%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : LCL888+1 : TPTP v9.2.1. Released v5.5.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n021.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 04:45:18 PM UTC 2026
% Result : Theorem 24.01s 18.87s
% Output : CNFRefutation 24.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 11
% Syntax : Number of formulae : 94 ( 69 unt; 0 def)
% Number of atoms : 130 ( 41 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 62 ( 26 ~; 23 |; 7 &)
% ( 1 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 142 ( 10 sgn 48 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(sos_07,axiom,
! [X9,X10,X11] :
( '>='('+'(X9,X10),X11)
<=> '>='(X10,'==>'(X9,X11)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_07) ).
fof(sos_03,axiom,
! [X1] : '+'(X1,'0') = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_03) ).
fof(sos_04,axiom,
! [X1] : '>='(X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_04) ).
fof(sos_06,axiom,
! [X7,X8] :
( ( '>='(X7,X8)
& '>='(X8,X7) )
=> X7 = X8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_06) ).
fof(sos_08,axiom,
! [X1] : '>='(X1,'0'),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_08) ).
fof(sos_02,axiom,
! [X1,X2] : '+'(X1,X2) = '+'(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_02) ).
fof(goals_13,conjecture,
! [X21,X22,X23] :
( ( X21 = '==>'(X21,X22)
& X23 = '==>'(X23,X22) )
=> X21 = X23 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals_13) ).
fof(sos_01,axiom,
! [X1,X2,X3] : '+'('+'(X1,X2),X3) = '+'(X1,'+'(X2,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_01) ).
fof(sos_11,axiom,
! [X18,X19,X20] :
( '>='(X18,X19)
=> '>='('==>'(X20,X18),'==>'(X20,X19)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_11) ).
fof(sos_12,axiom,
! [X1,X2] : '+'(X1,'==>'(X1,X2)) = '+'(X2,'==>'(X2,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_12) ).
fof(sos_05,axiom,
! [X4,X5,X6] :
( ( '>='(X4,X5)
& '>='(X5,X6) )
=> '>='(X4,X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_05) ).
fof(c_0_11,plain,
! [X66,X67,X68] :
( ( ~ '>='('+'(X66,X67),X68)
| '>='(X67,'==>'(X66,X68)) )
& ( ~ '>='(X67,'==>'(X66,X68))
| '>='('+'(X66,X67),X68) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos_07])]) ).
fof(c_0_12,plain,
! [X59] : '+'(X59,'0') = X59,
inference(variable_rename,[status(thm)],[sos_03]) ).
cnf(c_0_13,plain,
( '>='(X2,'==>'(X1,X3))
| ~ '>='('+'(X1,X2),X3) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_14,plain,
'+'(X1,'0') = X1,
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_15,plain,
! [X60] : '>='(X60,X60),
inference(variable_rename,[status(thm)],[sos_04]) ).
fof(c_0_16,plain,
! [X64,X65] :
( ~ '>='(X64,X65)
| ~ '>='(X65,X64)
| X64 = X65 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos_06])]) ).
cnf(c_0_17,plain,
( '>='('0','==>'(X1,X2))
| ~ '>='(X1,X2) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_18,plain,
'>='(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
fof(c_0_19,plain,
! [X69] : '>='(X69,'0'),
inference(variable_rename,[status(thm)],[sos_08]) ).
fof(c_0_20,plain,
! [X57,X58] : '+'(X57,X58) = '+'(X58,X57),
inference(variable_rename,[status(thm)],[sos_02]) ).
cnf(c_0_21,plain,
( X1 = X2
| ~ '>='(X1,X2)
| ~ '>='(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_22,plain,
'>='('0','==>'(X1,X1)),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_23,plain,
'>='(X1,'0'),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_24,plain,
'+'(X1,X2) = '+'(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_25,plain,
( '>='('+'(X2,X1),X3)
| ~ '>='(X1,'==>'(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_26,plain,
'==>'(X1,X1) = '0',
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23])]) ).
fof(c_0_27,negated_conjecture,
~ ! [X21,X22,X23] :
( ( X21 = '==>'(X21,X22)
& X23 = '==>'(X23,X22) )
=> X21 = X23 ),
inference(assume_negation,[status(cth)],[goals_13]) ).
cnf(c_0_28,plain,
( '>='(X1,'==>'(X2,X3))
| ~ '>='('+'(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_13,c_0_24]) ).
cnf(c_0_29,plain,
'>='('+'(X1,X2),X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_23])]) ).
