%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SWC118+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 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 01:04:44 PM UTC 2026
% Result : Theorem 0.18s 0.52s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 9
% Syntax : Number of formulae : 71 ( 25 unt; 5 def)
% Number of atoms : 274 ( 65 equ)
% Maximal formula atoms : 30 ( 3 avg)
% Number of connectives : 312 ( 109 ~; 116 |; 62 &)
% ( 9 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 29 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 6 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 82 ( 0 sgn 50 !; 32 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( segmentP(X0,X1)
<=> ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& app(app(X2,X1),X3) = X0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax7) ).
fof(f15,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( neq(X0,X1)
<=> X0 != X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax15) ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax17) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( X1 != X3
| X0 != X2
| ! [X4] :
( ssList(X4)
=> ! [X5] :
( ssList(X5)
=> ( app(app(X4,X2),X5) != X3
| ~ totalorderedP(X2)
| ? [X6] :
( ssItem(X6)
& ? [X7] :
( ssList(X7)
& app(X7,cons(X6,nil)) = X4
& ? [X8] :
( ssItem(X8)
& ? [X9] :
( ssList(X9)
& app(cons(X8,nil),X9) = X2
& leq(X6,X8) ) ) ) )
| ? [X10] :
( ssItem(X10)
& ? [X11] :
( ssList(X11)
& app(cons(X10,nil),X11) = X5
& ? [X12] :
( ssItem(X12)
& ? [X13] :
( ssList(X13)
& app(X13,cons(X12,nil)) = X2
& leq(X12,X10) ) ) ) ) ) ) )
| ( nil != X3
& nil = X2 )
| ( nil = X1
& nil = X0 )
| ( neq(X0,nil)
& segmentP(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
| ! [X4] :
( ssList(X4)
=> ! [X5] :
( ssList(X5)
=> ( app(app(X4,X2),X5) != X3
| ~ totalorderedP(X2)
| ? [X6] :
( ssItem(X6)
& ? [X7] :
( ssList(X7)
& app(X7,cons(X6,nil)) = X4
& ? [X8] :
( ssItem(X8)
& ? [X9] :
( ssList(X9)
& app(cons(X8,nil),X9) = X2
& leq(X6,X8) ) ) ) )
| ? [X10] :
( ssItem(X10)
& ? [X11] :
( ssList(X11)
& app(cons(X10,nil),X11) = X5
& ? [X12] :
( ssItem(X12)
& ? [X13] :
( ssList(X13)
& app(X13,cons(X12,nil)) = X2
& leq(X12,X10) ) ) ) ) ) ) )
| ( nil != X3
& nil = X2 )
| ( nil = X1
& nil = X0 )
| ( neq(X0,nil)
& segmentP(X1,X0) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f103,plain,
! [X0] :
( ! [X1] :
( ( segmentP(X0,X1)
<=> ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& app(app(X2,X1),X3) = X0 ) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f7]) ).
fof(f118,plain,
! [X0] :
( ! [X1] :
( ( neq(X0,X1)
<=> X0 != X1 )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f221,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& ? [X4] :
( ? [X5] :
( app(app(X4,X2),X5) = X3
& totalorderedP(X2)
& ! [X6] :
( ~ ssItem(X6)
| ! [X7] :
( ~ ssList(X7)
| app(X7,cons(X6,nil)) != X4
| ! [X8] :
( ~ ssItem(X8)
| ! [X9] :
( ~ ssList(X9)
| app(cons(X8,nil),X9) != X2
| ~ leq(X6,X8) ) ) ) )
& ! [X10] :
( ~ ssItem(X10)
| ! [X11] :
( ~ ssList(X11)
| app(cons(X10,nil),X11) != X5
| ! [X12] :
( ~ ssItem(X12)
| ! [X13] :
( ~ ssList(X13)
| app(X13,cons(X12,nil)) != X2
| ~ leq(X12,X10) ) ) ) )
& ssList(X5) )
& ssList(X4) )
& ( nil = X3
| nil != X2 )
& ( nil != X1
| nil != X0 )
& ( ~ neq(X0,nil)
| ~ segmentP(X1,X0) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(ennf_transformation,[],[f97]) ).
