%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SWC417+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 : n011.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 01:05:58 PM UTC 2026
% Result : Theorem 0.41s 0.30s
% Output : Refutation 0.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 14
% Syntax : Number of formulae : 83 ( 22 unt; 9 def)
% Number of atoms : 271 ( 62 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 330 ( 142 ~; 129 |; 34 &)
% ( 9 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 14 ( 12 usr; 10 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 66 ( 0 sgn 48 !; 18 ?)
% Comments :
%------------------------------------------------------------------------------
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(f28,axiom,
! [X0] :
( ssList(X0)
=> app(nil,X0) = X0 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax28) ).
fof(f84,axiom,
! [X0] :
( ssList(X0)
=> app(X0,nil) = X0 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax84) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( X1 != X3
| X0 != X2
| ( ( ~ neq(X1,nil)
| ? [X4] :
( ssItem(X4)
& ? [X5] :
( ssList(X5)
& ? [X6] :
( ssList(X6)
& app(app(X5,cons(X4,nil)),X6) = X1
& app(app(X6,cons(X4,nil)),X5) = X0 ) ) )
| ! [X7] :
( ssItem(X7)
=> ! [X8] :
( ssList(X8)
=> ( app(cons(X7,nil),X8) != X3
| app(X8,cons(X7,nil)) != X2 ) ) ) )
& ( ~ neq(X1,nil)
| neq(X3,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
| ( ( ~ neq(X1,nil)
| ? [X4] :
( ssItem(X4)
& ? [X5] :
( ssList(X5)
& ? [X6] :
( ssList(X6)
& app(app(X5,cons(X4,nil)),X6) = X1
& app(app(X6,cons(X4,nil)),X5) = X0 ) ) )
| ! [X7] :
( ssItem(X7)
=> ! [X8] :
( ssList(X8)
=> ( app(cons(X7,nil),X8) != X3
| app(X8,cons(X7,nil)) != X2 ) ) ) )
& ( ~ neq(X1,nil)
| neq(X3,nil) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f119,plain,
! [X0] :
( ! [X1] :
( ssList(cons(X1,X0))
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f16]) ).
fof(f134,plain,
! [X0] :
( app(nil,X0) = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f28]) ).
fof(f201,plain,
! [X0] :
( app(X0,nil) = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f84]) ).
fof(f221,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& ( ( neq(X1,nil)
& ! [X4] :
( ~ ssItem(X4)
| ! [X5] :
( ~ ssList(X5)
| ! [X6] :
( ~ ssList(X6)
| app(app(X5,cons(X4,nil)),X6) != X1
| app(app(X6,cons(X4,nil)),X5) != X0 ) ) )
& ? [X7] :
( ? [X8] :
( app(cons(X7,nil),X8) = X3
& app(X8,cons(X7,nil)) = X2
& ssList(X8) )
& ssItem(X7) ) )
| ( neq(X1,nil)
& ~ neq(X3,nil) ) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(ennf_transformation,[],[f97]) ).
fof(f222,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& ( ( neq(X1,nil)
& ! [X4] :
( ~ ssItem(X4)
| ! [X5] :
( ~ ssList(X5)
| ! [X6] :
( ~ ssList(X6)
| app(app(X5,cons(X4,nil)),X6) != X1
| app(app(X6,cons(X4,nil)),X5) != X0 ) ) )
& ? [X7] :
( ? [X8] :
( app(cons(X7,nil),X8) = X3
& app(X8,cons(X7,nil)) = X2
& ssList(X8) )
& ssItem(X7) ) )
| ( neq(X1,nil)
& ~ neq(X3,nil) ) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(flattening,[],[f221]) ).
fof(f305,plain,
! [X0,X1] :
( ~ ssItem(X1)
| ~ ssList(X0)
| ssList(cons(X1,X0)) ),
inference(cnf_transformation,[],[f119]) ).
fof(f306,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f320,plain,
! [X0] :
( ~ ssList(X0)
| app(nil,X0) = X0 ),
inference(cnf_transformation,[],[f134]) ).
fof(f397,plain,
! [X0] :
( ~ ssList(X0)
| app(X0,nil) = X0 ),
inference(cnf_transformation,[],[f201]) ).
fof(f411,plain,
! [X6,X4,X5] :
( ~ neq(sK50,nil)
| app(app(X6,cons(X4,nil)),X5) != sK47
| app(app(X5,cons(X4,nil)),X6) != sK48
| ~ ssList(X6)
| ~ ssList(X5)
| ~ ssItem(X4) ),
inference(cnf_transformation,[],[f222]) ).
