%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC355+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 : n016.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 01:03:36 PM UTC 2026
% Result : Theorem 3.53s 1.27s
% Output : Refutation 3.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 6
% Syntax : Number of formulae : 46 ( 12 unt; 0 def)
% Number of atoms : 186 ( 31 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 225 ( 85 ~; 76 |; 45 &)
% ( 2 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 74 ( 56 !; 18 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( segmentP(X0,X1)
<=> ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& app(app(X2,X1),X3) = X0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax7) ).
fof(f16,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> ssList(cons(X1,X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax16) ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax17) ).
fof(f26,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ssList(app(X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax26) ).
fof(f28,axiom,
! [X0] :
( ssList(X0)
=> app(nil,X0) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax28) ).
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)
=> app(X2,cons(X4,nil)) != X3 )
| segmentP(X1,X0) )
& ( ~ 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)
=> app(X2,cons(X4,nil)) != X3 )
| segmentP(X1,X0) )
& ( ~ 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] :
( app(X2,cons(X4,nil)) = X3
& ssItem(X4) )
& ~ segmentP(X1,X0) )
| ( 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] :
( app(X2,cons(X4,nil)) = X3
& ssItem(X4) )
& ~ segmentP(X1,X0) )
| ( neq(X1,nil)
& ~ neq(X3,nil) ) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(flattening,[],[f98]) ).
fof(f106,plain,
! [X0] :
( ! [X1] :
( ssList(cons(X1,X0))
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f16]) ).
fof(f115,plain,
! [X0] :
( app(nil,X0) = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f28]) ).
fof(f117,plain,
! [X0] :
( ! [X1] :
( ssList(app(X0,X1))
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f26]) ).
fof(f129,plain,
! [X0] :
( ! [X1] :
( ( segmentP(X0,X1)
<=> ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& app(app(X2,X1),X3) = X0 ) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f7]) ).
fof(f130,plain,
( sK1 = sK3
& sK0 = sK2
& ( ( neq(sK1,nil)
& sK3 = app(sK2,cons(sK4,nil))
& ssItem(sK4)
& ~ segmentP(sK1,sK0) )
| ( neq(sK1,nil)
& ~ neq(sK3,nil) ) )
& ssList(sK3)
& ssList(sK2)
& ssList(sK1)
& ssList(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X4,sK4)],[f99]) ).
fof(f138,plain,
! [X0] :
( ! [X1] :
( ( ( segmentP(X0,X1)
| ! [X2] :
( ~ ssList(X2)
| ! [X3] :
( ~ ssList(X3)
| app(app(X2,X1),X3) != X0 ) ) )
& ( ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& app(app(X2,X1),X3) = X0 ) )
| ~ segmentP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f129]) ).
fof(f139,plain,
! [X0] :
( ! [X1] :
( ( ( segmentP(X0,X1)
| ! [X2] :
( ~ ssList(X2)
| ! [X3] :
( ~ ssList(X3)
| app(app(X2,X1),X3) != X0 ) ) )
& ( ? [X4] :
( ssList(X4)
& ? [X5] :
( ssList(X5)
& app(app(X4,X1),X5) = X0 ) )
| ~ segmentP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(rectify,[],[f138]) ).
fof(f140,plain,
! [X0] :
( ! [X1] :
( ( ( segmentP(X0,X1)
| ! [X2] :
( ~ ssList(X2)
| ! [X3] :
( ~ ssList(X3)
| app(app(X2,X1),X3) != X0 ) ) )
& ( ( ssList(sK9(X0,X1))
& ssList(sK10(X0,X1))
& app(app(sK9(X0,X1),X1),sK10(X0,X1)) = X0 )
| ~ segmentP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9,sK10]),skolemize(X4,sK9(X0,X1)),skolemize(X5,sK10(X0,X1))],[f139]) ).
fof(f143,plain,
ssList(sK2),
inference(cnf_transformation,[],[f130]) ).
fof(f145,plain,
( ~ segmentP(sK1,sK0)
| ~ neq(sK3,nil) ),
inference(cnf_transformation,[],[f130]) ).
fof(f147,plain,
( ssItem(sK4)
| ~ neq(sK3,nil) ),
inference(cnf_transformation,[],[f130]) ).
fof(f149,plain,
( sK3 = app(sK2,cons(sK4,nil))
| ~ neq(sK3,nil) ),
inference(cnf_transformation,[],[f130]) ).
fof(f152,plain,
( neq(sK1,nil)
| neq(sK1,nil) ),
inference(cnf_transformation,[],[f130]) ).
fof(f153,plain,
sK0 = sK2,
inference(cnf_transformation,[],[f130]) ).
fof(f154,plain,
sK1 = sK3,
inference(cnf_transformation,[],[f130]) ).
fof(f165,plain,
! [X0,X1] :
( ssList(cons(X1,X0))
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f106]) ).
fof(f174,plain,
! [X0] :
( app(nil,X0) = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f115]) ).
fof(f176,plain,
! [X0,X1] :
( ssList(app(X0,X1))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f117]) ).
fof(f181,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f192,plain,
! [X2,X3,X0,X1] :
( segmentP(X0,X1)
| ~ ssList(X2)
| ~ ssList(X3)
| app(app(X2,X1),X3) != X0
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f140]) ).
fof(f193,plain,
( neq(sK3,nil)
| neq(sK3,nil) ),
inference(definition_unfolding,[],[f152,f154,f154]) ).
fof(f198,plain,
( ~ segmentP(sK3,sK2)
| ~ neq(sK3,nil) ),
inference(definition_unfolding,[],[f145,f154,f153]) ).
fof(f206,plain,
! [X2,X3,X1] :
( segmentP(app(app(X2,X1),X3),X1)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ ssList(X1)
| ~ ssList(app(app(X2,X1),X3)) ),
inference(equality_resolution,[],[f192]) ).