fof(f222,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& ? [X4] :
( ? [X5] :
( app(app(X4,X2),X5) = X3
& totalorderedP(X2)
& ! [X6] :
( ~ ssItem(X6)
| ! [X7] :
( ~ ssList(X7)
| app(X7,cons(X6,nil)) != X4
| ! [X8] :
( ~ ssItem(X8)
| ! [X9] :
( ~ ssList(X9)
| app(cons(X8,nil),X9) != X2
| ~ leq(X6,X8) ) ) ) )
& ! [X10] :
( ~ ssItem(X10)
| ! [X11] :
( ~ ssList(X11)
| app(cons(X10,nil),X11) != X5
| ! [X12] :
( ~ ssItem(X12)
| ! [X13] :
( ~ ssList(X13)
| app(X13,cons(X12,nil)) != X2
| ~ leq(X12,X10) ) ) ) )
& ssList(X5) )
& ssList(X4) )
& ( nil = X3
| nil != X2 )
& ( nil != X1
| nil != X0 )
& ( ~ neq(X0,nil)
| ~ segmentP(X1,X0) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(flattening,[],[f221]) ).
fof(f241,plain,
! [X2,X3,X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| app(app(X2,X1),X3) != X0
| ~ ssList(X3)
| ~ ssList(X2)
| segmentP(X0,X1) ),
inference(cnf_transformation,[],[f103]) ).
fof(f303,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| X0 = X1
| neq(X0,X1) ),
inference(cnf_transformation,[],[f118]) ).
fof(f306,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f413,plain,
ssList(sK52),
inference(cnf_transformation,[],[f222]) ).
fof(f415,plain,
sK50 = app(app(sK51,sK49),sK52),
inference(cnf_transformation,[],[f222]) ).
fof(f416,plain,
ssList(sK51),
inference(cnf_transformation,[],[f222]) ).
fof(f417,plain,
( nil != sK49
| nil = sK50 ),
inference(cnf_transformation,[],[f222]) ).
fof(f418,plain,
( nil != sK47
| nil != sK48 ),
inference(cnf_transformation,[],[f222]) ).
fof(f419,plain,
( ~ segmentP(sK48,sK47)
| ~ neq(sK47,nil) ),
inference(cnf_transformation,[],[f222]) ).
fof(f421,plain,
sK47 = sK49,
inference(cnf_transformation,[],[f222]) ).
fof(f422,plain,
sK48 = sK50,
inference(cnf_transformation,[],[f222]) ).
fof(f424,plain,
ssList(sK48),
inference(cnf_transformation,[],[f222]) ).
fof(f425,plain,
ssList(sK47),
inference(cnf_transformation,[],[f222]) ).
fof(f426,plain,
ssList(sK49),
inference(definition_unfolding,[],[f425,f421]) ).
fof(f427,plain,
ssList(sK50),
inference(definition_unfolding,[],[f424,f422]) ).
fof(f428,plain,
( ~ segmentP(sK50,sK49)
| ~ neq(sK49,nil) ),
inference(definition_unfolding,[],[f419,f422,f421,f421]) ).
fof(f429,plain,
( nil != sK49
| nil != sK50 ),
inference(definition_unfolding,[],[f418,f421,f422]) ).
fof(f435,plain,
! [X2,X3,X1] :
( ~ ssList(app(app(X2,X1),X3))
| ~ ssList(X1)
| ~ ssList(X3)
| ~ ssList(X2)
| segmentP(app(app(X2,X1),X3),X1) ),
inference(equality_resolution,[],[f241]) ).
fof(f473,plain,
! [X2,X3,X1] :
( ~ segmentP(app(app(X2,X1),X3),X1)
| ssList(X1)
| ssList(X3)
| ssList(X2)
| ssList(app(app(X2,X1),X3)) ),
inference(consistent_polarity_flipping,[],[f435]) ).
fof(f533,plain,
! [X0,X1] :
( ~ neq(X0,X1)
| ssList(X1)
| X0 = X1
| ssList(X0) ),
inference(consistent_polarity_flipping,[],[f303]) ).
fof(f535,plain,
~ ssList(nil),
inference(consistent_polarity_flipping,[],[f306]) ).
