%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC068-1 : 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 : n007.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 01:02:17 PM UTC 2026
% Result : Unsatisfiable 2.58s 1.25s
% Output : Refutation 2.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 18
% Syntax : Number of formulae : 67 ( 14 unt; 4 def)
% Number of atoms : 182 ( 37 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 229 ( 114 ~; 111 |; 0 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 5 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 42 ( 0 sgn 42 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause8) ).
fof(f57,axiom,
! [X0] :
( segmentP(X0,X0)
| ~ ssList(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause57) ).
fof(f74,axiom,
! [X0] :
( app(nil,X0) = X0
| ~ ssList(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause74) ).
fof(f85,axiom,
! [X0,X1] :
( ssList(app(X1,X0))
| ~ ssList(X1)
| ~ ssList(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause85) ).
fof(f101,axiom,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| neq(X1,X0)
| X1 = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause100) ).
fof(f102,plain,
! [X0,X1] :
( neq(X1,X0)
| ~ ssList(X1)
| ~ ssList(X0)
| X0 = X1 ),
inference(reorient_equations,[],[f101]) ).
fof(f156,axiom,
! [X0,X1] :
( nil != X0
| nil != X1
| ~ ssList(X1)
| ~ ssList(X0)
| app(X0,X1) = nil ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause145) ).
fof(f157,plain,
! [X0,X1] :
( nil != X0
| nil != X1
| ~ ssList(X1)
| ~ ssList(X0)
| nil = app(X0,X1) ),
inference(reorient_equations,[],[f156]) ).
fof(f161,axiom,
! [X2,X0,X1] :
( app(app(X2,X1),X0) = app(X2,app(X1,X0))
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause149) ).
fof(f187,axiom,
! [X2,X3,X0,X1] :
( app(app(X0,X1),X2) != X3
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X3)
| segmentP(X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause173) ).
fof(f203,negated_conjecture,
ssList(sk4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_4) ).
fof(f204,negated_conjecture,
app(sk4,sk4) = sk3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_5) ).
fof(f205,plain,
sk3 = app(sk4,sk4),
inference(reorient_equations,[],[f204]) ).
fof(f206,negated_conjecture,
sk2 = sk4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_6) ).
fof(f207,negated_conjecture,
sk1 = sk3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_7) ).
fof(f208,negated_conjecture,
! [X0] :
( ~ ssList(X0)
| ~ neq(X0,nil)
| ~ segmentP(sk2,X0)
| ~ segmentP(sk1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_8) ).
fof(f209,negated_conjecture,
( nil != sk2
| nil != sk1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_9) ).
fof(f212,plain,
! [X0] :
( ~ neq(X0,nil)
| ~ ssList(X0)
| ~ segmentP(sk4,X0)
| ~ segmentP(sk3,X0) ),
inference(definition_unfolding,[],[f208,f206,f207]) ).
fof(f213,plain,
( nil != sk4
| nil != sk3 ),
inference(definition_unfolding,[],[f209,f206,f207]) ).
fof(f214,plain,
! [X1] :
( nil != X1
| ~ ssList(X1)
| ~ ssList(nil)
| nil = app(nil,X1) ),
inference(equality_resolution,[],[f157]) ).
fof(f215,plain,
( ~ ssList(nil)
| ~ ssList(nil)
| nil = app(nil,nil) ),
inference(equality_resolution,[],[f214]) ).
fof(f216,plain,
! [X2,X0,X1] :
( ~ ssList(X2)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(app(app(X0,X1),X2))
| segmentP(app(app(X0,X1),X2),X1) ),
inference(equality_resolution,[],[f187]) ).
fof(f220,plain,
( ~ ssList(nil)
| nil = app(nil,nil) ),
inference(duplicate_literal_removal,[],[f215]) ).
fof(f225,definition,
( spl0_2
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f226,plain,
( ~ ssList(nil)
| spl0_2 ),
inference(avatar_component_clause,[],[f225]) ).
fof(f229,definition,
( spl0_3
<=> nil = app(nil,nil) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f230,plain,
( nil = app(nil,nil)
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f229]) ).
fof(f231,plain,
( spl0_3
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f220,f225,f229]) ).
fof(f233,definition,
( spl0_4
<=> nil = sk3 ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f234,plain,
( nil != sk3
| spl0_4 ),
inference(avatar_component_clause,[],[f233]) ).
