%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC101+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 : n018.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 01:02:27 PM UTC 2026
% Result : Theorem 3.53s 1.45s
% Output : Refutation 3.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 5
% Syntax : Number of formulae : 41 ( 12 unt; 0 def)
% Number of atoms : 205 ( 70 equ)
% Maximal formula atoms : 20 ( 5 avg)
% Number of connectives : 264 ( 100 ~; 85 |; 59 &)
% ( 4 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 73 ( 53 !; 20 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( frontsegP(X0,X1)
<=> ? [X2] :
( ssList(X2)
& app(X1,X2) = X0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax5) ).
fof(f15,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( neq(X0,X1)
<=> X0 != X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax15) ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax17) ).
fof(f26,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ssList(app(X0,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax26) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( X1 != X3
| X0 != X2
| ! [X4] :
( ssList(X4)
=> ( app(X2,X4) != X3
| ~ equalelemsP(X2)
| ? [X5] :
( ssItem(X5)
& ? [X6] :
( ssList(X6)
& app(cons(X5,nil),X6) = X4
& ? [X7] :
( ssList(X7)
& app(X7,cons(X5,nil)) = X2 ) ) ) ) )
| ( nil != X3
& nil = X2 )
| ( nil = X1
& nil = X0 )
| ( neq(X0,nil)
& frontsegP(X1,X0) ) ) ) ) ) ),
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
| ! [X4] :
( ssList(X4)
=> ( app(X2,X4) != X3
| ~ equalelemsP(X2)
| ? [X5] :
( ssItem(X5)
& ? [X6] :
( ssList(X6)
& app(cons(X5,nil),X6) = X4
& ? [X7] :
( ssList(X7)
& app(X7,cons(X5,nil)) = X2 ) ) ) ) )
| ( nil != X3
& nil = X2 )
| ( nil = X1
& nil = X0 )
| ( neq(X0,nil)
& frontsegP(X1,X0) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f98,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& ? [X4] :
( app(X2,X4) = X3
& equalelemsP(X2)
& ! [X5] :
( ~ ssItem(X5)
| ! [X6] :
( ~ ssList(X6)
| app(cons(X5,nil),X6) != X4
| ! [X7] :
( ~ ssList(X7)
| app(X7,cons(X5,nil)) != X2 ) ) )
& ssList(X4) )
& ( nil = X3
| nil != X2 )
& ( nil != X1
| nil != X0 )
& ( ~ neq(X0,nil)
| ~ frontsegP(X1,X0) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(ennf_transformation,[],[f97]) ).
fof(f99,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& ? [X4] :
( app(X2,X4) = X3
& equalelemsP(X2)
& ! [X5] :
( ~ ssItem(X5)
| ! [X6] :
( ~ ssList(X6)
| app(cons(X5,nil),X6) != X4
| ! [X7] :
( ~ ssList(X7)
| app(X7,cons(X5,nil)) != X2 ) ) )
& ssList(X4) )
& ( nil = X3
| nil != X2 )
& ( nil != X1
| nil != X0 )
& ( ~ neq(X0,nil)
| ~ frontsegP(X1,X0) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(flattening,[],[f98]) ).
fof(f117,plain,
! [X0] :
( ! [X1] :
( ssList(app(X0,X1))
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f26]) ).
fof(f118,plain,
! [X0] :
( ! [X1] :
( ( neq(X0,X1)
<=> X0 != X1 )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f130,plain,
! [X0] :
( ! [X1] :
( ( frontsegP(X0,X1)
<=> ? [X2] :
( ssList(X2)
& app(X1,X2) = X0 ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f5]) ).
fof(f134,plain,
( sK1 = sK3
& sK0 = sK2
& sK3 = app(sK2,sK4)
& equalelemsP(sK2)
& ! [X5] :
( ~ ssItem(X5)
| ! [X6] :
( ~ ssList(X6)
| app(cons(X5,nil),X6) != sK4
| ! [X7] :
( ~ ssList(X7)
| app(X7,cons(X5,nil)) != sK2 ) ) )
& ssList(sK4)
& ( nil = sK3
| nil != sK2 )
& ( nil != sK1
| nil != sK0 )
& ( ~ neq(sK0,nil)
| ~ frontsegP(sK1,sK0) )
& 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(f139,plain,
! [X0] :
( ! [X1] :
( ( ( neq(X0,X1)
| X0 = X1 )
& ( X0 != X1
| ~ neq(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f118]) ).
fof(f144,plain,
! [X0] :
( ! [X1] :
( ( ( frontsegP(X0,X1)
| ! [X2] :
( ~ ssList(X2)
| app(X1,X2) != X0 ) )
& ( ? [X2] :
( ssList(X2)
& app(X1,X2) = X0 )
| ~ frontsegP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f130]) ).
fof(f145,plain,
! [X0] :
( ! [X1] :
( ( ( frontsegP(X0,X1)
| ! [X2] :
( ~ ssList(X2)
| app(X1,X2) != X0 ) )
& ( ? [X3] :
( ssList(X3)
& app(X1,X3) = X0 )
| ~ frontsegP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(rectify,[],[f144]) ).
fof(f146,plain,
! [X0] :
( ! [X1] :
( ( ( frontsegP(X0,X1)
| ! [X2] :
( ~ ssList(X2)
| app(X1,X2) != X0 ) )
& ( ( ssList(sK9(X0,X1))
& app(X1,sK9(X0,X1)) = X0 )
| ~ frontsegP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(X3,sK9(X0,X1))],[f145]) ).
fof(f152,plain,
ssList(sK2),
inference(cnf_transformation,[],[f134]) ).
fof(f154,plain,
( ~ neq(sK0,nil)
| ~ frontsegP(sK1,sK0) ),
inference(cnf_transformation,[],[f134]) ).