fof(c_0_30,negated_conjecture,
( esk1_0 = '==>'(esk1_0,esk2_0)
& esk3_0 = '==>'(esk3_0,esk2_0)
& esk1_0 != esk3_0 ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_27])])]) ).
fof(c_0_31,plain,
! [X54,X55,X56] : '+'('+'(X54,X55),X56) = '+'(X54,'+'(X55,X56)),
inference(variable_rename,[status(thm)],[sos_01]) ).
cnf(c_0_32,plain,
'>='(X1,'==>'(X2,X1)),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_33,negated_conjecture,
esk1_0 = '==>'(esk1_0,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
fof(c_0_34,plain,
! [X76,X77,X78] :
( ~ '>='(X76,X77)
| '>='('==>'(X78,X76),'==>'(X78,X77)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos_11])]) ).
cnf(c_0_35,plain,
'+'('+'(X1,X2),X3) = '+'(X1,'+'(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_36,negated_conjecture,
esk3_0 = '==>'(esk3_0,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_37,negated_conjecture,
'>='(esk2_0,esk1_0),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_38,plain,
( '>='('==>'(X3,X1),'==>'(X3,X2))
| ~ '>='(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
fof(c_0_39,plain,
! [X79,X80] : '+'(X79,'==>'(X79,X80)) = '+'(X80,'==>'(X80,X79)),
inference(variable_rename,[status(thm)],[sos_12]) ).
cnf(c_0_40,plain,
'+'(X1,'+'(X2,X3)) = '+'(X3,'+'(X1,X2)),
inference(spm,[status(thm)],[c_0_24,c_0_35]) ).
cnf(c_0_41,negated_conjecture,
( '>='('+'(esk1_0,X1),esk2_0)
| ~ '>='(X1,esk1_0) ),
inference(spm,[status(thm)],[c_0_25,c_0_33]) ).
cnf(c_0_42,plain,
'>='('+'(X1,'==>'(X1,X2)),X2),
inference(spm,[status(thm)],[c_0_25,c_0_18]) ).
cnf(c_0_43,negated_conjecture,
( '>='('+'(esk3_0,X1),esk2_0)
| ~ '>='(X1,esk3_0) ),
inference(spm,[status(thm)],[c_0_25,c_0_36]) ).
cnf(c_0_44,negated_conjecture,
'>='('0','==>'(esk2_0,esk1_0)),
inference(spm,[status(thm)],[c_0_17,c_0_37]) ).
fof(c_0_45,plain,
! [X61,X62,X63] :
( ~ '>='(X61,X62)
| ~ '>='(X62,X63)
| '>='(X61,X63) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos_05])]) ).
cnf(c_0_46,plain,
'>='('==>'(X1,'+'(X2,X3)),'==>'(X1,X2)),
inference(spm,[status(thm)],[c_0_38,c_0_29]) ).
cnf(c_0_47,plain,
'+'(X1,'==>'(X1,X2)) = '+'(X2,'==>'(X2,X1)),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_48,plain,
( '>='('+'(X1,X2),'==>'(X3,X4))
| ~ '>='('+'(X2,'+'(X3,X1)),X4) ),
inference(spm,[status(thm)],[c_0_13,c_0_40]) ).
cnf(c_0_49,negated_conjecture,
'>='('+'(esk1_0,'+'(X1,'==>'(X1,esk1_0))),esk2_0),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_50,negated_conjecture,
'>='('+'(esk3_0,'+'(X1,'==>'(X1,esk3_0))),esk2_0),
inference(spm,[status(thm)],[c_0_43,c_0_42]) ).
cnf(c_0_51,negated_conjecture,
'==>'(esk2_0,esk1_0) = '0',
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_44]),c_0_23])]) ).
cnf(c_0_52,plain,
( '>='(X1,X3)
| ~ '>='(X1,X2)
| ~ '>='(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_53,negated_conjecture,
'>='('==>'(esk3_0,'+'(esk2_0,X1)),esk3_0),
inference(spm,[status(thm)],[c_0_46,c_0_36]) ).
cnf(c_0_54,plain,
'>='(X1,'==>'(X2,'+'(X2,X1))),
inference(spm,[status(thm)],[c_0_13,c_0_18]) ).
cnf(c_0_55,plain,
'+'(X1,'==>'(X1,'+'(X2,X3))) = '+'(X2,'+'(X3,'==>'('+'(X2,X3),X1))),
inference(spm,[status(thm)],[c_0_35,c_0_47]) ).
