%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC205+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 : n014.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 01:02:55 PM UTC 2026
% Result : Theorem 2.73s 1.35s
% Output : Refutation 2.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 7
% Syntax : Number of formulae : 50 ( 17 unt; 4 def)
% Number of atoms : 148 ( 46 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 160 ( 62 ~; 51 |; 32 &)
% ( 5 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 4 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 5 con; 0-0 aty)
% Number of variables : 24 ( 0 sgn 16 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
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(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( X1 != X3
| X0 != X2
| ~ neq(X1,nil)
| neq(X0,nil)
| ( nil != X3
& nil = X2 )
| ( nil != X2
& nil = X3 ) ) ) ) ) ),
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
| ~ neq(X1,nil)
| neq(X0,nil)
| ( nil != X3
& nil = X2 )
| ( nil != X2
& nil = X3 ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f99,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& neq(X1,nil)
& ~ neq(X0,nil)
& ( nil = X3
| nil != X2 )
& ( nil = X2
| nil != X3 )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(ennf_transformation,[],[f97]) ).
fof(f100,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& neq(X1,nil)
& ~ neq(X0,nil)
& ( nil = X3
| nil != X2 )
& ( nil = X2
| nil != X3 )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(flattening,[],[f99]) ).
fof(f101,plain,
! [X0] :
( ! [X1] :
( ( neq(X0,X1)
<=> X0 != X1 )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f102,plain,
( sK1 = sK3
& sK0 = sK2
& neq(sK1,nil)
& ~ neq(sK0,nil)
& ( nil = sK3
| nil != sK2 )
& ( nil = sK2
| nil != sK3 )
& 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)],[f100]) ).
fof(f103,plain,
! [X0] :
( ! [X1] :
( ( ( neq(X0,X1)
| X0 = X1 )
& ( X0 != X1
| ~ neq(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f101]) ).
fof(f104,plain,
ssList(sK0),
inference(cnf_transformation,[],[f102]) ).
fof(f109,plain,
( nil = sK3
| nil != sK2 ),
inference(cnf_transformation,[],[f102]) ).
fof(f110,plain,
~ neq(sK0,nil),
inference(cnf_transformation,[],[f102]) ).
fof(f111,plain,
neq(sK1,nil),
inference(cnf_transformation,[],[f102]) ).
fof(f112,plain,
sK0 = sK2,
inference(cnf_transformation,[],[f102]) ).
fof(f113,plain,
sK1 = sK3,
inference(cnf_transformation,[],[f102]) ).
fof(f115,plain,
! [X0,X1] :
( neq(X0,X1)
| X0 = X1
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f103]) ).
fof(f116,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f117,plain,
neq(sK3,nil),
inference(definition_unfolding,[],[f111,f113]) ).
fof(f118,plain,
~ neq(sK2,nil),
inference(definition_unfolding,[],[f110,f112]) ).
fof(f120,plain,
ssList(sK2),
inference(definition_unfolding,[],[f104,f112]) ).
fof(f121,definition,
~ sP4(nil),
introduced(definition,[new_symbols(definition,[sP4])],[inequality_splitting_name_introduction]) ).
fof(f122,plain,
( nil = sK3
| sP4(sK2) ),
inference(inequality_splitting,[],[f109,f121]) ).
fof(f132,definition,
( spl6_2
<=> nil = sK2 ),
introduced(definition,[new_symbols(definition,[spl6_2])],[avatar_definition]) ).
fof(f133,plain,
( nil != sK2
| spl6_2 ),
inference(avatar_component_clause,[],[f132]) ).
fof(f134,plain,
( nil = sK2
| ~ spl6_2 ),
inference(avatar_component_clause,[],[f132]) ).
fof(f137,definition,
( spl6_3
<=> sP4(sK2) ),
introduced(definition,[new_symbols(definition,[spl6_3])],[avatar_definition]) ).
fof(f139,plain,
( sP4(sK2)
| ~ spl6_3 ),
inference(avatar_component_clause,[],[f137]) ).
fof(f141,definition,
( spl6_4
<=> nil = sK3 ),
introduced(definition,[new_symbols(definition,[spl6_4])],[avatar_definition]) ).
fof(f143,plain,
( nil = sK3
| ~ spl6_4 ),
inference(avatar_component_clause,[],[f141]) ).
fof(f144,plain,
( spl6_3
| spl6_4 ),
inference(avatar_split_clause,[],[f122,f141,f137]) ).
fof(f145,plain,
( sP4(nil)
| ~ spl6_2
| ~ spl6_3 ),
inference(forward_demodulation,[],[f139,f134]) ).
fof(f146,plain,
( $false
| ~ spl6_2
| ~ spl6_3 ),
inference(forward_subsumption_resolution,[],[f145,f121]) ).
