%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC096+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n013.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 01:02:25 PM UTC 2026
% Result : Theorem 3.49s 1.38s
% Output : Refutation 3.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 2
% Syntax : Number of formulae : 30 ( 6 unt; 1 def)
% Number of atoms : 154 ( 45 equ)
% Maximal formula atoms : 17 ( 5 avg)
% Number of connectives : 199 ( 75 ~; 62 |; 54 &)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 8 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-4 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 113 ( 93 !; 20 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ~ ssList(X3)
| X1 != X3
| X0 != X2
| ( ( ~ neq(X1,nil)
| ? [X4] :
( ssItem(X4)
& ? [X5] :
( ssList(X5)
& cons(X4,nil) = X0
& app(X5,cons(X4,nil)) = X1 ) )
| ! [X6] :
( ssItem(X6)
=> ! [X7] :
( ~ ssList(X7)
| cons(X6,nil) != X2
| app(X7,cons(X6,nil)) != X3 ) ) )
& ( ~ neq(X1,nil)
| neq(X3,nil) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
fof(f97,negated_conjecture,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ~ ssList(X3)
| X1 != X3
| X0 != X2
| ( ( ~ neq(X1,nil)
| ? [X4] :
( ssItem(X4)
& ? [X5] :
( ssList(X5)
& cons(X4,nil) = X0
& app(X5,cons(X4,nil)) = X1 ) )
| ! [X6] :
( ssItem(X6)
=> ! [X7] :
( ~ ssList(X7)
| cons(X6,nil) != X2
| app(X7,cons(X6,nil)) != X3 ) ) )
& ( ~ neq(X1,nil)
| neq(X3,nil) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f98,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ssList(X3)
& X1 = X3
& X0 = X2
& ( ( neq(X1,nil)
& ! [X4] :
( ~ ssItem(X4)
| ! [X5] :
( ~ ssList(X5)
| cons(X4,nil) != X0
| app(X5,cons(X4,nil)) != X1 ) )
& ? [X6] :
( ? [X7] :
( ssList(X7)
& cons(X6,nil) = X2
& app(X7,cons(X6,nil)) = X3 )
& ssItem(X6) ) )
| ( neq(X1,nil)
& ~ neq(X3,nil) ) ) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(ennf_transformation,[],[f97]) ).
fof(f119,definition,
! [X1,X0,X2,X3] :
( ( neq(X1,nil)
& ! [X4] :
( ~ ssItem(X4)
| ! [X5] :
( ~ ssList(X5)
| cons(X4,nil) != X0
| app(X5,cons(X4,nil)) != X1 ) )
& ? [X6] :
( ? [X7] :
( ssList(X7)
& cons(X6,nil) = X2
& app(X7,cons(X6,nil)) = X3 )
& ssItem(X6) ) )
| ~ sP0(X1,X0,X2,X3) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f120,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ssList(X3)
& X1 = X3
& X0 = X2
& ( sP0(X1,X0,X2,X3)
| ( neq(X1,nil)
& ~ neq(X3,nil) ) ) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(definition_folding,[],[f98,f119]) ).
fof(f121,plain,
! [X1,X0,X2,X3] :
( ( neq(X1,nil)
& ! [X4] :
( ~ ssItem(X4)
| ! [X5] :
( ~ ssList(X5)
| cons(X4,nil) != X0
| app(X5,cons(X4,nil)) != X1 ) )
& ? [X6] :
( ? [X7] :
( ssList(X7)
& cons(X6,nil) = X2
& app(X7,cons(X6,nil)) = X3 )
& ssItem(X6) ) )
| ~ sP0(X1,X0,X2,X3) ),
inference(nnf_transformation,[],[f119]) ).
fof(f122,plain,
! [X0,X1,X2,X3] :
( ( neq(X0,nil)
& ! [X4] :
( ~ ssItem(X4)
| ! [X5] :
( ~ ssList(X5)
| cons(X4,nil) != X1
| app(X5,cons(X4,nil)) != X0 ) )
& ? [X6] :
( ? [X7] :
( ssList(X7)
& cons(X6,nil) = X2
& app(X7,cons(X6,nil)) = X3 )
& ssItem(X6) ) )
| ~ sP0(X0,X1,X2,X3) ),
inference(rectify,[],[f121]) ).