cnf(c_0_56,negated_conjecture,
'>='('+'(esk1_0,'==>'(X1,esk1_0)),'==>'(X1,esk2_0)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_24]) ).
cnf(c_0_57,negated_conjecture,
'>='('+'(esk3_0,'==>'(X1,esk3_0)),'==>'(X1,esk2_0)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_50]),c_0_24]) ).
cnf(c_0_58,negated_conjecture,
'>='('==>'(esk1_0,'+'(esk2_0,X1)),esk1_0),
inference(spm,[status(thm)],[c_0_46,c_0_33]) ).
cnf(c_0_59,negated_conjecture,
'+'(esk1_0,esk1_0) = esk2_0,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_33]),c_0_51]),c_0_14]) ).
cnf(c_0_60,negated_conjecture,
( '>='(X1,esk3_0)
| ~ '>='(X1,'==>'(esk3_0,'+'(esk2_0,X2))) ),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_61,plain,
'>='('+'(X1,'==>'('+'(X2,X1),X3)),'==>'(X2,'+'(X3,'==>'(X3,'+'(X2,X1))))),
inference(spm,[status(thm)],[c_0_54,c_0_55]) ).
cnf(c_0_62,negated_conjecture,
'>='('+'(esk1_0,'==>'(esk3_0,esk1_0)),esk3_0),
inference(spm,[status(thm)],[c_0_56,c_0_36]) ).
cnf(c_0_63,negated_conjecture,
'>='('+'(esk3_0,'==>'(esk1_0,esk3_0)),esk1_0),
inference(spm,[status(thm)],[c_0_57,c_0_33]) ).
cnf(c_0_64,negated_conjecture,
( '>='(X1,esk1_0)
| ~ '>='(X1,'==>'(esk1_0,'+'(esk2_0,X2))) ),
inference(spm,[status(thm)],[c_0_52,c_0_58]) ).
cnf(c_0_65,negated_conjecture,
'+'(esk1_0,'+'(esk1_0,X1)) = '+'(esk2_0,X1),
inference(spm,[status(thm)],[c_0_35,c_0_59]) ).
cnf(c_0_66,negated_conjecture,
'>='('+'(X1,'==>'('+'(esk3_0,X1),esk2_0)),esk3_0),
inference(spm,[status(thm)],[c_0_60,c_0_61]) ).
cnf(c_0_67,plain,
( '>='(X1,'==>'('+'(X2,X3),X4))
| ~ '>='('+'(X2,'+'(X3,X1)),X4) ),
inference(spm,[status(thm)],[c_0_13,c_0_35]) ).
cnf(c_0_68,negated_conjecture,
'>='('==>'(esk3_0,esk1_0),'==>'(esk1_0,esk3_0)),
inference(spm,[status(thm)],[c_0_13,c_0_62]) ).
cnf(c_0_69,negated_conjecture,
'>='('==>'(esk1_0,esk3_0),'==>'(esk3_0,esk1_0)),
inference(spm,[status(thm)],[c_0_13,c_0_63]) ).
cnf(c_0_70,negated_conjecture,
'>='('+'(X1,'==>'('+'(esk1_0,X1),esk2_0)),esk1_0),
inference(spm,[status(thm)],[c_0_64,c_0_61]) ).
cnf(c_0_71,negated_conjecture,
( '>='('+'(esk1_0,X1),'==>'(esk1_0,X2))
| ~ '>='('+'(esk2_0,X1),X2) ),
inference(spm,[status(thm)],[c_0_13,c_0_65]) ).
cnf(c_0_72,plain,
'>='('+'(X1,'+'(X2,'==>'(X2,'==>'(X1,X3)))),X3),
inference(spm,[status(thm)],[c_0_25,c_0_42]) ).
cnf(c_0_73,negated_conjecture,
'>='('==>'('+'(esk3_0,X1),esk2_0),'==>'(X1,esk3_0)),
inference(spm,[status(thm)],[c_0_13,c_0_66]) ).
cnf(c_0_74,negated_conjecture,
'>='('==>'(X1,esk3_0),'==>'('+'(esk3_0,X1),esk2_0)),
inference(spm,[status(thm)],[c_0_67,c_0_50]) ).
cnf(c_0_75,negated_conjecture,
'==>'(esk3_0,esk1_0) = '==>'(esk1_0,esk3_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_68]),c_0_69])]) ).