fof(f155,plain,
( nil != sK1
| nil != sK0 ),
inference(cnf_transformation,[],[f134]) ).
fof(f156,plain,
( nil != sK2
| nil = sK3 ),
inference(cnf_transformation,[],[f134]) ).
fof(f157,plain,
ssList(sK4),
inference(cnf_transformation,[],[f134]) ).
fof(f160,plain,
sK3 = app(sK2,sK4),
inference(cnf_transformation,[],[f134]) ).
fof(f161,plain,
sK0 = sK2,
inference(cnf_transformation,[],[f134]) ).
fof(f162,plain,
sK1 = sK3,
inference(cnf_transformation,[],[f134]) ).
fof(f184,plain,
! [X0,X1] :
( ssList(app(X0,X1))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f117]) ).
fof(f186,plain,
! [X0,X1] :
( neq(X0,X1)
| X0 = X1
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f139]) ).
fof(f189,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f202,plain,
! [X2,X0,X1] :
( frontsegP(X0,X1)
| ~ ssList(X2)
| app(X1,X2) != X0
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f146]) ).
fof(f212,plain,
( nil != sK3
| nil != sK2 ),
inference(definition_unfolding,[],[f155,f162,f161]) ).
fof(f213,plain,
( ~ frontsegP(sK3,sK2)
| ~ neq(sK2,nil) ),
inference(definition_unfolding,[],[f154,f161,f162,f161]) ).
fof(f222,plain,
! [X2,X1] :
( frontsegP(app(X1,X2),X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(app(X1,X2)) ),
inference(equality_resolution,[],[f202]) ).
fof(f228,plain,
nil != sK2,
inference(forward_subsumption_resolution,[],[f212,f156]) ).
fof(f286,plain,
! [X2,X1] :
( frontsegP(app(X1,X2),X1)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(forward_subsumption_resolution,[],[f222,f184]) ).
fof(f291,plain,
( frontsegP(sK3,sK2)
| ~ ssList(sK4)
| ~ ssList(sK2) ),
inference(superposition,[],[f286,f160]) ).
fof(f296,plain,
( frontsegP(sK3,sK2)
| ~ ssList(sK2) ),
inference(forward_subsumption_resolution,[],[f291,f157]) ).
fof(f298,plain,
frontsegP(sK3,sK2),
inference(forward_subsumption_resolution,[],[f296,f152]) ).
fof(f299,plain,
~ neq(sK2,nil),
inference(resolution,[],[f298,f213]) ).
fof(f317,plain,
( nil = sK2
| ~ ssList(nil)
| ~ ssList(sK2) ),
inference(resolution,[],[f299,f186]) ).
fof(f318,plain,
( ~ ssList(nil)
| ~ ssList(sK2) ),
inference(forward_subsumption_resolution,[],[f317,f228]) ).
fof(f320,plain,
~ ssList(sK2),
inference(forward_subsumption_resolution,[],[f318,f189]) ).
fof(f321,plain,
$false,
inference(forward_subsumption_resolution,[],[f320,f152]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC101+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n018.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 28 07:54:40 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 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
% 3.53/1.45 % (3216414)Detected formulas, will run a generic FOF schedule.
% 3.53/1.45 % (3216419)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=2064598488:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.53/1.45 % (3216424)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=264765348:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.53/1.45 % (3216423)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=455664083:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.53/1.45 % (3216420)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=632090208:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.53/1.45 % (3216421)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=4211289907:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.53/1.45 % (3216422)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3533120475:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.53/1.45 % (3216423)First to succeed.
% 3.53/1.45 % (3216422)Also succeeded, but the first one will report.
% 3.53/1.45 % (3216423)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3216414"
% 3.53/1.45 % (3216424)Also succeeded, but the first one will report.
% 3.53/1.45 % (3216425)dis-21_1_sil=8000:lcm=predicate:random_seed=1352970546: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)
% 3.53/1.45 % (3216425)Instruction limit reached!
% 3.53/1.45 % (3216425)------------------------------
% 3.53/1.45 % (3216425)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.53/1.45 % (3216425)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.53/1.45 % (3216425)CaDiCaL version: 2.1.3
% 3.53/1.45 % (3216425)Termination reason: Instruction limit
% 3.53/1.45 % (3216425)Termination phase: Saturation
% 3.53/1.45 % (3216425)Time elapsed: 0.078 s
% 3.53/1.45 % (3216425)Peak memory usage: 90 MB
% 3.53/1.45 % (3216425)Instructions burned: 129 (million)
% 3.53/1.45 % (3216433)lrs+10_1_sil=8000:sp=occurrence:random_seed=2616263733:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.53/1.45 % (3216433)Also succeeded, but the first one will report.
% 3.53/1.45 % (3216423)Refutation found. Thanks to Tanya!
% 3.53/1.45 % SZS status Theorem for theBenchmark
% 3.53/1.45 % SZS output start Proof for theBenchmark
% See solution above
% 3.53/1.45 % (3216423)------------------------------
% 3.53/1.45 % (3216423)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.53/1.45 % (3216423)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.53/1.45 % (3216423)CaDiCaL version: 2.1.3
% 3.53/1.45 % (3216423)Termination reason: Refutation
% 3.53/1.45 % (3216423)Time elapsed: 0.006 s
% 3.53/1.45 % (3216423)Peak memory usage: 88 MB
% 3.53/1.45 % (3216423)Instructions burned: 7 (million)
% 3.53/1.45 % (3216423)------------------------------
% 3.53/1.45 % (3216423)------------------------------
% 3.53/1.45 % (3216414)Success in time 0.419 s
% 3.53/1.45 % Vampire exiting
%------------------------------------------------------------------------------