%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC413+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 01:03:52 PM UTC 2026
% Result : Theorem 1.87s 1.14s
% Output : Refutation 3.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 3
% Syntax : Number of formulae : 52 ( 6 unt; 2 def)
% Number of atoms : 351 ( 90 equ)
% Maximal formula atoms : 28 ( 6 avg)
% Number of connectives : 440 ( 141 ~; 132 |; 128 &)
% ( 0 <=>; 39 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 9 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-4 aty)
% Number of functors : 16 ( 16 usr; 8 con; 0-2 aty)
% Number of variables : 234 ( 158 !; 76 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( X1 != X3
| X0 != X2
| ( ( ? [X4] :
( ssItem(X4)
& ? [X5] :
( ssItem(X5)
& ? [X6] :
( ssList(X6)
& app(app(cons(X4,nil),cons(X5,nil)),X6) = X1
& app(app(cons(X5,nil),cons(X4,nil)),X6) = X0 ) ) )
| ! [X7] :
( ssItem(X7)
=> ! [X8] :
( ssItem(X8)
=> ! [X9] :
( ssList(X9)
=> app(app(cons(X7,nil),cons(X8,nil)),X9) != X1 ) ) )
| ! [X10] :
( ssItem(X10)
=> ! [X11] :
( ssItem(X11)
=> ! [X12] :
( ssList(X12)
=> ( app(app(cons(X10,nil),cons(X11,nil)),X12) != X3
| app(app(cons(X11,nil),cons(X10,nil)),X12) != X2 ) ) ) ) )
& ( ? [X13] :
( ssItem(X13)
& ? [X14] :
( ssItem(X14)
& ? [X15] :
( ssList(X15)
& app(app(cons(X13,nil),cons(X14,nil)),X15) = X3 ) ) )
| ! [X7] :
( ssItem(X7)
=> ! [X8] :
( ssItem(X8)
=> ! [X9] :
( ssList(X9)
=> app(app(cons(X7,nil),cons(X8,nil)),X9) != X1 ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
fof(f97,negated_conjecture,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( X1 != X3
| X0 != X2
| ( ( ? [X4] :
( ssItem(X4)
& ? [X5] :
( ssItem(X5)
& ? [X6] :
( ssList(X6)
& app(app(cons(X4,nil),cons(X5,nil)),X6) = X1
& app(app(cons(X5,nil),cons(X4,nil)),X6) = X0 ) ) )
| ! [X7] :
( ssItem(X7)
=> ! [X8] :
( ssItem(X8)
=> ! [X9] :
( ssList(X9)
=> app(app(cons(X7,nil),cons(X8,nil)),X9) != X1 ) ) )
| ! [X10] :
( ssItem(X10)
=> ! [X11] :
( ssItem(X11)
=> ! [X12] :
( ssList(X12)
=> ( app(app(cons(X10,nil),cons(X11,nil)),X12) != X3
| app(app(cons(X11,nil),cons(X10,nil)),X12) != X2 ) ) ) ) )
& ( ? [X13] :
( ssItem(X13)
& ? [X14] :
( ssItem(X14)
& ? [X15] :
( ssList(X15)
& app(app(cons(X13,nil),cons(X14,nil)),X15) = X3 ) ) )
| ! [X7] :
( ssItem(X7)
=> ! [X8] :
( ssItem(X8)
=> ! [X9] :
( ssList(X9)
=> app(app(cons(X7,nil),cons(X8,nil)),X9) != X1 ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f98,plain,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( X1 != X3
| X0 != X2
| ( ( ? [X4] :
( ssItem(X4)
& ? [X5] :
( ssItem(X5)
& ? [X6] :
( ssList(X6)
& app(app(cons(X4,nil),cons(X5,nil)),X6) = X1
& app(app(cons(X5,nil),cons(X4,nil)),X6) = X0 ) ) )
| ! [X7] :
( ssItem(X7)
=> ! [X8] :
( ssItem(X8)
=> ! [X9] :
( ssList(X9)
=> app(app(cons(X7,nil),cons(X8,nil)),X9) != X1 ) ) )
| ! [X10] :
( ssItem(X10)
=> ! [X11] :
( ssItem(X11)
=> ! [X12] :
( ssList(X12)
=> ( app(app(cons(X10,nil),cons(X11,nil)),X12) != X3
| app(app(cons(X11,nil),cons(X10,nil)),X12) != X2 ) ) ) ) )
& ( ? [X13] :
( ssItem(X13)
& ? [X14] :
( ssItem(X14)
& ? [X15] :
( ssList(X15)
& app(app(cons(X13,nil),cons(X14,nil)),X15) = X3 ) ) )
| ! [X16] :
( ssItem(X16)
=> ! [X17] :
( ssItem(X17)
=> ! [X18] :
( ssList(X18)
=> app(app(cons(X16,nil),cons(X17,nil)),X18) != X1 ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f97]) ).