fof(f416,plain,
( ~ neq(sK50,nil)
| ssList(sK52) ),
inference(cnf_transformation,[],[f222]) ).
fof(f417,plain,
( ~ neq(sK50,nil)
| sK49 = app(sK52,cons(sK51,nil)) ),
inference(cnf_transformation,[],[f222]) ).
fof(f418,plain,
( ~ neq(sK50,nil)
| sK50 = app(cons(sK51,nil),sK52) ),
inference(cnf_transformation,[],[f222]) ).
fof(f419,plain,
( ~ neq(sK50,nil)
| ssItem(sK51) ),
inference(cnf_transformation,[],[f222]) ).
fof(f421,plain,
neq(sK48,nil),
inference(cnf_transformation,[],[f222]) ).
fof(f424,plain,
sK47 = sK49,
inference(cnf_transformation,[],[f222]) ).
fof(f425,plain,
sK48 = sK50,
inference(cnf_transformation,[],[f222]) ).
fof(f426,plain,
ssList(sK49),
inference(cnf_transformation,[],[f222]) ).
fof(f432,plain,
neq(sK50,nil),
inference(definition_unfolding,[],[f421,f425]) ).
fof(f438,plain,
! [X6,X4,X5] :
( ~ neq(sK50,nil)
| app(app(X6,cons(X4,nil)),X5) != sK49
| app(app(X5,cons(X4,nil)),X6) != sK50
| ~ ssList(X6)
| ~ ssList(X5)
| ~ ssItem(X4) ),
inference(definition_unfolding,[],[f411,f424,f425]) ).
fof(f472,definition,
( spl53_1
<=> ! [X6,X4,X5] :
( app(app(X6,cons(X4,nil)),X5) != sK49
| ~ ssItem(X4)
| ~ ssList(X5)
| ~ ssList(X6)
| app(app(X5,cons(X4,nil)),X6) != sK50 ) ),
introduced(definition,[new_symbols(definition,[spl53_1])],[avatar_definition]) ).
fof(f473,plain,
( ! [X6,X4,X5] :
( ~ ssItem(X4)
| app(app(X6,cons(X4,nil)),X5) != sK49
| ~ ssList(X5)
| ~ ssList(X6)
| app(app(X5,cons(X4,nil)),X6) != sK50 )
| ~ spl53_1 ),
inference(avatar_component_clause,[],[f472]) ).
fof(f475,definition,
( spl53_2
<=> neq(sK50,nil) ),
introduced(definition,[new_symbols(definition,[spl53_2])],[avatar_definition]) ).
fof(f478,plain,
( spl53_1
| ~ spl53_2 ),
inference(avatar_split_clause,[],[f438,f475,f472]) ).
fof(f481,definition,
( spl53_3
<=> ssList(sK52) ),
introduced(definition,[new_symbols(definition,[spl53_3])],[avatar_definition]) ).
fof(f483,plain,
( ssList(sK52)
| ~ spl53_3 ),
inference(avatar_component_clause,[],[f481]) ).
fof(f486,definition,
( spl53_4
<=> sK49 = app(sK52,cons(sK51,nil)) ),
introduced(definition,[new_symbols(definition,[spl53_4])],[avatar_definition]) ).
fof(f488,plain,
( sK49 = app(sK52,cons(sK51,nil))
| ~ spl53_4 ),
inference(avatar_component_clause,[],[f486]) ).
fof(f491,definition,
( spl53_5
<=> sK50 = app(cons(sK51,nil),sK52) ),
introduced(definition,[new_symbols(definition,[spl53_5])],[avatar_definition]) ).
fof(f493,plain,
( sK50 = app(cons(sK51,nil),sK52)
| ~ spl53_5 ),
inference(avatar_component_clause,[],[f491]) ).
fof(f495,plain,
( spl53_3
| ~ spl53_2 ),
inference(avatar_split_clause,[],[f416,f475,f481]) ).
fof(f496,plain,
( spl53_4
| ~ spl53_2 ),
inference(avatar_split_clause,[],[f417,f475,f486]) ).
fof(f497,plain,
( spl53_5
| ~ spl53_2 ),
inference(avatar_split_clause,[],[f418,f475,f491]) ).
fof(f499,definition,
( spl53_6
<=> ssItem(sK51) ),
introduced(definition,[new_symbols(definition,[spl53_6])],[avatar_definition]) ).
fof(f501,plain,
( ssItem(sK51)
| ~ spl53_6 ),
inference(avatar_component_clause,[],[f499]) ).
fof(f502,plain,
( spl53_6
| ~ spl53_2 ),
inference(avatar_split_clause,[],[f419,f475,f499]) ).
