%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC023+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 : n019.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 01:02:05 PM UTC 2026
% Result : Theorem 2.65s 1.35s
% Output : Refutation 2.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 2
% Syntax : Number of formulae : 43 ( 14 unt; 0 def)
% Number of atoms : 160 ( 39 equ)
% Maximal formula atoms : 17 ( 3 avg)
% Number of connectives : 182 ( 65 ~; 62 |; 44 &)
% ( 0 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 6 con; 0-0 aty)
% Number of variables : 31 ( 19 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f45,axiom,
! [X0] :
( ssList(X0)
=> frontsegP(X0,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax45) ).
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)
& frontsegP(X1,X4)
& frontsegP(X0,X4) )
| ( ! [X5] :
( ssList(X5)
=> ( ~ neq(X5,nil)
| ~ frontsegP(X3,X5)
| ~ frontsegP(X2,X5) ) )
& ( nil != X3
| nil != X2 ) ) ) ) ) ) ),
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] :
( ssList(X4)
& neq(X4,nil)
& frontsegP(X1,X4)
& frontsegP(X0,X4) )
| ( ! [X5] :
( ssList(X5)
=> ( ~ neq(X5,nil)
| ~ frontsegP(X3,X5)
| ~ frontsegP(X2,X5) ) )
& ( nil != X3
| nil != X2 ) ) ) ) ) ) ),
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)
| ~ frontsegP(X1,X4)
| ~ frontsegP(X0,X4) )
& ( ? [X5] :
( neq(X5,nil)
& frontsegP(X3,X5)
& frontsegP(X2,X5)
& ssList(X5) )
| ( nil = X3
& nil = X2 ) )
& 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)
| ~ frontsegP(X1,X4)
| ~ frontsegP(X0,X4) )
& ( ? [X5] :
( neq(X5,nil)
& frontsegP(X3,X5)
& frontsegP(X2,X5)
& ssList(X5) )
| ( nil = X3
& nil = X2 ) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(flattening,[],[f98]) ).
fof(f103,plain,
! [X0] :
( frontsegP(X0,nil)
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f45]) ).
fof(f131,plain,
( sK1 = sK3
& sK0 = sK2
& neq(sK1,nil)
& ! [X4] :
( ~ ssList(X4)
| ~ neq(X4,nil)
| ~ frontsegP(sK1,X4)
| ~ frontsegP(sK0,X4) )
& ( ( neq(sK4,nil)
& frontsegP(sK3,sK4)
& frontsegP(sK2,sK4)
& ssList(sK4) )
| ( nil = sK3
& nil = sK2 ) )
& 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(X5,sK4)],[f99]) ).
fof(f146,plain,
ssList(sK2),
inference(cnf_transformation,[],[f131]) ).
fof(f147,plain,
ssList(sK3),
inference(cnf_transformation,[],[f131]) ).
fof(f148,plain,
( nil = sK2
| ssList(sK4) ),
inference(cnf_transformation,[],[f131]) ).
fof(f149,plain,
( nil = sK3
| ssList(sK4) ),
inference(cnf_transformation,[],[f131]) ).
fof(f150,plain,
( frontsegP(sK2,sK4)
| nil = sK2 ),
inference(cnf_transformation,[],[f131]) ).
fof(f151,plain,
( frontsegP(sK2,sK4)
| nil = sK3 ),
inference(cnf_transformation,[],[f131]) ).
fof(f152,plain,
( frontsegP(sK3,sK4)
| nil = sK2 ),
inference(cnf_transformation,[],[f131]) ).
fof(f153,plain,
( frontsegP(sK3,sK4)
| nil = sK3 ),
inference(cnf_transformation,[],[f131]) ).
fof(f154,plain,
( neq(sK4,nil)
| nil = sK2 ),
inference(cnf_transformation,[],[f131]) ).
fof(f155,plain,
( neq(sK4,nil)
| nil = sK3 ),
inference(cnf_transformation,[],[f131]) ).
fof(f156,plain,
! [X4] :
( ~ ssList(X4)
| ~ neq(X4,nil)
| ~ frontsegP(sK1,X4)
| ~ frontsegP(sK0,X4) ),
inference(cnf_transformation,[],[f131]) ).
fof(f157,plain,
neq(sK1,nil),
inference(cnf_transformation,[],[f131]) ).
fof(f158,plain,
sK0 = sK2,
inference(cnf_transformation,[],[f131]) ).
fof(f159,plain,
sK1 = sK3,
inference(cnf_transformation,[],[f131]) ).
fof(f167,plain,
! [X0] :
( frontsegP(X0,nil)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f103]) ).
fof(f200,plain,
neq(sK3,nil),
inference(definition_unfolding,[],[f157,f159]) ).
fof(f201,plain,
! [X4] :
( ~ frontsegP(sK3,X4)
| ~ neq(X4,nil)
| ~ ssList(X4)
| ~ frontsegP(sK2,X4) ),
inference(definition_unfolding,[],[f156,f159,f158]) ).
fof(f237,plain,
( ~ neq(sK4,nil)
| ~ ssList(sK4)
| ~ frontsegP(sK2,sK4)
| nil = sK3 ),
inference(resolution,[],[f201,f153]) ).
fof(f238,plain,
( ~ neq(sK4,nil)
| ~ ssList(sK4)
| ~ frontsegP(sK2,sK4)
| nil = sK2 ),
inference(resolution,[],[f201,f152]) ).
fof(f241,plain,
( ~ ssList(sK4)
| ~ frontsegP(sK2,sK4)
| nil = sK2 ),
inference(forward_subsumption_resolution,[],[f238,f154]) ).