fof(f99,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& ( ( ! [X4] :
( ~ ssItem(X4)
| ! [X5] :
( ~ ssItem(X5)
| ! [X6] :
( ~ ssList(X6)
| app(app(cons(X4,nil),cons(X5,nil)),X6) != X1
| app(app(cons(X5,nil),cons(X4,nil)),X6) != X0 ) ) )
& ? [X7] :
( ? [X8] :
( ? [X9] :
( app(app(cons(X7,nil),cons(X8,nil)),X9) = X1
& ssList(X9) )
& ssItem(X8) )
& ssItem(X7) )
& ? [X10] :
( ? [X11] :
( ? [X12] :
( app(app(cons(X10,nil),cons(X11,nil)),X12) = X3
& app(app(cons(X11,nil),cons(X10,nil)),X12) = X2
& ssList(X12) )
& ssItem(X11) )
& ssItem(X10) ) )
| ( ! [X13] :
( ~ ssItem(X13)
| ! [X14] :
( ~ ssItem(X14)
| ! [X15] :
( ~ ssList(X15)
| app(app(cons(X13,nil),cons(X14,nil)),X15) != X3 ) ) )
& ? [X16] :
( ? [X17] :
( ? [X18] :
( app(app(cons(X16,nil),cons(X17,nil)),X18) = X1
& ssList(X18) )
& ssItem(X17) )
& ssItem(X16) ) ) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(ennf_transformation,[],[f98]) ).
fof(f100,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& ( ( ! [X4] :
( ~ ssItem(X4)
| ! [X5] :
( ~ ssItem(X5)
| ! [X6] :
( ~ ssList(X6)
| app(app(cons(X4,nil),cons(X5,nil)),X6) != X1
| app(app(cons(X5,nil),cons(X4,nil)),X6) != X0 ) ) )
& ? [X7] :
( ? [X8] :
( ? [X9] :
( app(app(cons(X7,nil),cons(X8,nil)),X9) = X1
& ssList(X9) )
& ssItem(X8) )
& ssItem(X7) )
& ? [X10] :
( ? [X11] :
( ? [X12] :
( app(app(cons(X10,nil),cons(X11,nil)),X12) = X3
& app(app(cons(X11,nil),cons(X10,nil)),X12) = X2
& ssList(X12) )
& ssItem(X11) )
& ssItem(X10) ) )
| ( ! [X13] :
( ~ ssItem(X13)
| ! [X14] :
( ~ ssItem(X14)
| ! [X15] :
( ~ ssList(X15)
| app(app(cons(X13,nil),cons(X14,nil)),X15) != X3 ) ) )
& ? [X16] :
( ? [X17] :
( ? [X18] :
( app(app(cons(X16,nil),cons(X17,nil)),X18) = X1
& ssList(X18) )
& ssItem(X17) )
& ssItem(X16) ) ) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(flattening,[],[f99]) ).
