%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC369+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 : 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 01:03:40 PM UTC 2026
% Result : Theorem 2.59s 1.16s
% Output : Refutation 2.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 10
% Syntax : Number of formulae : 60 ( 17 unt; 6 def)
% Number of atoms : 187 ( 40 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 199 ( 72 ~; 75 |; 33 &)
% ( 8 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 5 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 5 con; 0-0 aty)
% Number of variables : 29 ( 0 sgn 21 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f15,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( neq(X0,X1)
<=> X0 != X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax15) ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax17) ).
fof(f58,axiom,
! [X0] :
( ssList(X0)
=> ( segmentP(nil,X0)
<=> nil = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax58) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( X1 != X3
| X0 != X2
| segmentP(X1,X0)
| ( nil != X2
& nil = X3 )
| ( neq(X3,nil)
& ( ~ neq(X2,nil)
| ~ segmentP(X3,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
| segmentP(X1,X0)
| ( nil != X2
& nil = X3 )
| ( neq(X3,nil)
& ( ~ neq(X2,nil)
| ~ segmentP(X3,X2) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f99,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& ~ segmentP(X1,X0)
& ( nil = X2
| nil != X3 )
& ( ~ neq(X3,nil)
| ( neq(X2,nil)
& segmentP(X3,X2) ) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(ennf_transformation,[],[f97]) ).
fof(f100,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& ~ segmentP(X1,X0)
& ( nil = X2
| nil != X3 )
& ( ~ neq(X3,nil)
| ( neq(X2,nil)
& segmentP(X3,X2) ) )
& 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,
! [X0] :
( ( segmentP(nil,X0)
<=> nil = X0 )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f58]) ).
fof(f112,plain,
( sK1 = sK3
& sK0 = sK2
& ~ segmentP(sK1,sK0)
& ( nil = sK2
| nil != sK3 )
& ( ~ neq(sK3,nil)
| ( neq(sK2,nil)
& segmentP(sK3,sK2) ) )
& 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(f113,plain,
! [X0] :
( ! [X1] :
( ( ( neq(X0,X1)
| X0 = X1 )
& ( X0 != X1
| ~ neq(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f101]) ).
fof(f114,plain,
! [X0] :
( ( ( segmentP(nil,X0)
| nil != X0 )
& ( nil = X0
| ~ segmentP(nil,X0) ) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f102]) ).
fof(f119,plain,
ssList(sK1),
inference(cnf_transformation,[],[f112]) ).
fof(f122,plain,
( ~ neq(sK3,nil)
| segmentP(sK3,sK2) ),
inference(cnf_transformation,[],[f112]) ).
fof(f124,plain,
( nil = sK2
| nil != sK3 ),
inference(cnf_transformation,[],[f112]) ).
fof(f125,plain,
~ segmentP(sK1,sK0),
inference(cnf_transformation,[],[f112]) ).
fof(f126,plain,
sK0 = sK2,
inference(cnf_transformation,[],[f112]) ).
fof(f127,plain,
sK1 = sK3,
inference(cnf_transformation,[],[f112]) ).
fof(f129,plain,
! [X0,X1] :
( neq(X0,X1)
| X0 = X1
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f113]) ).
fof(f130,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f132,plain,
! [X0] :
( segmentP(nil,X0)
| nil != X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f114]) ).
fof(f142,plain,
~ segmentP(sK3,sK2),
inference(definition_unfolding,[],[f125,f127,f126]) ).
fof(f143,plain,
ssList(sK3),
inference(definition_unfolding,[],[f119,f127]) ).
fof(f145,definition,
~ sP6(nil),
introduced(definition,[new_symbols(definition,[sP6])],[inequality_splitting_name_introduction]) ).
fof(f146,plain,
( nil = sK2
| sP6(sK3) ),
inference(inequality_splitting,[],[f124,f145]) ).
fof(f147,definition,
~ sP7(nil),
introduced(definition,[new_symbols(definition,[sP7])],[inequality_splitting_name_introduction]) ).
