%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC060+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 : n002.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 01:02:15 PM UTC 2026
% Result : Theorem 2.66s 1.37s
% Output : Refutation 2.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 4
% Syntax : Number of formulae : 44 ( 8 unt; 0 def)
% Number of atoms : 172 ( 61 equ)
% Maximal formula atoms : 17 ( 3 avg)
% Number of connectives : 210 ( 82 ~; 80 |; 34 &)
% ( 4 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 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 : 37 ( 31 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f15,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( neq(X0,X1)
<=> X0 != X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax15) ).
fof(f55,axiom,
! [X0] :
( ssList(X0)
=> segmentP(X0,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax55) ).
fof(f58,axiom,
! [X0] :
( ssList(X0)
=> ( segmentP(nil,X0)
<=> nil = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax58) ).
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)
& segmentP(X1,X4)
& segmentP(X0,X4) ) ) )
| ( ( nil != X3
| nil != X2 )
& ( ~ neq(X2,nil)
| ~ segmentP(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)
& segmentP(X1,X4)
& segmentP(X0,X4) ) ) )
| ( ( nil != X3
| nil != X2 )
& ( ~ neq(X2,nil)
| ~ segmentP(X3,X2) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f98,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ssList(X3)
& X1 = X3
& X0 = X2
& ( ( nil = X1
& nil != X0 )
| ( neq(X1,nil)
& ! [X4] :
( ~ ssList(X4)
| ~ neq(X4,nil)
| ~ segmentP(X1,X4)
| ~ segmentP(X0,X4) ) ) )
& ( ( nil = X3
& nil = X2 )
| ( neq(X2,nil)
& segmentP(X3,X2) ) ) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(ennf_transformation,[],[f97]) ).
fof(f99,plain,
! [X0] :
( ! [X1] :
( ( neq(X0,X1)
<=> X0 != X1 )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f101,plain,
! [X0] :
( ( segmentP(nil,X0)
<=> nil = X0 )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f58]) ).
fof(f105,plain,
! [X0] :
( segmentP(X0,X0)
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f55]) ).
fof(f129,plain,
( ssList(sK3)
& sK1 = sK3
& sK0 = sK2
& ( ( nil = sK1
& nil != sK0 )
| ( neq(sK1,nil)
& ! [X4] :
( ~ ssList(X4)
| ~ neq(X4,nil)
| ~ segmentP(sK1,X4)
| ~ segmentP(sK0,X4) ) ) )
& ( ( nil = sK3
& nil = sK2 )
| ( neq(sK2,nil)
& segmentP(sK3,sK2) ) )
& 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)],[f98]) ).
fof(f130,plain,
! [X0] :
( ! [X1] :
( ( ( neq(X0,X1)
| X0 = X1 )
& ( X0 != X1
| ~ neq(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f99]) ).
fof(f132,plain,
! [X0] :
( ( ( segmentP(nil,X0)
| nil != X0 )
& ( nil = X0
| ~ segmentP(nil,X0) ) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f101]) ).
fof(f142,plain,
ssList(sK2),
inference(cnf_transformation,[],[f129]) ).
fof(f143,plain,
( segmentP(sK3,sK2)
| nil = sK2 ),
inference(cnf_transformation,[],[f129]) ).
fof(f145,plain,
( segmentP(sK3,sK2)
| nil = sK3 ),
inference(cnf_transformation,[],[f129]) ).
fof(f146,plain,
( neq(sK2,nil)
| nil = sK3 ),
inference(cnf_transformation,[],[f129]) ).
fof(f148,plain,
( nil != sK0
| neq(sK1,nil) ),
inference(cnf_transformation,[],[f129]) ).
fof(f149,plain,
! [X4] :
( nil = sK1
| ~ ssList(X4)
| ~ neq(X4,nil)
| ~ segmentP(sK1,X4)
| ~ segmentP(sK0,X4) ),
inference(cnf_transformation,[],[f129]) ).
fof(f151,plain,
sK0 = sK2,
inference(cnf_transformation,[],[f129]) ).
fof(f152,plain,
sK1 = sK3,
inference(cnf_transformation,[],[f129]) ).
fof(f154,plain,
! [X0,X1] :
( X0 != X1
| ~ neq(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f130]) ).
fof(f159,plain,
! [X0] :
( nil = X0
| ~ segmentP(nil,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f132]) ).
fof(f163,plain,
! [X0] :
( segmentP(X0,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f105]) ).
fof(f193,plain,
! [X4] :
( ~ segmentP(sK3,X4)
| ~ ssList(X4)
| ~ neq(X4,nil)
| nil = sK3
| ~ segmentP(sK2,X4) ),
inference(definition_unfolding,[],[f149,f152,f152,f151]) ).
fof(f194,plain,
( nil != sK2
| neq(sK3,nil) ),
inference(definition_unfolding,[],[f148,f151,f152]) ).
