%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC059+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 : 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 01:02:15 PM UTC 2026
% Result : Theorem 2.57s 1.24s
% Output : Refutation 2.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 11
% Syntax : Number of formulae : 77 ( 12 unt; 9 def)
% Number of atoms : 246 ( 47 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 286 ( 117 ~; 106 |; 45 &)
% ( 9 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 14 ( 12 usr; 10 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 5 con; 0-0 aty)
% Number of variables : 28 ( 0 sgn 18 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f55,axiom,
! [X0] :
( ssList(X0)
=> segmentP(X0,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax55) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( X1 != X3
| X0 != X2
| ( nil != X2
& nil = X3 )
| ( neq(X3,nil)
& ( ~ neq(X2,nil)
| ~ segmentP(X3,X2) ) )
| ( ( nil != X1
| nil = X0 )
& ( ~ neq(X1,nil)
| ? [X4] :
( ssList(X4)
& neq(X4,nil)
& segmentP(X1,X4)
& segmentP(X0,X4) ) ) ) ) ) ) ) ),
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
| ( nil != X2
& nil = X3 )
| ( neq(X3,nil)
& ( ~ neq(X2,nil)
| ~ segmentP(X3,X2) ) )
| ( ( nil != X1
| nil = X0 )
& ( ~ neq(X1,nil)
| ? [X4] :
( ssList(X4)
& neq(X4,nil)
& segmentP(X1,X4)
& segmentP(X0,X4) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f172,plain,
! [X0] :
( segmentP(X0,X0)
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f55]) ).
fof(f221,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& ( nil = X2
| nil != X3 )
& ( ~ neq(X3,nil)
| ( neq(X2,nil)
& segmentP(X3,X2) ) )
& ( ( nil = X1
& nil != X0 )
| ( neq(X1,nil)
& ! [X4] :
( ~ ssList(X4)
| ~ neq(X4,nil)
| ~ segmentP(X1,X4)
| ~ segmentP(X0,X4) ) ) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(ennf_transformation,[],[f97]) ).
fof(f222,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& ( nil = X2
| nil != X3 )
& ( ~ neq(X3,nil)
| ( neq(X2,nil)
& segmentP(X3,X2) ) )
& ( ( nil = X1
& nil != X0 )
| ( neq(X1,nil)
& ! [X4] :
( ~ ssList(X4)
| ~ neq(X4,nil)
| ~ segmentP(X1,X4)
| ~ segmentP(X0,X4) ) ) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(flattening,[],[f221]) ).
fof(f296,plain,
( sK54 = sK56
& sK53 = sK55
& ( nil = sK55
| nil != sK56 )
& ( ~ neq(sK56,nil)
| ( neq(sK55,nil)
& segmentP(sK56,sK55) ) )
& ( ( nil = sK54
& nil != sK53 )
| ( neq(sK54,nil)
& ! [X4] :
( ~ ssList(X4)
| ~ neq(X4,nil)
| ~ segmentP(sK54,X4)
| ~ segmentP(sK53,X4) ) ) )
& ssList(sK56)
& ssList(sK55)
& ssList(sK54)
& ssList(sK53) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK53,sK54,sK55,sK56]),skolemize(X0,sK53),skolemize(X1,sK54),skolemize(X2,sK55),skolemize(X3,sK56)],[f222]) ).
fof(f440,plain,
! [X0] :
( segmentP(X0,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f172]) ).
fof(f496,plain,
ssList(sK53),
inference(cnf_transformation,[],[f296]) ).
fof(f500,plain,
! [X4] :
( nil != sK53
| ~ ssList(X4)
| ~ neq(X4,nil)
| ~ segmentP(sK54,X4)
| ~ segmentP(sK53,X4) ),
inference(cnf_transformation,[],[f296]) ).
fof(f501,plain,
( nil != sK53
| neq(sK54,nil) ),
inference(cnf_transformation,[],[f296]) ).
