%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : LCL901+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 : n005.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 04:45:19 PM UTC 2026
% Result : Theorem 1.55s 1.82s
% Output : CNFRefutation 1.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 12
% Syntax : Number of formulae : 72 ( 56 unt; 0 def)
% Number of atoms : 93 ( 40 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 39 ( 18 ~; 15 |; 2 &)
% ( 1 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 131 ( 15 sgn 46 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(sos_03,axiom,
! [X1] : '+'(X1,'0') = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_03) ).
fof(sos_02,axiom,
! [X1,X2] : '+'(X1,X2) = '+'(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_02) ).
fof(sos_09,axiom,
! [X12,X13,X14] :
( '>='(X12,X13)
=> '>='('+'(X12,X14),'+'(X13,X14)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_09) ).
fof(sos_08,axiom,
! [X1] : '>='(X1,'0'),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_08) ).
fof(sos_06,axiom,
! [X7,X8] :
( ( '>='(X7,X8)
& '>='(X8,X7) )
=> X7 = X8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_06) ).
fof(sos_07,axiom,
! [X9,X10,X11] :
( '>='('+'(X9,X10),X11)
<=> '>='(X10,'==>'(X9,X11)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_07) ).
fof(sos_13,axiom,
! [X1,X2] : '==>'('==>'(X1,X2),X2) = '==>'('==>'(X2,X1),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_13) ).
fof(sos_14,axiom,
! [X1] : '+'(X1,X1) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_14) ).
fof(sos_04,axiom,
! [X1] : '>='(X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_04) ).
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(goals_15,conjecture,
! [X21] : '==>'('==>'('==>'(X21,'1'),X21),X21) = '0',
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals_15) ).
fof(c_0_12,plain,
! [X57] : '+'(X57,'0') = X57,
inference(variable_rename,[status(thm)],[sos_03]) ).
fof(c_0_13,plain,
! [X55,X56] : '+'(X55,X56) = '+'(X56,X55),
inference(variable_rename,[status(thm)],[sos_02]) ).
fof(c_0_14,plain,
! [X68,X69,X70] :
( ~ '>='(X68,X69)
| '>='('+'(X68,X70),'+'(X69,X70)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos_09])]) ).
fof(c_0_15,plain,
! [X67] : '>='(X67,'0'),
inference(variable_rename,[status(thm)],[sos_08]) ).
cnf(c_0_16,plain,
'+'(X1,'0') = X1,
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_17,plain,
'+'(X1,X2) = '+'(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
fof(c_0_18,plain,
! [X62,X63] :
( ~ '>='(X62,X63)
| ~ '>='(X63,X62)
| X62 = X63 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos_06])]) ).
fof(c_0_19,plain,
! [X64,X65,X66] :
( ( ~ '>='('+'(X64,X65),X66)
| '>='(X65,'==>'(X64,X66)) )
& ( ~ '>='(X65,'==>'(X64,X66))
| '>='('+'(X64,X65),X66) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos_07])]) ).
cnf(c_0_20,plain,
( '>='('+'(X1,X3),'+'(X2,X3))
| ~ '>='(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_21,plain,
'>='(X1,'0'),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_22,plain,
'+'('0',X1) = X1,
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_23,plain,
( X1 = X2
| ~ '>='(X1,X2)
| ~ '>='(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_24,plain,
( '>='(X2,'==>'(X1,X3))
| ~ '>='('+'(X1,X2),X3) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_25,plain,
'>='('+'(X1,X2),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22]) ).
cnf(c_0_26,plain,
( '0' = X1
| ~ '>='('0',X1) ),
inference(spm,[status(thm)],[c_0_23,c_0_21]) ).
cnf(c_0_27,plain,
'>='(X1,'==>'(X2,'0')),
inference(spm,[status(thm)],[c_0_24,c_0_21]) ).
fof(c_0_28,plain,
! [X78,X79] : '==>'('==>'(X78,X79),X79) = '==>'('==>'(X79,X78),X78),
inference(variable_rename,[status(thm)],[sos_13]) ).
cnf(c_0_29,plain,
'>='(X1,'==>'(X2,X1)),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
fof(c_0_30,plain,
! [X80] : '+'(X80,X80) = X80,
inference(variable_rename,[status(thm)],[sos_14]) ).
fof(c_0_31,plain,
! [X58] : '>='(X58,X58),
inference(variable_rename,[status(thm)],[sos_04]) ).
cnf(c_0_32,plain,
'==>'(X1,'0') = '0',
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_33,plain,
'==>'('==>'(X1,X2),X2) = '==>'('==>'(X2,X1),X1),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_34,plain,
'>='('+'(X1,X2),'+'('==>'(X3,X1),X2)),
inference(spm,[status(thm)],[c_0_20,c_0_29]) ).
cnf(c_0_35,plain,
'+'(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_36,plain,
( '>='('+'(X2,X1),X3)
| ~ '>='(X1,'==>'(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_37,plain,
'>='(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_38,plain,
'==>'('==>'('0',X1),X1) = '0',
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_39,plain,
( '>='('0','==>'(X1,X2))
| ~ '>='(X1,X2) ),
inference(spm,[status(thm)],[c_0_24,c_0_16]) ).
cnf(c_0_40,plain,
'>='(X1,'+'(X1,'==>'(X2,X1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_17]) ).
cnf(c_0_41,plain,
'>='('+'(X1,X2),X1),
inference(spm,[status(thm)],[c_0_25,c_0_17]) ).
cnf(c_0_42,plain,
'>='('+'(X1,'==>'(X1,X2)),X2),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_43,plain,
'>='('+'('==>'('0',X1),X2),X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_38]),c_0_21])]) ).
