%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : LCL903+1 : TPTP v9.2.1. Released v5.5.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n028.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 04:45:20 PM UTC 2026
% Result : Theorem 2.00s 1.93s
% Output : CNFRefutation 2.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 11
% Syntax : Number of formulae : 66 ( 49 unt; 0 def)
% Number of atoms : 88 ( 33 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 41 ( 19 ~; 16 |; 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 : 107 ( 12 sgn 38 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(sos_07,axiom,
! [X9,X10,X11] :
( '>='('+'(X9,X10),X11)
<=> '>='(X10,'==>'(X9,X11)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_07) ).
fof(sos_04,axiom,
! [X1] : '>='(X1,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_04) ).
fof(sos_12,axiom,
! [X1] : '+'(X1,'1') = '1',
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_12) ).
fof(sos_02,axiom,
! [X1,X2] : '+'(X1,X2) = '+'(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_02) ).
fof(sos_03,axiom,
! [X1] : '+'(X1,'0') = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_03) ).
fof(sos_06,axiom,
! [X7,X8] :
( ( '>='(X7,X8)
& '>='(X8,X7) )
=> X7 = X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_06) ).
fof(sos_09,axiom,
! [X12,X13,X14] :
( '>='(X12,X13)
=> '>='('+'(X12,X14),'+'(X13,X14)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_09) ).
fof(sos_08,axiom,
! [X1] : '>='(X1,'0'),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_08) ).
fof(sos_13,axiom,
! [X1] : '==>'('==>'('==>'(X1,'1'),X1),X1) = '0',
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_13) ).
fof(sos_10,axiom,
! [X15,X16,X17] :
( '>='(X15,X16)
=> '>='('==>'(X16,X17),'==>'(X15,X17)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_10) ).
fof(goals_14,conjecture,
! [X21] : '+'(X21,X21) = X21,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals_14) ).
fof(c_0_11,plain,
! [X62,X63,X64] :
( ( ~ '>='('+'(X62,X63),X64)
| '>='(X63,'==>'(X62,X64)) )
& ( ~ '>='(X63,'==>'(X62,X64))
| '>='('+'(X62,X63),X64) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos_07])]) ).
fof(c_0_12,plain,
! [X56] : '>='(X56,X56),
inference(variable_rename,[status(thm)],[sos_04]) ).
fof(c_0_13,plain,
! [X75] : '+'(X75,'1') = '1',
inference(variable_rename,[status(thm)],[sos_12]) ).
fof(c_0_14,plain,
! [X53,X54] : '+'(X53,X54) = '+'(X54,X53),
inference(variable_rename,[status(thm)],[sos_02]) ).
cnf(c_0_15,plain,
( '>='('+'(X2,X1),X3)
| ~ '>='(X1,'==>'(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_16,plain,
'>='(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_17,plain,
'+'(X1,'1') = '1',
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_18,plain,
'+'(X1,X2) = '+'(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
fof(c_0_19,plain,
! [X55] : '+'(X55,'0') = X55,
inference(variable_rename,[status(thm)],[sos_03]) ).
fof(c_0_20,plain,
! [X60,X61] :
( ~ '>='(X60,X61)
| ~ '>='(X61,X60)
| X60 = X61 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos_06])]) ).
cnf(c_0_21,plain,
'>='('+'(X1,'==>'(X1,X2)),X2),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_22,plain,
'+'('1',X1) = '1',
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
fof(c_0_23,plain,
! [X66,X67,X68] :
( ~ '>='(X66,X67)
| '>='('+'(X66,X68),'+'(X67,X68)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos_09])]) ).
fof(c_0_24,plain,
! [X65] : '>='(X65,'0'),
inference(variable_rename,[status(thm)],[sos_08]) ).
cnf(c_0_25,plain,
'+'(X1,'0') = X1,
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_26,plain,
( X1 = X2
| ~ '>='(X1,X2)
| ~ '>='(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_27,plain,
'>='('1',X1),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
fof(c_0_28,plain,
! [X76] : '==>'('==>'('==>'(X76,'1'),X76),X76) = '0',
inference(variable_rename,[status(thm)],[sos_13]) ).
cnf(c_0_29,plain,
( '>='('+'(X1,X3),'+'(X2,X3))
| ~ '>='(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_30,plain,
'>='(X1,'0'),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_31,plain,
'+'('0',X1) = X1,
inference(spm,[status(thm)],[c_0_25,c_0_18]) ).
cnf(c_0_32,plain,
( X1 = '1'
| ~ '>='(X1,'1') ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_33,plain,
'==>'('==>'('==>'(X1,'1'),X1),X1) = '0',
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_34,plain,
( '>='(X2,'==>'(X1,X3))
| ~ '>='('+'(X1,X2),X3) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_35,plain,
'>='('+'(X1,X2),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31]) ).