fof(f198,plain,
! [X1] :
( ~ neq(X1,X1)
| ~ ssList(X1)
| ~ ssList(X1) ),
inference(equality_resolution,[],[f154]) ).
fof(f206,plain,
! [X1] :
( ~ neq(X1,X1)
| ~ ssList(X1) ),
inference(duplicate_literal_removal,[],[f198]) ).
fof(f207,plain,
( ~ ssList(sK2)
| ~ neq(sK2,nil)
| nil = sK3
| ~ segmentP(sK2,sK2)
| nil = sK3 ),
inference(resolution,[],[f193,f145]) ).
fof(f209,plain,
( ~ ssList(sK2)
| ~ neq(sK2,nil)
| nil = sK3
| ~ segmentP(sK2,sK2) ),
inference(duplicate_literal_removal,[],[f207]) ).
fof(f211,plain,
( ~ ssList(sK2)
| nil = sK3
| ~ segmentP(sK2,sK2) ),
inference(forward_subsumption_resolution,[],[f209,f146]) ).
fof(f213,plain,
( ~ segmentP(sK2,sK2)
| nil = sK3 ),
inference(forward_subsumption_resolution,[],[f211,f142]) ).
fof(f220,plain,
( ~ ssList(sK2)
| nil = sK3 ),
inference(resolution,[],[f163,f213]) ).
fof(f222,plain,
nil = sK3,
inference(forward_subsumption_resolution,[],[f220,f142]) ).
fof(f228,plain,
( sK2 != sK3
| neq(sK3,sK3) ),
inference(superposition,[],[f194,f222]) ).
fof(f236,plain,
! [X0] :
( sK3 = X0
| ~ segmentP(nil,X0)
| ~ ssList(X0) ),
inference(forward_demodulation,[],[f159,f222]) ).
fof(f237,plain,
! [X0] :
( ~ segmentP(sK3,X0)
| sK3 = X0
| ~ ssList(X0) ),
inference(forward_demodulation,[],[f236,f222]) ).
fof(f239,plain,
( sK2 = sK3
| ~ ssList(sK2)
| nil = sK2 ),
inference(resolution,[],[f237,f143]) ).
fof(f245,plain,
( sK2 = sK3
| nil = sK2 ),
inference(forward_subsumption_resolution,[],[f239,f142]) ).
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,f142]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC060+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n002.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
% 0.11/0.38 % DateTime : Mon Sep 28 07:42:07 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 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
% 2.66/1.37 % (191923)Detected formulas, will run a generic FOF schedule.
% 2.66/1.37 % (191932)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=4076362271:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.66/1.37 % (191932)First to succeed.
% 2.66/1.37 % (191932)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-191923"
% 2.66/1.37 % (191929)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=1118799348:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.66/1.37 % (191931)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1751611615:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.66/1.37 % (191933)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3855479036:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.66/1.37 % (191928)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=4140900091:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.66/1.37 % (191930)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=1204806784:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.66/1.37 % (191931)Also succeeded, but the first one will report.
% 2.66/1.37 % (191934)dis-21_1_sil=8000:lcm=predicate:random_seed=4174299804: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)
% 2.66/1.37 % (191933)Also succeeded, but the first one will report.
% 2.66/1.37 % (191934)Instruction limit reached!
% 2.66/1.37 % (191934)------------------------------
% 2.66/1.37 % (191934)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.66/1.37 % (191934)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.66/1.37 % (191934)CaDiCaL version: 2.1.3
% 2.66/1.37 % (191934)Termination reason: Instruction limit
% 2.66/1.37 % (191934)Termination phase: Saturation
% 2.66/1.37 % (191934)Time elapsed: 0.078 s
% 2.66/1.37 % (191934)Peak memory usage: 90 MB
% 2.66/1.37 % (191934)Instructions burned: 131 (million)
% 2.66/1.37 % (191932)Refutation found. Thanks to Tanya!
% 2.66/1.37 % SZS status Theorem for theBenchmark
% 2.66/1.37 % SZS output start Proof for theBenchmark
% See solution above
% 2.66/1.37 % (191932)------------------------------
% 2.66/1.37 % (191932)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.66/1.37 % (191932)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.66/1.37 % (191932)CaDiCaL version: 2.1.3
% 2.66/1.37 % (191932)Termination reason: Refutation
% 2.66/1.37 % (191932)Time elapsed: 0.003 s
% 2.66/1.37 % (191932)Peak memory usage: 88 MB
% 2.66/1.37 % (191932)Instructions burned: 5 (million)
% 2.66/1.37 % (191932)------------------------------
% 2.66/1.37 % (191932)------------------------------
% 2.66/1.37 % (191923)Success in time 0.292 s
% 2.66/1.37 % Vampire exiting
%------------------------------------------------------------------------------