cnf(c_0_44,plain,
'>='('0','==>'(X1,'==>'(X2,X1))),
inference(spm,[status(thm)],[c_0_39,c_0_29]) ).
cnf(c_0_45,plain,
'+'(X1,'==>'(X2,X1)) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_40]),c_0_41])]) ).
cnf(c_0_46,plain,
'>='('0','==>'('+'(X1,'==>'(X1,X2)),X2)),
inference(spm,[status(thm)],[c_0_39,c_0_42]) ).
cnf(c_0_47,plain,
'>='('==>'('0',X1),X1),
inference(spm,[status(thm)],[c_0_43,c_0_16]) ).
fof(c_0_48,plain,
! [X52,X53,X54] : '+'('+'(X52,X53),X54) = '+'(X52,'+'(X53,X54)),
inference(variable_rename,[status(thm)],[sos_01]) ).
fof(c_0_49,plain,
! [X74,X75,X76] :
( ~ '>='(X74,X75)
| '>='('==>'(X76,X74),'==>'(X76,X75)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos_11])]) ).
cnf(c_0_50,plain,
'==>'(X1,'==>'(X2,X1)) = '0',
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_44]),c_0_21])]) ).
cnf(c_0_51,plain,
'>='(X1,'==>'(X2,'+'(X2,X1))),
inference(spm,[status(thm)],[c_0_24,c_0_37]) ).
cnf(c_0_52,plain,
'+'(X1,'==>'('==>'(X1,X2),X2)) = X1,
inference(spm,[status(thm)],[c_0_45,c_0_33]) ).
cnf(c_0_53,plain,
'==>'('+'(X1,'==>'(X1,X2)),X2) = '0',
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_46]),c_0_21])]) ).
cnf(c_0_54,plain,
'==>'('0',X1) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_47]),c_0_29])]) ).
cnf(c_0_55,plain,
'+'('+'(X1,X2),X3) = '+'(X1,'+'(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
cnf(c_0_56,plain,
( '>='('==>'(X3,X1),'==>'(X3,X2))
| ~ '>='(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_57,plain,
'==>'('==>'('==>'(X1,X2),X2),X2) = '==>'('0','==>'(X1,X2)),
inference(spm,[status(thm)],[c_0_33,c_0_50]) ).
cnf(c_0_58,plain,
( '==>'(X1,'+'(X1,X2)) = X2
| ~ '>='('==>'(X1,'+'(X1,X2)),X2) ),
inference(spm,[status(thm)],[c_0_23,c_0_51]) ).
cnf(c_0_59,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_52,c_0_53]),c_0_54]),c_0_55]),c_0_17]),c_0_45]) ).
cnf(c_0_60,plain,
'>='('==>'(X1,'+'(X2,X3)),'==>'(X1,X3)),
inference(spm,[status(thm)],[c_0_56,c_0_25]) ).
fof(c_0_61,negated_conjecture,
~ ! [X21] : '==>'('==>'('==>'(X21,'1'),X21),X21) = '0',
inference(assume_negation,[status(cth)],[goals_15]) ).
cnf(c_0_62,plain,
'==>'('==>'('==>'(X1,X2),X2),X2) = '==>'(X1,X2),
inference(rw,[status(thm)],[c_0_57,c_0_54]) ).
cnf(c_0_63,plain,
'==>'(X1,'+'(X1,X2)) = '==>'(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_59]),c_0_60])]) ).
cnf(c_0_64,plain,
'>='('0','==>'(X1,X1)),
inference(spm,[status(thm)],[c_0_39,c_0_37]) ).
fof(c_0_65,negated_conjecture,
'==>'('==>'('==>'(esk1_0,'1'),esk1_0),esk1_0) != '0',
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_61])])]) ).
cnf(c_0_66,plain,
'==>'('==>'('==>'(X1,X2),X2),X1) = '==>'(X2,X1),
inference(spm,[status(thm)],[c_0_62,c_0_33]) ).
cnf(c_0_67,plain,
'==>'(X1,'==>'(X1,X2)) = '==>'(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_59]),c_0_63]) ).
cnf(c_0_68,plain,
'==>'(X1,X1) = '0',
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_64]),c_0_21])]) ).
cnf(c_0_69,negated_conjecture,
'==>'('==>'('==>'(esk1_0,'1'),esk1_0),esk1_0) != '0',
inference(split_conjunct,[status(thm)],[c_0_65]) ).
cnf(c_0_70,plain,
'==>'('==>'(X1,X2),X1) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_67]),c_0_68]),c_0_54]) ).
cnf(c_0_71,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_69,c_0_70]),c_0_68])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : LCL901+1 : TPTP v9.2.1. Released v5.5.0.
% 0.00/0.11 % 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
% 0.15/0.32 % Computer : n005.cluster.edu
% 0.15/0.32 % Model : x86_64 x86_64
% 0.15/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.32 % Memory : 8042.1875MB
% 0.15/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.32 % CPULimit : 300
% 0.15/0.32 % WCLimit : 300
% 0.15/0.32 % DateTime : Mon May 4 23:14:45 EDT 2026
% 0.15/0.32 % CPUTime :
% 0.15/0.33 % start to proof: theBenchmark
% 1.55/1.82 % Version : CSE_E---1.7
% 1.55/1.82 % Problem : theBenchmark.p
% 1.55/1.82 % SZS status Theorem for theBenchmark.p
% 1.55/1.82 % SZS output start CNFRefutation
% See solution above
% 1.55/1.82 % Total time : 1.370s
%------------------------------------------------------------------------------