%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SWC218+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n006.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 01:05:08 PM UTC 2026
% Result : Theorem 0.17s 0.29s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 13
% Syntax : Number of formulae : 85 ( 22 unt; 5 def)
% Number of atoms : 250 ( 41 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 284 ( 119 ~; 102 |; 28 &)
% ( 13 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 6 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 72 ( 0 sgn 52 !; 20 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0] :
( ssList(X0)
=> ( singletonP(X0)
<=> ? [X1] :
( ssItem(X1)
& cons(X1,nil) = X0 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax4) ).
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/sandbox/benchmark/Axioms/SWC001+0.ax',ax7) ).
fof(f15,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( neq(X0,X1)
<=> X0 != X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax15) ).
fof(f16,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> ssList(cons(X1,X0)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax16) ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax17) ).
fof(f39,axiom,
~ singletonP(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax39) ).
fof(f58,axiom,
! [X0] :
( ssList(X0)
=> ( segmentP(nil,X0)
<=> nil = X0 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax58) ).
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(X4,X5) != X3
| ! [X6] :
( ssItem(X6)
=> app(app(X4,cons(X6,nil)),X5) != X2 ) ) ) )
| neq(X0,nil) ) ) ) ) ),
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
| ! [X4] :
( ssList(X4)
=> ! [X5] :
( ssList(X5)
=> ( app(X4,X5) != X3
| ! [X6] :
( ssItem(X6)
=> app(app(X4,cons(X6,nil)),X5) != X2 ) ) ) )
| neq(X0,nil) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f100,plain,
! [X0] :
( ( singletonP(X0)
<=> ? [X1] :
( ssItem(X1)
& cons(X1,nil) = X0 ) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f4]) ).
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(f119,plain,
! [X0] :
( ! [X1] :
( ssList(cons(X1,X0))
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f16]) ).
fof(f176,plain,
! [X0] :
( ( segmentP(nil,X0)
<=> nil = X0 )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f58]) ).
fof(f221,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& ? [X4] :
( ? [X5] :
( app(X4,X5) = X3
& ? [X6] :
( app(app(X4,cons(X6,nil)),X5) = X2
& ssItem(X6) )
& ssList(X5) )
& ssList(X4) )
& ~ neq(X0,nil)
& 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(X4,X5) = X3
& ? [X6] :
( app(app(X4,cons(X6,nil)),X5) = X2
& ssItem(X6) )
& ssList(X5) )
& ssList(X4) )
& ~ neq(X0,nil)
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(flattening,[],[f221]) ).
fof(f234,plain,
! [X0,X1] :
( ~ ssList(X0)
| cons(X1,nil) != X0
| ~ ssItem(X1)
| singletonP(X0) ),
inference(cnf_transformation,[],[f100]) ).
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(f305,plain,
! [X0,X1] :
( ssList(cons(X1,X0))
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f119]) ).
fof(f306,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f337,plain,
~ singletonP(nil),
inference(cnf_transformation,[],[f39]) ).
fof(f361,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ~ segmentP(nil,X0) ),
inference(cnf_transformation,[],[f176]) ).
fof(f411,plain,
ssItem(sK53),
inference(cnf_transformation,[],[f222]) ).
fof(f412,plain,
sK49 = app(app(sK51,cons(sK53,nil)),sK52),
inference(cnf_transformation,[],[f222]) ).
fof(f413,plain,
ssList(sK52),
inference(cnf_transformation,[],[f222]) ).
fof(f415,plain,
ssList(sK51),
inference(cnf_transformation,[],[f222]) ).
fof(f417,plain,
~ neq(sK47,nil),
inference(cnf_transformation,[],[f222]) ).
fof(f418,plain,
sK47 = sK49,
inference(cnf_transformation,[],[f222]) ).
fof(f420,plain,
ssList(sK49),
inference(cnf_transformation,[],[f222]) ).
fof(f425,plain,
~ neq(sK49,nil),
inference(definition_unfolding,[],[f417,f418]) ).
fof(f428,plain,
! [X1] :
( ~ ssList(cons(X1,nil))
| ~ ssItem(X1)
| singletonP(cons(X1,nil)) ),
inference(equality_resolution,[],[f234]) ).
fof(f431,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(f453,plain,
! [X1] :
( ~ singletonP(cons(X1,nil))
| ~ ssItem(X1)
| ~ ssList(cons(X1,nil)) ),
inference(consistent_polarity_flipping,[],[f428]) ).
fof(f459,plain,
! [X2,X3,X1] :
( ~ ssList(app(app(X2,X1),X3))
| ~ ssList(X1)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ segmentP(app(app(X2,X1),X3),X1) ),
inference(consistent_polarity_flipping,[],[f431]) ).
fof(f486,plain,
! [X0,X1] :
( ~ neq(X0,X1)
| ~ ssList(X1)
| X0 = X1
| ~ ssList(X0) ),
inference(consistent_polarity_flipping,[],[f303]) ).
fof(f489,plain,
singletonP(nil),
inference(consistent_polarity_flipping,[],[f337]) ).