cnf(c_0_76,negated_conjecture,
'>='('==>'('+'(esk1_0,X1),esk2_0),'==>'(X1,esk1_0)),
inference(spm,[status(thm)],[c_0_13,c_0_70]) ).
cnf(c_0_77,negated_conjecture,
'>='('==>'(X1,esk1_0),'==>'('+'(esk1_0,X1),esk2_0)),
inference(spm,[status(thm)],[c_0_67,c_0_49]) ).
cnf(c_0_78,negated_conjecture,
'>='('+'(esk1_0,'==>'(esk2_0,X1)),'==>'(esk1_0,X1)),
inference(spm,[status(thm)],[c_0_71,c_0_42]) ).
cnf(c_0_79,negated_conjecture,
'>='('+'(esk2_0,'==>'(esk1_0,'==>'(esk1_0,X1))),X1),
inference(spm,[status(thm)],[c_0_72,c_0_65]) ).
cnf(c_0_80,negated_conjecture,
'>='(esk2_0,esk3_0),
inference(spm,[status(thm)],[c_0_32,c_0_36]) ).
cnf(c_0_81,negated_conjecture,
'==>'('+'(esk3_0,X1),esk2_0) = '==>'(X1,esk3_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_73]),c_0_74])]) ).
cnf(c_0_82,negated_conjecture,
'+'(esk3_0,'==>'(esk1_0,esk3_0)) = '+'(esk1_0,'==>'(esk1_0,esk3_0)),
inference(spm,[status(thm)],[c_0_47,c_0_75]) ).
cnf(c_0_83,negated_conjecture,
'==>'('+'(esk1_0,X1),esk2_0) = '==>'(X1,esk1_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_76]),c_0_77])]) ).
cnf(c_0_84,plain,
'>='('0','==>'(X1,'==>'(X2,X1))),
inference(spm,[status(thm)],[c_0_17,c_0_32]) ).
cnf(c_0_85,negated_conjecture,
'>='('==>'(esk2_0,X1),'==>'(esk1_0,'==>'(esk1_0,X1))),
inference(spm,[status(thm)],[c_0_13,c_0_78]) ).
cnf(c_0_86,negated_conjecture,
'>='('==>'(esk1_0,'==>'(esk1_0,X1)),'==>'(esk2_0,X1)),
inference(spm,[status(thm)],[c_0_13,c_0_79]) ).
cnf(c_0_87,negated_conjecture,
'>='('0','==>'(esk2_0,esk3_0)),
inference(spm,[status(thm)],[c_0_17,c_0_80]) ).
cnf(c_0_88,negated_conjecture,
'==>'('==>'(esk1_0,esk3_0),esk3_0) = '==>'('==>'(esk1_0,esk3_0),esk1_0),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_82]),c_0_83]) ).
cnf(c_0_89,plain,
'==>'(X1,'==>'(X2,X1)) = '0',
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_84]),c_0_23])]) ).
cnf(c_0_90,negated_conjecture,
'==>'(esk1_0,'==>'(esk1_0,X1)) = '==>'(esk2_0,X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_85]),c_0_86])]) ).
cnf(c_0_91,negated_conjecture,
'==>'(esk2_0,esk3_0) = '0',
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_87]),c_0_23])]) ).
cnf(c_0_92,negated_conjecture,
esk1_0 != esk3_0,
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_93,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[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_47,c_0_88]),c_0_89]),c_0_14]),c_0_47]),c_0_90]),c_0_91]),c_0_14]),c_0_92]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.21 % Problem : LCL888+1 : TPTP v9.2.1. Released v5.5.0.
% 0.03/0.21 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.12/0.44 % Computer : n021.cluster.edu
% 0.12/0.44 % Model : x86_64 x86_64
% 0.12/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.44 % Memory : 8042.1875MB
% 0.12/0.44 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.44 % CPULimit : 300
% 0.12/0.44 % WCLimit : 300
% 0.12/0.44 % DateTime : Mon May 4 23:15:10 EDT 2026
% 0.10/0.45 % CPUTime :
% 0.10/0.46 % start to proof: theBenchmark
% 24.01/18.87 % Version : CSE_E---1.7
% 24.01/18.87 % Problem : theBenchmark.p
% 24.01/18.87 % SZS status Theorem for theBenchmark.p
% 24.01/18.87 % SZS output start CNFRefutation
% See solution above
% 24.11/18.98 % Total time : 14.513s
%------------------------------------------------------------------------------