%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWC065+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 : n015.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 05:18:07 PM UTC 2026
% Result : Theorem 1.71s 1.84s
% Output : CNFRefutation 1.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 8
% Syntax : Number of formulae : 46 ( 13 unt; 0 def)
% Number of atoms : 214 ( 71 equ)
% Maximal formula atoms : 30 ( 4 avg)
% Number of connectives : 276 ( 108 ~; 104 |; 41 &)
% ( 3 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 65 ( 0 sgn 36 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
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(co1,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ! [X5] :
( ssList(X5)
=> ( app(X3,X5) != X4
| ~ equalelemsP(X3)
| ? [X6] :
( ssItem(X6)
& ? [X7] :
( ssList(X7)
& app(cons(X6,nil),X7) = X5
& ? [X8] :
( ssList(X8)
& app(X8,cons(X6,nil)) = X3 ) ) ) ) )
| ( nil != X4
& nil = X3 )
| ( ( nil != X2
| nil = X1 )
& ( ~ neq(X2,nil)
| ? [X9] :
( ssList(X9)
& neq(X9,nil)
& segmentP(X2,X9)
& segmentP(X1,X9) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
fof(ax28,axiom,
! [X1] :
( ssList(X1)
=> app(nil,X1) = X1 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax28) ).
fof(ax26,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ssList(app(X1,X2)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax26) ).
fof(ax55,axiom,
! [X1] :
( ssList(X1)
=> segmentP(X1,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax55) ).
fof(ax17,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax17) ).
fof(ax83,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( nil = app(X1,X2)
<=> ( nil = X2
& nil = X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax83) ).
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(c_0_8,plain,
! [X243,X244,X247,X248] :
( ( ssList(esk8_2(X243,X244))
| ~ segmentP(X243,X244)
| ~ ssList(X244)
| ~ ssList(X243) )
& ( ssList(esk9_2(X243,X244))
| ~ segmentP(X243,X244)
| ~ ssList(X244)
| ~ ssList(X243) )
& ( app(app(esk8_2(X243,X244),X244),esk9_2(X243,X244)) = X243
| ~ segmentP(X243,X244)
| ~ ssList(X244)
| ~ ssList(X243) )
& ( ~ ssList(X247)
| ~ ssList(X248)
| app(app(X247,X244),X248) != X243
| segmentP(X243,X244)
| ~ ssList(X244)
| ~ ssList(X243) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax7])])])])]) ).
fof(c_0_9,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ! [X5] :
( ssList(X5)
=> ( app(X3,X5) != X4
| ~ equalelemsP(X3)
| ? [X6] :
( ssItem(X6)
& ? [X7] :
( ssList(X7)
& app(cons(X6,nil),X7) = X5
& ? [X8] :
( ssList(X8)
& app(X8,cons(X6,nil)) = X3 ) ) ) ) )
| ( nil != X4
& nil = X3 )
| ( ( nil != X2
| nil = X1 )
& ( ~ neq(X2,nil)
| ? [X9] :
( ssList(X9)
& neq(X9,nil)
& segmentP(X2,X9)
& segmentP(X1,X9) ) ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[co1])]) ).
cnf(c_0_10,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_8]) ).
fof(c_0_11,plain,
! [X350] :
( ~ ssList(X350)
| app(nil,X350) = X350 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax28])]) ).
fof(c_0_12,plain,
! [X345,X346] :
( ~ ssList(X345)
| ~ ssList(X346)
| ssList(app(X345,X346)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax26])])]) ).
fof(c_0_13,negated_conjecture,
! [X471,X472,X473,X474] :
( ssList(esk48_0)
& ssList(esk49_0)
& ssList(esk50_0)
& ssList(esk51_0)
& esk49_0 = esk51_0
& esk48_0 = esk50_0
& ssList(esk52_0)
& app(esk50_0,esk52_0) = esk51_0
& equalelemsP(esk50_0)
& ( ~ ssItem(X471)
| ~ ssList(X472)
| app(cons(X471,nil),X472) != esk52_0
| ~ ssList(X473)
| app(X473,cons(X471,nil)) != esk50_0 )
& ( nil = esk51_0
| nil != esk50_0 )
& ( neq(esk49_0,nil)
| nil = esk49_0 )
& ( ~ ssList(X474)
| ~ neq(X474,nil)
| ~ segmentP(esk49_0,X474)
| ~ segmentP(esk48_0,X474)
| nil = esk49_0 )
& ( neq(esk49_0,nil)
| nil != esk48_0 )
& ( ~ ssList(X474)
| ~ neq(X474,nil)
| ~ segmentP(esk49_0,X474)
| ~ segmentP(esk48_0,X474)
| nil != esk48_0 ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])])])])]) ).
