%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC259+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 : n013.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 01:03:10 PM UTC 2026
% Result : Theorem 0.19s 1.31s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 8
% Syntax : Number of formulae : 48 ( 13 unt; 5 def)
% Number of atoms : 200 ( 40 equ)
% Maximal formula atoms : 20 ( 4 avg)
% Number of connectives : 239 ( 87 ~; 73 |; 64 &)
% ( 4 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 5 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-2 aty)
% Number of variables : 65 ( 0 sgn 41 !; 24 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f65,axiom,
! [X0] :
( ssItem(X0)
=> totalorderedP(cons(X0,nil)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax65) ).
fof(f66,axiom,
totalorderedP(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax66) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ~ ssList(X3)
| X1 != X3
| X0 != X2
| totalorderedP(X0)
| ( ! [X4] :
( ssItem(X4)
=> ! [X5] :
( ssList(X5)
=> ! [X6] :
( ~ ssList(X6)
| cons(X4,nil) != X2
| app(app(X5,X2),X6) != X3
| ? [X7] :
( ssItem(X7)
& memberP(X5,X7)
& lt(X4,X7) )
| ? [X8] :
( ssItem(X8)
& memberP(X6,X8)
& lt(X8,X4) ) ) ) )
& ( nil != X3
| nil != X2 ) ) ) ) ) ),
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
| totalorderedP(X0)
| ( ! [X4] :
( ssItem(X4)
=> ! [X5] :
( ssList(X5)
=> ! [X6] :
( ~ ssList(X6)
| cons(X4,nil) != X2
| app(app(X5,X2),X6) != X3
| ? [X7] :
( ssItem(X7)
& memberP(X5,X7)
& lt(X4,X7) )
| ? [X8] :
( ssItem(X8)
& memberP(X6,X8)
& lt(X8,X4) ) ) ) )
& ( nil != X3
| nil != X2 ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f180,plain,
! [X0] :
( totalorderedP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f65]) ).
fof(f221,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ssList(X3)
& X1 = X3
& X0 = X2
& ~ totalorderedP(X0)
& ( ? [X4] :
( ? [X5] :
( ? [X6] :
( ssList(X6)
& cons(X4,nil) = X2
& app(app(X5,X2),X6) = X3
& ! [X7] :
( ~ ssItem(X7)
| ~ memberP(X5,X7)
| ~ lt(X4,X7) )
& ! [X8] :
( ~ ssItem(X8)
| ~ memberP(X6,X8)
| ~ lt(X8,X4) ) )
& ssList(X5) )
& ssItem(X4) )
| ( nil = X3
& nil = X2 ) ) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(ennf_transformation,[],[f97]) ).
fof(f231,definition,
! [X2,X3] :
( ? [X4] :
( ? [X5] :
( ? [X6] :
( ssList(X6)
& cons(X4,nil) = X2
& app(app(X5,X2),X6) = X3
& ! [X7] :
( ~ ssItem(X7)
| ~ memberP(X5,X7)
| ~ lt(X4,X7) )
& ! [X8] :
( ~ ssItem(X8)
| ~ memberP(X6,X8)
| ~ lt(X8,X4) ) )
& ssList(X5) )
& ssItem(X4) )
| ~ sP6(X2,X3) ),
introduced(definition,[new_symbols(definition,[sP6])],[predicate_definition_introduction]) ).
fof(f232,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ssList(X3)
& X1 = X3
& X0 = X2
& ~ totalorderedP(X0)
& ( sP6(X2,X3)
| ( nil = X3
& nil = X2 ) ) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(definition_folding,[],[f221,f231]) ).
fof(f297,plain,
! [X2,X3] :
( ? [X4] :
( ? [X5] :
( ? [X6] :
( ssList(X6)
& cons(X4,nil) = X2
& app(app(X5,X2),X6) = X3
& ! [X7] :
( ~ ssItem(X7)
| ~ memberP(X5,X7)
| ~ lt(X4,X7) )
& ! [X8] :
( ~ ssItem(X8)
| ~ memberP(X6,X8)
| ~ lt(X8,X4) ) )
& ssList(X5) )
& ssItem(X4) )
| ~ sP6(X2,X3) ),
inference(nnf_transformation,[],[f231]) ).
fof(f298,plain,
! [X0,X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ssList(X4)
& cons(X2,nil) = X0
& app(app(X3,X0),X4) = X1
& ! [X5] :
( ~ ssItem(X5)
| ~ memberP(X3,X5)
| ~ lt(X2,X5) )
& ! [X6] :
( ~ ssItem(X6)
| ~ memberP(X4,X6)
| ~ lt(X6,X2) ) )
& ssList(X3) )
& ssItem(X2) )
| ~ sP6(X0,X1) ),
inference(rectify,[],[f297]) ).