fof(f504,plain,
spl53_2,
inference(avatar_split_clause,[],[f432,f475]) ).
fof(f506,definition,
( spl53_7
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[spl53_7])],[avatar_definition]) ).
fof(f507,plain,
( ssList(nil)
| ~ spl53_7 ),
inference(avatar_component_clause,[],[f506]) ).
fof(f534,plain,
spl53_7,
inference(avatar_split_clause,[],[f306,f506]) ).
fof(f537,plain,
( ! [X0,X1] :
( ~ ssList(X1)
| ~ ssList(X0)
| sK49 != app(app(X0,cons(sK51,nil)),X1)
| sK50 != app(app(X1,cons(sK51,nil)),X0) )
| ~ spl53_1
| ~ spl53_6 ),
inference(resolution,[],[f473,f501]) ).
fof(f547,plain,
( ! [X0] :
( ~ ssList(X0)
| sK49 != app(app(sK52,cons(sK51,nil)),X0)
| sK50 != app(app(X0,cons(sK51,nil)),sK52) )
| ~ spl53_1
| ~ spl53_3
| ~ spl53_6 ),
inference(resolution,[],[f537,f483]) ).
fof(f548,plain,
( ! [X0] :
( ~ ssList(X0)
| sK49 != app(sK49,X0)
| sK50 != app(app(X0,cons(sK51,nil)),sK52) )
| ~ spl53_1
| ~ spl53_3
| ~ spl53_4
| ~ spl53_6 ),
inference(forward_demodulation,[],[f547,f488]) ).
fof(f550,plain,
( sK49 != app(sK49,nil)
| sK50 != app(app(nil,cons(sK51,nil)),sK52)
| ~ spl53_1
| ~ spl53_3
| ~ spl53_4
| ~ spl53_6
| ~ spl53_7 ),
inference(resolution,[],[f548,f507]) ).
fof(f574,definition,
( spl53_17
<=> sK50 = app(app(nil,cons(sK51,nil)),sK52) ),
introduced(definition,[new_symbols(definition,[spl53_17])],[avatar_definition]) ).
fof(f576,plain,
( sK50 != app(app(nil,cons(sK51,nil)),sK52)
| spl53_17 ),
inference(avatar_component_clause,[],[f574]) ).
fof(f578,definition,
( spl53_18
<=> sK49 = app(sK49,nil) ),
introduced(definition,[new_symbols(definition,[spl53_18])],[avatar_definition]) ).
fof(f580,plain,
( sK49 != app(sK49,nil)
| spl53_18 ),
inference(avatar_component_clause,[],[f578]) ).
fof(f581,plain,
( ~ spl53_17
| ~ spl53_18
| ~ spl53_1
| ~ spl53_3
| ~ spl53_4
| ~ spl53_6
| ~ spl53_7 ),
inference(avatar_split_clause,[],[f550,f506,f499,f486,f481,f472,f578,f574]) ).
fof(f1008,plain,
sK49 = app(sK49,nil),
inference(resolution,[],[f397,f426]) ).
fof(f1011,plain,
( $false
| spl53_18 ),
inference(forward_subsumption_resolution,[],[f1008,f580]) ).
fof(f1012,plain,
spl53_18,
inference(avatar_contradiction_clause,[],[f1011]) ).
fof(f1013,plain,
( ! [X0] :
( ssList(cons(sK51,X0))
| ~ ssList(X0) )
| ~ spl53_6 ),
inference(resolution,[],[f305,f501]) ).
fof(f1107,plain,
( ! [X0] :
( ~ ssList(X0)
| cons(sK51,X0) = app(nil,cons(sK51,X0)) )
| ~ spl53_6 ),
inference(resolution,[],[f1013,f320]) ).
fof(f1178,plain,
( cons(sK51,nil) = app(nil,cons(sK51,nil))
| ~ spl53_6
| ~ spl53_7 ),
inference(resolution,[],[f1107,f507]) ).
fof(f1185,plain,
( sK50 != app(cons(sK51,nil),sK52)
| ~ spl53_6
| ~ spl53_7
| spl53_17 ),
inference(superposition,[],[f576,f1178]) ).
fof(f1191,plain,
( $false
| ~ spl53_5
| ~ spl53_6
| ~ spl53_7
| spl53_17 ),
inference(forward_subsumption_resolution,[],[f1185,f493]) ).
fof(f1192,plain,
( ~ spl53_5
| ~ spl53_6
| ~ spl53_7
| spl53_17 ),
inference(avatar_contradiction_clause,[],[f1191]) ).
cnf(s1,plain,
( spl53_1
| ~ spl53_2 ),
inference(sat_conversion,[],[f478]) ).