fof(f502,plain,
! [X4] :
( nil = sK54
| ~ ssList(X4)
| ~ neq(X4,nil)
| ~ segmentP(sK54,X4)
| ~ segmentP(sK53,X4) ),
inference(cnf_transformation,[],[f296]) ).
fof(f503,plain,
( nil = sK54
| neq(sK54,nil) ),
inference(cnf_transformation,[],[f296]) ).
fof(f504,plain,
( ~ neq(sK56,nil)
| segmentP(sK56,sK55) ),
inference(cnf_transformation,[],[f296]) ).
fof(f505,plain,
( ~ neq(sK56,nil)
| neq(sK55,nil) ),
inference(cnf_transformation,[],[f296]) ).
fof(f506,plain,
( nil = sK55
| nil != sK56 ),
inference(cnf_transformation,[],[f296]) ).
fof(f507,plain,
sK53 = sK55,
inference(cnf_transformation,[],[f296]) ).
fof(f508,plain,
sK54 = sK56,
inference(cnf_transformation,[],[f296]) ).
fof(f544,definition,
( spl57_1
<=> ! [X4] :
( ~ ssList(X4)
| ~ segmentP(sK53,X4)
| ~ segmentP(sK54,X4)
| ~ neq(X4,nil) ) ),
introduced(definition,[new_symbols(definition,[spl57_1])],[avatar_definition]) ).
fof(f545,plain,
( ! [X4] :
( ~ segmentP(sK53,X4)
| ~ ssList(X4)
| ~ segmentP(sK54,X4)
| ~ neq(X4,nil) )
| ~ spl57_1 ),
inference(avatar_component_clause,[],[f544]) ).
fof(f547,definition,
( spl57_2
<=> nil = sK53 ),
introduced(definition,[new_symbols(definition,[spl57_2])],[avatar_definition]) ).
fof(f549,plain,
( nil != sK53
| spl57_2 ),
inference(avatar_component_clause,[],[f547]) ).
fof(f550,plain,
( spl57_1
| ~ spl57_2 ),
inference(avatar_split_clause,[],[f500,f547,f544]) ).
fof(f552,definition,
( spl57_3
<=> neq(sK54,nil) ),
introduced(definition,[new_symbols(definition,[spl57_3])],[avatar_definition]) ).
fof(f555,plain,
( spl57_3
| ~ spl57_2 ),
inference(avatar_split_clause,[],[f501,f547,f552]) ).
fof(f557,definition,
( spl57_4
<=> nil = sK54 ),
introduced(definition,[new_symbols(definition,[spl57_4])],[avatar_definition]) ).
fof(f560,plain,
( spl57_1
| spl57_4 ),
inference(avatar_split_clause,[],[f502,f557,f544]) ).
fof(f561,plain,
( spl57_3
| spl57_4 ),
inference(avatar_split_clause,[],[f503,f557,f552]) ).
fof(f563,definition,
( spl57_5
<=> segmentP(sK56,sK55) ),
introduced(definition,[new_symbols(definition,[spl57_5])],[avatar_definition]) ).
fof(f565,plain,
( segmentP(sK56,sK55)
| ~ spl57_5 ),
inference(avatar_component_clause,[],[f563]) ).
fof(f567,definition,
( spl57_6
<=> neq(sK56,nil) ),
introduced(definition,[new_symbols(definition,[spl57_6])],[avatar_definition]) ).
fof(f569,plain,
( ~ neq(sK56,nil)
| spl57_6 ),
inference(avatar_component_clause,[],[f567]) ).
fof(f570,plain,
( spl57_5
| ~ spl57_6 ),
inference(avatar_split_clause,[],[f504,f567,f563]) ).
fof(f572,definition,
( spl57_7
<=> neq(sK55,nil) ),
introduced(definition,[new_symbols(definition,[spl57_7])],[avatar_definition]) ).
fof(f574,plain,
( neq(sK55,nil)
| ~ spl57_7 ),
inference(avatar_component_clause,[],[f572]) ).
