%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC095+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 : n026.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 3.35s 1.36s
% Output : Refutation 3.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 3
% Syntax : Number of formulae : 23 ( 12 unt; 2 def)
% Number of atoms : 105 ( 32 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 129 ( 47 ~; 42 |; 30 &)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 7 con; 0-2 aty)
% Number of variables : 42 ( 29 !; 13 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ~ ssList(X3)
| X1 != X3
| X0 != X2
| ? [X4] :
( ssList(X4)
& ? [X5] :
( ssList(X5)
& ? [X6] :
( ssList(X6)
& app(app(X4,X5),X6) = X0
& app(X4,X6) = X1 ) ) )
| ! [X7] :
( ssList(X7)
=> ! [X8] :
( ssList(X8)
=> ! [X9] :
( ~ ssList(X9)
| app(app(X7,X8),X9) != X2
| app(X7,X9) != X3 ) ) ) ) ) ) ),
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
| ? [X4] :
( ssList(X4)
& ? [X5] :
( ssList(X5)
& ? [X6] :
( ssList(X6)
& app(app(X4,X5),X6) = X0
& app(X4,X6) = X1 ) ) )
| ! [X7] :
( ssList(X7)
=> ! [X8] :
( ssList(X8)
=> ! [X9] :
( ~ ssList(X9)
| app(app(X7,X8),X9) != X2
| app(X7,X9) != X3 ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f100,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ssList(X3)
& X1 = X3
& X0 = X2
& ! [X4] :
( ~ ssList(X4)
| ! [X5] :
( ~ ssList(X5)
| ! [X6] :
( ~ ssList(X6)
| app(app(X4,X5),X6) != X0
| app(X4,X6) != X1 ) ) )
& ? [X7] :
( ? [X8] :
( ? [X9] :
( ssList(X9)
& app(app(X7,X8),X9) = X2
& app(X7,X9) = X3 )
& ssList(X8) )
& ssList(X7) ) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(ennf_transformation,[],[f97]) ).
fof(f110,plain,
( ssList(sK3)
& sK1 = sK3
& sK0 = sK2
& ! [X4] :
( ~ ssList(X4)
| ! [X5] :
( ~ ssList(X5)
| ! [X6] :
( ~ ssList(X6)
| app(app(X4,X5),X6) != sK0
| app(X4,X6) != sK1 ) ) )
& ssList(sK6)
& sK2 = app(app(sK4,sK5),sK6)
& sK3 = app(sK4,sK6)
& ssList(sK5)
& ssList(sK4)
& ssList(sK2)
& ssList(sK1)
& ssList(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5,sK6]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X7,sK4),skolemize(X8,sK5),skolemize(X9,sK6)],[f100]) ).
fof(f116,plain,
ssList(sK4),
inference(cnf_transformation,[],[f110]) ).
fof(f117,plain,
ssList(sK5),
inference(cnf_transformation,[],[f110]) ).
fof(f118,plain,
sK3 = app(sK4,sK6),
inference(cnf_transformation,[],[f110]) ).
fof(f119,plain,
sK2 = app(app(sK4,sK5),sK6),
inference(cnf_transformation,[],[f110]) ).
fof(f120,plain,
ssList(sK6),
inference(cnf_transformation,[],[f110]) ).
fof(f121,plain,
! [X6,X4,X5] :
( ~ ssList(X4)
| ~ ssList(X5)
| ~ ssList(X6)
| app(app(X4,X5),X6) != sK0
| app(X4,X6) != sK1 ),
inference(cnf_transformation,[],[f110]) ).
fof(f122,plain,
sK0 = sK2,
inference(cnf_transformation,[],[f110]) ).
fof(f123,plain,
sK1 = sK3,
inference(cnf_transformation,[],[f110]) ).
fof(f134,plain,
! [X6,X4,X5] :
( ~ ssList(X4)
| ~ ssList(X5)
| ~ ssList(X6)
| app(app(X4,X5),X6) != sK2
| app(X4,X6) != sK3 ),
inference(definition_unfolding,[],[f121,f122,f123]) ).
