%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC048+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 01:02:11 PM UTC 2026
% Result : Theorem 3.29s 1.39s
% Output : Refutation 3.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 4
% Syntax : Number of formulae : 45 ( 8 unt; 0 def)
% Number of atoms : 189 ( 67 equ)
% Maximal formula atoms : 17 ( 4 avg)
% Number of connectives : 229 ( 85 ~; 83 |; 45 &)
% ( 4 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 5 con; 0-0 aty)
% Number of variables : 42 ( 32 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f15,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( neq(X0,X1)
<=> X0 != X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax15) ).
fof(f49,axiom,
! [X0] :
( ssList(X0)
=> rearsegP(X0,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax49) ).
fof(f52,axiom,
! [X0] :
( ssList(X0)
=> ( rearsegP(nil,X0)
<=> nil = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax52) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( X1 != X3
| X0 != X2
| ( ( nil != X1
| nil = X0 )
& ( ~ neq(X1,nil)
| ? [X4] :
( ssList(X4)
& neq(X4,nil)
& rearsegP(X1,X4)
& rearsegP(X0,X4) ) ) )
| ( ( nil != X3
| nil != X2 )
& ( ~ neq(X2,nil)
| ~ rearsegP(X3,X2) ) ) ) ) ) ) ),
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
| ( ( nil != X1
| nil = X0 )
& ( ~ neq(X1,nil)
| ? [X4] :
( ssList(X4)
& neq(X4,nil)
& rearsegP(X1,X4)
& rearsegP(X0,X4) ) ) )
| ( ( nil != X3
| nil != X2 )
& ( ~ neq(X2,nil)
| ~ rearsegP(X3,X2) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f98,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& ( ( nil = X1
& nil != X0 )
| ( neq(X1,nil)
& ! [X4] :
( ~ ssList(X4)
| ~ neq(X4,nil)
| ~ rearsegP(X1,X4)
| ~ rearsegP(X0,X4) ) ) )
& ( ( nil = X3
& nil = X2 )
| ( neq(X2,nil)
& rearsegP(X3,X2) ) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(ennf_transformation,[],[f97]) ).
fof(f99,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& ( ( nil = X1
& nil != X0 )
| ( neq(X1,nil)
& ! [X4] :
( ~ ssList(X4)
| ~ neq(X4,nil)
| ~ rearsegP(X1,X4)
| ~ rearsegP(X0,X4) ) ) )
& ( ( nil = X3
& nil = X2 )
| ( neq(X2,nil)
& rearsegP(X3,X2) ) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(flattening,[],[f98]) ).
fof(f100,plain,
! [X0] :
( ! [X1] :
( ( neq(X0,X1)
<=> X0 != X1 )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f102,plain,
! [X0] :
( ( rearsegP(nil,X0)
<=> nil = X0 )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f52]) ).
fof(f106,plain,
! [X0] :
( rearsegP(X0,X0)
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f49]) ).
fof(f130,plain,
( sK1 = sK3
& sK0 = sK2
& ( ( nil = sK1
& nil != sK0 )
| ( neq(sK1,nil)
& ! [X4] :
( ~ ssList(X4)
| ~ neq(X4,nil)
| ~ rearsegP(sK1,X4)
| ~ rearsegP(sK0,X4) ) ) )
& ( ( nil = sK3
& nil = sK2 )
| ( neq(sK2,nil)
& rearsegP(sK3,sK2) ) )
& ssList(sK3)
& ssList(sK2)
& ssList(sK1)
& ssList(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f99]) ).
fof(f131,plain,
! [X0] :
( ! [X1] :
( ( ( neq(X0,X1)
| X0 = X1 )
& ( X0 != X1
| ~ neq(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f100]) ).
fof(f133,plain,
! [X0] :
( ( ( rearsegP(nil,X0)
| nil != X0 )
& ( nil = X0
| ~ rearsegP(nil,X0) ) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f102]) ).
fof(f143,plain,
ssList(sK2),
inference(cnf_transformation,[],[f130]) ).
