%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWC165+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 : 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 05:18:33 PM UTC 2026
% Result : Theorem 1.64s 1.84s
% Output : CNFRefutation 1.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 10
% Syntax : Number of formulae : 52 ( 21 unt; 0 def)
% Number of atoms : 247 ( 68 equ)
% Maximal formula atoms : 48 ( 4 avg)
% Number of connectives : 290 ( 95 ~; 109 |; 43 &)
% ( 2 <=>; 41 =>; 0 <=; 0 <~>)
% Maximal formula depth : 32 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 19 ( 19 usr; 12 con; 0-2 aty)
% Number of variables : 86 ( 0 sgn 60 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ! [X5] :
( ssItem(X5)
=> ! [X6] :
( ssItem(X6)
=> ! [X7] :
( ssList(X7)
=> ! [X8] :
( ssList(X8)
=> ( app(app(app(X7,cons(X5,nil)),cons(X6,nil)),X8) != X1
| neq(X5,X6) ) ) ) ) )
| ( ! [X9] :
( ssItem(X9)
=> ! [X10] :
( ssList(X10)
=> ! [X11] :
( ssList(X11)
=> ( cons(X9,nil) != X3
| app(app(X10,X3),X11) != X4
| ? [X12] :
( ssItem(X12)
& memberP(X10,X12)
& lt(X9,X12) )
| ? [X13] :
( ssItem(X13)
& memberP(X11,X13)
& lt(X13,X9) ) ) ) ) )
& ( nil != X4
| nil != X3 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
fof(ax1,axiom,
! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ( neq(X1,X2)
<=> X1 != X2 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax1) ).
fof(ax82,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> app(app(X1,X2),X3) = app(X1,app(X2,X3)) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax82) ).
fof(ax16,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> ssList(cons(X2,X1)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax16) ).
fof(ax17,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax17) ).
fof(ax26,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ssList(app(X1,X2)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax26) ).
fof(ax13,axiom,
! [X1] :
( ssList(X1)
=> ( duplicatefreeP(X1)
<=> ! [X2] :
( ssItem(X2)
=> ! [X3] :
( ssItem(X3)
=> ! [X4] :
( ssList(X4)
=> ! [X5] :
( ssList(X5)
=> ! [X6] :
( ssList(X6)
=> ( app(app(X4,cons(X2,X5)),cons(X3,X6)) = X1
=> X2 != X3 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax13) ).
fof(ax81,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> cons(X2,X1) = app(cons(X2,nil),X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax81) ).
fof(ax71,axiom,
! [X1] :
( ssItem(X1)
=> duplicatefreeP(cons(X1,nil)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax71) ).
fof(ax72,axiom,
duplicatefreeP(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax72) ).
fof(c_0_10,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ! [X5] :
( ssItem(X5)
=> ! [X6] :
( ssItem(X6)
=> ! [X7] :
( ssList(X7)
=> ! [X8] :
( ssList(X8)
=> ( app(app(app(X7,cons(X5,nil)),cons(X6,nil)),X8) != X1
| neq(X5,X6) ) ) ) ) )
| ( ! [X9] :
( ssItem(X9)
=> ! [X10] :
( ssList(X10)
=> ! [X11] :
( ssList(X11)
=> ( cons(X9,nil) != X3
| app(app(X10,X3),X11) != X4
| ? [X12] :
( ssItem(X12)
& memberP(X10,X12)
& lt(X9,X12) )
| ? [X13] :
( ssItem(X13)
& memberP(X11,X13)
& lt(X13,X9) ) ) ) ) )
& ( nil != X4
| nil != X3 ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[co1]) ).
