%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SWC153-1 : 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 01:04:53 PM UTC 2026
% Result : Unsatisfiable 0.17s 0.47s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 27
% Syntax : Number of formulae : 100 ( 35 unt; 13 def)
% Number of atoms : 330 ( 17 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 407 ( 177 ~; 217 |; 0 &)
% ( 13 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 19 ( 17 usr; 14 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 59 ( 0 sgn 59 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f206,negated_conjecture,
sk3 = sk1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_6) ).
fof(f207,plain,
sk1 = sk3,
inference(reorient_equations,[],[f206]) ).
fof(f208,negated_conjecture,
! [X2,X3,X0,X1,X4] :
( ~ ssItem(X0)
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ ssList(X4)
| app(app(app(app(X2,cons(X0,nil)),X3),cons(X1,nil)),X4) != sk3
| ~ leq(X1,X0)
| leq(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_7) ).
fof(f209,plain,
! [X2,X3,X0,X1,X4] :
( ~ ssItem(X0)
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ ssList(X4)
| sk3 != app(app(app(app(X2,cons(X0,nil)),X3),cons(X1,nil)),X4)
| ~ leq(X1,X0)
| leq(X0,X1) ),
inference(reorient_equations,[],[f208]) ).
fof(f210,negated_conjecture,
! [X2,X3,X0,X1,X4,X5] :
( ~ ssItem(X0)
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ ssList(X4)
| app(app(app(app(X2,cons(X0,nil)),X3),cons(X1,nil)),X4) != sk3
| ~ leq(X1,X0)
| ~ ssItem(X5)
| ~ memberP(X3,X5)
| leq(X0,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_8) ).
fof(f211,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ ssItem(X0)
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ ssList(X4)
| sk3 != app(app(app(app(X2,cons(X0,nil)),X3),cons(X1,nil)),X4)
| ~ leq(X1,X0)
| ~ ssItem(X5)
| ~ memberP(X3,X5)
| leq(X0,X5) ),
inference(reorient_equations,[],[f210]) ).
fof(f212,negated_conjecture,
! [X2,X3,X0,X1,X4,X5] :
( ~ ssItem(X0)
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ ssList(X4)
| app(app(app(app(X2,cons(X0,nil)),X3),cons(X1,nil)),X4) != sk3
| ~ leq(X1,X0)
| ~ ssItem(X5)
| ~ memberP(X3,X5)
| leq(X5,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_9) ).
fof(f213,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ ssItem(X0)
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ ssList(X4)
| sk3 != app(app(app(app(X2,cons(X0,nil)),X3),cons(X1,nil)),X4)
| ~ leq(X1,X0)
| ~ ssItem(X5)
| ~ memberP(X3,X5)
| leq(X5,X1) ),
inference(reorient_equations,[],[f212]) ).
fof(f214,negated_conjecture,
ssItem(sk5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_10) ).
fof(f215,negated_conjecture,
ssItem(sk6),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_11) ).
fof(f216,negated_conjecture,
ssList(sk7),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_12) ).
fof(f217,negated_conjecture,
ssList(sk8),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_13) ).
fof(f218,negated_conjecture,
ssList(sk9),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_14) ).
fof(f219,negated_conjecture,
app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)),sk9) = sk1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_15) ).
fof(f220,plain,
sk1 = app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)),sk9),
inference(reorient_equations,[],[f219]) ).
fof(f221,negated_conjecture,
leq(sk6,sk5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_16) ).
fof(f222,negated_conjecture,
( ssItem(sk10)
| ~ leq(sk5,sk6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_17) ).
fof(f223,negated_conjecture,
( memberP(sk8,sk10)
| ~ leq(sk5,sk6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_18) ).
fof(f224,negated_conjecture,
( ~ leq(sk10,sk6)
| ~ leq(sk5,sk10)
| ~ leq(sk5,sk6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_19) ).
fof(f227,plain,
sk3 = app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)),sk9),
inference(definition_unfolding,[],[f220,f207]) ).
