%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC050+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 : n004.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 01:02:12 PM UTC 2026
% Result : Theorem 2.55s 1.27s
% Output : Refutation 2.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 2
% Syntax : Number of formulae : 29 ( 6 unt; 1 def)
% Number of atoms : 166 ( 14 equ)
% Maximal formula atoms : 17 ( 5 avg)
% Number of connectives : 210 ( 73 ~; 61 |; 66 &)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 8 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-4 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 84 ( 65 !; 19 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( X1 != X3
| X0 != X2
| ( ( ~ neq(X1,nil)
| ? [X4] :
( ssList(X4)
& neq(X4,nil)
& rearsegP(X1,X4)
& rearsegP(X0,X4) )
| ! [X5] :
( ssList(X5)
=> ( ~ neq(X5,nil)
| ~ rearsegP(X3,X5)
| ~ rearsegP(X2,X5) ) ) )
& ( ~ neq(X1,nil)
| neq(X3,nil) ) ) ) ) ) ) ),
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
| ( ( ~ neq(X1,nil)
| ? [X4] :
( ssList(X4)
& neq(X4,nil)
& rearsegP(X1,X4)
& rearsegP(X0,X4) )
| ! [X5] :
( ssList(X5)
=> ( ~ neq(X5,nil)
| ~ rearsegP(X3,X5)
| ~ rearsegP(X2,X5) ) ) )
& ( ~ neq(X1,nil)
| neq(X3,nil) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f98,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& ( ( neq(X1,nil)
& ! [X4] :
( ~ ssList(X4)
| ~ neq(X4,nil)
| ~ rearsegP(X1,X4)
| ~ rearsegP(X0,X4) )
& ? [X5] :
( neq(X5,nil)
& rearsegP(X3,X5)
& rearsegP(X2,X5)
& ssList(X5) ) )
| ( neq(X1,nil)
& ~ neq(X3,nil) ) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(ennf_transformation,[],[f97]) ).
fof(f99,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& ( ( neq(X1,nil)
& ! [X4] :
( ~ ssList(X4)
| ~ neq(X4,nil)
| ~ rearsegP(X1,X4)
| ~ rearsegP(X0,X4) )
& ? [X5] :
( neq(X5,nil)
& rearsegP(X3,X5)
& rearsegP(X2,X5)
& ssList(X5) ) )
| ( neq(X1,nil)
& ~ neq(X3,nil) ) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(flattening,[],[f98]) ).
fof(f130,definition,
! [X1,X0,X3,X2] :
( ( neq(X1,nil)
& ! [X4] :
( ~ ssList(X4)
| ~ neq(X4,nil)
| ~ rearsegP(X1,X4)
| ~ rearsegP(X0,X4) )
& ? [X5] :
( neq(X5,nil)
& rearsegP(X3,X5)
& rearsegP(X2,X5)
& ssList(X5) ) )
| ~ sP0(X1,X0,X3,X2) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f131,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& ( sP0(X1,X0,X3,X2)
| ( neq(X1,nil)
& ~ neq(X3,nil) ) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(definition_folding,[],[f99,f130]) ).
fof(f132,plain,
! [X1,X0,X3,X2] :
( ( neq(X1,nil)
& ! [X4] :
( ~ ssList(X4)
| ~ neq(X4,nil)
| ~ rearsegP(X1,X4)
| ~ rearsegP(X0,X4) )
& ? [X5] :
( neq(X5,nil)
& rearsegP(X3,X5)
& rearsegP(X2,X5)
& ssList(X5) ) )
| ~ sP0(X1,X0,X3,X2) ),
inference(nnf_transformation,[],[f130]) ).
fof(f133,plain,
! [X0,X1,X2,X3] :
( ( neq(X0,nil)
& ! [X4] :
( ~ ssList(X4)
| ~ neq(X4,nil)
| ~ rearsegP(X0,X4)
| ~ rearsegP(X1,X4) )
& ? [X5] :
( neq(X5,nil)
& rearsegP(X2,X5)
& rearsegP(X3,X5)
& ssList(X5) ) )
| ~ sP0(X0,X1,X2,X3) ),
inference(rectify,[],[f132]) ).
