%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWC076+1 : TPTP v9.2.1. Released v2.4.0.
% 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 : n024.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 05:18:10 PM UTC 2026
% Result : Theorem 1.16s 1.63s
% Output : CNFRefutation 1.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 34 ( 15 unt; 0 def)
% Number of atoms : 172 ( 51 equ)
% Maximal formula atoms : 28 ( 5 avg)
% Number of connectives : 217 ( 79 ~; 73 |; 46 &)
% ( 2 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 7 con; 0-2 aty)
% Number of variables : 59 ( 0 sgn 31 !; 16 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ? [X5] :
( ssList(X5)
& neq(X5,nil)
& segmentP(X2,X5)
& segmentP(X1,X5) )
| ! [X6] :
( ssList(X6)
=> ! [X7] :
( ssList(X7)
=> ( app(app(X6,X3),X7) != X4
| ~ equalelemsP(X3)
| ? [X8] :
( ssItem(X8)
& ? [X9] :
( ssList(X9)
& app(X9,cons(X8,nil)) = X6
& ? [X10] :
( ssList(X10)
& app(cons(X8,nil),X10) = X3 ) ) )
| ? [X11] :
( ssItem(X11)
& ? [X12] :
( ssList(X12)
& app(cons(X11,nil),X12) = X7
& ? [X13] :
( ssList(X13)
& app(X13,cons(X11,nil)) = X3 ) ) ) ) ) )
| ( nil != X4
& nil = X3 )
| ( nil = X2
& nil = X1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
fof(ax7,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( segmentP(X1,X2)
<=> ? [X3] :
( ssList(X3)
& ? [X4] :
( ssList(X4)
& app(app(X3,X2),X4) = X1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax7) ).
fof(ax55,axiom,
! [X1] :
( ssList(X1)
=> segmentP(X1,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax55) ).
fof(ax15,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( neq(X1,X2)
<=> X1 != X2 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax15) ).
fof(ax17,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax17) ).
fof(c_0_5,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ? [X5] :
( ssList(X5)
& neq(X5,nil)
& segmentP(X2,X5)
& segmentP(X1,X5) )
| ! [X6] :
( ssList(X6)
=> ! [X7] :
( ssList(X7)
=> ( app(app(X6,X3),X7) != X4
| ~ equalelemsP(X3)
| ? [X8] :
( ssItem(X8)
& ? [X9] :
( ssList(X9)
& app(X9,cons(X8,nil)) = X6
& ? [X10] :
( ssList(X10)
& app(cons(X8,nil),X10) = X3 ) ) )
| ? [X11] :
( ssItem(X11)
& ? [X12] :
( ssList(X12)
& app(cons(X11,nil),X12) = X7
& ? [X13] :
( ssList(X13)
& app(X13,cons(X11,nil)) = X3 ) ) ) ) ) )
| ( nil != X4
& nil = X3 )
| ( nil = X2
& nil = X1 ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[co1])]) ).
fof(c_0_6,negated_conjecture,
! [X478,X481,X482,X483,X484,X485,X486] :
( ssList(esk48_0)
& ssList(esk49_0)
& ssList(esk50_0)
& ssList(esk51_0)
& esk49_0 = esk51_0
& esk48_0 = esk50_0
& ( ~ ssList(X478)
| ~ neq(X478,nil)
| ~ segmentP(esk49_0,X478)
| ~ segmentP(esk48_0,X478) )
& ssList(esk52_0)
& ssList(esk53_0)
& app(app(esk52_0,esk50_0),esk53_0) = esk51_0
& equalelemsP(esk50_0)
& ( ~ ssItem(X481)
| ~ ssList(X482)
| app(X482,cons(X481,nil)) != esk52_0
| ~ ssList(X483)
| app(cons(X481,nil),X483) != esk50_0 )
& ( ~ ssItem(X484)
| ~ ssList(X485)
| app(cons(X484,nil),X485) != esk53_0
| ~ ssList(X486)
| app(X486,cons(X484,nil)) != esk50_0 )
& ( nil = esk51_0
| nil != esk50_0 )
& ( nil != esk49_0
| nil != esk48_0 ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])])]) ).
fof(c_0_7,plain,
! [X251,X252,X255,X256] :
( ( ssList(esk8_2(X251,X252))
| ~ segmentP(X251,X252)
| ~ ssList(X252)
| ~ ssList(X251) )
& ( ssList(esk9_2(X251,X252))
| ~ segmentP(X251,X252)
| ~ ssList(X252)
| ~ ssList(X251) )
& ( app(app(esk8_2(X251,X252),X252),esk9_2(X251,X252)) = X251
| ~ segmentP(X251,X252)
| ~ ssList(X252)
| ~ ssList(X251) )
& ( ~ ssList(X255)
| ~ ssList(X256)
| app(app(X255,X252),X256) != X251
| segmentP(X251,X252)
| ~ ssList(X252)
| ~ ssList(X251) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax7])])])])]) ).