fof(f145,plain,
( rearsegP(sK3,sK2)
| nil = sK2 ),
inference(cnf_transformation,[],[f130]) ).
fof(f147,plain,
( rearsegP(sK3,sK2)
| nil = sK3 ),
inference(cnf_transformation,[],[f130]) ).
fof(f148,plain,
( neq(sK2,nil)
| nil = sK3 ),
inference(cnf_transformation,[],[f130]) ).
fof(f150,plain,
( nil != sK0
| neq(sK1,nil) ),
inference(cnf_transformation,[],[f130]) ).
fof(f151,plain,
! [X4] :
( nil = sK1
| ~ ssList(X4)
| ~ neq(X4,nil)
| ~ rearsegP(sK1,X4)
| ~ rearsegP(sK0,X4) ),
inference(cnf_transformation,[],[f130]) ).
fof(f153,plain,
sK0 = sK2,
inference(cnf_transformation,[],[f130]) ).
fof(f154,plain,
sK1 = sK3,
inference(cnf_transformation,[],[f130]) ).
fof(f155,plain,
! [X0,X1] :
( X0 != X1
| ~ neq(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f131]) ).
fof(f160,plain,
! [X0] :
( nil = X0
| ~ rearsegP(nil,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f133]) ).
fof(f164,plain,
! [X0] :
( rearsegP(X0,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f106]) ).
fof(f193,plain,
! [X4] :
( ~ rearsegP(sK3,X4)
| ~ ssList(X4)
| ~ neq(X4,nil)
| nil = sK3
| ~ rearsegP(sK2,X4) ),
inference(definition_unfolding,[],[f151,f154,f154,f153]) ).
fof(f194,plain,
( nil != sK2
| neq(sK3,nil) ),
inference(definition_unfolding,[],[f150,f153,f154]) ).
fof(f198,plain,
! [X1] :
( ~ neq(X1,X1)
| ~ ssList(X1)
| ~ ssList(X1) ),
inference(equality_resolution,[],[f155]) ).
fof(f206,plain,
! [X1] :
( ~ neq(X1,X1)
| ~ ssList(X1) ),
inference(duplicate_literal_removal,[],[f198]) ).
fof(f207,plain,
( ~ ssList(sK2)
| ~ neq(sK2,nil)
| nil = sK3
| ~ rearsegP(sK2,sK2)
| nil = sK3 ),
inference(resolution,[],[f193,f147]) ).
fof(f209,plain,
( ~ ssList(sK2)
| ~ neq(sK2,nil)
| nil = sK3
| ~ rearsegP(sK2,sK2) ),
inference(duplicate_literal_removal,[],[f207]) ).
fof(f211,plain,
( ~ ssList(sK2)
| nil = sK3
| ~ rearsegP(sK2,sK2) ),
inference(forward_subsumption_resolution,[],[f209,f148]) ).
fof(f213,plain,
( ~ rearsegP(sK2,sK2)
| nil = sK3 ),
inference(forward_subsumption_resolution,[],[f211,f143]) ).
fof(f220,plain,
( ~ ssList(sK2)
| nil = sK3 ),
inference(resolution,[],[f164,f213]) ).
fof(f222,plain,
nil = sK3,
inference(forward_subsumption_resolution,[],[f220,f143]) ).
fof(f228,plain,
( sK2 != sK3
| neq(sK3,sK3) ),
inference(superposition,[],[f194,f222]) ).
fof(f236,plain,
! [X0] :
( sK3 = X0
| ~ rearsegP(nil,X0)
| ~ ssList(X0) ),
inference(forward_demodulation,[],[f160,f222]) ).
fof(f237,plain,
! [X0] :
( ~ rearsegP(sK3,X0)
| sK3 = X0
| ~ ssList(X0) ),
inference(forward_demodulation,[],[f236,f222]) ).
fof(f239,plain,
( sK2 = sK3
| ~ ssList(sK2)
| nil = sK2 ),
inference(resolution,[],[f237,f145]) ).