fof(f134,plain,
! [X0,X1,X2,X3] :
( ( neq(X0,nil)
& ! [X4] :
( ~ ssList(X4)
| ~ neq(X4,nil)
| ~ rearsegP(X0,X4)
| ~ rearsegP(X1,X4) )
& neq(sK1(X2,X3),nil)
& rearsegP(X2,sK1(X2,X3))
& rearsegP(X3,sK1(X2,X3))
& ssList(sK1(X2,X3)) )
| ~ sP0(X0,X1,X2,X3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X5,sK1(X2,X3))],[f133]) ).
fof(f135,plain,
( sK3 = sK5
& sK2 = sK4
& ( sP0(sK3,sK2,sK5,sK4)
| ( neq(sK3,nil)
& ~ neq(sK5,nil) ) )
& ssList(sK5)
& ssList(sK4)
& ssList(sK3)
& ssList(sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4,sK5]),skolemize(X0,sK2),skolemize(X1,sK3),skolemize(X2,sK4),skolemize(X3,sK5)],[f131]) ).
fof(f146,plain,
! [X2,X3,X0,X1] :
( ~ sP0(X0,X1,X2,X3)
| ssList(sK1(X2,X3)) ),
inference(cnf_transformation,[],[f134]) ).
fof(f147,plain,
! [X2,X3,X0,X1] :
( rearsegP(X3,sK1(X2,X3))
| ~ sP0(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f134]) ).
fof(f148,plain,
! [X2,X3,X0,X1] :
( rearsegP(X2,sK1(X2,X3))
| ~ sP0(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f134]) ).
fof(f149,plain,
! [X2,X3,X0,X1] :
( neq(sK1(X2,X3),nil)
| ~ sP0(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f134]) ).
fof(f150,plain,
! [X2,X3,X0,X1,X4] :
( ~ sP0(X0,X1,X2,X3)
| ~ neq(X4,nil)
| ~ rearsegP(X0,X4)
| ~ rearsegP(X1,X4)
| ~ ssList(X4) ),
inference(cnf_transformation,[],[f134]) ).
fof(f156,plain,
( sP0(sK3,sK2,sK5,sK4)
| ~ neq(sK5,nil) ),
inference(cnf_transformation,[],[f135]) ).
fof(f157,plain,
( sP0(sK3,sK2,sK5,sK4)
| neq(sK3,nil) ),
inference(cnf_transformation,[],[f135]) ).
fof(f158,plain,
sK2 = sK4,
inference(cnf_transformation,[],[f135]) ).
fof(f159,plain,
sK3 = sK5,
inference(cnf_transformation,[],[f135]) ).
fof(f197,plain,
( sP0(sK5,sK4,sK5,sK4)
| neq(sK5,nil) ),
inference(definition_unfolding,[],[f157,f159,f158,f159]) ).
fof(f198,plain,
( sP0(sK5,sK4,sK5,sK4)
| ~ neq(sK5,nil) ),
inference(definition_unfolding,[],[f156,f159,f158]) ).
fof(f210,plain,
sP0(sK5,sK4,sK5,sK4),
inference(forward_subsumption_resolution,[],[f198,f197]) ).
fof(f332,plain,
! [X0] :
( ~ rearsegP(sK5,X0)
| ~ neq(X0,nil)
| ~ rearsegP(sK4,X0)
| ~ ssList(X0) ),
inference(resolution,[],[f150,f210]) ).
fof(f339,plain,
! [X2,X0,X1] :
( ~ neq(sK1(sK5,X0),nil)
| ~ rearsegP(sK4,sK1(sK5,X0))
| ~ ssList(sK1(sK5,X0))
| ~ sP0(X1,X2,sK5,X0) ),
inference(resolution,[],[f332,f148]) ).