fof(f119,definition,
! [X3,X2] :
( ? [X10] :
( ? [X11] :
( ? [X12] :
( app(app(cons(X10,nil),cons(X11,nil)),X12) = X3
& app(app(cons(X11,nil),cons(X10,nil)),X12) = X2
& ssList(X12) )
& ssItem(X11) )
& ssItem(X10) )
| ~ sP0(X3,X2) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f120,definition,
! [X1,X0,X2,X3] :
( ( ! [X4] :
( ~ ssItem(X4)
| ! [X5] :
( ~ ssItem(X5)
| ! [X6] :
( ~ ssList(X6)
| app(app(cons(X4,nil),cons(X5,nil)),X6) != X1
| app(app(cons(X5,nil),cons(X4,nil)),X6) != X0 ) ) )
& ? [X7] :
( ? [X8] :
( ? [X9] :
( app(app(cons(X7,nil),cons(X8,nil)),X9) = X1
& ssList(X9) )
& ssItem(X8) )
& ssItem(X7) )
& sP0(X3,X2) )
| ~ sP1(X1,X0,X2,X3) ),
introduced(definition,[new_symbols(definition,[sP1])],[predicate_definition_introduction]) ).
fof(f121,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& ( sP1(X1,X0,X2,X3)
| ( ! [X13] :
( ~ ssItem(X13)
| ! [X14] :
( ~ ssItem(X14)
| ! [X15] :
( ~ ssList(X15)
| app(app(cons(X13,nil),cons(X14,nil)),X15) != X3 ) ) )
& ? [X16] :
( ? [X17] :
( ? [X18] :
( app(app(cons(X16,nil),cons(X17,nil)),X18) = X1
& ssList(X18) )
& ssItem(X17) )
& ssItem(X16) ) ) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(definition_folding,[],[f100,f120,f119]) ).
fof(f122,plain,
! [X1,X0,X2,X3] :
( ( ! [X4] :
( ~ ssItem(X4)
| ! [X5] :
( ~ ssItem(X5)
| ! [X6] :
( ~ ssList(X6)
| app(app(cons(X4,nil),cons(X5,nil)),X6) != X1
| app(app(cons(X5,nil),cons(X4,nil)),X6) != X0 ) ) )
& ? [X7] :
( ? [X8] :
( ? [X9] :
( app(app(cons(X7,nil),cons(X8,nil)),X9) = X1
& ssList(X9) )
& ssItem(X8) )
& ssItem(X7) )
& sP0(X3,X2) )
| ~ sP1(X1,X0,X2,X3) ),
inference(nnf_transformation,[],[f120]) ).
fof(f123,plain,
! [X0,X1,X2,X3] :
( ( ! [X4] :
( ~ ssItem(X4)
| ! [X5] :
( ~ ssItem(X5)
| ! [X6] :
( ~ ssList(X6)
| app(app(cons(X4,nil),cons(X5,nil)),X6) != X0
| app(app(cons(X5,nil),cons(X4,nil)),X6) != X1 ) ) )
& ? [X7] :
( ? [X8] :
( ? [X9] :
( app(app(cons(X7,nil),cons(X8,nil)),X9) = X0
& ssList(X9) )
& ssItem(X8) )
& ssItem(X7) )
& sP0(X3,X2) )
| ~ sP1(X0,X1,X2,X3) ),
inference(rectify,[],[f122]) ).
fof(f124,plain,
! [X0,X1,X2,X3] :
( ( ! [X4] :
( ~ ssItem(X4)
| ! [X5] :
( ~ ssItem(X5)
| ! [X6] :
( ~ ssList(X6)
| app(app(cons(X4,nil),cons(X5,nil)),X6) != X0
| app(app(cons(X5,nil),cons(X4,nil)),X6) != X1 ) ) )
& app(app(cons(sK2(X0),nil),cons(sK3(X0),nil)),sK4(X0)) = X0
& ssList(sK4(X0))
& ssItem(sK3(X0))
& ssItem(sK2(X0))
& sP0(X3,X2) )
| ~ sP1(X0,X1,X2,X3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4]),skolemize(X7,sK2(X0)),skolemize(X8,sK3(X0)),skolemize(X9,sK4(X0))],[f123]) ).
