%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : LCL896+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 : n019.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 6.75s 4.72s
% Output : CNFRefutation 6.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 11
% Syntax : Number of formulae : 52 ( 37 unt; 0 def)
% Number of atoms : 72 ( 28 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 37 ( 17 ~; 14 |; 2 &)
% ( 1 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 6 ( 2 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 : 106 ( 5 sgn 48 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(sos_03,axiom,
! [X1] : '+'(X1,'0') = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_03) ).
fof(sos_02,axiom,
! [X1,X2] : '+'(X1,X2) = '+'(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_02) ).
fof(sos_07,axiom,
! [X9,X10,X11] :
( '>='('+'(X9,X10),X11)
<=> '>='(X10,'==>'(X9,X11)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_07) ).
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_04,axiom,
! [X1] : '>='(X1,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_04) ).
fof(sos_06,axiom,
! [X7,X8] :
( ( '>='(X7,X8)
& '>='(X8,X7) )
=> X7 = X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_06) ).
fof(sos_11,axiom,
! [X18,X19,X20] :
( '>='(X18,X19)
=> '>='('==>'(X20,X18),'==>'(X20,X19)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_11) ).
fof(sos_12,axiom,
! [X1,X2,X3] : '+'('+'(X1,'==>'(X1,X2)),'==>'('+'(X1,'==>'(X1,X2)),X3)) = '+'(X1,'==>'(X1,'+'(X2,'==>'(X2,X3)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_12) ).
fof(sos_01,axiom,
! [X1,X2,X3] : '+'('+'(X1,X2),X3) = '+'(X1,'+'(X2,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_01) ).
fof(goals_13,conjecture,
! [X21,X22] : '+'(X21,'==>'(X21,X22)) = '+'(X22,'==>'(X22,X21)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals_13) ).
fof(c_0_11,plain,
! [X58] : '+'(X58,'0') = X58,
inference(variable_rename,[status(thm)],[sos_03]) ).
fof(c_0_12,plain,
! [X56,X57] : '+'(X56,X57) = '+'(X57,X56),
inference(variable_rename,[status(thm)],[sos_02]) ).
fof(c_0_13,plain,
! [X65,X66,X67] :
( ( ~ '>='('+'(X65,X66),X67)
| '>='(X66,'==>'(X65,X67)) )
& ( ~ '>='(X66,'==>'(X65,X67))
| '>='('+'(X65,X66),X67) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos_07])]) ).
fof(c_0_14,plain,
! [X69,X70,X71] :
( ~ '>='(X69,X70)
| '>='('+'(X69,X71),'+'(X70,X71)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos_09])]) ).
fof(c_0_15,plain,
! [X68] : '>='(X68,'0'),
inference(variable_rename,[status(thm)],[sos_08]) ).
cnf(c_0_16,plain,
'+'(X1,'0') = X1,
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_17,plain,
'+'(X1,X2) = '+'(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_18,plain,
( '>='(X2,'==>'(X1,X3))
| ~ '>='('+'(X1,X2),X3) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_19,plain,
( '>='('+'(X1,X3),'+'(X2,X3))
| ~ '>='(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_20,plain,
'>='(X1,'0'),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_21,plain,
'+'('0',X1) = X1,
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
fof(c_0_22,plain,
! [X59] : '>='(X59,X59),
inference(variable_rename,[status(thm)],[sos_04]) ).
fof(c_0_23,plain,
! [X63,X64] :
( ~ '>='(X63,X64)
| ~ '>='(X64,X63)
| X63 = X64 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos_06])]) ).
cnf(c_0_24,plain,
( '>='('0','==>'(X1,X2))
| ~ '>='(X1,X2) ),
inference(spm,[status(thm)],[c_0_18,c_0_16]) ).
cnf(c_0_25,plain,
'>='('+'(X1,X2),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21]) ).
cnf(c_0_26,plain,
'>='(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
fof(c_0_27,plain,
! [X75,X76,X77] :
( ~ '>='(X75,X76)
| '>='('==>'(X77,X75),'==>'(X77,X76)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos_11])]) ).