fof(f495,plain,
! [X0] :
( segmentP(nil,X0)
| nil = X0
| ~ ssList(X0) ),
inference(consistent_polarity_flipping,[],[f361]) ).
fof(f509,plain,
neq(sK49,nil),
inference(consistent_polarity_flipping,[],[f425]) ).
fof(f522,definition,
( spl54_2
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[spl54_2])],[avatar_definition]) ).
fof(f523,plain,
( ssList(nil)
| ~ spl54_2 ),
inference(avatar_component_clause,[],[f522]) ).
fof(f551,plain,
spl54_2,
inference(avatar_split_clause,[],[f306,f522]) ).
fof(f743,definition,
( spl54_15
<=> nil = sK49 ),
introduced(definition,[new_symbols(definition,[spl54_15])],[avatar_definition]) ).
fof(f745,plain,
( nil = sK49
| ~ spl54_15 ),
inference(avatar_component_clause,[],[f743]) ).
fof(f829,plain,
( ~ ssList(nil)
| nil = sK49
| ~ ssList(sK49) ),
inference(resolution,[],[f486,f509]) ).
fof(f1006,plain,
( nil = sK49
| ~ ssList(sK49)
| ~ spl54_2 ),
inference(forward_subsumption_resolution,[],[f829,f523]) ).
fof(f1019,plain,
( nil = sK49
| ~ spl54_2 ),
inference(forward_subsumption_resolution,[],[f1006,f420]) ).
fof(f1021,plain,
( spl54_15
| ~ spl54_2 ),
inference(avatar_split_clause,[],[f1019,f522,f743]) ).
fof(f1960,definition,
( spl54_57
<=> ssList(cons(sK53,nil)) ),
introduced(definition,[new_symbols(definition,[spl54_57])],[avatar_definition]) ).
fof(f1961,plain,
( ssList(cons(sK53,nil))
| ~ spl54_57 ),
inference(avatar_component_clause,[],[f1960]) ).
fof(f1962,plain,
( ~ ssList(cons(sK53,nil))
| spl54_57 ),
inference(avatar_component_clause,[],[f1960]) ).
fof(f1968,plain,
( ~ ssItem(sK53)
| ~ ssList(nil)
| spl54_57 ),
inference(resolution,[],[f1962,f305]) ).
fof(f1969,plain,
( ~ ssList(nil)
| spl54_57 ),
inference(forward_subsumption_resolution,[],[f1968,f411]) ).
fof(f1970,plain,
( $false
| ~ spl54_2
| spl54_57 ),
inference(forward_subsumption_resolution,[],[f1969,f523]) ).
fof(f1971,plain,
( ~ spl54_2
| spl54_57 ),
inference(avatar_contradiction_clause,[],[f1970]) ).
fof(f1987,plain,
( ~ ssList(sK49)
| ~ ssList(cons(sK53,nil))
| ~ ssList(sK52)
| ~ ssList(sK51)
| ~ segmentP(sK49,cons(sK53,nil)) ),
inference(superposition,[],[f459,f412]) ).
fof(f1990,plain,
( ~ ssList(cons(sK53,nil))
| ~ ssList(sK52)
| ~ ssList(sK51)
| ~ segmentP(sK49,cons(sK53,nil)) ),
inference(forward_subsumption_resolution,[],[f1987,f420]) ).
fof(f1998,plain,
( ~ ssList(cons(sK53,nil))
| ~ ssList(sK51)
| ~ segmentP(sK49,cons(sK53,nil)) ),
inference(forward_subsumption_resolution,[],[f1990,f413]) ).
fof(f2005,plain,
( ~ ssList(cons(sK53,nil))
| ~ segmentP(sK49,cons(sK53,nil)) ),
inference(forward_subsumption_resolution,[],[f1998,f415]) ).
fof(f2008,plain,
( ~ segmentP(nil,cons(sK53,nil))
| ~ ssList(cons(sK53,nil))
| ~ spl54_15 ),
inference(forward_demodulation,[],[f2005,f745]) ).
fof(f2015,definition,
( spl54_60
<=> segmentP(nil,cons(sK53,nil)) ),
introduced(definition,[new_symbols(definition,[spl54_60])],[avatar_definition]) ).
fof(f2017,plain,
( ~ segmentP(nil,cons(sK53,nil))
| spl54_60 ),
inference(avatar_component_clause,[],[f2015]) ).
fof(f2018,plain,
( ~ spl54_57
| ~ spl54_60
| ~ spl54_15 ),
inference(avatar_split_clause,[],[f2008,f743,f2015,f1960]) ).
fof(f2036,definition,
( spl54_62
<=> nil = cons(sK53,nil) ),
introduced(definition,[new_symbols(definition,[spl54_62])],[avatar_definition]) ).
fof(f2038,plain,
( nil = cons(sK53,nil)
| ~ spl54_62 ),
inference(avatar_component_clause,[],[f2036]) ).
