%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC104+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 : n008.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 01:02:27 PM UTC 2026
% Result : Theorem 2.72s 1.30s
% Output : Refutation 3.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 10
% Syntax : Number of formulae : 76 ( 21 unt; 6 def)
% Number of atoms : 283 ( 61 equ)
% Maximal formula atoms : 21 ( 3 avg)
% Number of connectives : 334 ( 127 ~; 123 |; 61 &)
% ( 9 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 14 ( 12 usr; 6 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 70 ( 0 sgn 48 !; 22 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( frontsegP(X0,X1)
<=> ? [X2] :
( ssList(X2)
& app(X1,X2) = X0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax5) ).
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(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( X1 != X3
| X0 != X2
| ~ neq(X1,nil)
| ! [X4] :
( ssList(X4)
=> ( app(X2,X4) != X3
| ~ totalorderedP(X2)
| ? [X5] :
( ssItem(X5)
& ? [X6] :
( ssList(X6)
& app(cons(X5,nil),X6) = X4
& ? [X7] :
( ssItem(X7)
& ? [X8] :
( ssList(X8)
& app(X8,cons(X7,nil)) = X2
& leq(X7,X5) ) ) ) ) ) )
| ( nil != X3
& nil = X2 )
| ( neq(X0,nil)
& frontsegP(X1,X0) ) ) ) ) ) ),
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
| ~ neq(X1,nil)
| ! [X4] :
( ssList(X4)
=> ( app(X2,X4) != X3
| ~ totalorderedP(X2)
| ? [X5] :
( ssItem(X5)
& ? [X6] :
( ssList(X6)
& app(cons(X5,nil),X6) = X4
& ? [X7] :
( ssItem(X7)
& ? [X8] :
( ssList(X8)
& app(X8,cons(X7,nil)) = X2
& leq(X7,X5) ) ) ) ) ) )
| ( nil != X3
& nil = X2 )
| ( neq(X0,nil)
& frontsegP(X1,X0) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f98,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& neq(X1,nil)
& ? [X4] :
( app(X2,X4) = X3
& totalorderedP(X2)
& ! [X5] :
( ~ ssItem(X5)
| ! [X6] :
( ~ ssList(X6)
| app(cons(X5,nil),X6) != X4
| ! [X7] :
( ~ ssItem(X7)
| ! [X8] :
( ~ ssList(X8)
| app(X8,cons(X7,nil)) != X2
| ~ leq(X7,X5) ) ) ) )
& ssList(X4) )
& ( nil = X3
| nil != X2 )
& ( ~ neq(X0,nil)
| ~ frontsegP(X1,X0) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(ennf_transformation,[],[f97]) ).
fof(f99,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& neq(X1,nil)
& ? [X4] :
( app(X2,X4) = X3
& totalorderedP(X2)
& ! [X5] :
( ~ ssItem(X5)
| ! [X6] :
( ~ ssList(X6)
| app(cons(X5,nil),X6) != X4
| ! [X7] :
( ~ ssItem(X7)
| ! [X8] :
( ~ ssList(X8)
| app(X8,cons(X7,nil)) != X2
| ~ leq(X7,X5) ) ) ) )
& ssList(X4) )
& ( nil = X3
| nil != X2 )
& ( ~ neq(X0,nil)
| ~ frontsegP(X1,X0) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(flattening,[],[f98]) ).
fof(f118,plain,
! [X0] :
( ! [X1] :
( ( neq(X0,X1)
<=> X0 != X1 )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f130,plain,
! [X0] :
( ! [X1] :
( ( frontsegP(X0,X1)
<=> ? [X2] :
( ssList(X2)
& app(X1,X2) = X0 ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f5]) ).
fof(f140,plain,
( sK1 = sK3
& sK0 = sK2
& neq(sK1,nil)
& sK3 = app(sK2,sK4)
& totalorderedP(sK2)
& ! [X5] :
( ~ ssItem(X5)
| ! [X6] :
( ~ ssList(X6)
| app(cons(X5,nil),X6) != sK4
| ! [X7] :
( ~ ssItem(X7)
| ! [X8] :
( ~ ssList(X8)
| app(X8,cons(X7,nil)) != sK2
| ~ leq(X7,X5) ) ) ) )
& ssList(sK4)
& ( nil = sK3
| nil != sK2 )
& ( ~ neq(sK0,nil)
| ~ frontsegP(sK1,sK0) )
& ssList(sK3)
& ssList(sK2)
& ssList(sK1)
& ssList(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X4,sK4)],[f99]) ).