cnf(c_0_28,plain,
( '>='('+'(X2,X1),X3)
| ~ '>='(X1,'==>'(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
fof(c_0_29,plain,
! [X78,X79,X80] : '+'('+'(X78,'==>'(X78,X79)),'==>'('+'(X78,'==>'(X78,X79)),X80)) = '+'(X78,'==>'(X78,'+'(X79,'==>'(X79,X80)))),
inference(variable_rename,[status(thm)],[sos_12]) ).
fof(c_0_30,plain,
! [X53,X54,X55] : '+'('+'(X53,X54),X55) = '+'(X53,'+'(X54,X55)),
inference(variable_rename,[status(thm)],[sos_01]) ).
cnf(c_0_31,plain,
( X1 = X2
| ~ '>='(X1,X2)
| ~ '>='(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_32,plain,
'>='('0','==>'('+'(X1,X2),X2)),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_33,plain,
'>='(X1,'==>'(X2,'+'(X2,X1))),
inference(spm,[status(thm)],[c_0_18,c_0_26]) ).
cnf(c_0_34,plain,
( '>='('==>'(X3,X1),'==>'(X3,X2))
| ~ '>='(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_35,plain,
'>='('+'(X1,'==>'(X1,X2)),X2),
inference(spm,[status(thm)],[c_0_28,c_0_26]) ).
cnf(c_0_36,plain,
'+'('+'(X1,'==>'(X1,X2)),'==>'('+'(X1,'==>'(X1,X2)),X3)) = '+'(X1,'==>'(X1,'+'(X2,'==>'(X2,X3)))),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_37,plain,
'+'('+'(X1,X2),X3) = '+'(X1,'+'(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_38,plain,
'==>'('+'(X1,X2),X2) = '0',
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_20])]) ).
cnf(c_0_39,plain,
( '==>'(X1,'+'(X1,X2)) = X2
| ~ '>='('==>'(X1,'+'(X1,X2)),X2) ),
inference(spm,[status(thm)],[c_0_31,c_0_33]) ).
cnf(c_0_40,plain,
'>='('==>'(X1,'+'(X2,'==>'(X2,X3))),'==>'(X1,X3)),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_41,plain,
'+'(X1,'+'('==>'(X1,X2),'==>'('+'(X1,'==>'(X1,X2)),X3))) = '+'(X1,'==>'(X1,'+'(X2,'==>'(X2,X3)))),
inference(rw,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_42,plain,
'==>'('+'(X1,X2),X1) = '0',
inference(spm,[status(thm)],[c_0_38,c_0_17]) ).
cnf(c_0_43,plain,
'==>'(X1,'+'(X1,'==>'(X1,X2))) = '==>'(X1,X2),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_44,plain,
'+'(X1,'==>'(X1,'+'(X2,'==>'(X2,X1)))) = '+'(X1,'==>'(X1,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_16]) ).
fof(c_0_45,negated_conjecture,
~ ! [X21,X22] : '+'(X21,'==>'(X21,X22)) = '+'(X22,'==>'(X22,X21)),
inference(assume_negation,[status(cth)],[goals_13]) ).
cnf(c_0_46,plain,
'==>'(X1,'+'(X2,'==>'(X2,X1))) = '==>'(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_43]) ).
fof(c_0_47,negated_conjecture,
'+'(esk1_0,'==>'(esk1_0,esk2_0)) != '+'(esk2_0,'==>'(esk2_0,esk1_0)),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_45])])]) ).
cnf(c_0_48,plain,
'>='('+'(X1,'==>'(X1,X2)),'+'(X2,'==>'(X2,X1))),
inference(spm,[status(thm)],[c_0_35,c_0_46]) ).
cnf(c_0_49,negated_conjecture,
'+'(esk1_0,'==>'(esk1_0,esk2_0)) != '+'(esk2_0,'==>'(esk2_0,esk1_0)),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_50,plain,
'+'(X1,'==>'(X1,X2)) = '+'(X2,'==>'(X2,X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_48]),c_0_48])]) ).
cnf(c_0_51,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_49,c_0_50])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LCL896+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
% 0.15/0.33 % Computer : n019.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Mon May 4 23:15:14 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 6.75/4.72 % Version : CSE_E---1.7
% 6.75/4.72 % Problem : theBenchmark.p
% 6.75/4.72 % SZS status Theorem for theBenchmark.p
% 6.75/4.72 % SZS output start CNFRefutation
% See solution above
% 6.75/4.74 % Total time : 3.374s
%------------------------------------------------------------------------------