fof(c_0_14,plain,
! [X404] :
( ~ ssList(X404)
| segmentP(X404,X404) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax55])]) ).
cnf(c_0_15,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_10]) ).
cnf(c_0_16,plain,
( app(nil,X1) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_17,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[ax17]) ).
cnf(c_0_18,plain,
( ssList(app(X1,X2))
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_19,negated_conjecture,
app(esk50_0,esk52_0) = esk51_0,
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_20,negated_conjecture,
esk48_0 = esk50_0,
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_21,negated_conjecture,
esk49_0 = esk51_0,
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_22,negated_conjecture,
( nil = esk49_0
| ~ ssList(X1)
| ~ neq(X1,nil)
| ~ segmentP(esk49_0,X1)
| ~ segmentP(esk48_0,X1) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_23,plain,
( segmentP(X1,X1)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_24,negated_conjecture,
ssList(esk48_0),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_25,plain,
( segmentP(app(X1,X2),X1)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17])]),c_0_18]) ).
cnf(c_0_26,negated_conjecture,
app(esk48_0,esk52_0) = esk49_0,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_19,c_0_20]),c_0_21]) ).
cnf(c_0_27,negated_conjecture,
ssList(esk52_0),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
fof(c_0_28,plain,
! [X440,X441] :
( ( nil = X441
| nil != app(X440,X441)
| ~ ssList(X441)
| ~ ssList(X440) )
& ( nil = X440
| nil != app(X440,X441)
| ~ ssList(X441)
| ~ ssList(X440) )
& ( nil != X441
| nil != X440
| nil = app(X440,X441)
| ~ ssList(X441)
| ~ ssList(X440) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax83])])])]) ).
cnf(c_0_29,negated_conjecture,
( esk49_0 = nil
| ~ segmentP(esk49_0,esk48_0)
| ~ neq(esk48_0,nil) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24])]) ).
cnf(c_0_30,negated_conjecture,
segmentP(esk49_0,esk48_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_24]),c_0_27])]) ).
fof(c_0_31,plain,
! [X324,X325] :
( ( ~ neq(X324,X325)
| X324 != X325
| ~ ssList(X325)
| ~ ssList(X324) )
& ( X324 = X325
| neq(X324,X325)
| ~ ssList(X325)
| ~ ssList(X324) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax15])])])]) ).
cnf(c_0_32,negated_conjecture,
( nil = esk51_0
| nil != esk50_0 ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_33,negated_conjecture,
( ~ ssList(X1)
| ~ neq(X1,nil)
| ~ segmentP(esk49_0,X1)
| ~ segmentP(esk48_0,X1)
| nil != esk48_0 ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_34,plain,
( nil = X1
| nil != app(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_35,negated_conjecture,
( esk49_0 = nil
| ~ neq(esk48_0,nil) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_29,c_0_30])]) ).
cnf(c_0_36,plain,
( X1 = X2
| neq(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_37,negated_conjecture,
( esk49_0 = nil
| esk48_0 != nil ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_32,c_0_21]),c_0_20]) ).
cnf(c_0_38,negated_conjecture,
( esk48_0 != nil
| ~ segmentP(esk49_0,esk48_0)
| ~ neq(esk48_0,nil) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_23]),c_0_24])]) ).
cnf(c_0_39,negated_conjecture,
( esk48_0 = nil
| esk49_0 != nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_26]),c_0_27]),c_0_24])]) ).
cnf(c_0_40,negated_conjecture,
esk49_0 = nil,
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_17]),c_0_24])]),c_0_37]) ).
cnf(c_0_41,negated_conjecture,
( esk48_0 != nil
| ~ neq(esk48_0,nil) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_38,c_0_30])]) ).
cnf(c_0_42,negated_conjecture,
esk48_0 = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_39,c_0_40])]) ).
cnf(c_0_43,negated_conjecture,
( neq(esk49_0,nil)
| nil != esk48_0 ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_44,negated_conjecture,
~ neq(nil,nil),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_41,c_0_42]),c_0_42])]) ).
cnf(c_0_45,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_43,c_0_40]),c_0_42])]),c_0_44]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWC065+1 : TPTP v9.2.1. Released v2.4.0.
% 0.00/0.12 % 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
% 0.16/0.33 % Computer : n015.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue May 5 04:21:31 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 1.71/1.84 % Version : CSE_E---1.7
% 1.71/1.84 % Problem : theBenchmark.p
% 1.71/1.84 % SZS status Theorem for theBenchmark.p
% 1.71/1.84 % SZS output start CNFRefutation
% See solution above
% 1.71/1.85 % Total time : 1.374s
%------------------------------------------------------------------------------