fof(f145,plain,
! [X0] :
( ! [X1] :
( ( ( neq(X0,X1)
| X0 = X1 )
& ( X0 != X1
| ~ neq(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f118]) ).
fof(f150,plain,
! [X0] :
( ! [X1] :
( ( ( frontsegP(X0,X1)
| ! [X2] :
( ~ ssList(X2)
| app(X1,X2) != X0 ) )
& ( ? [X2] :
( ssList(X2)
& app(X1,X2) = X0 )
| ~ frontsegP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f130]) ).
fof(f151,plain,
! [X0] :
( ! [X1] :
( ( ( frontsegP(X0,X1)
| ! [X2] :
( ~ ssList(X2)
| app(X1,X2) != X0 ) )
& ( ? [X3] :
( ssList(X3)
& app(X1,X3) = X0 )
| ~ frontsegP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(rectify,[],[f150]) ).
fof(f152,plain,
! [X0] :
( ! [X1] :
( ( ( frontsegP(X0,X1)
| ! [X2] :
( ~ ssList(X2)
| app(X1,X2) != X0 ) )
& ( ( ssList(sK9(X0,X1))
& app(X1,sK9(X0,X1)) = X0 )
| ~ frontsegP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(X3,sK9(X0,X1))],[f151]) ).
fof(f158,plain,
ssList(sK0),
inference(cnf_transformation,[],[f140]) ).
fof(f159,plain,
ssList(sK1),
inference(cnf_transformation,[],[f140]) ).
fof(f162,plain,
( ~ neq(sK0,nil)
| ~ frontsegP(sK1,sK0) ),
inference(cnf_transformation,[],[f140]) ).
fof(f163,plain,
( nil = sK3
| nil != sK2 ),
inference(cnf_transformation,[],[f140]) ).
fof(f164,plain,
ssList(sK4),
inference(cnf_transformation,[],[f140]) ).
fof(f167,plain,
sK3 = app(sK2,sK4),
inference(cnf_transformation,[],[f140]) ).
fof(f168,plain,
neq(sK1,nil),
inference(cnf_transformation,[],[f140]) ).
fof(f169,plain,
sK0 = sK2,
inference(cnf_transformation,[],[f140]) ).
fof(f170,plain,
sK1 = sK3,
inference(cnf_transformation,[],[f140]) ).
fof(f194,plain,
! [X0,X1] :
( neq(X0,X1)
| X0 = X1
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f145]) ).
fof(f197,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f210,plain,
! [X2,X0,X1] :
( frontsegP(X0,X1)
| ~ ssList(X2)
| app(X1,X2) != X0
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f152]) ).
fof(f229,plain,
neq(sK3,nil),
inference(definition_unfolding,[],[f168,f170]) ).
fof(f230,plain,
( ~ neq(sK2,nil)
| ~ frontsegP(sK3,sK2) ),
inference(definition_unfolding,[],[f162,f169,f170,f169]) ).
fof(f231,plain,
ssList(sK3),
inference(definition_unfolding,[],[f159,f170]) ).
fof(f232,plain,
ssList(sK2),
inference(definition_unfolding,[],[f158,f169]) ).
fof(f236,definition,
~ sP17(nil),
introduced(definition,[new_symbols(definition,[sP17])],[inequality_splitting_name_introduction]) ).
fof(f237,plain,
( nil = sK3
| sP17(sK2) ),
inference(inequality_splitting,[],[f163,f236]) ).
fof(f258,plain,
! [X2,X1] :
( frontsegP(app(X1,X2),X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(app(X1,X2)) ),
inference(equality_resolution,[],[f210]) ).
fof(f268,definition,
( spl29_1
<=> frontsegP(sK3,sK2) ),
introduced(definition,[new_symbols(definition,[spl29_1])],[avatar_definition]) ).
fof(f270,plain,
( ~ frontsegP(sK3,sK2)
| spl29_1 ),
inference(avatar_component_clause,[],[f268]) ).