fof(f210,plain,
neq(sK3,nil),
inference(duplicate_literal_removal,[],[f193]) ).
fof(f211,plain,
ssItem(sK4),
inference(forward_subsumption_resolution,[],[f147,f210]) ).
fof(f212,plain,
~ segmentP(sK3,sK2),
inference(forward_subsumption_resolution,[],[f198,f210]) ).
fof(f213,plain,
sK3 = app(sK2,cons(sK4,nil)),
inference(forward_subsumption_resolution,[],[f149,f210]) ).
fof(f556,plain,
! [X0,X1] :
( segmentP(app(X0,X1),X0)
| ~ ssList(nil)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(app(X0,X1))
| ~ ssList(X0) ),
inference(superposition,[],[f206,f174]) ).
fof(f565,plain,
! [X0,X1] :
( segmentP(app(X0,X1),X0)
| ~ ssList(nil)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(app(X0,X1)) ),
inference(duplicate_literal_removal,[],[f556]) ).
fof(f574,plain,
! [X0,X1] :
( segmentP(app(X0,X1),X0)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(app(X0,X1)) ),
inference(forward_subsumption_resolution,[],[f565,f181]) ).
fof(f580,plain,
! [X0,X1] :
( segmentP(app(X0,X1),X0)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[],[f574,f176]) ).
fof(f692,plain,
( segmentP(sK3,sK2)
| ~ ssList(cons(sK4,nil))
| ~ ssList(sK2) ),
inference(superposition,[],[f580,f213]) ).
fof(f704,plain,
( ~ ssList(cons(sK4,nil))
| ~ ssList(sK2) ),
inference(forward_subsumption_resolution,[],[f692,f212]) ).
fof(f710,plain,
~ ssList(cons(sK4,nil)),
inference(forward_subsumption_resolution,[],[f704,f143]) ).
fof(f711,plain,
( ~ ssItem(sK4)
| ~ ssList(nil) ),
inference(resolution,[],[f710,f165]) ).
fof(f712,plain,
~ ssList(nil),
inference(forward_subsumption_resolution,[],[f711,f211]) ).
fof(f713,plain,
$false,
inference(forward_subsumption_resolution,[],[f712,f181]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC355+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.18 % Computer : n016.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Mon Sep 28 09:19:48 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.22 Running first-order theorem proving
% 0.07/0.22 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
% 3.53/1.27 % (3501132)Detected formulas, will run a generic FOF schedule.
% 3.53/1.27 % (3501143)dis-21_1_sil=8000:lcm=predicate:random_seed=305816804: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)
% 3.53/1.27 % (3501137)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=1644603767:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.53/1.27 % (3501138)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=2550582771:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.53/1.27 % (3501139)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=1989867246:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.53/1.27 % (3501140)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3445456596:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.53/1.27 % (3501141)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=191388679:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.53/1.27 % (3501142)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2038826498:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.53/1.27 % (3501143)Instruction limit reached!
% 3.53/1.27 % (3501143)------------------------------
% 3.53/1.27 % (3501143)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.53/1.27 % (3501143)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.53/1.27 % (3501143)CaDiCaL version: 2.1.3
% 3.53/1.27 % (3501143)Termination reason: Instruction limit
% 3.53/1.27 % (3501143)Termination phase: Saturation
% 3.53/1.27 % (3501143)Time elapsed: 0.042 s
% 3.53/1.27 % (3501143)Peak memory usage: 90 MB
% 3.53/1.27 % (3501143)Instructions burned: 131 (million)
% 3.53/1.27 % (3501141)First to succeed.
% 3.53/1.27 % (3501141)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3501132"
% 3.53/1.27 % (3501142)Also succeeded, but the first one will report.
% 3.53/1.27 % (3501140)Instruction limit reached!
% 3.53/1.27 % (3501140)------------------------------
% 3.53/1.27 % (3501140)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.53/1.27 % (3501140)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.53/1.27 % (3501140)CaDiCaL version: 2.1.3
% 3.53/1.27 % (3501140)Termination reason: Instruction limit
% 3.53/1.27 % (3501140)Termination phase: Saturation
% 3.53/1.27 % (3501140)Time elapsed: 0.071 s
% 3.53/1.27 % (3501140)Peak memory usage: 90 MB
% 3.53/1.27 % (3501140)Instructions burned: 109 (million)
% 3.53/1.27 % (3501151)lrs+10_1_sil=8000:sp=occurrence:random_seed=1933558758:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 3.53/1.27 % (3501151)Also succeeded, but the first one will report.
% 3.53/1.27 % (3501152)lrs+10_1_sil=32000:urr=on:br=off:random_seed=4155656026:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 3.53/1.27 % (3501141)Refutation found. Thanks to Tanya!
% 3.53/1.27 % SZS status Theorem for theBenchmark
% 3.53/1.27 % SZS output start Proof for theBenchmark
% See solution above
% 3.53/1.27 % (3501141)------------------------------
% 3.53/1.27 % (3501141)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.53/1.27 % (3501141)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.53/1.27 % (3501141)CaDiCaL version: 2.1.3
% 3.53/1.27 % (3501141)Termination reason: Refutation
% 3.53/1.27 % (3501141)Time elapsed: 0.012 s
% 3.53/1.27 % (3501141)Peak memory usage: 88 MB
% 3.53/1.27 % (3501141)Instructions burned: 18 (million)
% 3.53/1.27 % (3501141)------------------------------
% 3.53/1.27 % (3501141)------------------------------
% 3.53/1.27 % (3501132)Success in time 0.42 s
% 3.53/1.27 % Vampire exiting
%------------------------------------------------------------------------------