fof(f363,plain,
! [X2,X3,X0,X1,X4] :
( sk3 != app(app(app(app(X2,cons(X0,nil)),X3),cons(X1,nil)),X4)
| ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ ssList(X4)
| ssItem(X0)
| leq(X1,X0)
| ~ leq(X0,X1) ),
inference(consistent_polarity_flipping,[],[f209]) ).
fof(f364,plain,
! [X2,X3,X0,X1,X4,X5] :
( sk3 != app(app(app(app(X2,cons(X0,nil)),X3),cons(X1,nil)),X4)
| ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ ssList(X4)
| ssItem(X0)
| leq(X1,X0)
| ssItem(X5)
| ~ memberP(X3,X5)
| ~ leq(X0,X5) ),
inference(consistent_polarity_flipping,[],[f211]) ).
fof(f365,plain,
! [X2,X3,X0,X1,X4,X5] :
( sk3 != app(app(app(app(X2,cons(X0,nil)),X3),cons(X1,nil)),X4)
| ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ ssList(X4)
| ssItem(X0)
| leq(X1,X0)
| ssItem(X5)
| ~ memberP(X3,X5)
| ~ leq(X5,X1) ),
inference(consistent_polarity_flipping,[],[f213]) ).
fof(f366,plain,
~ ssItem(sk5),
inference(consistent_polarity_flipping,[],[f214]) ).
fof(f367,plain,
~ ssItem(sk6),
inference(consistent_polarity_flipping,[],[f215]) ).
fof(f368,plain,
~ leq(sk6,sk5),
inference(consistent_polarity_flipping,[],[f221]) ).
fof(f369,plain,
( ~ ssItem(sk10)
| leq(sk5,sk6) ),
inference(consistent_polarity_flipping,[],[f222]) ).
fof(f370,plain,
( memberP(sk8,sk10)
| leq(sk5,sk6) ),
inference(consistent_polarity_flipping,[],[f223]) ).
fof(f371,plain,
( leq(sk10,sk6)
| leq(sk5,sk10)
| leq(sk5,sk6) ),
inference(consistent_polarity_flipping,[],[f224]) ).
fof(f379,definition,
( spl0_1
<=> leq(sk5,sk6) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f383,definition,
( spl0_2
<=> leq(sk5,sk10) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f387,definition,
( spl0_3
<=> leq(sk10,sk6) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f390,plain,
( spl0_1
| spl0_2
| spl0_3 ),
inference(avatar_split_clause,[],[f371,f387,f383,f379]) ).
fof(f392,definition,
( spl0_4
<=> memberP(sk8,sk10) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f394,plain,
( memberP(sk8,sk10)
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f392]) ).
fof(f395,plain,
( spl0_1
| spl0_4 ),
inference(avatar_split_clause,[],[f370,f392,f379]) ).
fof(f397,definition,
( spl0_5
<=> ssItem(sk10) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f400,plain,
( spl0_1
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f369,f397,f379]) ).
fof(f444,plain,
( sk3 != sk3
| ssItem(sk6)
| ~ ssList(sk7)
| ~ ssList(sk8)
| ~ ssList(sk9)
| ssItem(sk5)
| leq(sk6,sk5)
| ~ leq(sk5,sk6) ),
inference(superposition,[],[f363,f227]) ).
fof(f445,plain,
( ssItem(sk6)
| ~ ssList(sk7)
| ~ ssList(sk8)
| ~ ssList(sk9)
| ssItem(sk5)
| leq(sk6,sk5)
| ~ leq(sk5,sk6) ),
inference(trivial_inequality_removal,[],[f444]) ).
fof(f447,definition,
( spl0_15
<=> ssItem(sk6) ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
fof(f451,definition,
( spl0_16
<=> ssList(sk9) ),
introduced(definition,[new_symbols(definition,[spl0_16])],[avatar_definition]) ).