fof(f272,definition,
( spl29_2
<=> neq(sK2,nil) ),
introduced(definition,[new_symbols(definition,[spl29_2])],[avatar_definition]) ).
fof(f274,plain,
( ~ neq(sK2,nil)
| spl29_2 ),
inference(avatar_component_clause,[],[f272]) ).
fof(f275,plain,
( ~ spl29_1
| ~ spl29_2 ),
inference(avatar_split_clause,[],[f230,f272,f268]) ).
fof(f277,definition,
( spl29_3
<=> sP17(sK2) ),
introduced(definition,[new_symbols(definition,[spl29_3])],[avatar_definition]) ).
fof(f279,plain,
( sP17(sK2)
| ~ spl29_3 ),
inference(avatar_component_clause,[],[f277]) ).
fof(f281,definition,
( spl29_4
<=> nil = sK3 ),
introduced(definition,[new_symbols(definition,[spl29_4])],[avatar_definition]) ).
fof(f283,plain,
( nil = sK3
| ~ spl29_4 ),
inference(avatar_component_clause,[],[f281]) ).
fof(f284,plain,
( spl29_3
| spl29_4 ),
inference(avatar_split_clause,[],[f237,f281,f277]) ).
fof(f296,plain,
( frontsegP(sK3,sK2)
| ~ ssList(sK4)
| ~ ssList(sK2)
| ~ ssList(sK3) ),
inference(superposition,[],[f258,f167]) ).
fof(f297,plain,
( ~ ssList(sK4)
| ~ ssList(sK2)
| ~ ssList(sK3)
| spl29_1 ),
inference(forward_subsumption_resolution,[],[f296,f270]) ).
fof(f308,plain,
( ~ ssList(sK2)
| ~ ssList(sK3)
| spl29_1 ),
inference(forward_subsumption_resolution,[],[f297,f164]) ).
fof(f319,plain,
( ~ ssList(sK3)
| spl29_1 ),
inference(forward_subsumption_resolution,[],[f308,f232]) ).
fof(f321,definition,
( spl29_5
<=> nil = sK2 ),
introduced(definition,[new_symbols(definition,[spl29_5])],[avatar_definition]) ).
fof(f322,plain,
( nil != sK2
| spl29_5 ),
inference(avatar_component_clause,[],[f321]) ).
fof(f323,plain,
( nil = sK2
| ~ spl29_5 ),
inference(avatar_component_clause,[],[f321]) ).
fof(f348,plain,
( $false
| spl29_1 ),
inference(forward_subsumption_resolution,[],[f319,f231]) ).
fof(f349,plain,
spl29_1,
inference(avatar_contradiction_clause,[],[f348]) ).
fof(f363,plain,
( nil = sK2
| ~ ssList(nil)
| ~ ssList(sK2)
| spl29_2 ),
inference(resolution,[],[f274,f194]) ).
fof(f365,plain,
( neq(nil,nil)
| ~ spl29_4 ),
inference(superposition,[],[f229,f283]) ).
fof(f373,plain,
( ~ neq(nil,nil)
| spl29_2
| ~ spl29_5 ),
inference(superposition,[],[f274,f323]) ).
fof(f374,plain,
( sP17(nil)
| ~ spl29_3
| ~ spl29_5 ),
inference(superposition,[],[f279,f323]) ).
fof(f375,plain,
( $false
| ~ spl29_3
| ~ spl29_5 ),
inference(forward_subsumption_resolution,[],[f374,f236]) ).
fof(f376,plain,
( ~ spl29_3
| ~ spl29_5 ),
inference(avatar_contradiction_clause,[],[f375]) ).
fof(f377,plain,
( $false
| spl29_2
| ~ spl29_4
| ~ spl29_5 ),
inference(forward_subsumption_resolution,[],[f373,f365]) ).
fof(f378,plain,
( spl29_2
| ~ spl29_4
| ~ spl29_5 ),
inference(avatar_contradiction_clause,[],[f377]) ).
fof(f384,plain,
( ~ ssList(nil)
| ~ ssList(sK2)
| spl29_2
| spl29_5 ),
inference(forward_subsumption_resolution,[],[f363,f322]) ).
fof(f389,plain,
( ~ ssList(sK2)
| spl29_2
| spl29_5 ),
inference(forward_subsumption_resolution,[],[f384,f197]) ).