fof(c_0_11,negated_conjecture,
! [X485,X486] :
( ssList(esk48_0)
& ssList(esk49_0)
& ssList(esk50_0)
& ssList(esk51_0)
& esk49_0 = esk51_0
& esk48_0 = esk50_0
& ssItem(esk52_0)
& ssItem(esk53_0)
& ssList(esk54_0)
& ssList(esk55_0)
& app(app(app(esk54_0,cons(esk52_0,nil)),cons(esk53_0,nil)),esk55_0) = esk48_0
& ~ neq(esk52_0,esk53_0)
& ( nil = esk51_0
| ssItem(esk56_0) )
& ( nil = esk50_0
| ssItem(esk56_0) )
& ( nil = esk51_0
| ssList(esk57_0) )
& ( nil = esk50_0
| ssList(esk57_0) )
& ( nil = esk51_0
| ssList(esk58_0) )
& ( nil = esk50_0
| ssList(esk58_0) )
& ( nil = esk51_0
| cons(esk56_0,nil) = esk50_0 )
& ( nil = esk50_0
| cons(esk56_0,nil) = esk50_0 )
& ( nil = esk51_0
| app(app(esk57_0,esk50_0),esk58_0) = esk51_0 )
& ( nil = esk50_0
| app(app(esk57_0,esk50_0),esk58_0) = esk51_0 )
& ( nil = esk51_0
| ~ ssItem(X485)
| ~ memberP(esk57_0,X485)
| ~ lt(esk56_0,X485) )
& ( nil = esk50_0
| ~ ssItem(X485)
| ~ memberP(esk57_0,X485)
| ~ lt(esk56_0,X485) )
& ( nil = esk51_0
| ~ ssItem(X486)
| ~ memberP(esk58_0,X486)
| ~ lt(X486,esk56_0) )
& ( nil = esk50_0
| ~ ssItem(X486)
| ~ memberP(esk58_0,X486)
| ~ lt(X486,esk56_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_10])])])])]) ).
fof(c_0_12,plain,
! [X230,X231] :
( ( ~ neq(X230,X231)
| X230 != X231
| ~ ssItem(X231)
| ~ ssItem(X230) )
& ( X230 = X231
| neq(X230,X231)
| ~ ssItem(X231)
| ~ ssItem(X230) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax1])])])]) ).
cnf(c_0_13,negated_conjecture,
app(app(app(esk54_0,cons(esk52_0,nil)),cons(esk53_0,nil)),esk55_0) = esk48_0,
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_14,negated_conjecture,
esk48_0 = esk50_0,
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_15,negated_conjecture,
~ neq(esk52_0,esk53_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_16,plain,
( X1 = X2
| neq(X1,X2)
| ~ ssItem(X2)
| ~ ssItem(X1) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_17,negated_conjecture,
ssItem(esk53_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_18,negated_conjecture,
ssItem(esk52_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_19,negated_conjecture,
app(app(app(esk54_0,cons(esk52_0,nil)),cons(esk53_0,nil)),esk55_0) = esk50_0,
inference(rw,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_20,negated_conjecture,
esk53_0 = esk52_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17]),c_0_18])]) ).
fof(c_0_21,plain,
! [X445,X446,X447] :
( ~ ssList(X445)
| ~ ssList(X446)
| ~ ssList(X447)
| app(app(X445,X446),X447) = app(X445,app(X446,X447)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax82])])]) ).
cnf(c_0_22,negated_conjecture,
app(app(app(esk54_0,cons(esk52_0,nil)),cons(esk52_0,nil)),esk55_0) = esk50_0,
inference(rw,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_23,plain,
( app(app(X1,X2),X3) = app(X1,app(X2,X3))
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_24,negated_conjecture,
ssList(esk55_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_25,plain,
! [X334,X335] :
( ~ ssList(X334)
| ~ ssItem(X335)
| ssList(cons(X335,X334)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax16])])]) ).
cnf(c_0_26,negated_conjecture,
( app(app(esk54_0,cons(esk52_0,nil)),app(cons(esk52_0,nil),esk55_0)) = esk50_0
| ~ ssList(app(esk54_0,cons(esk52_0,nil)))
| ~ ssList(cons(esk52_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_27,plain,
( ssList(cons(X2,X1))
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_28,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[ax17]) ).
fof(c_0_29,plain,
! [X353,X354] :
( ~ ssList(X353)
| ~ ssList(X354)
| ssList(app(X353,X354)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax26])])]) ).
cnf(c_0_30,negated_conjecture,
( app(app(esk54_0,cons(esk52_0,nil)),app(cons(esk52_0,nil),esk55_0)) = esk50_0
| ~ ssList(app(esk54_0,cons(esk52_0,nil))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_28]),c_0_18])]) ).