fof(f148,plain,
! [X0] :
( segmentP(nil,X0)
| sP7(X0)
| ~ ssList(X0) ),
inference(inequality_splitting,[],[f132,f147]) ).
fof(f153,definition,
( spl8_1
<=> segmentP(sK3,sK2) ),
introduced(definition,[new_symbols(definition,[spl8_1])],[avatar_definition]) ).
fof(f154,plain,
( ~ segmentP(sK3,sK2)
| spl8_1 ),
inference(avatar_component_clause,[],[f153]) ).
fof(f157,definition,
( spl8_2
<=> neq(sK3,nil) ),
introduced(definition,[new_symbols(definition,[spl8_2])],[avatar_definition]) ).
fof(f159,plain,
( ~ neq(sK3,nil)
| spl8_2 ),
inference(avatar_component_clause,[],[f157]) ).
fof(f160,plain,
( spl8_1
| ~ spl8_2 ),
inference(avatar_split_clause,[],[f122,f157,f153]) ).
fof(f167,definition,
( spl8_4
<=> sP6(sK3) ),
introduced(definition,[new_symbols(definition,[spl8_4])],[avatar_definition]) ).
fof(f169,plain,
( sP6(sK3)
| ~ spl8_4 ),
inference(avatar_component_clause,[],[f167]) ).
fof(f171,definition,
( spl8_5
<=> nil = sK2 ),
introduced(definition,[new_symbols(definition,[spl8_5])],[avatar_definition]) ).
fof(f173,plain,
( nil = sK2
| ~ spl8_5 ),
inference(avatar_component_clause,[],[f171]) ).
fof(f174,plain,
( spl8_4
| spl8_5 ),
inference(avatar_split_clause,[],[f146,f171,f167]) ).
fof(f175,plain,
~ spl8_1,
inference(avatar_split_clause,[],[f142,f153]) ).
fof(f176,plain,
( nil = sK3
| ~ ssList(nil)
| ~ ssList(sK3)
| spl8_2 ),
inference(resolution,[],[f159,f129]) ).
fof(f177,plain,
( nil = sK3
| ~ ssList(sK3)
| spl8_2 ),
inference(forward_subsumption_resolution,[],[f176,f130]) ).
fof(f178,plain,
( nil = sK3
| spl8_2 ),
inference(forward_subsumption_resolution,[],[f177,f143]) ).
fof(f181,plain,
( sP6(nil)
| spl8_2
| ~ spl8_4 ),
inference(superposition,[],[f169,f178]) ).
fof(f183,plain,
( $false
| spl8_2
| ~ spl8_4 ),
inference(forward_subsumption_resolution,[],[f181,f145]) ).
fof(f184,plain,
( spl8_2
| ~ spl8_4 ),
inference(avatar_contradiction_clause,[],[f183]) ).
fof(f186,plain,
( ~ segmentP(sK3,nil)
| spl8_1
| ~ spl8_5 ),
inference(superposition,[],[f154,f173]) ).
fof(f188,plain,
( ~ segmentP(nil,nil)
| spl8_1
| spl8_2
| ~ spl8_5 ),
inference(forward_demodulation,[],[f186,f178]) ).
fof(f189,plain,
( sP7(nil)
| ~ ssList(nil)
| spl8_1
| spl8_2
| ~ spl8_5 ),
inference(resolution,[],[f188,f148]) ).
fof(f196,plain,
( ~ ssList(nil)
| spl8_1
| spl8_2
| ~ spl8_5 ),
inference(forward_subsumption_resolution,[],[f189,f147]) ).
fof(f197,plain,
( $false
| spl8_1
| spl8_2
| ~ spl8_5 ),
inference(forward_subsumption_resolution,[],[f196,f130]) ).
fof(f198,plain,
( spl8_1
| spl8_2
| ~ spl8_5 ),
inference(avatar_contradiction_clause,[],[f197]) ).
cnf(s1,plain,
( spl8_1
| ~ spl8_2 ),
inference(sat_conversion,[],[f160]) ).