fof(f399,plain,
( $false
| spl29_2
| spl29_5 ),
inference(forward_subsumption_resolution,[],[f389,f232]) ).
fof(f400,plain,
( spl29_2
| spl29_5 ),
inference(avatar_contradiction_clause,[],[f399]) ).
cnf(s1,plain,
( ~ spl29_1
| ~ spl29_2 ),
inference(sat_conversion,[],[f275]) ).
cnf(s2,plain,
( spl29_3
| spl29_4 ),
inference(sat_conversion,[],[f284]) ).
cnf(s7,plain,
spl29_1,
inference(sat_conversion,[],[f349]) ).
cnf(s8,plain,
( ~ spl29_3
| ~ spl29_5 ),
inference(sat_conversion,[],[f376]) ).
cnf(s9,plain,
( spl29_2
| ~ spl29_4
| ~ spl29_5 ),
inference(sat_conversion,[],[f378]) ).
cnf(s12,plain,
( spl29_2
| spl29_5 ),
inference(sat_conversion,[],[f400]) ).
cnf(s13,plain,
~ spl29_2,
inference(rat,[],[s1,s7]) ).
cnf(s14,plain,
spl29_5,
inference(rat,[],[s12,s13]) ).
cnf(s15,plain,
~ spl29_4,
inference(rat,[],[s9,s14,s13]) ).
cnf(s16,plain,
~ spl29_3,
inference(rat,[],[s8,s14]) ).
cnf(s17,plain,
$false,
inference(rat,[],[s2,s15,s16]) ).
fof(f401,plain,
$false,
inference(avatar_sat_refutation,[],[s17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC104+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n008.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Mon Sep 28 07:53:54 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 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
% 2.72/1.30 % (2088084)Detected formulas, will run a generic FOF schedule.
% 2.72/1.30 % (2088090)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=3475964030:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.72/1.30 % (2088093)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2156028861:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.72/1.30 % (2088092)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=79532814:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.72/1.30 % (2088089)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=2735132994:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.72/1.30 % (2088091)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=4274169399:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.72/1.30 % (2088092)First to succeed.
% 2.72/1.30 % (2088092)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2088084"
% 2.72/1.30 % (2088093)Also succeeded, but the first one will report.
% 2.72/1.30 % (2088095)dis-21_1_sil=8000:lcm=predicate:random_seed=1420919586: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)
% 2.72/1.30 % (2088094)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3614869642:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.72/1.30 % (2088094)Also succeeded, but the first one will report.
% 2.72/1.30 % (2088095)Instruction limit reached!
% 2.72/1.30 % (2088095)------------------------------
% 2.72/1.30 % (2088095)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.72/1.30 % (2088095)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.72/1.30 % (2088095)CaDiCaL version: 2.1.3
% 2.72/1.30 % (2088095)Termination reason: Instruction limit
% 2.72/1.30 % (2088095)Termination phase: Saturation
% 2.72/1.30 % (2088095)Time elapsed: 0.074 s
% 2.72/1.30 % (2088095)Peak memory usage: 90 MB
% 2.72/1.30 % (2088095)Instructions burned: 130 (million)
% 2.72/1.30 % (2088103)lrs+10_1_sil=8000:sp=occurrence:random_seed=1439899675:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 2.72/1.30 % (2088092)Refutation found. Thanks to Tanya!
% 2.72/1.30 % SZS status Theorem for theBenchmark
% 2.72/1.30 % SZS output start Proof for theBenchmark
% See solution above
% 3.51/1.39 % (2088092)------------------------------
% 3.51/1.39 % (2088092)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.51/1.39 % (2088092)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.51/1.39 % (2088092)CaDiCaL version: 2.1.3
% 3.51/1.39 % (2088092)Termination reason: Refutation
% 3.51/1.39 % (2088092)Time elapsed: 0.008 s
% 3.51/1.39 % (2088092)Peak memory usage: 89 MB
% 3.51/1.39 % (2088092)Instructions burned: 9 (million)
% 3.51/1.39 % (2088092)------------------------------
% 3.51/1.39 % (2088092)------------------------------
% 3.51/1.39 % (2088084)Success in time 0.435 s
% 3.51/1.39 % Vampire exiting
%------------------------------------------------------------------------------