fof(f453,plain,
( ~ ssList(sk9)
| spl0_16 ),
inference(avatar_component_clause,[],[f451]) ).
fof(f462,plain,
( $false
| spl0_16 ),
inference(resolution,[],[f453,f218]) ).
fof(f463,plain,
spl0_16,
inference(avatar_contradiction_clause,[],[f462]) ).
fof(f465,plain,
! [X0] :
( sk3 != sk3
| ssItem(sk6)
| ~ ssList(sk7)
| ~ ssList(sk8)
| ~ ssList(sk9)
| ssItem(sk5)
| leq(sk6,sk5)
| ssItem(X0)
| ~ memberP(sk8,X0)
| ~ leq(sk5,X0) ),
inference(superposition,[],[f364,f227]) ).
fof(f466,plain,
! [X0] :
( ssItem(sk6)
| ~ ssList(sk7)
| ~ ssList(sk8)
| ~ ssList(sk9)
| ssItem(sk5)
| leq(sk6,sk5)
| ssItem(X0)
| ~ memberP(sk8,X0)
| ~ leq(sk5,X0) ),
inference(trivial_inequality_removal,[],[f465]) ).
fof(f468,definition,
( spl0_19
<=> ! [X0] :
( ssItem(X0)
| ~ leq(sk5,X0)
| ~ memberP(sk8,X0) ) ),
introduced(definition,[new_symbols(definition,[spl0_19])],[avatar_definition]) ).
fof(f469,plain,
( ! [X0] :
( ~ memberP(sk8,X0)
| ~ leq(sk5,X0)
| ssItem(X0) )
| ~ spl0_19 ),
inference(avatar_component_clause,[],[f468]) ).
fof(f471,definition,
( spl0_20
<=> leq(sk6,sk5) ),
introduced(definition,[new_symbols(definition,[spl0_20])],[avatar_definition]) ).
fof(f473,plain,
( leq(sk6,sk5)
| ~ spl0_20 ),
inference(avatar_component_clause,[],[f471]) ).
fof(f475,definition,
( spl0_21
<=> ssItem(sk5) ),
introduced(definition,[new_symbols(definition,[spl0_21])],[avatar_definition]) ).
fof(f479,definition,
( spl0_22
<=> ssList(sk8) ),
introduced(definition,[new_symbols(definition,[spl0_22])],[avatar_definition]) ).
fof(f481,plain,
( ~ ssList(sk8)
| spl0_22 ),
inference(avatar_component_clause,[],[f479]) ).
fof(f483,definition,
( spl0_23
<=> ssList(sk7) ),
introduced(definition,[new_symbols(definition,[spl0_23])],[avatar_definition]) ).
fof(f485,plain,
( ~ ssList(sk7)
| spl0_23 ),
inference(avatar_component_clause,[],[f483]) ).
fof(f486,plain,
( spl0_19
| spl0_20
| spl0_21
| ~ spl0_16
| ~ spl0_22
| ~ spl0_23
| spl0_15 ),
inference(avatar_split_clause,[],[f466,f447,f483,f479,f451,f475,f471,f468]) ).
fof(f487,plain,
( $false
| spl0_22 ),
inference(resolution,[],[f481,f217]) ).
fof(f488,plain,
spl0_22,
inference(avatar_contradiction_clause,[],[f487]) ).
fof(f489,plain,
( $false
| spl0_23 ),
inference(resolution,[],[f485,f216]) ).
fof(f490,plain,
spl0_23,
inference(avatar_contradiction_clause,[],[f489]) ).
fof(f493,plain,
~ spl0_15,
inference(avatar_split_clause,[],[f367,f447]) ).
fof(f494,plain,
~ spl0_21,
inference(avatar_split_clause,[],[f366,f475]) ).
fof(f495,plain,
( ~ leq(sk5,sk10)
| ssItem(sk10)
| ~ spl0_4
| ~ spl0_19 ),
inference(resolution,[],[f469,f394]) ).
