%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SWC323+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 : n010.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 01:05:32 PM UTC 2026
% Result : Theorem 0.08s 0.27s
% Output : Refutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 15
% Syntax : Number of formulae : 97 ( 18 unt; 9 def)
% Number of atoms : 304 ( 84 equ)
% Maximal formula atoms : 17 ( 3 avg)
% Number of connectives : 364 ( 157 ~; 141 |; 34 &)
% ( 13 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 4 avg)
% Maximal term depth : 3 ( 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 : 60 ( 0 sgn 44 !; 16 ?)
% Comments :
%------------------------------------------------------------------------------
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(f83,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( nil = app(X0,X1)
<=> ( nil = X1
& nil = X0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax83) ).
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
| ? [X4] :
( ssList(X4)
& ? [X5] :
( ssList(X5)
& app(X4,X5) = X1
& app(X5,X4) = X0 ) )
| ( nil != X2
& nil = X3 )
| ( ! [X6] :
( ssItem(X6)
=> ! [X7] :
( ssList(X7)
=> ( app(cons(X6,nil),X7) != X3
| app(X7,cons(X6,nil)) != X2 ) ) )
& 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
| ? [X4] :
( ssList(X4)
& ? [X5] :
( ssList(X5)
& app(X4,X5) = X1
& app(X5,X4) = X0 ) )
| ( nil != X2
& nil = X3 )
| ( ! [X6] :
( ssItem(X6)
=> ! [X7] :
( ssList(X7)
=> ( app(cons(X6,nil),X7) != X3
| app(X7,cons(X6,nil)) != X2 ) ) )
& neq(X3,nil) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
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(f200,plain,
! [X0] :
( ! [X1] :
( ( nil = app(X0,X1)
<=> ( nil = X1
& nil = X0 ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f83]) ).
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
& ! [X4] :
( ~ ssList(X4)
| ! [X5] :
( ~ ssList(X5)
| app(X4,X5) != X1
| app(X5,X4) != X0 ) )
& ( nil = X2
| nil != X3 )
& ( ? [X6] :
( ? [X7] :
( app(cons(X6,nil),X7) = X3
& app(X7,cons(X6,nil)) = X2
& ssList(X7) )
& ssItem(X6) )
| ~ 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
& ! [X4] :
( ~ ssList(X4)
| ! [X5] :
( ~ ssList(X5)
| app(X4,X5) != X1
| app(X5,X4) != X0 ) )
& ( nil = X2
| nil != X3 )
& ( ? [X6] :
( ? [X7] :
( app(cons(X6,nil),X7) = X3
& app(X7,cons(X6,nil)) = X2
& ssList(X7) )
& ssItem(X6) )
| ~ neq(X3,nil) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(flattening,[],[f221]) ).
fof(f303,plain,
! [X0,X1] :
( neq(X0,X1)
| ~ ssList(X1)
| X0 = X1
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f118]) ).
fof(f305,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssItem(X1)
| ssList(cons(X1,X0)) ),
inference(cnf_transformation,[],[f119]) ).
fof(f306,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f396,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| nil != X0
| nil != X1
| nil = app(X0,X1) ),
inference(cnf_transformation,[],[f200]) ).
fof(f397,plain,
! [X0] :
( ~ ssList(X0)
| app(X0,nil) = X0 ),
inference(cnf_transformation,[],[f201]) ).
fof(f411,plain,
( ~ neq(sK50,nil)
| ssList(sK52) ),
inference(cnf_transformation,[],[f222]) ).
fof(f412,plain,
( ~ neq(sK50,nil)
| sK49 = app(sK52,cons(sK51,nil)) ),
inference(cnf_transformation,[],[f222]) ).
fof(f413,plain,
( ~ neq(sK50,nil)
| sK50 = app(cons(sK51,nil),sK52) ),
inference(cnf_transformation,[],[f222]) ).
fof(f414,plain,
! [X4,X5] :
( app(X5,X4) != sK47
| app(X4,X5) != sK48
| ~ ssList(X5)
| ~ ssList(X4) ),
inference(cnf_transformation,[],[f222]) ).