fof(f236,definition,
( spl0_5
<=> nil = sk4 ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f237,plain,
( nil != sk4
| spl0_5 ),
inference(avatar_component_clause,[],[f236]) ).
fof(f238,plain,
( ~ spl0_4
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f213,f236,f233]) ).
fof(f240,plain,
( $false
| spl0_2 ),
inference(forward_subsumption_resolution,[],[f226,f8]) ).
fof(f241,plain,
spl0_2,
inference(avatar_contradiction_clause,[],[f240]) ).
fof(f253,plain,
! [X0] :
( ~ ssList(X0)
| ~ ssList(nil)
| nil = X0
| ~ ssList(X0)
| ~ segmentP(sk4,X0)
| ~ segmentP(sk3,X0) ),
inference(resolution,[],[f102,f212]) ).
fof(f256,plain,
! [X0] :
( ~ ssList(X0)
| ~ ssList(nil)
| nil = X0
| ~ segmentP(sk4,X0)
| ~ segmentP(sk3,X0) ),
inference(duplicate_literal_removal,[],[f253]) ).
fof(f257,plain,
! [X0] :
( ~ segmentP(sk4,X0)
| nil = X0
| ~ ssList(X0)
| ~ segmentP(sk3,X0) ),
inference(forward_subsumption_resolution,[],[f256,f8]) ).
fof(f259,plain,
( nil = sk4
| ~ ssList(sk4)
| ~ segmentP(sk3,sk4)
| ~ ssList(sk4) ),
inference(resolution,[],[f257,f57]) ).
fof(f260,plain,
( nil = sk4
| ~ ssList(sk4)
| ~ segmentP(sk3,sk4) ),
inference(duplicate_literal_removal,[],[f259]) ).
fof(f261,plain,
( ~ ssList(sk4)
| ~ segmentP(sk3,sk4)
| spl0_5 ),
inference(forward_subsumption_resolution,[],[f260,f237]) ).
fof(f262,plain,
( ~ segmentP(sk3,sk4)
| spl0_5 ),
inference(forward_subsumption_resolution,[],[f261,f203]) ).
fof(f265,plain,
( ~ segmentP(app(sk4,sk4),sk4)
| spl0_5 ),
inference(superposition,[],[f262,f205]) ).
fof(f420,plain,
! [X2,X0,X1] :
( ~ ssList(X2)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(app(X0,app(X1,X2)))
| segmentP(app(app(X0,X1),X2),X1) ),
inference(forward_subsumption_demodulation,[],[f216,f161]) ).
fof(f421,plain,
! [X2,X0,X1] :
( segmentP(app(X0,app(X1,X2)),X1)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(app(X0,app(X1,X2)))
| ~ ssList(X2) ),
inference(forward_subsumption_demodulation,[],[f420,f161]) ).
fof(f437,plain,
! [X0,X1] :
( segmentP(app(X0,X1),X0)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(app(X0,X1))
| ~ ssList(X1)
| ~ ssList(app(X0,X1)) ),
inference(superposition,[],[f421,f74]) ).
fof(f439,plain,
! [X0,X1] :
( segmentP(app(X0,X1),X0)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(app(X0,X1))
| ~ ssList(X1) ),
inference(duplicate_literal_removal,[],[f437]) ).
fof(f446,plain,
! [X0,X1] :
( segmentP(app(X0,X1),X0)
| ~ ssList(X0)
| ~ ssList(app(X0,X1))
| ~ ssList(X1) ),
inference(forward_subsumption_resolution,[],[f439,f8]) ).
fof(f450,plain,
! [X0,X1] :
( segmentP(app(X0,X1),X0)
| ~ ssList(X0)
| ~ ssList(X1) ),
inference(forward_subsumption_resolution,[],[f446,f85]) ).
fof(f464,plain,
( ~ ssList(sk4)
| ~ ssList(sk4)
| spl0_5 ),
inference(resolution,[],[f450,f265]) ).
fof(f475,plain,
( ~ ssList(sk4)
| spl0_5 ),
inference(duplicate_literal_removal,[],[f464]) ).
fof(f479,plain,
( $false
| spl0_5 ),
inference(forward_subsumption_resolution,[],[f475,f203]) ).
fof(f480,plain,
spl0_5,
inference(avatar_contradiction_clause,[],[f479]) ).