fof(f575,plain,
( spl57_7
| ~ spl57_6 ),
inference(avatar_split_clause,[],[f505,f567,f572]) ).
fof(f577,definition,
( spl57_8
<=> nil = sK56 ),
introduced(definition,[new_symbols(definition,[spl57_8])],[avatar_definition]) ).
fof(f579,plain,
( nil != sK56
| spl57_8 ),
inference(avatar_component_clause,[],[f577]) ).
fof(f581,definition,
( spl57_9
<=> nil = sK55 ),
introduced(definition,[new_symbols(definition,[spl57_9])],[avatar_definition]) ).
fof(f583,plain,
( nil = sK55
| ~ spl57_9 ),
inference(avatar_component_clause,[],[f581]) ).
fof(f584,plain,
( ~ spl57_8
| spl57_9 ),
inference(avatar_split_clause,[],[f506,f581,f577]) ).
fof(f624,plain,
( ~ neq(sK54,nil)
| spl57_6 ),
inference(forward_demodulation,[],[f569,f508]) ).
fof(f626,plain,
( nil != sK54
| spl57_8 ),
inference(forward_demodulation,[],[f579,f508]) ).
fof(f633,plain,
( nil = sK53
| ~ spl57_9 ),
inference(superposition,[],[f583,f507]) ).
fof(f639,plain,
( $false
| spl57_2
| ~ spl57_9 ),
inference(forward_subsumption_resolution,[],[f633,f549]) ).
fof(f640,plain,
( spl57_2
| ~ spl57_9 ),
inference(avatar_contradiction_clause,[],[f639]) ).
fof(f642,plain,
( ~ spl57_4
| spl57_8 ),
inference(avatar_split_clause,[],[f626,f577,f557]) ).
fof(f644,plain,
( ~ spl57_3
| spl57_6 ),
inference(avatar_split_clause,[],[f624,f567,f552]) ).
fof(f645,plain,
( segmentP(sK56,sK53)
| ~ spl57_5 ),
inference(forward_demodulation,[],[f565,f507]) ).
fof(f647,plain,
( neq(sK53,nil)
| ~ spl57_7 ),
inference(forward_demodulation,[],[f574,f507]) ).
fof(f648,plain,
( segmentP(sK54,sK53)
| ~ spl57_5 ),
inference(forward_demodulation,[],[f645,f508]) ).
fof(f650,plain,
( ~ ssList(sK53)
| ~ ssList(sK53)
| ~ segmentP(sK54,sK53)
| ~ neq(sK53,nil)
| ~ spl57_1 ),
inference(resolution,[],[f440,f545]) ).
fof(f651,plain,
( ~ ssList(sK53)
| ~ segmentP(sK54,sK53)
| ~ neq(sK53,nil)
| ~ spl57_1 ),
inference(duplicate_literal_removal,[],[f650]) ).
fof(f652,plain,
( ~ segmentP(sK54,sK53)
| ~ neq(sK53,nil)
| ~ spl57_1 ),
inference(forward_subsumption_resolution,[],[f651,f496]) ).
fof(f653,plain,
( ~ neq(sK53,nil)
| ~ spl57_1
| ~ spl57_5 ),
inference(forward_subsumption_resolution,[],[f652,f648]) ).
fof(f654,plain,
( $false
| ~ spl57_1
| ~ spl57_5
| ~ spl57_7 ),
inference(forward_subsumption_resolution,[],[f653,f647]) ).
fof(f655,plain,
( ~ spl57_1
| ~ spl57_5
| ~ spl57_7 ),
inference(avatar_contradiction_clause,[],[f654]) ).
cnf(s1,plain,
( spl57_1
| ~ spl57_2 ),
inference(sat_conversion,[],[f550]) ).
cnf(s2,plain,
( ~ spl57_2
| spl57_3 ),
inference(sat_conversion,[],[f555]) ).