fof(f618,plain,
~ ssList(sK49),
inference(consistent_polarity_flipping,[],[f426]) ).
fof(f619,plain,
~ ssList(sK50),
inference(consistent_polarity_flipping,[],[f427]) ).
fof(f622,plain,
( segmentP(sK50,sK49)
| neq(sK49,nil) ),
inference(consistent_polarity_flipping,[],[f428]) ).
fof(f623,plain,
~ ssList(sK51),
inference(consistent_polarity_flipping,[],[f416]) ).
fof(f624,plain,
~ ssList(sK52),
inference(consistent_polarity_flipping,[],[f413]) ).
fof(f635,definition,
( spl53_1
<=> nil = sK50 ),
introduced(definition,[new_symbols(definition,[spl53_1])],[avatar_definition]) ).
fof(f639,definition,
( spl53_2
<=> nil = sK49 ),
introduced(definition,[new_symbols(definition,[spl53_2])],[avatar_definition]) ).
fof(f641,plain,
( nil != sK49
| spl53_2 ),
inference(avatar_component_clause,[],[f639]) ).
fof(f642,plain,
( spl53_1
| ~ spl53_2 ),
inference(avatar_split_clause,[],[f417,f639,f635]) ).
fof(f643,plain,
( ~ spl53_1
| ~ spl53_2 ),
inference(avatar_split_clause,[],[f429,f639,f635]) ).
fof(f645,definition,
( spl53_3
<=> neq(sK49,nil) ),
introduced(definition,[new_symbols(definition,[spl53_3])],[avatar_definition]) ).
fof(f647,plain,
( neq(sK49,nil)
| ~ spl53_3 ),
inference(avatar_component_clause,[],[f645]) ).
fof(f649,definition,
( spl53_4
<=> segmentP(sK50,sK49) ),
introduced(definition,[new_symbols(definition,[spl53_4])],[avatar_definition]) ).
fof(f651,plain,
( segmentP(sK50,sK49)
| ~ spl53_4 ),
inference(avatar_component_clause,[],[f649]) ).
fof(f652,plain,
( spl53_3
| spl53_4 ),
inference(avatar_split_clause,[],[f622,f649,f645]) ).
fof(f658,definition,
( spl53_6
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[spl53_6])],[avatar_definition]) ).
fof(f659,plain,
( ~ ssList(nil)
| spl53_6 ),
inference(avatar_component_clause,[],[f658]) ).
fof(f687,plain,
~ spl53_6,
inference(avatar_split_clause,[],[f535,f658]) ).
fof(f791,plain,
( ssList(nil)
| nil = sK49
| ssList(sK49)
| ~ spl53_3 ),
inference(resolution,[],[f533,f647]) ).
fof(f796,plain,
( nil = sK49
| ssList(sK49)
| ~ spl53_3
| spl53_6 ),
inference(forward_subsumption_resolution,[],[f791,f659]) ).
fof(f797,plain,
( ssList(sK49)
| spl53_2
| ~ spl53_3
| spl53_6 ),
inference(forward_subsumption_resolution,[],[f796,f641]) ).
fof(f798,plain,
( $false
| spl53_2
| ~ spl53_3
| spl53_6 ),
inference(forward_subsumption_resolution,[],[f797,f618]) ).
fof(f799,plain,
( spl53_2
| ~ spl53_3
| spl53_6 ),
inference(avatar_contradiction_clause,[],[f798]) ).
fof(f2370,plain,
( ~ segmentP(sK50,sK49)
| ssList(sK49)
| ssList(sK52)
| ssList(sK51)
| ssList(sK50) ),
inference(superposition,[],[f473,f415]) ).
fof(f2375,plain,
( ssList(sK49)
| ssList(sK52)
| ssList(sK51)
| ssList(sK50)
| ~ spl53_4 ),
inference(forward_subsumption_resolution,[],[f2370,f651]) ).
fof(f2381,plain,
( ssList(sK52)
| ssList(sK51)
| ssList(sK50)
| ~ spl53_4 ),
inference(forward_subsumption_resolution,[],[f2375,f618]) ).
fof(f2387,plain,
( ssList(sK51)
| ssList(sK50)
| ~ spl53_4 ),
inference(forward_subsumption_resolution,[],[f2381,f624]) ).