cnf(c_0_31,plain,
( ssList(app(X1,X2))
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_32,negated_conjecture,
ssList(esk54_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_33,plain,
! [X312,X313,X314,X315,X316,X317] :
( ( ~ duplicatefreeP(X312)
| ~ ssItem(X313)
| ~ ssItem(X314)
| ~ ssList(X315)
| ~ ssList(X316)
| ~ ssList(X317)
| app(app(X315,cons(X313,X316)),cons(X314,X317)) != X312
| X313 != X314
| ~ ssList(X312) )
& ( ssItem(esk35_1(X312))
| duplicatefreeP(X312)
| ~ ssList(X312) )
& ( ssItem(esk36_1(X312))
| duplicatefreeP(X312)
| ~ ssList(X312) )
& ( ssList(esk37_1(X312))
| duplicatefreeP(X312)
| ~ ssList(X312) )
& ( ssList(esk38_1(X312))
| duplicatefreeP(X312)
| ~ ssList(X312) )
& ( ssList(esk39_1(X312))
| duplicatefreeP(X312)
| ~ ssList(X312) )
& ( app(app(esk37_1(X312),cons(esk35_1(X312),esk38_1(X312))),cons(esk36_1(X312),esk39_1(X312))) = X312
| duplicatefreeP(X312)
| ~ ssList(X312) )
& ( esk35_1(X312) = esk36_1(X312)
| duplicatefreeP(X312)
| ~ ssList(X312) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax13])])])])]) ).
cnf(c_0_34,negated_conjecture,
( app(app(esk54_0,cons(esk52_0,nil)),app(cons(esk52_0,nil),esk55_0)) = esk50_0
| ~ ssList(cons(esk52_0,nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_32])]) ).
fof(c_0_35,plain,
! [X443,X444] :
( ~ ssList(X443)
| ~ ssItem(X444)
| cons(X444,X443) = app(cons(X444,nil),X443) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax81])])]) ).
fof(c_0_36,plain,
! [X428] :
( ~ ssItem(X428)
| duplicatefreeP(cons(X428,nil)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax71])]) ).
cnf(c_0_37,plain,
( ~ duplicatefreeP(X1)
| ~ ssItem(X2)
| ~ ssItem(X3)
| ~ ssList(X4)
| ~ ssList(X5)
| ~ ssList(X6)
| app(app(X4,cons(X2,X5)),cons(X3,X6)) != X1
| X2 != X3
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_38,negated_conjecture,
app(app(esk54_0,cons(esk52_0,nil)),app(cons(esk52_0,nil),esk55_0)) = esk50_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_27]),c_0_28]),c_0_18])]) ).
cnf(c_0_39,plain,
( cons(X2,X1) = app(cons(X2,nil),X1)
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_40,negated_conjecture,
ssList(esk48_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_41,plain,
( duplicatefreeP(cons(X1,nil))
| ~ ssItem(X1) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_42,negated_conjecture,
( nil = esk50_0
| cons(esk56_0,nil) = esk50_0 ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_43,negated_conjecture,
( nil = esk50_0
| ssItem(esk56_0) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_44,plain,
( ~ duplicatefreeP(app(app(X1,cons(X2,X3)),cons(X2,X4)))
| ~ ssList(app(app(X1,cons(X2,X3)),cons(X2,X4)))
| ~ ssList(X4)
| ~ ssList(X3)
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_37])]) ).
cnf(c_0_45,negated_conjecture,
app(app(esk54_0,cons(esk52_0,nil)),cons(esk52_0,esk55_0)) = esk50_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_24]),c_0_18])]) ).
cnf(c_0_46,negated_conjecture,
ssList(esk50_0),
inference(rw,[status(thm)],[c_0_40,c_0_14]) ).
cnf(c_0_47,negated_conjecture,
( esk50_0 = nil
| duplicatefreeP(esk50_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_43]) ).
cnf(c_0_48,negated_conjecture,
~ duplicatefreeP(esk50_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_46]),c_0_24]),c_0_28]),c_0_32]),c_0_18])]) ).
cnf(c_0_49,negated_conjecture,
esk50_0 = nil,
inference(sr,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_50,plain,
duplicatefreeP(nil),
inference(split_conjunct,[status(thm)],[ax72]) ).
cnf(c_0_51,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_48,c_0_49]),c_0_50])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SWC165+1 : TPTP v9.2.1. Released v2.4.0.
% 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
% 0.16/0.32 % Computer : n028.cluster.edu
% 0.16/0.32 % Model : x86_64 x86_64
% 0.16/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.32 % Memory : 8042.1875MB
% 0.16/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.32 % CPULimit : 300
% 0.16/0.32 % WCLimit : 300
% 0.16/0.32 % DateTime : Tue May 5 04:30:45 EDT 2026
% 0.16/0.32 % CPUTime :
% 0.16/0.33 % start to proof: theBenchmark
% 1.64/1.84 % Version : CSE_E---1.7
% 1.64/1.84 % Problem : theBenchmark.p
% 1.64/1.84 % SZS status Theorem for theBenchmark.p
% 1.64/1.84 % SZS output start CNFRefutation
% See solution above
% 1.64/1.84 % Total time : 1.372s
%------------------------------------------------------------------------------