fof(f415,plain,
( ~ neq(sK50,nil)
| ssItem(sK51) ),
inference(cnf_transformation,[],[f222]) ).
fof(f416,plain,
( nil != sK50
| nil = sK49 ),
inference(cnf_transformation,[],[f222]) ).
fof(f417,plain,
ssList(sK50),
inference(cnf_transformation,[],[f222]) ).
fof(f418,plain,
sK47 = sK49,
inference(cnf_transformation,[],[f222]) ).
fof(f419,plain,
sK48 = sK50,
inference(cnf_transformation,[],[f222]) ).
fof(f420,plain,
ssList(sK49),
inference(cnf_transformation,[],[f222]) ).
fof(f425,plain,
! [X4,X5] :
( app(X5,X4) != sK49
| app(X4,X5) != sK50
| ~ ssList(X5)
| ~ ssList(X4) ),
inference(definition_unfolding,[],[f414,f418,f419]) ).
fof(f448,plain,
! [X1] :
( ~ ssList(nil)
| ~ ssList(X1)
| nil != X1
| nil = app(nil,X1) ),
inference(equality_resolution,[],[f396]) ).
fof(f449,plain,
( ~ ssList(nil)
| ~ ssList(nil)
| nil = app(nil,nil) ),
inference(equality_resolution,[],[f448]) ).
fof(f498,plain,
! [X0,X1] :
( ssList(cons(X1,X0))
| ssItem(X1)
| ~ ssList(X0) ),
inference(consistent_polarity_flipping,[],[f305]) ).
fof(f565,plain,
( ~ neq(sK50,nil)
| ~ ssItem(sK51) ),
inference(consistent_polarity_flipping,[],[f415]) ).
fof(f567,plain,
( ~ ssList(nil)
| nil = app(nil,nil) ),
inference(duplicate_literal_removal,[],[f449]) ).
fof(f574,definition,
( spl53_1
<=> ssList(sK52) ),
introduced(definition,[new_symbols(definition,[spl53_1])],[avatar_definition]) ).
fof(f576,plain,
( ssList(sK52)
| ~ spl53_1 ),
inference(avatar_component_clause,[],[f574]) ).
fof(f578,definition,
( spl53_2
<=> neq(sK50,nil) ),
introduced(definition,[new_symbols(definition,[spl53_2])],[avatar_definition]) ).
fof(f580,plain,
( ~ neq(sK50,nil)
| spl53_2 ),
inference(avatar_component_clause,[],[f578]) ).
fof(f581,plain,
( spl53_1
| ~ spl53_2 ),
inference(avatar_split_clause,[],[f411,f578,f574]) ).
fof(f583,definition,
( spl53_3
<=> sK49 = app(sK52,cons(sK51,nil)) ),
introduced(definition,[new_symbols(definition,[spl53_3])],[avatar_definition]) ).
fof(f585,plain,
( sK49 = app(sK52,cons(sK51,nil))
| ~ spl53_3 ),
inference(avatar_component_clause,[],[f583]) ).
fof(f586,plain,
( spl53_3
| ~ spl53_2 ),
inference(avatar_split_clause,[],[f412,f578,f583]) ).
fof(f588,definition,
( spl53_4
<=> sK50 = app(cons(sK51,nil),sK52) ),
introduced(definition,[new_symbols(definition,[spl53_4])],[avatar_definition]) ).
fof(f590,plain,
( sK50 = app(cons(sK51,nil),sK52)
| ~ spl53_4 ),
inference(avatar_component_clause,[],[f588]) ).
fof(f591,plain,
( spl53_4
| ~ spl53_2 ),
inference(avatar_split_clause,[],[f413,f578,f588]) ).
fof(f593,definition,
( spl53_5
<=> ssItem(sK51) ),
introduced(definition,[new_symbols(definition,[spl53_5])],[avatar_definition]) ).
fof(f595,plain,
( ~ ssItem(sK51)
| spl53_5 ),
inference(avatar_component_clause,[],[f593]) ).