fof(f125,plain,
! [X3,X2] :
( ? [X10] :
( ? [X11] :
( ? [X12] :
( app(app(cons(X10,nil),cons(X11,nil)),X12) = X3
& app(app(cons(X11,nil),cons(X10,nil)),X12) = X2
& ssList(X12) )
& ssItem(X11) )
& ssItem(X10) )
| ~ sP0(X3,X2) ),
inference(nnf_transformation,[],[f119]) ).
fof(f126,plain,
! [X0,X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( app(app(cons(X2,nil),cons(X3,nil)),X4) = X0
& app(app(cons(X3,nil),cons(X2,nil)),X4) = X1
& ssList(X4) )
& ssItem(X3) )
& ssItem(X2) )
| ~ sP0(X0,X1) ),
inference(rectify,[],[f125]) ).
fof(f127,plain,
! [X0,X1] :
( ( app(app(cons(sK5(X0,X1),nil),cons(sK6(X0,X1),nil)),sK7(X0,X1)) = X0
& app(app(cons(sK6(X0,X1),nil),cons(sK5(X0,X1),nil)),sK7(X0,X1)) = X1
& ssList(sK7(X0,X1))
& ssItem(sK6(X0,X1))
& ssItem(sK5(X0,X1)) )
| ~ sP0(X0,X1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5,sK6,sK7]),skolemize(X2,sK5(X0,X1)),skolemize(X3,sK6(X0,X1)),skolemize(X4,sK7(X0,X1))],[f126]) ).
fof(f128,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& ( sP1(X1,X0,X2,X3)
| ( ! [X4] :
( ~ ssItem(X4)
| ! [X5] :
( ~ ssItem(X5)
| ! [X6] :
( ~ ssList(X6)
| app(app(cons(X4,nil),cons(X5,nil)),X6) != X3 ) ) )
& ? [X7] :
( ? [X8] :
( ? [X9] :
( app(app(cons(X7,nil),cons(X8,nil)),X9) = X1
& ssList(X9) )
& ssItem(X8) )
& ssItem(X7) ) ) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(rectify,[],[f121]) ).
fof(f129,plain,
( sK9 = sK11
& sK8 = sK10
& ( sP1(sK9,sK8,sK10,sK11)
| ( ! [X4] :
( ~ ssItem(X4)
| ! [X5] :
( ~ ssItem(X5)
| ! [X6] :
( ~ ssList(X6)
| app(app(cons(X4,nil),cons(X5,nil)),X6) != sK11 ) ) )
& sK9 = app(app(cons(sK12,nil),cons(sK13,nil)),sK14)
& ssList(sK14)
& ssItem(sK13)
& ssItem(sK12) ) )
& ssList(sK11)
& ssList(sK10)
& ssList(sK9)
& ssList(sK8) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8,sK9,sK10,sK11,sK12,sK13,sK14]),skolemize(X0,sK8),skolemize(X1,sK9),skolemize(X2,sK10),skolemize(X3,sK11),skolemize(X7,sK12),skolemize(X8,sK13),skolemize(X9,sK14)],[f128]) ).
fof(f134,plain,
! [X2,X3,X0,X1] :
( ~ sP1(X0,X1,X2,X3)
| sP0(X3,X2) ),
inference(cnf_transformation,[],[f124]) ).
fof(f139,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( ~ ssItem(X4)
| ~ ssItem(X5)
| ~ ssList(X6)
| app(app(cons(X4,nil),cons(X5,nil)),X6) != X0
| app(app(cons(X5,nil),cons(X4,nil)),X6) != X1
| ~ sP1(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f124]) ).
fof(f140,plain,
! [X0,X1] :
( ssItem(sK5(X0,X1))
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f127]) ).
fof(f141,plain,
! [X0,X1] :
( ssItem(sK6(X0,X1))
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f127]) ).
