%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWC302+1 : TPTP v9.2.1. Released v2.4.0.
% 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 : n021.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 05:19:05 PM UTC 2026
% Result : Theorem 1.62s 1.80s
% Output : CNFRefutation 1.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 10
% Syntax : Number of formulae : 58 ( 24 unt; 0 def)
% Number of atoms : 228 ( 38 equ)
% Maximal formula atoms : 30 ( 3 avg)
% Number of connectives : 272 ( 102 ~; 98 |; 25 &)
% ( 2 <=>; 45 =>; 0 <=; 0 <~>)
% Maximal formula depth : 26 ( 5 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 10 con; 0-2 aty)
% Number of variables : 88 ( 0 sgn 62 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ~ segmentP(X4,X3)
| ~ totalorderedP(X3)
| ! [X5] :
( ssItem(X5)
=> ! [X6] :
( ssItem(X6)
=> ! [X7] :
( ssList(X7)
=> ! [X8] :
( ssList(X8)
=> ! [X9] :
( ssList(X9)
=> ( app(app(app(app(X7,cons(X5,nil)),X8),cons(X6,nil)),X9) != X1
| ~ lt(X6,X5) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
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/sandbox2/benchmark/Axioms/SWC001+0.ax',ax82) ).
fof(ax16,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> ssList(cons(X2,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax16) ).
fof(ax17,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax17) ).
fof(ax81,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> cons(X2,X1) = app(cons(X2,nil),X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax81) ).
fof(ax26,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ssList(app(X1,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax26) ).
fof(ax93,axiom,
! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ( lt(X1,X2)
<=> ( X1 != X2
& leq(X1,X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax93) ).
fof(ax11,axiom,
! [X1] :
( ssList(X1)
=> ( totalorderedP(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
=> leq(X2,X3) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax11) ).
fof(ax33,axiom,
! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ( lt(X1,X2)
=> ~ lt(X2,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax33) ).
fof(ax29,axiom,
! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ( ( leq(X1,X2)
& leq(X2,X1) )
=> X1 = X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax29) ).
fof(c_0_10,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ~ segmentP(X4,X3)
| ~ totalorderedP(X3)
| ! [X5] :
( ssItem(X5)
=> ! [X6] :
( ssItem(X6)
=> ! [X7] :
( ssList(X7)
=> ! [X8] :
( ssList(X8)
=> ! [X9] :
( ssList(X9)
=> ( app(app(app(app(X7,cons(X5,nil)),X8),cons(X6,nil)),X9) != X1
| ~ lt(X6,X5) ) ) ) ) ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[co1])]) ).
fof(c_0_11,negated_conjecture,
( ssList(esk48_0)
& ssList(esk49_0)
& ssList(esk50_0)
& ssList(esk51_0)
& esk49_0 = esk51_0
& esk48_0 = esk50_0
& segmentP(esk51_0,esk50_0)
& totalorderedP(esk50_0)
& ssItem(esk52_0)
& ssItem(esk53_0)
& ssList(esk54_0)
& ssList(esk55_0)
& ssList(esk56_0)
& app(app(app(app(esk54_0,cons(esk52_0,nil)),esk55_0),cons(esk53_0,nil)),esk56_0) = esk48_0
& lt(esk53_0,esk52_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])])]) ).
cnf(c_0_12,negated_conjecture,
app(app(app(app(esk54_0,cons(esk52_0,nil)),esk55_0),cons(esk53_0,nil)),esk56_0) = esk48_0,
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_13,negated_conjecture,
esk48_0 = esk50_0,
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_14,plain,
! [X437,X438,X439] :
( ~ ssList(X437)
| ~ ssList(X438)
| ~ ssList(X439)
| app(app(X437,X438),X439) = app(X437,app(X438,X439)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax82])])]) ).
cnf(c_0_15,negated_conjecture,
app(app(app(app(esk54_0,cons(esk52_0,nil)),esk55_0),cons(esk53_0,nil)),esk56_0) = esk50_0,
inference(rw,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_16,plain,
( app(app(X1,X2),X3) = app(X1,app(X2,X3))
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_17,negated_conjecture,
ssList(esk55_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_18,negated_conjecture,
ssList(esk54_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_19,plain,
! [X326,X327] :
( ~ ssList(X326)
| ~ ssItem(X327)
| ssList(cons(X327,X326)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax16])])]) ).