cnf(s6,plain,
( ~ spl53_2
| spl53_3 ),
inference(sat_conversion,[],[f495]) ).
cnf(s7,plain,
( ~ spl53_2
| spl53_4 ),
inference(sat_conversion,[],[f496]) ).
cnf(s8,plain,
( ~ spl53_2
| spl53_5 ),
inference(sat_conversion,[],[f497]) ).
cnf(s9,plain,
( ~ spl53_2
| spl53_6 ),
inference(sat_conversion,[],[f502]) ).
cnf(s11,plain,
spl53_2,
inference(sat_conversion,[],[f504]) ).
cnf(s19,plain,
spl53_7,
inference(sat_conversion,[],[f534]) ).
cnf(s22,plain,
( ~ spl53_1
| ~ spl53_3
| ~ spl53_4
| ~ spl53_6
| ~ spl53_7
| ~ spl53_17
| ~ spl53_18 ),
inference(sat_conversion,[],[f581]) ).
cnf(s60,plain,
spl53_18,
inference(sat_conversion,[],[f1012]) ).
cnf(s61,plain,
( ~ spl53_5
| ~ spl53_6
| ~ spl53_7
| spl53_17 ),
inference(sat_conversion,[],[f1192]) ).
cnf(s62,plain,
( ~ spl53_1
| ~ spl53_3
| ~ spl53_4
| ~ spl53_6
| ~ spl53_7
| ~ spl53_17 ),
inference(rat,[],[s22,s60]) ).
cnf(s66,plain,
spl53_6,
inference(rat,[],[s9,s11]) ).
cnf(s67,plain,
spl53_5,
inference(rat,[],[s8,s11]) ).
cnf(s68,plain,
spl53_17,
inference(rat,[],[s61,s66,s19,s67]) ).
cnf(s69,plain,
spl53_4,
inference(rat,[],[s7,s11]) ).
cnf(s70,plain,
spl53_3,
inference(rat,[],[s6,s11]) ).
cnf(s71,plain,
~ spl53_1,
inference(rat,[],[s62,s68,s19,s66,s69,s70]) ).
cnf(s72,plain,
$false,
inference(rat,[],[s1,s11,s71]) ).
fof(f1193,plain,
$false,
inference(avatar_sat_refutation,[],[s72]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC417+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.18 % Computer : n011.cluster.edu
% 0.10/0.18 % Model : x86_64 x86_64
% 0.10/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.18 % Memory : 8046.5625MB
% 0.10/0.18 % OS : Linux 6.8.0-71-generic
% 0.10/0.18 % CPULimit : 300
% 0.10/0.18 % WCLimit : 300
% 0.10/0.18 % DateTime : Mon Sep 28 09:33:46 UTC 2026
% 0.10/0.18 % CPUTime :
% 0.10/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.21 Running first-order model finding
% 0.10/0.21 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
% 0.41/0.30 % (3272621)Will run a generic schedule for satisfiability detection.
% 0.41/0.30 % (3272632)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2363995674:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.41/0.30 % (3272627)% WARNING: option uhcvi not known.
% 0.41/0.30 % (3272626)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1452579613_2999 on theBenchmark for (2999ds/0Mi)
% 0.41/0.30 % (3272628)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=630735417:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.41/0.30 % (3272629)dis+10_1_sil=32000:sp=arity:random_seed=1355277679:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.41/0.30 % (3272630)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1715777563:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.41/0.30 % (3272631)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1108973059:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.41/0.30 % (3272627)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3660854245:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.41/0.30 % TRYING [1]
% 0.41/0.30 % TRYING [2]
% 0.41/0.30 % TRYING [3]
% 0.41/0.30 % (3272630) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3272621-3272630"...
% 0.41/0.30 % (3272630)...printing done.
% 0.41/0.30 % (3272630)Refutation found. Thanks to Tanya!
% 0.41/0.30 % SZS status Theorem for theBenchmark
% 0.41/0.30 % SZS output start Proof for theBenchmark
% See solution above
% 0.41/0.30 % (3272630)------------------------------
% 0.41/0.30 % (3272630)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.41/0.30 % (3272630)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.41/0.30 % (3272630)CaDiCaL version: 2.1.3
% 0.41/0.30 % (3272630)Termination reason: Refutation
% 0.41/0.30 % (3272630)Time elapsed: 0.027 s
% 0.41/0.30 % (3272630)Peak memory usage: 13 MB
% 0.41/0.30 % (3272630)Instructions burned: 47 (million)
% 0.41/0.30 % (3272621)Success in time 0.076 s
% 0.41/0.30 % Vampire exiting
%------------------------------------------------------------------------------