fof(f343,plain,
! [X2,X0,X1] :
( ~ rearsegP(sK4,sK1(sK5,X0))
| ~ ssList(sK1(sK5,X0))
| ~ sP0(X1,X2,sK5,X0) ),
inference(forward_subsumption_resolution,[],[f339,f149]) ).
fof(f348,plain,
! [X2,X0,X1] :
( ~ sP0(X1,X2,sK5,X0)
| ~ rearsegP(sK4,sK1(sK5,X0)) ),
inference(forward_subsumption_resolution,[],[f343,f146]) ).
fof(f528,plain,
~ rearsegP(sK4,sK1(sK5,sK4)),
inference(resolution,[],[f348,f210]) ).
fof(f538,plain,
! [X0,X1] : ~ sP0(X0,X1,sK5,sK4),
inference(resolution,[],[f528,f147]) ).
fof(f545,plain,
$false,
inference(resolution,[],[f538,f210]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC050+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.38 % Computer : n004.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Mon Sep 28 07:37:47 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 2.55/1.27 % (184336)Detected formulas, will run a generic FOF schedule.
% 2.55/1.27 % (184345)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=647076636:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.55/1.27 % (184345)First to succeed.
% 2.55/1.27 % (184345)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-184336"
% 2.55/1.27 % (184341)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=2259368604:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.55/1.27 % (184342)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=1453456482:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.55/1.27 % (184344)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2502885568:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.55/1.27 % (184343)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=3024362378:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.55/1.27 % (184344)Also succeeded, but the first one will report.
% 2.55/1.27 % (184347)dis-21_1_sil=8000:lcm=predicate:random_seed=4226742482: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)
% 2.55/1.27 % (184346)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3346433858:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.55/1.27 % (184347)Instruction limit reached!
% 2.55/1.27 % (184347)------------------------------
% 2.55/1.27 % (184347)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.55/1.27 % (184347)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.55/1.27 % (184347)CaDiCaL version: 2.1.3
% 2.55/1.27 % (184347)Termination reason: Instruction limit
% 2.55/1.27 % (184347)Termination phase: Saturation
% 2.55/1.27 % (184347)Time elapsed: 0.074 s
% 2.55/1.27 % (184347)Peak memory usage: 90 MB
% 2.55/1.27 % (184347)Instructions burned: 130 (million)
% 2.55/1.27 % (184346)Instruction limit reached!
% 2.55/1.27 % (184346)------------------------------
% 2.55/1.27 % (184346)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.55/1.27 % (184346)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.55/1.27 % (184346)CaDiCaL version: 2.1.3
% 2.55/1.27 % (184346)Termination reason: Instruction limit
% 2.55/1.27 % (184346)Termination phase: Saturation
% 2.55/1.27 % (184346)Time elapsed: 0.091 s
% 2.55/1.27 % (184346)Peak memory usage: 90 MB
% 2.55/1.27 % (184346)Instructions burned: 140 (million)
% 2.55/1.27 % (184345)Refutation found. Thanks to Tanya!
% 2.55/1.27 % SZS status Theorem for theBenchmark
% 2.55/1.27 % SZS output start Proof for theBenchmark
% See solution above
% 2.55/1.27 % (184345)------------------------------
% 2.55/1.27 % (184345)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.55/1.27 % (184345)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.55/1.27 % (184345)CaDiCaL version: 2.1.3
% 2.55/1.27 % (184345)Termination reason: Refutation
% 2.55/1.27 % (184345)Time elapsed: 0.005 s
% 2.55/1.27 % (184345)Peak memory usage: 88 MB
% 2.55/1.27 % (184345)Instructions burned: 12 (million)
% 2.55/1.27 % (184345)------------------------------
% 2.55/1.27 % (184345)------------------------------
% 2.55/1.27 % (184336)Success in time 0.29 s
% 2.55/1.27 % Vampire exiting
%------------------------------------------------------------------------------