fof(f496,plain,
( spl0_5
| ~ spl0_2
| ~ spl0_4
| ~ spl0_19 ),
inference(avatar_split_clause,[],[f495,f468,f392,f383,f397]) ).
fof(f498,plain,
! [X0] :
( sk3 != sk3
| ssItem(sk6)
| ~ ssList(sk7)
| ~ ssList(sk8)
| ~ ssList(sk9)
| ssItem(sk5)
| leq(sk6,sk5)
| ssItem(X0)
| ~ memberP(sk8,X0)
| ~ leq(X0,sk6) ),
inference(superposition,[],[f365,f227]) ).
fof(f499,plain,
! [X0] :
( ssItem(sk6)
| ~ ssList(sk7)
| ~ ssList(sk8)
| ~ ssList(sk9)
| ssItem(sk5)
| leq(sk6,sk5)
| ssItem(X0)
| ~ memberP(sk8,X0)
| ~ leq(X0,sk6) ),
inference(trivial_inequality_removal,[],[f498]) ).
fof(f501,definition,
( spl0_24
<=> ! [X0] :
( ssItem(X0)
| ~ leq(X0,sk6)
| ~ memberP(sk8,X0) ) ),
introduced(definition,[new_symbols(definition,[spl0_24])],[avatar_definition]) ).
fof(f502,plain,
( ! [X0] :
( ~ memberP(sk8,X0)
| ~ leq(X0,sk6)
| ssItem(X0) )
| ~ spl0_24 ),
inference(avatar_component_clause,[],[f501]) ).
fof(f503,plain,
( spl0_24
| spl0_20
| spl0_21
| ~ spl0_16
| ~ spl0_22
| ~ spl0_23
| spl0_15 ),
inference(avatar_split_clause,[],[f499,f447,f483,f479,f451,f475,f471,f501]) ).
fof(f504,plain,
( $false
| ~ spl0_20 ),
inference(resolution,[],[f473,f368]) ).
fof(f505,plain,
~ spl0_20,
inference(avatar_contradiction_clause,[],[f504]) ).
fof(f506,plain,
( ~ leq(sk10,sk6)
| ssItem(sk10)
| ~ spl0_4
| ~ spl0_24 ),
inference(resolution,[],[f502,f394]) ).
fof(f507,plain,
( spl0_5
| ~ spl0_3
| ~ spl0_4
| ~ spl0_24 ),
inference(avatar_split_clause,[],[f506,f501,f392,f387,f397]) ).
fof(f508,plain,
( ~ spl0_1
| spl0_20
| spl0_21
| ~ spl0_16
| ~ spl0_22
| ~ spl0_23
| spl0_15 ),
inference(avatar_split_clause,[],[f445,f447,f483,f479,f451,f475,f471,f379]) ).
cnf(s1,plain,
( spl0_1
| spl0_2
| spl0_3 ),
inference(sat_conversion,[],[f390]) ).
cnf(s2,plain,
( spl0_1
| spl0_4 ),
inference(sat_conversion,[],[f395]) ).
cnf(s3,plain,
( spl0_1
| ~ spl0_5 ),
inference(sat_conversion,[],[f400]) ).
cnf(s15,plain,
spl0_16,
inference(sat_conversion,[],[f463]) ).
cnf(s16,plain,
( spl0_15
| ~ spl0_16
| spl0_19
| spl0_20
| spl0_21
| ~ spl0_22
| ~ spl0_23 ),
inference(sat_conversion,[],[f486]) ).
cnf(s17,plain,
spl0_22,
inference(sat_conversion,[],[f488]) ).
cnf(s18,plain,
spl0_23,
inference(sat_conversion,[],[f490]) ).
cnf(s20,plain,
~ spl0_15,
inference(sat_conversion,[],[f493]) ).
cnf(s21,plain,
~ spl0_21,
inference(sat_conversion,[],[f494]) ).