fof(f245,plain,
( sK2 = sK3
| nil = sK2 ),
inference(forward_subsumption_resolution,[],[f239,f143]) ).
fof(f246,plain,
( sK2 = sK3
| sK2 = sK3 ),
inference(forward_demodulation,[],[f245,f222]) ).
fof(f247,plain,
sK2 = sK3,
inference(duplicate_literal_removal,[],[f246]) ).
fof(f254,plain,
( sK2 != sK2
| neq(sK2,sK2) ),
inference(superposition,[],[f228,f247]) ).
fof(f262,plain,
neq(sK2,sK2),
inference(trivial_inequality_removal,[],[f254]) ).
fof(f269,plain,
~ ssList(sK2),
inference(resolution,[],[f262,f206]) ).
fof(f271,plain,
$false,
inference(forward_subsumption_resolution,[],[f269,f143]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC048+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.42 % Computer : n004.cluster.edu
% 0.13/0.42 % Model : x86_64 x86_64
% 0.13/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.42 % Memory : 8046.5625MB
% 0.13/0.42 % OS : Linux 6.8.0-71-generic
% 0.13/0.42 % CPULimit : 300
% 0.13/0.42 % WCLimit : 300
% 0.13/0.42 % DateTime : Mon Sep 28 07:36:08 UTC 2026
% 0.13/0.42 % CPUTime :
% 0.13/0.42 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.45 Running first-order theorem proving
% 0.13/0.45 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
% 3.29/1.39 % (183527)Detected formulas, will run a generic FOF schedule.
% 3.29/1.39 % (183534)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=3086694832:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.29/1.39 % (183536)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1248839367:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.29/1.39 % (183535)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=121447809:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.29/1.39 % (183532)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=3461232152:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.29/1.39 % (183537)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=247019616:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.29/1.39 % (183533)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=604149332:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.29/1.39 % (183536)First to succeed.
% 3.29/1.39 % (183535)Also succeeded, but the first one will report.
% 3.29/1.39 % (183536)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-183527"
% 3.29/1.39 % (183537)Also succeeded, but the first one will report.
% 3.29/1.39 % (183538)dis-21_1_sil=8000:lcm=predicate:random_seed=2192493068: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)
% 3.29/1.39 % (183538)Instruction limit reached!
% 3.29/1.39 % (183538)------------------------------
% 3.29/1.39 % (183538)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.29/1.39 % (183538)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.29/1.39 % (183538)CaDiCaL version: 2.1.3
% 3.29/1.39 % (183538)Termination reason: Instruction limit
% 3.29/1.39 % (183538)Termination phase: Saturation
% 3.29/1.39 % (183538)Time elapsed: 0.075 s
% 3.29/1.39 % (183538)Peak memory usage: 90 MB
% 3.29/1.39 % (183538)Instructions burned: 129 (million)
% 3.29/1.39 % (183546)lrs+10_1_sil=8000:sp=occurrence:random_seed=1012123476:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.29/1.39 % (183546)Also succeeded, but the first one will report.
% 3.29/1.39 % (183536)Refutation found. Thanks to Tanya!
% 3.29/1.39 % SZS status Theorem for theBenchmark
% 3.29/1.39 % SZS output start Proof for theBenchmark
% See solution above
% 3.29/1.39 % (183536)------------------------------
% 3.29/1.39 % (183536)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.29/1.39 % (183536)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.29/1.39 % (183536)CaDiCaL version: 2.1.3
% 3.29/1.39 % (183536)Termination reason: Refutation
% 3.29/1.39 % (183536)Time elapsed: 0.005 s
% 3.29/1.39 % (183536)Peak memory usage: 88 MB
% 3.29/1.39 % (183536)Instructions burned: 5 (million)
% 3.29/1.39 % (183536)------------------------------
% 3.29/1.39 % (183536)------------------------------
% 3.29/1.39 % (183527)Success in time 0.402 s
% 3.29/1.39 % Vampire exiting
%------------------------------------------------------------------------------