98/0.65 cnf(c_0_66, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64, c_0_65]), c_0_61])]), ['proof']).
% 0.98/0.65 % SZS output end Proof
% 0.98/0.65 % User time : 0.116 s
% 0.98/0.65 % System time : 0.012 s
% 0.98/0.65 % Total time : 0.128 s
% 0.98/0.65 % User time : 0.632 s
% 0.98/0.65 % System time : 0.029 s
% 0.98/0.65 % Total time : 0.661 s
% 0.98/0.65
%------------------------------------------------------------------------------