fof(f486,plain,
( nil = sk4
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f236]) ).
fof(f488,plain,
( nil != app(sk4,sk4)
| spl0_4 ),
inference(superposition,[],[f234,f205]) ).
fof(f492,plain,
( nil != app(nil,nil)
| spl0_4
| ~ spl0_5 ),
inference(superposition,[],[f488,f486]) ).
fof(f493,plain,
( $false
| ~ spl0_3
| spl0_4
| ~ spl0_5 ),
inference(forward_subsumption_resolution,[],[f492,f230]) ).
fof(f494,plain,
( ~ spl0_3
| spl0_4
| ~ spl0_5 ),
inference(avatar_contradiction_clause,[],[f493]) ).
cnf(s2,plain,
( ~ spl0_2
| spl0_3 ),
inference(sat_conversion,[],[f231]) ).
cnf(s3,plain,
( ~ spl0_4
| ~ spl0_5 ),
inference(sat_conversion,[],[f238]) ).
cnf(s4,plain,
spl0_2,
inference(sat_conversion,[],[f241]) ).
cnf(s5,plain,
spl0_5,
inference(sat_conversion,[],[f480]) ).
cnf(s7,plain,
( ~ spl0_3
| spl0_4
| ~ spl0_5 ),
inference(sat_conversion,[],[f494]) ).
cnf(s8,plain,
~ spl0_4,
inference(rat,[],[s3,s5]) ).
cnf(s9,plain,
~ spl0_3,
inference(rat,[],[s7,s5,s8]) ).
cnf(s10,plain,
$false,
inference(rat,[],[s2,s9,s4]) ).
fof(f495,plain,
$false,
inference(avatar_sat_refutation,[],[s10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC068-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n007.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 07:40:55 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 2.58/1.25 % (2227766)Input is clausal, will run a generic CNF schedule.
% 2.58/1.25 % (2227775)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=2567756586:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.58/1.25 % (2227775)First to succeed.
% 2.58/1.25 % (2227775)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2227766"
% 2.58/1.25 % (2227771)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=4185381723:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.58/1.25 % (2227773)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=3097241962:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.58/1.25 % (2227774)lrs+10_1_sil=8000:sp=occurrence:random_seed=2111814830:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.58/1.25 % (2227772)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=537546503:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.58/1.25 % (2227774)Also succeeded, but the first one will report.
% 2.58/1.25 % (2227776)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=401537380:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.58/1.25 % (2227777)dis-21_1_sil=8000:lcm=predicate:random_seed=350543709:st=5:avsq=on:i=117:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/117Mi)
% 2.58/1.25 % (2227776)Also succeeded, but the first one will report.
% 2.58/1.25 % (2227777)Instruction limit reached!
% 2.58/1.25 % (2227777)------------------------------
% 2.58/1.25 % (2227777)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.58/1.25 % (2227777)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.58/1.25 % (2227777)CaDiCaL version: 2.1.3
% 2.58/1.25 % (2227777)Termination reason: Instruction limit
% 2.58/1.25 % (2227777)Termination phase: Saturation
% 2.58/1.25 % (2227777)Time elapsed: 0.069 s
% 2.58/1.25 % (2227777)Peak memory usage: 89 MB
% 2.58/1.25 % (2227777)Instructions burned: 117 (million)
% 2.58/1.25 % (2227775)Refutation found. Thanks to Tanya!
% 2.58/1.25 % SZS status Unsatisfiable for theBenchmark
% 2.58/1.25 % SZS output start Proof for theBenchmark
% See solution above
% 2.58/1.25 % (2227775)------------------------------
% 2.58/1.25 % (2227775)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.58/1.25 % (2227775)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.58/1.25 % (2227775)CaDiCaL version: 2.1.3
% 2.58/1.25 % (2227775)Termination reason: Refutation
% 2.58/1.25 % (2227775)Time elapsed: 0.006 s
% 2.58/1.25 % (2227775)Peak memory usage: 89 MB
% 2.58/1.25 % (2227775)Instructions burned: 14 (million)
% 2.58/1.25 % (2227775)------------------------------
% 2.58/1.25 % (2227775)------------------------------
% 2.58/1.25 % (2227766)Success in time 0.298 s
% 2.58/1.25 % Vampire exiting
%------------------------------------------------------------------------------