cnf(c_0_8,negated_conjecture,
( ~ ssList(X1)
| ~ neq(X1,nil)
| ~ segmentP(esk49_0,X1)
| ~ segmentP(esk48_0,X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_9,negated_conjecture,
esk48_0 = esk50_0,
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,negated_conjecture,
esk49_0 = esk51_0,
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_11,plain,
! [X412] :
( ~ ssList(X412)
| segmentP(X412,X412) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax55])]) ).
cnf(c_0_12,negated_conjecture,
ssList(esk48_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_13,plain,
( segmentP(X4,X3)
| ~ ssList(X1)
| ~ ssList(X2)
| app(app(X1,X3),X2) != X4
| ~ ssList(X3)
| ~ ssList(X4) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_14,negated_conjecture,
ssList(esk49_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_15,negated_conjecture,
( ~ segmentP(esk50_0,X1)
| ~ segmentP(esk51_0,X1)
| ~ ssList(X1)
| ~ neq(X1,nil) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_8,c_0_9]),c_0_10]) ).
cnf(c_0_16,plain,
( segmentP(X1,X1)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_17,negated_conjecture,
ssList(esk50_0),
inference(rw,[status(thm)],[c_0_12,c_0_9]) ).
cnf(c_0_18,plain,
( segmentP(app(app(X1,X2),X3),X2)
| ~ ssList(app(app(X1,X2),X3))
| ~ ssList(X2)
| ~ ssList(X3)
| ~ ssList(X1) ),
inference(er,[status(thm)],[c_0_13]) ).
cnf(c_0_19,negated_conjecture,
app(app(esk52_0,esk50_0),esk53_0) = esk51_0,
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_20,negated_conjecture,
ssList(esk51_0),
inference(rw,[status(thm)],[c_0_14,c_0_10]) ).
cnf(c_0_21,negated_conjecture,
ssList(esk53_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_22,negated_conjecture,
ssList(esk52_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_23,negated_conjecture,
( nil != esk49_0
| nil != esk48_0 ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_24,negated_conjecture,
( ~ segmentP(esk51_0,esk50_0)
| ~ neq(esk50_0,nil) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17])]) ).
cnf(c_0_25,negated_conjecture,
segmentP(esk51_0,esk50_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20]),c_0_17]),c_0_21]),c_0_22])]) ).
fof(c_0_26,plain,
! [X332,X333] :
( ( ~ neq(X332,X333)
| X332 != X333
| ~ ssList(X333)
| ~ ssList(X332) )
& ( X332 = X333
| neq(X332,X333)
| ~ ssList(X333)
| ~ ssList(X332) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax15])])])]) ).
cnf(c_0_27,negated_conjecture,
( nil = esk51_0
| nil != esk50_0 ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_28,negated_conjecture,
( esk50_0 != nil
| esk51_0 != nil ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_23,c_0_9]),c_0_10]) ).
cnf(c_0_29,negated_conjecture,
~ neq(esk50_0,nil),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_24,c_0_25])]) ).
cnf(c_0_30,plain,
( X1 = X2
| neq(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_31,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[ax17]) ).
cnf(c_0_32,negated_conjecture,
esk50_0 != nil,
inference(csr,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_33,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31]),c_0_17])]),c_0_32]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : SWC076+1 : TPTP v9.2.1. Released v2.4.0.
% 0.00/0.06 % 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
% 0.05/0.24 % Computer : n024.cluster.edu
% 0.05/0.24 % Model : x86_64 x86_64
% 0.05/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.05/0.24 % Memory : 8042.1875MB
% 0.05/0.24 % OS : Linux 3.10.0-693.el7.x86_64
% 0.05/0.24 % CPULimit : 300
% 0.05/0.24 % WCLimit : 300
% 0.05/0.24 % DateTime : Mon May 4 23:24:11 EDT 2026
% 0.05/0.24 % CPUTime :
% 0.05/0.24 % start to proof: theBenchmark
% 1.16/1.63 % Version : CSE_E---1.7
% 1.16/1.63 % Problem : theBenchmark.p
% 1.16/1.63 % SZS status Theorem for theBenchmark.p
% 1.16/1.63 % SZS output start CNFRefutation
% See solution above
% 1.16/1.63 % Total time : 1.368s
%------------------------------------------------------------------------------