cnf(c_0_20,negated_conjecture,
( app(app(app(esk54_0,app(cons(esk52_0,nil),esk55_0)),cons(esk53_0,nil)),esk56_0) = esk50_0
| ~ ssList(cons(esk52_0,nil)) ),
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])]) ).
cnf(c_0_21,plain,
( ssList(cons(X2,X1))
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_22,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[ax17]) ).
cnf(c_0_23,negated_conjecture,
ssItem(esk52_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_24,plain,
! [X435,X436] :
( ~ ssList(X435)
| ~ ssItem(X436)
| cons(X436,X435) = app(cons(X436,nil),X435) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax81])])]) ).
cnf(c_0_25,negated_conjecture,
app(app(app(esk54_0,app(cons(esk52_0,nil),esk55_0)),cons(esk53_0,nil)),esk56_0) = esk50_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22]),c_0_23])]) ).
cnf(c_0_26,plain,
( cons(X2,X1) = app(cons(X2,nil),X1)
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_27,negated_conjecture,
app(app(app(esk54_0,cons(esk52_0,esk55_0)),cons(esk53_0,nil)),esk56_0) = esk50_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_17]),c_0_23])]) ).
cnf(c_0_28,negated_conjecture,
ssList(esk56_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_29,negated_conjecture,
( app(app(esk54_0,cons(esk52_0,esk55_0)),app(cons(esk53_0,nil),esk56_0)) = esk50_0
| ~ ssList(app(esk54_0,cons(esk52_0,esk55_0)))
| ~ ssList(cons(esk53_0,nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_27]),c_0_28])]) ).
cnf(c_0_30,negated_conjecture,
ssItem(esk53_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_31,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])])]) ).
cnf(c_0_32,negated_conjecture,
( app(app(esk54_0,cons(esk52_0,esk55_0)),app(cons(esk53_0,nil),esk56_0)) = esk50_0
| ~ ssList(app(esk54_0,cons(esk52_0,esk55_0))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_21]),c_0_22]),c_0_30])]) ).
cnf(c_0_33,plain,
( ssList(app(X1,X2))
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
fof(c_0_34,plain,
! [X459,X460] :
( ( X459 != X460
| ~ lt(X459,X460)
| ~ ssItem(X460)
| ~ ssItem(X459) )
& ( leq(X459,X460)
| ~ lt(X459,X460)
| ~ ssItem(X460)
| ~ ssItem(X459) )
& ( X459 = X460
| ~ leq(X459,X460)
| lt(X459,X460)
| ~ ssItem(X460)
| ~ ssItem(X459) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax93])])])]) ).
fof(c_0_35,plain,
! [X282,X283,X284,X285,X286,X287] :
( ( ~ totalorderedP(X282)
| ~ ssItem(X283)
| ~ ssItem(X284)
| ~ ssList(X285)
| ~ ssList(X286)
| ~ ssList(X287)
| app(app(X285,cons(X283,X286)),cons(X284,X287)) != X282
| leq(X283,X284)
| ~ ssList(X282) )
& ( ssItem(esk25_1(X282))
| totalorderedP(X282)
| ~ ssList(X282) )
& ( ssItem(esk26_1(X282))
| totalorderedP(X282)
| ~ ssList(X282) )
& ( ssList(esk27_1(X282))
| totalorderedP(X282)
| ~ ssList(X282) )
& ( ssList(esk28_1(X282))
| totalorderedP(X282)
| ~ ssList(X282) )
& ( ssList(esk29_1(X282))
| totalorderedP(X282)
| ~ ssList(X282) )
& ( app(app(esk27_1(X282),cons(esk25_1(X282),esk28_1(X282))),cons(esk26_1(X282),esk29_1(X282))) = X282
| totalorderedP(X282)
| ~ ssList(X282) )
& ( ~ leq(esk25_1(X282),esk26_1(X282))
| totalorderedP(X282)
| ~ ssList(X282) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax11])])])])]) ).
cnf(c_0_36,negated_conjecture,
( app(app(esk54_0,cons(esk52_0,esk55_0)),app(cons(esk53_0,nil),esk56_0)) = esk50_0
| ~ ssList(cons(esk52_0,esk55_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_18])]) ).