fof(f142,plain,
! [X0,X1] :
( ssList(sK7(X0,X1))
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f127]) ).
fof(f143,plain,
! [X0,X1] :
( app(app(cons(sK6(X0,X1),nil),cons(sK5(X0,X1),nil)),sK7(X0,X1)) = X1
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f127]) ).
fof(f144,plain,
! [X0,X1] :
( app(app(cons(sK5(X0,X1),nil),cons(sK6(X0,X1),nil)),sK7(X0,X1)) = X0
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f127]) ).
fof(f149,plain,
( sP1(sK9,sK8,sK10,sK11)
| ssItem(sK12) ),
inference(cnf_transformation,[],[f129]) ).
fof(f150,plain,
( sP1(sK9,sK8,sK10,sK11)
| ssItem(sK13) ),
inference(cnf_transformation,[],[f129]) ).
fof(f151,plain,
( sP1(sK9,sK8,sK10,sK11)
| ssList(sK14) ),
inference(cnf_transformation,[],[f129]) ).
fof(f152,plain,
( sP1(sK9,sK8,sK10,sK11)
| sK9 = app(app(cons(sK12,nil),cons(sK13,nil)),sK14) ),
inference(cnf_transformation,[],[f129]) ).
fof(f153,plain,
! [X6,X4,X5] :
( sP1(sK9,sK8,sK10,sK11)
| ~ ssItem(X4)
| ~ ssItem(X5)
| ~ ssList(X6)
| app(app(cons(X4,nil),cons(X5,nil)),X6) != sK11 ),
inference(cnf_transformation,[],[f129]) ).
fof(f154,plain,
sK8 = sK10,
inference(cnf_transformation,[],[f129]) ).
fof(f155,plain,
sK9 = sK11,
inference(cnf_transformation,[],[f129]) ).
fof(f179,plain,
! [X6,X4,X5] :
( app(app(cons(X4,nil),cons(X5,nil)),X6) != sK11
| ~ ssItem(X4)
| ~ ssItem(X5)
| ~ ssList(X6)
| sP1(sK11,sK10,sK10,sK11) ),
inference(definition_unfolding,[],[f153,f155,f154]) ).
fof(f180,plain,
( sK11 = app(app(cons(sK12,nil),cons(sK13,nil)),sK14)
| sP1(sK11,sK10,sK10,sK11) ),
inference(definition_unfolding,[],[f152,f155,f154,f155]) ).
fof(f181,plain,
( sP1(sK11,sK10,sK10,sK11)
| ssList(sK14) ),
inference(definition_unfolding,[],[f151,f155,f154]) ).
fof(f182,plain,
( sP1(sK11,sK10,sK10,sK11)
| ssItem(sK13) ),
inference(definition_unfolding,[],[f150,f155,f154]) ).
fof(f183,plain,
( sP1(sK11,sK10,sK10,sK11)
| ssItem(sK12) ),
inference(definition_unfolding,[],[f149,f155,f154]) ).
fof(f186,plain,
! [X2,X3,X1,X6,X4,X5] :
( ~ ssItem(X4)
| ~ ssItem(X5)
| ~ ssList(X6)
| app(app(cons(X5,nil),cons(X4,nil)),X6) != X1
| ~ sP1(app(app(cons(X4,nil),cons(X5,nil)),X6),X1,X2,X3) ),
inference(equality_resolution,[],[f139]) ).
fof(f187,plain,
! [X2,X3,X6,X4,X5] :
( ~ sP1(app(app(cons(X4,nil),cons(X5,nil)),X6),app(app(cons(X5,nil),cons(X4,nil)),X6),X2,X3)
| ~ ssItem(X5)
| ~ ssList(X6)
| ~ ssItem(X4) ),
inference(equality_resolution,[],[f186]) ).