fof(f299,plain,
! [X0,X1] :
( ( ssList(sK56(X0,X1))
& cons(sK54(X0,X1),nil) = X0
& app(app(sK55(X0,X1),X0),sK56(X0,X1)) = X1
& ! [X5] :
( ~ ssItem(X5)
| ~ memberP(sK55(X0,X1),X5)
| ~ lt(sK54(X0,X1),X5) )
& ! [X6] :
( ~ ssItem(X6)
| ~ memberP(sK56(X0,X1),X6)
| ~ lt(X6,sK54(X0,X1)) )
& ssList(sK55(X0,X1))
& ssItem(sK54(X0,X1)) )
| ~ sP6(X0,X1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK54,sK55,sK56]),skolemize(X2,sK54(X0,X1)),skolemize(X3,sK55(X0,X1)),skolemize(X4,sK56(X0,X1))],[f298]) ).
fof(f300,plain,
( ssList(sK60)
& sK58 = sK60
& sK57 = sK59
& ~ totalorderedP(sK57)
& ( sP6(sK59,sK60)
| ( nil = sK60
& nil = sK59 ) )
& ssList(sK59)
& ssList(sK58)
& ssList(sK57) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK57,sK58,sK59,sK60]),skolemize(X0,sK57),skolemize(X1,sK58),skolemize(X2,sK59),skolemize(X3,sK60)],[f232]) ).
fof(f455,plain,
! [X0] :
( totalorderedP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f180]) ).
fof(f456,plain,
totalorderedP(nil),
inference(cnf_transformation,[],[f66]) ).
fof(f500,plain,
! [X0,X1] :
( ssItem(sK54(X0,X1))
| ~ sP6(X0,X1) ),
inference(cnf_transformation,[],[f299]) ).
fof(f505,plain,
! [X0,X1] :
( ~ sP6(X0,X1)
| cons(sK54(X0,X1),nil) = X0 ),
inference(cnf_transformation,[],[f299]) ).
fof(f510,plain,
( sP6(sK59,sK60)
| nil = sK59 ),
inference(cnf_transformation,[],[f300]) ).
fof(f512,plain,
~ totalorderedP(sK57),
inference(cnf_transformation,[],[f300]) ).
fof(f513,plain,
sK57 = sK59,
inference(cnf_transformation,[],[f300]) ).
fof(f551,definition,
( spl61_1
<=> nil = sK59 ),
introduced(definition,[new_symbols(definition,[spl61_1])],[avatar_definition]) ).
fof(f553,plain,
( nil = sK59
| ~ spl61_1 ),
inference(avatar_component_clause,[],[f551]) ).
fof(f555,definition,
( spl61_2
<=> sP6(sK59,sK60) ),
introduced(definition,[new_symbols(definition,[spl61_2])],[avatar_definition]) ).
fof(f557,plain,
( sP6(sK59,sK60)
| ~ spl61_2 ),
inference(avatar_component_clause,[],[f555]) ).
fof(f558,plain,
( spl61_1
| spl61_2 ),
inference(avatar_split_clause,[],[f510,f555,f551]) ).
fof(f579,definition,
( spl61_7
<=> ! [X0] :
( totalorderedP(cons(X0,nil))
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[spl61_7])],[avatar_definition]) ).
fof(f580,plain,
( ! [X0] :
( totalorderedP(cons(X0,nil))
| ~ ssItem(X0) )
| ~ spl61_7 ),
inference(avatar_component_clause,[],[f579]) ).
fof(f582,plain,
spl61_7,
inference(avatar_split_clause,[],[f455,f579]) ).
fof(f599,plain,
~ totalorderedP(sK59),
inference(superposition,[],[f512,f513]) ).
fof(f647,plain,
( sK59 = cons(sK54(sK59,sK60),nil)
| ~ spl61_2 ),
inference(resolution,[],[f505,f557]) ).
fof(f655,plain,
( totalorderedP(sK59)
| ~ ssItem(sK54(sK59,sK60))
| ~ spl61_2
| ~ spl61_7 ),
inference(superposition,[],[f580,f647]) ).
fof(f667,plain,
( ~ ssItem(sK54(sK59,sK60))
| ~ spl61_2
| ~ spl61_7 ),
inference(forward_subsumption_resolution,[],[f655,f599]) ).
fof(f669,definition,
( spl61_11
<=> ssItem(sK54(sK59,sK60)) ),
introduced(definition,[new_symbols(definition,[spl61_11])],[avatar_definition]) ).
fof(f671,plain,
( ~ ssItem(sK54(sK59,sK60))
| spl61_11 ),
inference(avatar_component_clause,[],[f669]) ).
fof(f720,plain,
( ~ spl61_11
| ~ spl61_2
| ~ spl61_7 ),
inference(avatar_split_clause,[],[f667,f579,f555,f669]) ).