cnf(s3,plain,
( spl57_1
| spl57_4 ),
inference(sat_conversion,[],[f560]) ).
cnf(s4,plain,
( spl57_3
| spl57_4 ),
inference(sat_conversion,[],[f561]) ).
cnf(s5,plain,
( spl57_5
| ~ spl57_6 ),
inference(sat_conversion,[],[f570]) ).
cnf(s6,plain,
( ~ spl57_6
| spl57_7 ),
inference(sat_conversion,[],[f575]) ).
cnf(s7,plain,
( ~ spl57_8
| spl57_9 ),
inference(sat_conversion,[],[f584]) ).
cnf(s22,plain,
( spl57_2
| ~ spl57_9 ),
inference(sat_conversion,[],[f640]) ).
cnf(s23,plain,
( ~ spl57_4
| spl57_8 ),
inference(sat_conversion,[],[f642]) ).
cnf(s24,plain,
( ~ spl57_3
| spl57_6 ),
inference(sat_conversion,[],[f644]) ).
cnf(s27,plain,
( ~ spl57_1
| ~ spl57_5
| ~ spl57_7 ),
inference(sat_conversion,[],[f655]) ).
cnf(s32,plain,
spl57_1,
inference(rat,[],[s7,s22,s23,s1,s3]) ).
cnf(s33,plain,
~ spl57_6,
inference(rat,[],[s27,s5,s6,s32]) ).
cnf(s34,plain,
~ spl57_3,
inference(rat,[],[s24,s33]) ).
cnf(s35,plain,
spl57_4,
inference(rat,[],[s4,s34]) ).
cnf(s36,plain,
~ spl57_2,
inference(rat,[],[s2,s34]) ).
cnf(s37,plain,
spl57_8,
inference(rat,[],[s23,s35]) ).
cnf(s38,plain,
~ spl57_9,
inference(rat,[],[s22,s36]) ).
cnf(s39,plain,
$false,
inference(rat,[],[s7,s38,s37]) ).
fof(f656,plain,
$false,
inference(avatar_sat_refutation,[],[s39]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC059+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.37 % Computer : n002.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Mon Sep 28 07:42:22 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
% 2.57/1.24 % (192328)Detected formulas, will run a generic FOF schedule.
% 2.57/1.24 % (192338)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3698933650:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.57/1.24 % (192338)First to succeed.
% 2.57/1.24 % (192338)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-192328"
% 2.57/1.24 % (192337)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1953477540:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.57/1.24 % (192335)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=35065645:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.57/1.24 % (192333)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=3011655527:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.57/1.24 % (192339)dis-21_1_sil=8000:lcm=predicate:random_seed=1421234019: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)
% 2.57/1.24 % (192336)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2010911645:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.57/1.24 % (192334)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=2911455757:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.57/1.24 % (192337)Also succeeded, but the first one will report.
% 2.57/1.24 % (192336)Also succeeded, but the first one will report.
% 2.57/1.24 % (192339)Also succeeded, but the first one will report.
% 2.57/1.24 % (192338)Refutation found. Thanks to Tanya!
% 2.57/1.24 % SZS status Theorem for theBenchmark
% 2.57/1.24 % SZS output start Proof for theBenchmark
% See solution above
% 2.57/1.24 % (192338)------------------------------
% 2.57/1.24 % (192338)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.57/1.24 % (192338)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.57/1.24 % (192338)CaDiCaL version: 2.1.3
% 2.57/1.24 % (192338)Termination reason: Refutation
% 2.57/1.24 % (192338)Time elapsed: 0.005 s
% 2.57/1.24 % (192338)Peak memory usage: 90 MB
% 2.57/1.24 % (192338)Instructions burned: 12 (million)
% 2.57/1.24 % (192338)------------------------------
% 2.57/1.24 % (192338)------------------------------
% 2.57/1.24 % (192328)Success in time 0.295 s
% 2.57/1.24 % Vampire exiting
%------------------------------------------------------------------------------