fof(f191,plain,
( sK11 != sK11
| ~ ssItem(sK12)
| ~ ssItem(sK13)
| ~ ssList(sK14)
| sP1(sK11,sK10,sK10,sK11)
| sP1(sK11,sK10,sK10,sK11) ),
inference(superposition,[],[f179,f180]) ).
fof(f192,plain,
( sK11 != sK11
| ~ ssItem(sK12)
| ~ ssItem(sK13)
| ~ ssList(sK14)
| sP1(sK11,sK10,sK10,sK11) ),
inference(duplicate_literal_removal,[],[f191]) ).
fof(f193,plain,
( ~ ssItem(sK12)
| ~ ssItem(sK13)
| ~ ssList(sK14)
| sP1(sK11,sK10,sK10,sK11) ),
inference(trivial_inequality_removal,[],[f192]) ).
fof(f194,plain,
( ~ ssItem(sK13)
| ~ ssList(sK14)
| sP1(sK11,sK10,sK10,sK11) ),
inference(forward_subsumption_resolution,[],[f193,f183]) ).
fof(f195,plain,
( ~ ssList(sK14)
| sP1(sK11,sK10,sK10,sK11) ),
inference(forward_subsumption_resolution,[],[f194,f182]) ).
fof(f196,plain,
sP1(sK11,sK10,sK10,sK11),
inference(forward_subsumption_resolution,[],[f195,f181]) ).
fof(f198,plain,
sP0(sK11,sK10),
inference(resolution,[],[f134,f196]) ).
fof(f703,plain,
! [X2,X3,X0,X1] :
( ~ sP1(app(app(cons(sK5(X1,X0),nil),cons(sK6(X1,X0),nil)),sK7(X1,X0)),X0,X2,X3)
| ~ ssItem(sK6(X1,X0))
| ~ ssList(sK7(X1,X0))
| ~ ssItem(sK5(X1,X0))
| ~ sP0(X1,X0) ),
inference(superposition,[],[f187,f143]) ).
fof(f717,plain,
! [X2,X3,X0,X1] :
( ~ sP1(app(app(cons(sK5(X1,X0),nil),cons(sK6(X1,X0),nil)),sK7(X1,X0)),X0,X2,X3)
| ~ ssList(sK7(X1,X0))
| ~ ssItem(sK5(X1,X0))
| ~ sP0(X1,X0) ),
inference(forward_subsumption_resolution,[],[f703,f141]) ).
fof(f726,plain,
! [X2,X3,X0,X1] :
( ~ sP1(app(app(cons(sK5(X1,X0),nil),cons(sK6(X1,X0),nil)),sK7(X1,X0)),X0,X2,X3)
| ~ ssItem(sK5(X1,X0))
| ~ sP0(X1,X0) ),
inference(forward_subsumption_resolution,[],[f717,f142]) ).
fof(f732,plain,
! [X2,X3,X0,X1] :
( ~ sP1(app(app(cons(sK5(X1,X0),nil),cons(sK6(X1,X0),nil)),sK7(X1,X0)),X0,X2,X3)
| ~ sP0(X1,X0) ),
inference(forward_subsumption_resolution,[],[f726,f140]) ).
fof(f2115,plain,
! [X2,X3,X0,X1] :
( ~ sP1(X0,X1,X2,X3)
| ~ sP0(X0,X1)
| ~ sP0(X0,X1) ),
inference(superposition,[],[f732,f144]) ).
fof(f2117,plain,
! [X2,X3,X0,X1] :
( ~ sP1(X0,X1,X2,X3)
| ~ sP0(X0,X1) ),
inference(duplicate_literal_removal,[],[f2115]) ).
fof(f2140,plain,
~ sP0(sK11,sK10),
inference(resolution,[],[f2117,f196]) ).
fof(f2147,plain,
$false,
inference(forward_subsumption_resolution,[],[f2140,f198]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC413+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n003.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Mon Sep 28 09:33:57 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 Running first-order theorem proving
% 0.09/0.22 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.87/1.14 % (1461204)Detected formulas, will run a generic FOF schedule.