fof(c_0_37,plain,
! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ( lt(X1,X2)
=> ~ lt(X2,X1) ) ) ),
inference(fof_simplification,[status(thm)],[ax33]) ).
fof(c_0_38,plain,
! [X351,X352] :
( ~ ssItem(X351)
| ~ ssItem(X352)
| ~ leq(X351,X352)
| ~ leq(X352,X351)
| X351 = X352 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax29])])]) ).
cnf(c_0_39,plain,
( leq(X1,X2)
| ~ lt(X1,X2)
| ~ ssItem(X2)
| ~ ssItem(X1) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_40,negated_conjecture,
lt(esk53_0,esk52_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_41,plain,
( leq(X2,X3)
| ~ totalorderedP(X1)
| ~ ssItem(X2)
| ~ ssItem(X3)
| ~ ssList(X4)
| ~ ssList(X5)
| ~ ssList(X6)
| app(app(X4,cons(X2,X5)),cons(X3,X6)) != X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_42,negated_conjecture,
app(app(esk54_0,cons(esk52_0,esk55_0)),app(cons(esk53_0,nil),esk56_0)) = esk50_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_21]),c_0_17]),c_0_23])]) ).
cnf(c_0_43,negated_conjecture,
ssList(esk48_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_44,plain,
! [X359,X360] :
( ~ ssItem(X359)
| ~ ssItem(X360)
| ~ lt(X359,X360)
| ~ lt(X360,X359) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_37])])]) ).
cnf(c_0_45,plain,
( X1 = X2
| ~ ssItem(X1)
| ~ ssItem(X2)
| ~ leq(X1,X2)
| ~ leq(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_46,negated_conjecture,
leq(esk53_0,esk52_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_23]),c_0_30])]) ).
cnf(c_0_47,plain,
( leq(X1,X2)
| ~ totalorderedP(app(app(X3,cons(X1,X4)),cons(X2,X5)))
| ~ ssList(app(app(X3,cons(X1,X4)),cons(X2,X5)))
| ~ ssList(X5)
| ~ ssList(X4)
| ~ ssList(X3)
| ~ ssItem(X2)
| ~ ssItem(X1) ),
inference(er,[status(thm)],[c_0_41]) ).
cnf(c_0_48,negated_conjecture,
app(app(esk54_0,cons(esk52_0,esk55_0)),cons(esk53_0,esk56_0)) = esk50_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_26]),c_0_28]),c_0_30])]) ).
cnf(c_0_49,negated_conjecture,
totalorderedP(esk50_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_50,negated_conjecture,
ssList(esk50_0),
inference(rw,[status(thm)],[c_0_43,c_0_13]) ).
cnf(c_0_51,plain,
( ~ ssItem(X1)
| ~ ssItem(X2)
| ~ lt(X1,X2)
| ~ lt(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_52,negated_conjecture,
( esk53_0 = esk52_0
| ~ leq(esk52_0,esk53_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_30]),c_0_23])]) ).
cnf(c_0_53,negated_conjecture,
leq(esk52_0,esk53_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(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_49]),c_0_50]),c_0_28]),c_0_17]),c_0_18]),c_0_30]),c_0_23])]) ).
cnf(c_0_54,negated_conjecture,
~ lt(esk52_0,esk53_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_40]),c_0_30]),c_0_23])]) ).
cnf(c_0_55,negated_conjecture,
esk53_0 = esk52_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_52,c_0_53])]) ).
cnf(c_0_56,negated_conjecture,
~ lt(esk52_0,esk52_0),
inference(rw,[status(thm)],[c_0_54,c_0_55]) ).
cnf(c_0_57,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_40,c_0_55]),c_0_56]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWC302+1 : TPTP v9.2.1. Released v2.4.0.
% 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
% 0.16/0.33 % Computer : n021.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 04:43:55 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.35 % start to proof: theBenchmark
% 1.62/1.80 % Version : CSE_E---1.7
% 1.62/1.80 % Problem : theBenchmark.p
% 1.62/1.80 % SZS status Theorem for theBenchmark.p
% 1.62/1.80 % SZS output start CNFRefutation
% See solution above
% 1.62/1.80 % Total time : 1.374s
%------------------------------------------------------------------------------