fof(f2119,plain,
( nil = cons(sK53,nil)
| ~ ssList(cons(sK53,nil))
| spl54_60 ),
inference(resolution,[],[f2017,f495]) ).
fof(f2122,plain,
( nil = cons(sK53,nil)
| ~ spl54_57
| spl54_60 ),
inference(forward_subsumption_resolution,[],[f2119,f1961]) ).
fof(f2124,plain,
( spl54_62
| ~ spl54_57
| spl54_60 ),
inference(avatar_split_clause,[],[f2122,f2015,f1960,f2036]) ).
fof(f2168,plain,
( ~ singletonP(nil)
| ~ ssItem(sK53)
| ~ ssList(nil)
| ~ spl54_62 ),
inference(superposition,[],[f453,f2038]) ).
fof(f2226,plain,
( ~ ssItem(sK53)
| ~ ssList(nil)
| ~ spl54_62 ),
inference(forward_subsumption_resolution,[],[f2168,f489]) ).
fof(f2253,plain,
( ~ ssList(nil)
| ~ spl54_62 ),
inference(forward_subsumption_resolution,[],[f2226,f411]) ).
fof(f2258,plain,
( $false
| ~ spl54_2
| ~ spl54_62 ),
inference(forward_subsumption_resolution,[],[f2253,f523]) ).
fof(f2259,plain,
( ~ spl54_2
| ~ spl54_62 ),
inference(avatar_contradiction_clause,[],[f2258]) ).
cnf(s9,plain,
spl54_2,
inference(sat_conversion,[],[f551]) ).
cnf(s28,plain,
( ~ spl54_2
| spl54_15 ),
inference(sat_conversion,[],[f1021]) ).
cnf(s86,plain,
( ~ spl54_2
| spl54_57 ),
inference(sat_conversion,[],[f1971]) ).
cnf(s88,plain,
( ~ spl54_15
| ~ spl54_57
| ~ spl54_60 ),
inference(sat_conversion,[],[f2018]) ).
cnf(s97,plain,
( ~ spl54_57
| spl54_60
| spl54_62 ),
inference(sat_conversion,[],[f2124]) ).
cnf(s105,plain,
( ~ spl54_2
| ~ spl54_62 ),
inference(sat_conversion,[],[f2259]) ).
cnf(s106,plain,
~ spl54_62,
inference(rat,[],[s105,s9]) ).
cnf(s107,plain,
spl54_57,
inference(rat,[],[s86,s9]) ).
cnf(s108,plain,
spl54_15,
inference(rat,[],[s28,s9]) ).
cnf(s110,plain,
spl54_60,
inference(rat,[],[s97,s106,s107]) ).
cnf(s115,plain,
$false,
inference(rat,[],[s88,s110,s107,s108]) ).
fof(f2260,plain,
$false,
inference(avatar_sat_refutation,[],[s115]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC218+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.07/0.20 % Computer : n006.cluster.edu
% 0.07/0.20 % Model : x86_64 x86_64
% 0.07/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.20 % Memory : 8046.5625MB
% 0.07/0.20 % OS : Linux 6.8.0-71-generic
% 0.07/0.20 % CPULimit : 300
% 0.07/0.20 % WCLimit : 300
% 0.07/0.20 % DateTime : Mon Sep 28 08:31:55 UTC 2026
% 0.07/0.20 % CPUTime :
% 0.07/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.07/0.22 Running first-order model finding
% 0.07/0.22 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.29 % (3819443)Will run a generic schedule for satisfiability detection.
% 0.17/0.29 % (3819449)% WARNING: option uhcvi not known.
% 0.17/0.29 % (3819449)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3943079116:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.17/0.29 % (3819448)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3726180919_2999 on theBenchmark for (2999ds/0Mi)
% 0.17/0.29 % (3819451)dis+10_1_sil=32000:sp=arity:random_seed=3533457800:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.17/0.29 % (3819450)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2578040903:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.17/0.29 % (3819452)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2707109406:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.17/0.29 % (3819453)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2184625323:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.17/0.29 % (3819454)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3715639865:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.17/0.29 % TRYING [1]
% 0.17/0.29 % TRYING [2]
% 0.17/0.29 % (3819449) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3819443-3819449"...
% 0.17/0.29 % (3819449)...printing done.
% 0.17/0.29 % (3819449)Refutation found. Thanks to Tanya!
% 0.17/0.29 % SZS status Theorem for theBenchmark
% 0.17/0.29 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/0.29 % (3819449)------------------------------
% 0.17/0.29 % (3819449)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.17/0.29 % (3819449)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/0.29 % (3819449)CaDiCaL version: 2.1.3
% 0.17/0.29 % (3819449)Termination reason: Refutation
% 0.17/0.29 % (3819449)Time elapsed: 0.025 s
% 0.17/0.29 % (3819449)Peak memory usage: 14 MB
% 0.17/0.29 % (3819449)Instructions burned: 74 (million)
% 0.17/0.29 % (3819443)Success in time 0.057 s
% 0.17/0.29 % Vampire exiting
%------------------------------------------------------------------------------