fof(f123,plain,
! [X0,X1,X2,X3] :
( ( neq(X0,nil)
& ! [X4] :
( ~ ssItem(X4)
| ! [X5] :
( ~ ssList(X5)
| cons(X4,nil) != X1
| app(X5,cons(X4,nil)) != X0 ) )
& ssList(sK2(X2,X3))
& cons(sK1(X2,X3),nil) = X2
& app(sK2(X2,X3),cons(sK1(X2,X3),nil)) = X3
& ssItem(sK1(X2,X3)) )
| ~ sP0(X0,X1,X2,X3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2]),skolemize(X6,sK1(X2,X3)),skolemize(X7,sK2(X2,X3))],[f122]) ).
fof(f124,plain,
( ssList(sK6)
& sK4 = sK6
& sK3 = sK5
& ( sP0(sK4,sK3,sK5,sK6)
| ( neq(sK4,nil)
& ~ neq(sK6,nil) ) )
& ssList(sK5)
& ssList(sK4)
& ssList(sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4,sK5,sK6]),skolemize(X0,sK3),skolemize(X1,sK4),skolemize(X2,sK5),skolemize(X3,sK6)],[f120]) ).
fof(f131,plain,
! [X2,X3,X0,X1] :
( ~ sP0(X0,X1,X2,X3)
| ssItem(sK1(X2,X3)) ),
inference(cnf_transformation,[],[f123]) ).
fof(f132,plain,
! [X2,X3,X0,X1] :
( app(sK2(X2,X3),cons(sK1(X2,X3),nil)) = X3
| ~ sP0(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f123]) ).
fof(f133,plain,
! [X2,X3,X0,X1] :
( cons(sK1(X2,X3),nil) = X2
| ~ sP0(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f123]) ).
fof(f134,plain,
! [X2,X3,X0,X1] :
( ~ sP0(X0,X1,X2,X3)
| ssList(sK2(X2,X3)) ),
inference(cnf_transformation,[],[f123]) ).
fof(f135,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ ssItem(X4)
| ~ ssList(X5)
| cons(X4,nil) != X1
| app(X5,cons(X4,nil)) != X0
| ~ sP0(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f123]) ).
fof(f140,plain,
( sP0(sK4,sK3,sK5,sK6)
| ~ neq(sK6,nil) ),
inference(cnf_transformation,[],[f124]) ).
fof(f141,plain,
( sP0(sK4,sK3,sK5,sK6)
| neq(sK4,nil) ),
inference(cnf_transformation,[],[f124]) ).
fof(f142,plain,
sK3 = sK5,
inference(cnf_transformation,[],[f124]) ).
fof(f143,plain,
sK4 = sK6,
inference(cnf_transformation,[],[f124]) ).
fof(f172,plain,
( sP0(sK6,sK5,sK5,sK6)
| neq(sK6,nil) ),
inference(definition_unfolding,[],[f141,f143,f142,f143]) ).
fof(f173,plain,
( sP0(sK6,sK5,sK5,sK6)
| ~ neq(sK6,nil) ),
inference(definition_unfolding,[],[f140,f143,f142]) ).
fof(f176,plain,
! [X2,X3,X0,X4,X5] :
( ~ ssItem(X4)
| ~ ssList(X5)
| app(X5,cons(X4,nil)) != X0
| ~ sP0(X0,cons(X4,nil),X2,X3) ),
inference(equality_resolution,[],[f135]) ).
fof(f177,plain,
! [X2,X3,X4,X5] :
( ~ sP0(app(X5,cons(X4,nil)),cons(X4,nil),X2,X3)
| ~ ssList(X5)
| ~ ssItem(X4) ),
inference(equality_resolution,[],[f176]) ).
fof(f185,plain,
sP0(sK6,sK5,sK5,sK6),
inference(forward_subsumption_resolution,[],[f173,f172]) ).
fof(f248,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ sP0(X0,cons(sK1(X1,X0),nil),X2,X3)
| ~ ssList(sK2(X1,X0))
| ~ ssItem(sK1(X1,X0))
| ~ sP0(X4,X5,X1,X0) ),
inference(superposition,[],[f177,f132]) ).
fof(f257,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ sP0(X0,cons(sK1(X1,X0),nil),X2,X3)
| ~ ssItem(sK1(X1,X0))
| ~ sP0(X4,X5,X1,X0) ),
inference(forward_subsumption_resolution,[],[f248,f134]) ).
fof(f258,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ sP0(X0,cons(sK1(X1,X0),nil),X2,X3)
| ~ sP0(X4,X5,X1,X0) ),
inference(forward_subsumption_resolution,[],[f257,f131]) ).
fof(f898,plain,
! [X0,X1] : ~ sP0(X0,cons(sK1(X1,X0),nil),X1,X0),
inference(factoring,[],[f258]) ).
