%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SWC200+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 : n016.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 01:05:04 PM UTC 2026
% Result : Theorem 0.16s 0.56s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 7
% Syntax : Number of formulae : 52 ( 13 unt; 1 def)
% Number of atoms : 164 ( 33 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 185 ( 73 ~; 68 |; 24 &)
% ( 5 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 2 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 54 ( 0 sgn 38 !; 16 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
? [X0] :
( ssItem(X0)
& ? [X1] :
( ssItem(X1)
& X0 != X1 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax2) ).
fof(f4,axiom,
! [X0] :
( ssList(X0)
=> ( singletonP(X0)
<=> ? [X1] :
( ssItem(X1)
& cons(X1,nil) = X0 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax4) ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax17) ).
fof(f37,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssList(X2)
=> ( memberP(cons(X1,X2),X0)
<=> ( X0 = X1
| memberP(X2,X0) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax37) ).
fof(f38,axiom,
! [X0] :
( ssItem(X0)
=> ~ memberP(nil,X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax38) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( X1 != X3
| X0 != X2
| ~ singletonP(X2)
| ? [X4] :
( ssItem(X4)
& ! [X5] :
( ssItem(X5)
=> ( ~ memberP(X0,X5)
| X4 = X5 ) ) ) ) ) ) ) ),
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
| ~ singletonP(X2)
| ? [X4] :
( ssItem(X4)
& ! [X5] :
( ssItem(X5)
=> ( ~ memberP(X0,X5)
| X4 = X5 ) ) ) ) ) ) ) ),
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(f147,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( memberP(cons(X1,X2),X0)
<=> ( X0 = X1
| memberP(X2,X0) ) )
| ~ ssList(X2) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f37]) ).
fof(f148,plain,
! [X0] :
( ~ memberP(nil,X0)
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f38]) ).
fof(f221,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& singletonP(X2)
& ! [X4] :
( ~ ssItem(X4)
| ? [X5] :
( memberP(X0,X5)
& X4 != X5
& ssItem(X5) ) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(ennf_transformation,[],[f97]) ).
fof(f222,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& singletonP(X2)
& ! [X4] :
( ~ ssItem(X4)
| ? [X5] :
( memberP(X0,X5)
& X4 != X5
& ssItem(X5) ) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(flattening,[],[f221]) ).
fof(f227,plain,
ssItem(sK0),
inference(cnf_transformation,[],[f2]) ).
fof(f232,plain,
! [X0] :
( ~ singletonP(X0)
| cons(sK4(X0),nil) = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f100]) ).
fof(f233,plain,
! [X0] :
( ssItem(sK4(X0))
| ~ ssList(X0)
| ~ singletonP(X0) ),
inference(cnf_transformation,[],[f100]) ).
fof(f306,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f333,plain,
! [X2,X0,X1] :
( ~ memberP(cons(X1,X2),X0)
| ~ ssItem(X1)
| ~ ssList(X2)
| memberP(X2,X0)
| X0 = X1
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f147]) ).
fof(f336,plain,
! [X0] :
( ~ memberP(nil,X0)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f148]) ).
fof(f411,plain,
! [X4] :
( ssItem(sK51(X4))
| ~ ssItem(X4) ),
inference(cnf_transformation,[],[f222]) ).
fof(f412,plain,
! [X4] :
( sK51(X4) != X4
| ~ ssItem(X4) ),
inference(cnf_transformation,[],[f222]) ).
fof(f413,plain,
! [X4] :
( memberP(sK47,sK51(X4))
| ~ ssItem(X4) ),
inference(cnf_transformation,[],[f222]) ).
fof(f415,plain,
singletonP(sK49),
inference(cnf_transformation,[],[f222]) ).
fof(f416,plain,
sK47 = sK49,
inference(cnf_transformation,[],[f222]) ).
fof(f418,plain,
ssList(sK49),
inference(cnf_transformation,[],[f222]) ).
fof(f423,plain,
! [X4] :
( memberP(sK49,sK51(X4))
| ~ ssItem(X4) ),
inference(definition_unfolding,[],[f413,f416]) ).
fof(f488,plain,
( sK49 = cons(sK4(sK49),nil)
| ~ ssList(sK49) ),
inference(resolution,[],[f232,f415]) ).
fof(f489,plain,
sK49 = cons(sK4(sK49),nil),
inference(forward_subsumption_resolution,[],[f488,f418]) ).
fof(f493,definition,
( spl52_8
<=> ssItem(sK4(sK49)) ),
introduced(definition,[new_symbols(definition,[spl52_8])],[avatar_definition]) ).
fof(f494,plain,
( ssItem(sK4(sK49))
| ~ spl52_8 ),
inference(avatar_component_clause,[],[f493]) ).