fof(f2390,plain,
( ssList(sK50)
| ~ spl53_4 ),
inference(forward_subsumption_resolution,[],[f2387,f623]) ).
fof(f2392,plain,
( $false
| ~ spl53_4 ),
inference(forward_subsumption_resolution,[],[f2390,f619]) ).
fof(f2393,plain,
~ spl53_4,
inference(avatar_contradiction_clause,[],[f2392]) ).
cnf(s1,plain,
( spl53_1
| ~ spl53_2 ),
inference(sat_conversion,[],[f642]) ).
cnf(s2,plain,
( ~ spl53_1
| ~ spl53_2 ),
inference(sat_conversion,[],[f643]) ).
cnf(s3,plain,
( spl53_3
| spl53_4 ),
inference(sat_conversion,[],[f652]) ).
cnf(s12,plain,
~ spl53_6,
inference(sat_conversion,[],[f687]) ).
cnf(s14,plain,
( spl53_2
| ~ spl53_3
| spl53_6 ),
inference(sat_conversion,[],[f799]) ).
cnf(s70,plain,
~ spl53_4,
inference(sat_conversion,[],[f2393]) ).
cnf(s78,plain,
spl53_3,
inference(rat,[],[s3,s70]) ).
cnf(s79,plain,
spl53_2,
inference(rat,[],[s14,s12,s78]) ).
cnf(s80,plain,
~ spl53_1,
inference(rat,[],[s2,s79]) ).
cnf(s85,plain,
$false,
inference(rat,[],[s1,s79,s80]) ).
fof(f2394,plain,
$false,
inference(avatar_sat_refutation,[],[s85]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC118+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.13/0.38 % Computer : n008.cluster.edu
% 0.13/0.38 % Model : x86_64 x86_64
% 0.13/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.38 % Memory : 8046.5625MB
% 0.13/0.38 % OS : Linux 6.8.0-71-generic
% 0.13/0.38 % CPULimit : 300
% 0.13/0.38 % WCLimit : 300
% 0.13/0.38 % DateTime : Mon Sep 28 08:00:09 UTC 2026
% 0.13/0.39 % CPUTime :
% 0.13/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.13/0.42 Running first-order model finding
% 0.13/0.42 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.52 % (2089777)Will run a generic schedule for satisfiability detection.
% 0.18/0.52 % (2089782)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1747582115_2999 on theBenchmark for (2999ds/0Mi)
% 0.18/0.52 % (2089783)% WARNING: option uhcvi not known.
% 0.18/0.52 % (2089783)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=608043853:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.18/0.52 % (2089787)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2717627060:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.18/0.52 % (2089784)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=4188830969:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.18/0.52 % (2089785)dis+10_1_sil=32000:sp=arity:random_seed=2395774845:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.18/0.52 % TRYING [1]
% 0.18/0.52 % (2089786)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=281698797:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.18/0.52 % (2089788)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1063862571:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.18/0.52 % TRYING [2]
% 0.18/0.52 % TRYING [3]
% 0.18/0.52 % TRYING [4]
% 0.18/0.52 % TRYING [5]
% 0.18/0.52 % (2089783) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2089777-2089783"...
% 0.18/0.52 % (2089783)...printing done.
% 0.18/0.52 % (2089785) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2089777-2089785"...
% 0.18/0.52 % (2089783)Refutation found. Thanks to Tanya!
% 0.18/0.52 % SZS status Theorem for theBenchmark
% 0.18/0.52 % SZS output start Proof for theBenchmark
% See solution above
% 0.18/0.52 % (2089783)------------------------------
% 0.18/0.52 % (2089783)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.52 % (2089783)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.52 % (2089783)CaDiCaL version: 2.1.3
% 0.18/0.52 % (2089783)Termination reason: Refutation
% 0.18/0.52 % (2089783)Time elapsed: 0.047 s
% 0.18/0.52 % (2089783)Peak memory usage: 14 MB
% 0.18/0.52 % (2089783)Instructions burned: 78 (million)
% 0.18/0.52 % (2089777)Success in time 0.088 s
% 0.18/0.52 % Vampire exiting
%------------------------------------------------------------------------------