fof(f900,plain,
! [X2,X3,X0,X1] :
( ~ sP0(X2,X3,X0,X1)
| ~ sP0(X1,X0,X0,X1) ),
inference(superposition,[],[f898,f133]) ).
fof(f901,plain,
~ sP0(sK6,sK5,sK5,sK6),
inference(resolution,[],[f900,f185]) ).
fof(f904,plain,
$false,
inference(forward_subsumption_resolution,[],[f901,f185]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC096+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n013.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.39 % DateTime : Mon Sep 28 07:51:18 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.49/1.38 % (1008754)Detected formulas, will run a generic FOF schedule.
% 3.49/1.38 % (1008765)dis-21_1_sil=8000:lcm=predicate:random_seed=3143516790: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)
% 3.49/1.38 % (1008759)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=2007878527:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.49/1.38 % (1008762)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3471575728:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.49/1.38 % (1008760)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=1758880199:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.49/1.38 % (1008761)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=1685055378:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.49/1.38 % (1008764)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1215810747:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.49/1.38 % (1008765)Instruction limit reached!
% 3.49/1.38 % (1008765)------------------------------
% 3.49/1.38 % (1008765)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.49/1.38 % (1008765)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.49/1.38 % (1008765)CaDiCaL version: 2.1.3
% 3.49/1.38 % (1008765)Termination reason: Instruction limit
% 3.49/1.38 % (1008765)Termination phase: Saturation
% 3.49/1.38 % (1008765)Time elapsed: 0.042 s
% 3.49/1.38 % (1008765)Peak memory usage: 90 MB
% 3.49/1.38 % (1008765)Instructions burned: 131 (million)
% 3.49/1.38 % (1008763)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1472592997:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.49/1.38 % (1008763)First to succeed.
% 3.49/1.38 % (1008763)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1008754"
% 3.49/1.38 % (1008762)Instruction limit reached!
% 3.49/1.38 % (1008762)------------------------------
% 3.49/1.38 % (1008762)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.49/1.38 % (1008762)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.49/1.38 % (1008762)CaDiCaL version: 2.1.3
% 3.49/1.38 % (1008762)Termination reason: Instruction limit
% 3.49/1.38 % (1008762)Termination phase: Saturation
% 3.49/1.38 % (1008762)Time elapsed: 0.070 s
% 3.49/1.38 % (1008762)Peak memory usage: 89 MB
% 3.49/1.38 % (1008762)Instructions burned: 109 (million)
% 3.49/1.38 % (1008764)Instruction limit reached!
% 3.49/1.38 % (1008764)------------------------------
% 3.49/1.38 % (1008764)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.49/1.38 % (1008764)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.49/1.38 % (1008764)CaDiCaL version: 2.1.3
% 3.49/1.38 % (1008764)Termination reason: Instruction limit
% 3.49/1.38 % (1008764)Termination phase: Saturation
% 3.49/1.38 % (1008764)Time elapsed: 0.093 s
% 3.49/1.38 % (1008764)Peak memory usage: 90 MB
% 3.49/1.38 % (1008764)Instructions burned: 139 (million)
% 3.49/1.38 % (1008773)lrs+10_1_sil=8000:sp=occurrence:random_seed=2965317477:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 3.49/1.38 % (1008773)Also succeeded, but the first one will report.
% 3.49/1.38 % (1008774)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3624902633:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 3.49/1.38 % (1008776)lrs+1011_1_sil=32000:sp=occurrence:random_seed=62328547:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 3.49/1.38 % (1008763)Refutation found. Thanks to Tanya!
% 3.49/1.38 % SZS status Theorem for theBenchmark
% 3.49/1.38 % SZS output start Proof for theBenchmark
% See solution above
% 3.49/1.38 % (1008763)------------------------------
% 3.49/1.38 % (1008763)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.49/1.38 % (1008763)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.49/1.38 % (1008763)CaDiCaL version: 2.1.3
% 3.49/1.38 % (1008763)Termination reason: Refutation
% 3.49/1.38 % (1008763)Time elapsed: 0.015 s
% 3.49/1.38 % (1008763)Peak memory usage: 88 MB
% 3.49/1.38 % (1008763)Instructions burned: 23 (million)
% 3.49/1.38 % (1008763)------------------------------
% 3.49/1.38 % (1008763)------------------------------
% 3.49/1.38 % (1008754)Success in time 0.427 s
% 3.49/1.38 % Vampire exiting
%------------------------------------------------------------------------------