fof(f495,plain,
( ~ ssItem(sK4(sK49))
| spl52_8 ),
inference(avatar_component_clause,[],[f493]) ).
fof(f503,plain,
( ~ ssList(sK49)
| ~ singletonP(sK49)
| spl52_8 ),
inference(resolution,[],[f495,f233]) ).
fof(f504,plain,
( ~ singletonP(sK49)
| spl52_8 ),
inference(forward_subsumption_resolution,[],[f503,f418]) ).
fof(f505,plain,
( $false
| spl52_8 ),
inference(forward_subsumption_resolution,[],[f504,f415]) ).
fof(f506,plain,
spl52_8,
inference(avatar_contradiction_clause,[],[f505]) ).
fof(f515,plain,
! [X0] :
( ~ memberP(sK49,X0)
| ~ ssItem(sK4(sK49))
| ~ ssList(nil)
| memberP(nil,X0)
| sK4(sK49) = X0
| ~ ssItem(X0) ),
inference(superposition,[],[f333,f489]) ).
fof(f518,plain,
( ! [X0] :
( ~ memberP(sK49,X0)
| ~ ssList(nil)
| memberP(nil,X0)
| sK4(sK49) = X0
| ~ ssItem(X0) )
| ~ spl52_8 ),
inference(forward_subsumption_resolution,[],[f515,f494]) ).
fof(f519,plain,
( ! [X0] :
( ~ memberP(sK49,X0)
| memberP(nil,X0)
| sK4(sK49) = X0
| ~ ssItem(X0) )
| ~ spl52_8 ),
inference(forward_subsumption_resolution,[],[f518,f306]) ).
fof(f520,plain,
( ! [X0] :
( ~ memberP(sK49,X0)
| sK4(sK49) = X0
| ~ ssItem(X0) )
| ~ spl52_8 ),
inference(forward_subsumption_resolution,[],[f519,f336]) ).
fof(f521,plain,
( ! [X0] :
( sK51(X0) = sK4(sK49)
| ~ ssItem(sK51(X0))
| ~ ssItem(X0) )
| ~ spl52_8 ),
inference(resolution,[],[f520,f423]) ).
fof(f523,plain,
( ! [X0] :
( ~ ssItem(X0)
| sK51(X0) = sK4(sK49) )
| ~ spl52_8 ),
inference(forward_subsumption_resolution,[],[f521,f411]) ).
fof(f524,plain,
( sK4(sK49) = sK51(sK0)
| ~ spl52_8 ),
inference(resolution,[],[f523,f227]) ).
fof(f527,plain,
( sK4(sK49) = sK51(sK4(sK49))
| ~ spl52_8 ),
inference(resolution,[],[f523,f494]) ).
fof(f530,plain,
( ssItem(sK51(sK0))
| ~ spl52_8 ),
inference(superposition,[],[f494,f524]) ).
fof(f546,plain,
( sK51(sK0) = sK51(sK51(sK0))
| ~ spl52_8 ),
inference(forward_demodulation,[],[f527,f524]) ).
fof(f550,plain,
( sK51(sK0) != sK51(sK0)
| ~ ssItem(sK51(sK0))
| ~ spl52_8 ),
inference(superposition,[],[f412,f546]) ).
fof(f552,plain,
( ~ ssItem(sK51(sK0))
| ~ spl52_8 ),
inference(trivial_inequality_removal,[],[f550]) ).
fof(f553,plain,
( $false
| ~ spl52_8 ),
inference(forward_subsumption_resolution,[],[f552,f530]) ).
fof(f554,plain,
~ spl52_8,
inference(avatar_contradiction_clause,[],[f553]) ).
cnf(s9,plain,
spl52_8,
inference(sat_conversion,[],[f506]) ).
cnf(s10,plain,
~ spl52_8,
inference(sat_conversion,[],[f554]) ).
cnf(s11,plain,
$false,
inference(rat,[],[s9,s10]) ).
fof(f555,plain,
$false,
inference(avatar_sat_refutation,[],[s11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC200+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.13/0.39 % Computer : n016.cluster.edu
% 0.13/0.39 % Model : x86_64 x86_64
% 0.13/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.39 % Memory : 8046.5625MB
% 0.13/0.39 % OS : Linux 6.8.0-71-generic
% 0.13/0.39 % CPULimit : 300
% 0.13/0.39 % WCLimit : 300
% 0.13/0.39 % DateTime : Mon Sep 28 08:31:18 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
% 0.16/0.56 % (3475922)Will run a generic schedule for satisfiability detection.