cnf(s22,plain,
( ~ spl0_2
| ~ spl0_4
| spl0_5
| ~ spl0_19 ),
inference(sat_conversion,[],[f496]) ).
cnf(s23,plain,
( spl0_15
| ~ spl0_16
| spl0_20
| spl0_21
| ~ spl0_22
| ~ spl0_23
| spl0_24 ),
inference(sat_conversion,[],[f503]) ).
cnf(s24,plain,
~ spl0_20,
inference(sat_conversion,[],[f505]) ).
cnf(s25,plain,
( ~ spl0_3
| ~ spl0_4
| spl0_5
| ~ spl0_24 ),
inference(sat_conversion,[],[f507]) ).
cnf(s26,plain,
( ~ spl0_1
| spl0_15
| ~ spl0_16
| spl0_20
| spl0_21
| ~ spl0_22
| ~ spl0_23 ),
inference(sat_conversion,[],[f508]) ).
cnf(s27,plain,
( spl0_15
| ~ spl0_16
| spl0_21
| ~ spl0_22
| ~ spl0_23
| spl0_24 ),
inference(rat,[],[s23,s24]) ).
cnf(s28,plain,
( ~ spl0_16
| spl0_19 ),
inference(rat,[],[s16,s18,s17,s21,s24,s20]) ).
cnf(s29,plain,
spl0_24,
inference(rat,[],[s27,s17,s18,s20,s21,s15]) ).
cnf(s30,plain,
~ spl0_1,
inference(rat,[],[s26,s18,s17,s21,s24,s20,s15]) ).
cnf(s31,plain,
spl0_19,
inference(rat,[],[s28,s15]) ).
cnf(s37,plain,
~ spl0_5,
inference(rat,[],[s3,s30]) ).
cnf(s38,plain,
spl0_4,
inference(rat,[],[s2,s30]) ).
cnf(s39,plain,
~ spl0_3,
inference(rat,[],[s25,s29,s37,s38]) ).
cnf(s40,plain,
~ spl0_2,
inference(rat,[],[s22,s31,s37,s38]) ).
cnf(s41,plain,
$false,
inference(rat,[],[s1,s39,s40,s30]) ).
fof(f509,plain,
$false,
inference(avatar_sat_refutation,[],[s41]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC153-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.40 % Computer : n016.cluster.edu
% 0.12/0.40 % Model : x86_64 x86_64
% 0.12/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.40 % Memory : 8046.5625MB
% 0.12/0.40 % OS : Linux 6.8.0-71-generic
% 0.12/0.40 % CPULimit : 300
% 0.12/0.40 % WCLimit : 300
% 0.12/0.40 % DateTime : Mon Sep 28 08:15:19 UTC 2026
% 0.12/0.40 % CPUTime :
% 0.12/0.40 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.44 Running first-order model finding
% 0.12/0.44 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
% 0.17/0.47 % (3470402)Will run a generic schedule for satisfiability detection.
% 0.17/0.47 % (3470413)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3332240011:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.17/0.47 % (3470408)% WARNING: option uhcvi not known.
% 0.17/0.47 % (3470413) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3470402-3470413"...
% 0.17/0.47 % (3470413)...printing done.
% 0.17/0.47 % (3470413)Refutation found. Thanks to Tanya!
% 0.17/0.47 % SZS status Unsatisfiable for theBenchmark
% 0.17/0.47 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/0.47 % (3470413)------------------------------
% 0.17/0.47 % (3470413)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.17/0.47 % (3470413)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/0.47 % (3470413)CaDiCaL version: 2.1.3
% 0.17/0.47 % (3470413)Termination reason: Refutation
% 0.17/0.47 % (3470413)Time elapsed: 0.005 s
% 0.17/0.47 % (3470413)Peak memory usage: 13 MB
% 0.17/0.47 % (3470413)Instructions burned: 13 (million)
% 0.17/0.47 % (3470402)Success in time 0.032 s
% 0.17/0.47 % Vampire exiting
%------------------------------------------------------------------------------