fof(f137,definition,
~ sP7(sK2),
introduced(definition,[new_symbols(definition,[sP7])],[inequality_splitting_name_introduction]) ).
fof(f138,definition,
~ sP8(sK3),
introduced(definition,[new_symbols(definition,[sP8])],[inequality_splitting_name_introduction]) ).
fof(f139,plain,
! [X6,X4,X5] :
( sP7(app(app(X4,X5),X6))
| ~ ssList(X5)
| ~ ssList(X6)
| ~ ssList(X4)
| sP8(app(X4,X6)) ),
inference(inequality_splitting,[],[f134,f138,f137]) ).
fof(f289,plain,
( sP7(sK2)
| ~ ssList(sK5)
| ~ ssList(sK6)
| ~ ssList(sK4)
| sP8(app(sK4,sK6)) ),
inference(superposition,[],[f139,f119]) ).
fof(f300,plain,
( ~ ssList(sK5)
| ~ ssList(sK6)
| ~ ssList(sK4)
| sP8(app(sK4,sK6)) ),
inference(forward_subsumption_resolution,[],[f289,f137]) ).
fof(f334,plain,
( ~ ssList(sK6)
| ~ ssList(sK4)
| sP8(app(sK4,sK6)) ),
inference(forward_subsumption_resolution,[],[f300,f117]) ).
fof(f336,plain,
( ~ ssList(sK4)
| sP8(app(sK4,sK6)) ),
inference(forward_subsumption_resolution,[],[f334,f120]) ).
fof(f337,plain,
sP8(app(sK4,sK6)),
inference(forward_subsumption_resolution,[],[f336,f116]) ).
fof(f338,plain,
sP8(sK3),
inference(forward_demodulation,[],[f337,f118]) ).
fof(f339,plain,
$false,
inference(forward_subsumption_resolution,[],[f338,f138]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC095+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n026.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Mon Sep 28 07:53:31 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 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
% 3.35/1.36 % (3682460)Detected formulas, will run a generic FOF schedule.
% 3.35/1.36 % (3682467)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=960327070:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.35/1.36 % (3682468)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=4025690830:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.35/1.36 % (3682470)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=4165762929:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.35/1.36 % (3682465)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=2245689681:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.35/1.36 % (3682466)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=255160513:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.35/1.36 % (3682468)First to succeed.
% 3.35/1.36 % (3682468)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3682460"
% 3.35/1.36 % (3682470)Also succeeded, but the first one will report.
% 3.35/1.36 % (3682469)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=279401146:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.35/1.36 % (3682471)dis-21_1_sil=8000:lcm=predicate:random_seed=3650256536: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)
% 3.35/1.36 % (3682469)Also succeeded, but the first one will report.
% 3.35/1.36 % (3682471)Also succeeded, but the first one will report.
% 3.35/1.36 % (3682468)Refutation found. Thanks to Tanya!
% 3.35/1.36 % SZS status Theorem for theBenchmark
% 3.35/1.36 % SZS output start Proof for theBenchmark
% See solution above
% 3.35/1.36 % (3682468)------------------------------
% 3.35/1.36 % (3682468)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.35/1.36 % (3682468)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.35/1.36 % (3682468)CaDiCaL version: 2.1.3
% 3.35/1.36 % (3682468)Termination reason: Refutation
% 3.35/1.36 % (3682468)Time elapsed: 0.005 s
% 3.35/1.36 % (3682468)Peak memory usage: 89 MB
% 3.35/1.36 % (3682468)Instructions burned: 5 (million)
% 3.35/1.36 % (3682468)------------------------------
% 3.35/1.36 % (3682468)------------------------------
% 3.35/1.36 % (3682460)Success in time 0.408 s
% 3.35/1.36 % Vampire exiting
%------------------------------------------------------------------------------