fof(f726,plain,
( ~ sP6(sK59,sK60)
| spl61_11 ),
inference(resolution,[],[f671,f500]) ).
fof(f729,plain,
( ~ spl61_2
| spl61_11 ),
inference(avatar_split_clause,[],[f726,f669,f555]) ).
fof(f731,plain,
( ~ totalorderedP(nil)
| ~ spl61_1 ),
inference(superposition,[],[f599,f553]) ).
fof(f733,plain,
( $false
| ~ spl61_1 ),
inference(forward_subsumption_resolution,[],[f731,f456]) ).
fof(f734,plain,
~ spl61_1,
inference(avatar_contradiction_clause,[],[f733]) ).
cnf(s1,plain,
( spl61_1
| spl61_2 ),
inference(sat_conversion,[],[f558]) ).
cnf(s7,plain,
spl61_7,
inference(sat_conversion,[],[f582]) ).
cnf(s23,plain,
( ~ spl61_2
| ~ spl61_7
| ~ spl61_11 ),
inference(sat_conversion,[],[f720]) ).
cnf(s26,plain,
( ~ spl61_2
| spl61_11 ),
inference(sat_conversion,[],[f729]) ).
cnf(s27,plain,
~ spl61_1,
inference(sat_conversion,[],[f734]) ).
cnf(s32,plain,
spl61_2,
inference(rat,[],[s1,s27]) ).
cnf(s33,plain,
spl61_11,
inference(rat,[],[s26,s32]) ).
cnf(s34,plain,
$false,
inference(rat,[],[s23,s7,s33,s32]) ).
fof(f735,plain,
$false,
inference(avatar_sat_refutation,[],[s34]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC259+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n013.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Mon Sep 28 08:44:45 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 Running first-order theorem proving
% 0.09/0.22 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
% 0.19/1.31 % (1031270)Detected formulas, will run a generic FOF schedule.
% 0.19/1.31 % (1031301)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=663382120:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 0.19/1.31 % (1031301)First to succeed.
% 0.19/1.31 % (1031301)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1031270"
% 0.19/1.31 % (1031296)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=3867357275:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 0.19/1.31 % (1031297)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=1039849868:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 0.19/1.31 % (1031299)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2037229535:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 0.19/1.31 % (1031302)dis-21_1_sil=8000:lcm=predicate:random_seed=1652420344: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)
% 0.19/1.31 % (1031298)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=2108169611:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 0.19/1.31 % (1031299)Refutation not found, incomplete strategy
% 0.19/1.31 % (1031299)------------------------------
% 0.19/1.31 % (1031299)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.19/1.31 % (1031299)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/1.31 % (1031299)CaDiCaL version: 2.1.3
% 0.19/1.31 % (1031299)Termination reason: Refutation not found, incomplete strategy
% 0.19/1.31 % (1031299)Time elapsed: 0.007 s
% 0.19/1.31 % (1031299)Peak memory usage: 88 MB
% 0.19/1.31 % (1031299)Instructions burned: 5 (million)
% 0.19/1.31 % (1031300)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1642655074:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 0.19/1.31 % (1031300)Also succeeded, but the first one will report.
% 0.19/1.31 % (1031302)Instruction limit reached!
% 0.19/1.31 % (1031302)------------------------------
% 0.19/1.31 % (1031302)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.19/1.31 % (1031302)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/1.31 % (1031302)CaDiCaL version: 2.1.3
% 0.19/1.31 % (1031302)Termination reason: Instruction limit
% 0.19/1.31 % (1031302)Termination phase: Saturation
% 0.19/1.31 % (1031302)Time elapsed: 0.121 s
% 0.19/1.31 % (1031302)Peak memory usage: 91 MB
% 0.19/1.31 % (1031302)Instructions burned: 129 (million)
% 0.19/1.31 % (1031301)Refutation found. Thanks to Tanya!
% 0.19/1.31 % SZS status Theorem for theBenchmark
% 0.19/1.31 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/1.31 % (1031301)------------------------------
% 0.19/1.31 % (1031301)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.19/1.31 % (1031301)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/1.31 % (1031301)CaDiCaL version: 2.1.3
% 0.19/1.31 % (1031301)Termination reason: Refutation
% 0.19/1.31 % (1031301)Time elapsed: 0.012 s
% 0.19/1.31 % (1031301)Peak memory usage: 90 MB
% 0.19/1.31 % (1031301)Instructions burned: 18 (million)
% 0.19/1.31 % (1031301)------------------------------
% 0.19/1.31 % (1031301)------------------------------
% 0.19/1.31 % (1031270)Success in time 0.409 s
% 0.19/1.31 % Vampire exiting
%------------------------------------------------------------------------------