cnf(c_0_36,plain,
'+'(X1,'==>'(X1,'1')) = '1',
inference(spm,[status(thm)],[c_0_32,c_0_21]) ).
cnf(c_0_37,plain,
'>='('==>'('==>'(X1,'1'),X1),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_33]),c_0_25]) ).
cnf(c_0_38,plain,
'>='(X1,'==>'(X2,X1)),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_39,plain,
'>='('==>'(X1,'1'),'==>'(X1,X2)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_36]),c_0_27])]) ).
cnf(c_0_40,plain,
'==>'('==>'(X1,'1'),X1) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_37]),c_0_38])]) ).
cnf(c_0_41,plain,
( '>='(X1,'==>'(X2,X3))
| ~ '>='('+'(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_34,c_0_18]) ).
fof(c_0_42,plain,
! [X69,X70,X71] :
( ~ '>='(X69,X70)
| '>='('==>'(X70,X71),'==>'(X69,X71)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos_10])]) ).
cnf(c_0_43,plain,
'>='('==>'('==>'(X1,'1'),'1'),X1),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_44,plain,
'>='(X1,'==>'('==>'(X1,'1'),X2)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_36]),c_0_27])]) ).
cnf(c_0_45,plain,
( '>='('==>'(X2,X3),'==>'(X1,X3))
| ~ '>='(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_46,plain,
'==>'('==>'(X1,'1'),'1') = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_43]),c_0_44])]) ).
cnf(c_0_47,plain,
'>='('==>'('==>'(X1,X2),X3),'==>'('==>'(X1,'1'),X3)),
inference(spm,[status(thm)],[c_0_45,c_0_39]) ).
cnf(c_0_48,plain,
'==>'(X1,'==>'(X1,'1')) = '==>'(X1,'1'),
inference(spm,[status(thm)],[c_0_40,c_0_46]) ).
cnf(c_0_49,plain,
( '>='('0','==>'(X1,X2))
| ~ '>='(X1,X2) ),
inference(spm,[status(thm)],[c_0_34,c_0_25]) ).
cnf(c_0_50,plain,
'>='(X1,'==>'(X2,'+'(X2,X1))),
inference(spm,[status(thm)],[c_0_34,c_0_16]) ).
cnf(c_0_51,plain,
'>='('==>'('==>'(X1,X2),X1),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_46]),c_0_46]) ).
cnf(c_0_52,plain,
'>='('0','==>'(X1,'==>'(X2,'+'(X2,X1)))),
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_53,plain,
'==>'('==>'(X1,X2),X1) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_51]),c_0_38])]) ).
cnf(c_0_54,plain,
'>='('0','==>'(X1,X1)),
inference(spm,[status(thm)],[c_0_49,c_0_16]) ).
fof(c_0_55,negated_conjecture,
~ ! [X21] : '+'(X21,X21) = X21,
inference(assume_negation,[status(cth)],[goals_14]) ).
cnf(c_0_56,plain,
'==>'(X1,'==>'(X2,'+'(X2,X1))) = '0',
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_52]),c_0_30])]) ).
cnf(c_0_57,plain,
'==>'(X1,'==>'(X1,X2)) = '==>'(X1,X2),
inference(spm,[status(thm)],[c_0_53,c_0_53]) ).
cnf(c_0_58,plain,
'==>'(X1,X1) = '0',
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_54]),c_0_30])]) ).
fof(c_0_59,negated_conjecture,
'+'(esk1_0,esk1_0) != esk1_0,
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_55])])]) ).
cnf(c_0_60,plain,
( '+'(X1,'==>'(X1,X2)) = X2
| ~ '>='(X2,'+'(X1,'==>'(X1,X2))) ),
inference(spm,[status(thm)],[c_0_26,c_0_21]) ).
cnf(c_0_61,plain,
'==>'(X1,'+'(X1,X1)) = '0',
inference(spm,[status(thm)],[c_0_56,c_0_57]) ).
cnf(c_0_62,plain,
'>='('+'(X1,X2),X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_58]),c_0_30])]) ).
cnf(c_0_63,negated_conjecture,
'+'(esk1_0,esk1_0) != esk1_0,
inference(split_conjunct,[status(thm)],[c_0_59]) ).
cnf(c_0_64,plain,
'+'(X1,X1) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61]),c_0_25]),c_0_25]),c_0_62])]) ).
cnf(c_0_65,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_63,c_0_64])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LCL903+1 : TPTP v9.2.1. Released v5.5.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.14/0.33 % Computer : n028.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Mon May 4 23:15:46 EDT 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.34 % start to proof: theBenchmark
% 2.00/1.93 % Version : CSE_E---1.7
% 2.00/1.93 % Problem : theBenchmark.p
% 2.00/1.93 % SZS status Theorem for theBenchmark.p
% 2.00/1.93 % SZS output start CNFRefutation
% See solution above
% 2.00/1.93 % Total time : 1.370s
%------------------------------------------------------------------------------