fof(f242,plain,
( ~ ssList(sK4)
| ~ frontsegP(sK2,sK4)
| nil = sK3 ),
inference(forward_subsumption_resolution,[],[f237,f155]) ).
fof(f243,plain,
( ~ frontsegP(sK2,sK4)
| nil = sK2 ),
inference(forward_subsumption_resolution,[],[f241,f148]) ).
fof(f244,plain,
( ~ frontsegP(sK2,sK4)
| nil = sK3 ),
inference(forward_subsumption_resolution,[],[f242,f149]) ).
fof(f245,plain,
nil = sK2,
inference(forward_subsumption_resolution,[],[f243,f150]) ).
fof(f246,plain,
nil = sK3,
inference(forward_subsumption_resolution,[],[f244,f151]) ).
fof(f255,plain,
sK2 = sK3,
inference(forward_demodulation,[],[f246,f245]) ).
fof(f259,plain,
neq(sK2,nil),
inference(superposition,[],[f200,f255]) ).
fof(f266,plain,
neq(sK2,sK2),
inference(forward_demodulation,[],[f259,f245]) ).
fof(f268,plain,
! [X0] :
( frontsegP(X0,sK2)
| ~ ssList(X0) ),
inference(forward_demodulation,[],[f167,f245]) ).
fof(f269,plain,
( ~ ssList(sK3)
| ~ neq(sK2,nil)
| ~ ssList(sK2)
| ~ frontsegP(sK2,sK2) ),
inference(resolution,[],[f268,f201]) ).
fof(f270,plain,
( ~ neq(sK2,nil)
| ~ ssList(sK2)
| ~ frontsegP(sK2,sK2) ),
inference(forward_subsumption_resolution,[],[f269,f147]) ).
fof(f271,plain,
( ~ neq(sK2,nil)
| ~ frontsegP(sK2,sK2) ),
inference(forward_subsumption_resolution,[],[f270,f146]) ).
fof(f272,plain,
( ~ neq(sK2,sK2)
| ~ frontsegP(sK2,sK2) ),
inference(forward_demodulation,[],[f271,f245]) ).
fof(f273,plain,
~ frontsegP(sK2,sK2),
inference(forward_subsumption_resolution,[],[f272,f266]) ).
fof(f274,plain,
~ ssList(sK2),
inference(resolution,[],[f273,f268]) ).
fof(f275,plain,
$false,
inference(forward_subsumption_resolution,[],[f274,f146]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC023+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.38 % Computer : n019.cluster.edu
% 0.13/0.38 % Model : x86_64 x86_64
% 0.13/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.38 % Memory : 8046.5625MB
% 0.13/0.38 % OS : Linux 6.8.0-71-generic
% 0.13/0.39 % CPULimit : 300
% 0.13/0.39 % WCLimit : 300
% 0.13/0.39 % DateTime : Mon Sep 28 07:29:33 UTC 2026
% 0.13/0.39 % CPUTime :
% 0.13/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.41 Running first-order theorem proving
% 0.13/0.41 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
% 2.65/1.35 % (3828741)Detected formulas, will run a generic FOF schedule.
% 2.65/1.35 % (3828750)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1959247539:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.65/1.35 % (3828750)First to succeed.
% 2.65/1.35 % (3828750)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3828741"
% 2.65/1.35 % (3828749)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=4213830364:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.65/1.35 % (3828748)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=3077991269:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.65/1.35 % (3828752)dis-21_1_sil=8000:lcm=predicate:random_seed=556326052: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)
% 2.65/1.35 % (3828746)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=721682335:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.65/1.35 % (3828747)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=1109448586:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.65/1.35 % (3828751)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3399266527:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.65/1.35 % (3828749)Also succeeded, but the first one will report.
% 2.65/1.35 % (3828751)Also succeeded, but the first one will report.
% 2.65/1.35 % (3828752)Instruction limit reached!
% 2.65/1.35 % (3828752)------------------------------
% 2.65/1.35 % (3828752)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.65/1.35 % (3828752)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.65/1.35 % (3828752)CaDiCaL version: 2.1.3
% 2.65/1.35 % (3828752)Termination reason: Instruction limit
% 2.65/1.35 % (3828752)Termination phase: Saturation
% 2.65/1.35 % (3828752)Time elapsed: 0.074 s
% 2.65/1.35 % (3828752)Peak memory usage: 90 MB
% 2.65/1.35 % (3828752)Instructions burned: 129 (million)
% 2.65/1.35 % (3828750)Refutation found. Thanks to Tanya!
% 2.65/1.35 % SZS status Theorem for theBenchmark
% 2.65/1.35 % SZS output start Proof for theBenchmark
% See solution above
% 2.65/1.35 % (3828750)------------------------------
% 2.65/1.35 % (3828750)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.65/1.35 % (3828750)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.65/1.35 % (3828750)CaDiCaL version: 2.1.3
% 2.65/1.35 % (3828750)Termination reason: Refutation
% 2.65/1.35 % (3828750)Time elapsed: 0.002 s
% 2.65/1.35 % (3828750)Peak memory usage: 88 MB
% 2.65/1.35 % (3828750)Instructions burned: 4 (million)
% 2.65/1.35 % (3828750)------------------------------
% 2.65/1.35 % (3828750)------------------------------
% 2.65/1.35 % (3828741)Success in time 0.294 s
% 2.65/1.35 % Vampire exiting
%------------------------------------------------------------------------------