fof(f147,plain,
( ~ spl6_2
| ~ spl6_3 ),
inference(avatar_contradiction_clause,[],[f146]) ).
fof(f148,plain,
( nil = sK2
| ~ ssList(nil)
| ~ ssList(sK2) ),
inference(resolution,[],[f118,f115]) ).
fof(f149,plain,
( ~ ssList(nil)
| ~ ssList(sK2)
| spl6_2 ),
inference(forward_subsumption_resolution,[],[f148,f133]) ).
fof(f150,plain,
( ~ ssList(sK2)
| spl6_2 ),
inference(forward_subsumption_resolution,[],[f149,f116]) ).
fof(f151,plain,
( $false
| spl6_2 ),
inference(forward_subsumption_resolution,[],[f150,f120]) ).
fof(f152,plain,
spl6_2,
inference(avatar_contradiction_clause,[],[f151]) ).
fof(f154,plain,
( ~ neq(nil,nil)
| ~ spl6_2 ),
inference(superposition,[],[f118,f134]) ).
fof(f156,plain,
( neq(nil,nil)
| ~ spl6_4 ),
inference(superposition,[],[f117,f143]) ).
fof(f161,plain,
( $false
| ~ spl6_2
| ~ spl6_4 ),
inference(forward_subsumption_resolution,[],[f156,f154]) ).
fof(f162,plain,
( ~ spl6_2
| ~ spl6_4 ),
inference(avatar_contradiction_clause,[],[f161]) ).
cnf(s2,plain,
( spl6_3
| spl6_4 ),
inference(sat_conversion,[],[f144]) ).
cnf(s3,plain,
( ~ spl6_2
| ~ spl6_3 ),
inference(sat_conversion,[],[f147]) ).
cnf(s4,plain,
spl6_2,
inference(sat_conversion,[],[f152]) ).
cnf(s6,plain,
( ~ spl6_2
| ~ spl6_4 ),
inference(sat_conversion,[],[f162]) ).
cnf(s7,plain,
~ spl6_4,
inference(rat,[],[s6,s4]) ).
cnf(s8,plain,
~ spl6_3,
inference(rat,[],[s3,s4]) ).
cnf(s9,plain,
$false,
inference(rat,[],[s2,s7,s8]) ).
fof(f163,plain,
$false,
inference(avatar_sat_refutation,[],[s9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC205+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.36 % Computer : n014.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 28 08:27:01 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.40 Running first-order theorem proving
% 0.09/0.40 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
% 2.73/1.35 % (1631576)Detected formulas, will run a generic FOF schedule.
% 2.73/1.35 % (1631584)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3966806192:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.73/1.35 % (1631584)First to succeed.
% 2.73/1.35 % (1631584)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1631576"
% 2.73/1.35 % (1631586)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3771984452:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.73/1.35 % (1631582)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=3469887330:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.73/1.35 % (1631581)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=1094224178:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.73/1.35 % (1631583)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=2944072417:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.73/1.35 % (1631585)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1272532741:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.73/1.35 % (1631587)dis-21_1_sil=8000:lcm=predicate:random_seed=1462514280: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)
% 2.73/1.35 % (1631585)Also succeeded, but the first one will report.
% 2.73/1.35 % (1631586)Also succeeded, but the first one will report.
% 2.73/1.35 % (1631587)Instruction limit reached!
% 2.73/1.35 % (1631587)------------------------------
% 2.73/1.35 % (1631587)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.73/1.35 % (1631587)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.73/1.35 % (1631587)CaDiCaL version: 2.1.3
% 2.73/1.35 % (1631587)Termination reason: Instruction limit
% 2.73/1.35 % (1631587)Termination phase: Saturation
% 2.73/1.35 % (1631587)Time elapsed: 0.076 s
% 2.73/1.35 % (1631587)Peak memory usage: 90 MB
% 2.73/1.35 % (1631587)Instructions burned: 131 (million)
% 2.73/1.35 % (1631584)Refutation found. Thanks to Tanya!
% 2.73/1.35 % SZS status Theorem for theBenchmark
% 2.73/1.35 % SZS output start Proof for theBenchmark
% See solution above
% 2.73/1.35 % (1631584)------------------------------
% 2.73/1.35 % (1631584)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.73/1.35 % (1631584)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.73/1.35 % (1631584)CaDiCaL version: 2.1.3
% 2.73/1.35 % (1631584)Termination reason: Refutation
% 2.73/1.35 % (1631584)Time elapsed: 0.002 s
% 2.73/1.35 % (1631584)Peak memory usage: 89 MB
% 2.73/1.35 % (1631584)Instructions burned: 2 (million)
% 2.73/1.35 % (1631584)------------------------------
% 2.73/1.35 % (1631584)------------------------------
% 2.73/1.35 % (1631576)Success in time 0.305 s
% 2.73/1.35 % Vampire exiting
%------------------------------------------------------------------------------