% 0.16/0.56 % (3475933)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2432153891:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.16/0.56 % (3475928)% WARNING: option uhcvi not known.
% 0.16/0.56 % (3475931)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=179518983:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.16/0.56 % (3475927)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2501243579_2999 on theBenchmark for (2999ds/0Mi)
% 0.16/0.56 % (3475929)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3108376242:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.16/0.56 % (3475928)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1487879904:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.16/0.56 % (3475930)dis+10_1_sil=32000:sp=arity:random_seed=1896654902:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.16/0.56 % (3475932)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3064733982:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.16/0.56 % TRYING [1]
% 0.16/0.56 % TRYING [2]
% 0.16/0.56 % TRYING [3]
% 0.16/0.56 % TRYING [4]
% 0.16/0.56 % (3475933)Instruction limit reached!
% 0.16/0.56 % (3475933)------------------------------
% 0.16/0.56 % (3475933)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.16/0.56 % (3475933)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/0.56 % (3475933)CaDiCaL version: 2.1.3
% 0.16/0.56 % (3475933)Termination reason: Instruction limit
% 0.16/0.56 % (3475933)Termination phase: Saturation
% 0.16/0.56 % (3475933)Time elapsed: 0.057 s
% 0.16/0.56 % (3475933)Peak memory usage: 15 MB
% 0.16/0.56 % (3475933)Instructions burned: 161 (million)
% 0.16/0.56 % (3475930)Instruction limit reached!
% 0.16/0.56 % (3475930)------------------------------
% 0.16/0.56 % (3475930)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.16/0.56 % (3475930)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/0.56 % (3475930)CaDiCaL version: 2.1.3
% 0.16/0.56 % (3475930)Termination reason: Instruction limit
% 0.16/0.56 % (3475930)Termination phase: Saturation
% 0.16/0.56 % (3475930)Time elapsed: 0.060 s
% 0.16/0.56 % (3475930)Peak memory usage: 13 MB
% 0.16/0.56 % (3475930)Instructions burned: 103 (million)
% 0.16/0.56 % (3475941)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=2084021357:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.16/0.56 % (3475931)Instruction limit reached!
% 0.16/0.56 % (3475931)------------------------------
% 0.16/0.56 % (3475931)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.16/0.56 % (3475931)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/0.56 % (3475931)CaDiCaL version: 2.1.3
% 0.16/0.56 % (3475931)Termination reason: Instruction limit
% 0.16/0.56 % (3475931)Termination phase: Saturation
% 0.16/0.56 % (3475931)Time elapsed: 0.065 s
% 0.16/0.56 % (3475931)Peak memory usage: 13 MB
% 0.16/0.56 % (3475931)Instructions burned: 117 (million)
% 0.16/0.56 % TRYING [1]
% 0.16/0.56 % TRYING [2]
% 0.16/0.56 % TRYING [3]
% 0.16/0.56 % (3475932)Instruction limit reached!
% 0.16/0.56 % (3475932)------------------------------
% 0.16/0.56 % (3475932)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.16/0.56 % (3475932)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/0.56 % (3475932)CaDiCaL version: 2.1.3
% 0.16/0.56 % (3475932)Termination reason: Instruction limit
% 0.16/0.56 % (3475932)Termination phase: Saturation
% 0.16/0.56 % (3475932)Time elapsed: 0.076 s
% 0.16/0.56 % (3475932)Peak memory usage: 14 MB
% 0.16/0.56 % (3475932)Instructions burned: 131 (million)
% 0.16/0.56 % (3475942)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=2629656938:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 0.16/0.56 % TRYING [4]
% 0.16/0.56 % (3475944)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=3261395743:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 0.16/0.56 % TRYING [5]
% 0.16/0.56 % (3475944) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3475922-3475944"...
% 0.16/0.56 % (3475944)...printing done.
% 0.16/0.56 % (3475945)ott-21_1_sil=16000:fs=off:random_seed=2450478263:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 0.16/0.56 % (3475944)Refutation found. Thanks to Tanya!
% 0.16/0.56 % SZS status Theorem for theBenchmark
% 0.16/0.56 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.56 % (3475944)------------------------------
% 0.16/0.56 % (3475944)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.16/0.56 % (3475944)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/0.56 % (3475944)CaDiCaL version: 2.1.3
% 0.16/0.56 % (3475944)Termination reason: Refutation
% 0.16/0.56 % (3475944)Time elapsed: 0.009 s
% 0.16/0.56 % (3475944)Peak memory usage: 12 MB
% 0.16/0.56 % (3475944)Instructions burned: 12 (million)
% 0.16/0.56 % (3475922)Success in time 0.131 s
% 0.16/0.56 % Vampire exiting
%------------------------------------------------------------------------------