cnf(s3,plain,
( spl8_4
| spl8_5 ),
inference(sat_conversion,[],[f174]) ).
cnf(s4,plain,
~ spl8_1,
inference(sat_conversion,[],[f175]) ).
cnf(s5,plain,
( spl8_2
| ~ spl8_4 ),
inference(sat_conversion,[],[f184]) ).
cnf(s8,plain,
( spl8_1
| spl8_2
| ~ spl8_5 ),
inference(sat_conversion,[],[f198]) ).
cnf(s9,plain,
~ spl8_2,
inference(rat,[],[s1,s4]) ).
cnf(s10,plain,
~ spl8_5,
inference(rat,[],[s8,s4,s9]) ).
cnf(s11,plain,
~ spl8_4,
inference(rat,[],[s5,s9]) ).
cnf(s12,plain,
$false,
inference(rat,[],[s3,s10,s11]) ).
fof(f199,plain,
$false,
inference(avatar_sat_refutation,[],[s12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SWC369+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.23 % Computer : n002.cluster.edu
% 0.11/0.23 % Model : x86_64 x86_64
% 0.11/0.23 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.23 % Memory : 8046.5625MB
% 0.11/0.23 % OS : Linux 6.8.0-71-generic
% 0.11/0.23 % CPULimit : 300
% 0.11/0.23 % WCLimit : 300
% 0.11/0.23 % DateTime : Mon Sep 28 09:23:07 UTC 2026
% 0.11/0.23 % CPUTime :
% 0.11/0.23 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.26 Running first-order theorem proving
% 0.11/0.26 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
% 2.59/1.16 % (229615)Detected formulas, will run a generic FOF schedule.
% 2.59/1.16 % (229736)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2368259504:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.59/1.16 % (229736)First to succeed.
% 2.59/1.16 % (229736)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-229615"
% 2.59/1.16 % (229735)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=2981884659:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.59/1.16 % (229733)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=1327526619:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.59/1.16 % (229739)dis-21_1_sil=8000:lcm=predicate:random_seed=3167005830: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)
% 2.59/1.16 % (229734)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=2799271274:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.59/1.16 % (229737)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3628273338:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.59/1.16 % (229737)Also succeeded, but the first one will report.
% 2.59/1.16 % (229738)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1293537117:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.59/1.16 % (229738)Also succeeded, but the first one will report.
% 2.59/1.16 % (229739)Instruction limit reached!
% 2.59/1.16 % (229739)------------------------------
% 2.59/1.16 % (229739)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.59/1.16 % (229739)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.59/1.16 % (229739)CaDiCaL version: 2.1.3
% 2.59/1.16 % (229739)Termination reason: Instruction limit
% 2.59/1.16 % (229739)Termination phase: Saturation
% 2.59/1.16 % (229739)Time elapsed: 0.076 s
% 2.59/1.16 % (229739)Peak memory usage: 90 MB
% 2.59/1.16 % (229739)Instructions burned: 130 (million)
% 2.59/1.16 % (229736)Refutation found. Thanks to Tanya!
% 2.59/1.16 % SZS status Theorem for theBenchmark
% 2.59/1.16 % SZS output start Proof for theBenchmark
% See solution above
% 2.59/1.16 % (229736)------------------------------
% 2.59/1.16 % (229736)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.59/1.16 % (229736)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.59/1.16 % (229736)CaDiCaL version: 2.1.3
% 2.59/1.16 % (229736)Termination reason: Refutation
% 2.59/1.16 % (229736)Time elapsed: 0.002 s
% 2.59/1.16 % (229736)Peak memory usage: 89 MB
% 2.59/1.16 % (229736)Instructions burned: 3 (million)
% 2.59/1.16 % (229736)------------------------------
% 2.59/1.16 % (229736)------------------------------
% 2.59/1.16 % (229615)Success in time 0.264 s
% 2.59/1.16 % Vampire exiting
%------------------------------------------------------------------------------