% 1.87/1.14 % (1461212)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1379343065:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 1.87/1.14 % (1461212)Refutation not found, incomplete strategy
% 1.87/1.14 % (1461212)------------------------------
% 1.87/1.14 % (1461212)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.87/1.14 % (1461212)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.87/1.14 % (1461212)CaDiCaL version: 2.1.3
% 1.87/1.14 % (1461212)Termination reason: Refutation not found, incomplete strategy
% 1.87/1.14 % (1461212)Time elapsed: 0.002 s
% 1.87/1.14 % (1461212)Peak memory usage: 88 MB
% 1.87/1.14 % (1461212)Instructions burned: 4 (million)
% 1.87/1.14 % (1461214)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2478028029:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 1.87/1.14 % (1461213)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=860696711:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 1.87/1.14 % (1461211)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=98927205:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 1.87/1.14 % (1461210)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=2003057021:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 1.87/1.14 % (1461209)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=987742844:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 1.87/1.14 % (1461215)dis-21_1_sil=8000:lcm=predicate:random_seed=620995151:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 1.87/1.14 % (1461213)First to succeed.
% 1.87/1.14 % (1461213)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1461204"
% 1.87/1.14 % (1461215)Instruction limit reached!
% 1.87/1.14 % (1461215)------------------------------
% 1.87/1.14 % (1461215)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.87/1.14 % (1461215)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.87/1.14 % (1461215)CaDiCaL version: 2.1.3
% 1.87/1.14 % (1461215)Termination reason: Instruction limit
% 1.87/1.14 % (1461215)Termination phase: Saturation
% 1.87/1.14 % (1461215)Time elapsed: 0.072 s
% 1.87/1.14 % (1461215)Peak memory usage: 90 MB
% 1.87/1.14 % (1461215)Instructions burned: 129 (million)
% 1.87/1.14 % (1461214)Instruction limit reached!
% 1.87/1.14 % (1461214)------------------------------
% 1.87/1.14 % (1461214)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.87/1.14 % (1461214)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.87/1.14 % (1461214)CaDiCaL version: 2.1.3
% 1.87/1.14 % (1461214)Termination reason: Instruction limit
% 1.87/1.14 % (1461214)Termination phase: Saturation
% 1.87/1.14 % (1461214)Time elapsed: 0.087 s
% 1.87/1.14 % (1461214)Peak memory usage: 90 MB
% 1.87/1.14 % (1461214)Instructions burned: 139 (million)
% 1.87/1.14 % (1461212)------------------------------
% 1.87/1.14 % (1461212)------------------------------
% 1.87/1.14 % (1461223)lrs+10_1_sil=8000:sp=occurrence:random_seed=395795775:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 1.87/1.14 % (1461224)lrs+10_1_sil=32000:urr=on:br=off:random_seed=2536072629:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 1.87/1.14 % (1461225)lrs+1011_1_sil=32000:sp=occurrence:random_seed=1152170026:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 1.87/1.14 % (1461213)Refutation found. Thanks to Tanya!
% 1.87/1.14 % SZS status Theorem for theBenchmark
% 1.87/1.14 % SZS output start Proof for theBenchmark
% See solution above
% 3.90/1.23 % (1461213)------------------------------
% 3.90/1.23 % (1461213)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.90/1.23 % (1461213)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.90/1.23 % (1461213)CaDiCaL version: 2.1.3
% 3.90/1.23 % (1461213)Termination reason: Refutation
% 3.90/1.23 % (1461213)Time elapsed: 0.045 s
% 3.90/1.23 % (1461213)Peak memory usage: 89 MB
% 3.90/1.23 % (1461213)Instructions burned: 76 (million)
% 3.90/1.23 % (1461213)------------------------------
% 3.90/1.23 % (1461213)------------------------------
% 3.90/1.23 % (1461204)Success in time 0.472 s
% 3.90/1.23 % Vampire exiting
%------------------------------------------------------------------------------