fof(f596,plain,
( ~ spl53_5
| ~ spl53_2 ),
inference(avatar_split_clause,[],[f565,f578,f593]) ).
fof(f598,definition,
( spl53_6
<=> nil = sK49 ),
introduced(definition,[new_symbols(definition,[spl53_6])],[avatar_definition]) ).
fof(f600,plain,
( nil = sK49
| ~ spl53_6 ),
inference(avatar_component_clause,[],[f598]) ).
fof(f602,definition,
( spl53_7
<=> nil = sK50 ),
introduced(definition,[new_symbols(definition,[spl53_7])],[avatar_definition]) ).
fof(f605,plain,
( spl53_6
| ~ spl53_7 ),
inference(avatar_split_clause,[],[f416,f602,f598]) ).
fof(f607,definition,
( spl53_8
<=> nil = app(nil,nil) ),
introduced(definition,[new_symbols(definition,[spl53_8])],[avatar_definition]) ).
fof(f609,plain,
( nil = app(nil,nil)
| ~ spl53_8 ),
inference(avatar_component_clause,[],[f607]) ).
fof(f611,definition,
( spl53_9
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[spl53_9])],[avatar_definition]) ).
fof(f612,plain,
( ssList(nil)
| ~ spl53_9 ),
inference(avatar_component_clause,[],[f611]) ).
fof(f614,plain,
( spl53_8
| ~ spl53_9 ),
inference(avatar_split_clause,[],[f567,f611,f607]) ).
fof(f640,plain,
spl53_9,
inference(avatar_split_clause,[],[f306,f611]) ).
fof(f677,plain,
sK49 = app(sK49,nil),
inference(resolution,[],[f397,f420]) ).
fof(f687,plain,
( sK49 != sK49
| sK50 != app(nil,sK49)
| ~ ssList(sK49)
| ~ ssList(nil) ),
inference(superposition,[],[f425,f677]) ).
fof(f688,plain,
( sK50 != app(nil,sK49)
| ~ ssList(sK49)
| ~ ssList(nil) ),
inference(trivial_inequality_removal,[],[f687]) ).
fof(f689,plain,
( sK50 != app(nil,sK49)
| ~ ssList(nil) ),
inference(forward_subsumption_resolution,[],[f688,f420]) ).
fof(f690,plain,
( sK50 != app(nil,sK49)
| ~ spl53_9 ),
inference(forward_subsumption_resolution,[],[f689,f612]) ).
fof(f725,plain,
( ~ ssList(nil)
| nil = sK50
| ~ ssList(sK50)
| spl53_2 ),
inference(resolution,[],[f303,f580]) ).
fof(f730,plain,
( nil = sK50
| ~ ssList(sK50)
| spl53_2
| ~ spl53_9 ),
inference(forward_subsumption_resolution,[],[f725,f612]) ).
fof(f735,plain,
( nil = sK50
| spl53_2
| ~ spl53_9 ),
inference(forward_subsumption_resolution,[],[f730,f417]) ).
fof(f737,plain,
( spl53_7
| spl53_2
| ~ spl53_9 ),
inference(avatar_split_clause,[],[f735,f611,f578,f602]) ).
fof(f745,plain,
( sK50 != app(nil,nil)
| ~ spl53_6
| ~ spl53_9 ),
inference(superposition,[],[f690,f600]) ).
fof(f746,plain,
( nil != sK50
| ~ spl53_6
| ~ spl53_8
| ~ spl53_9 ),
inference(forward_demodulation,[],[f745,f609]) ).
fof(f749,plain,
( ~ spl53_7
| ~ spl53_6
| ~ spl53_8
| ~ spl53_9 ),
inference(avatar_split_clause,[],[f746,f611,f607,f598,f602]) ).
fof(f803,plain,
( sK49 != sK49
| sK50 != app(cons(sK51,nil),sK52)
| ~ ssList(sK52)
| ~ ssList(cons(sK51,nil))
| ~ spl53_3 ),
inference(superposition,[],[f425,f585]) ).
fof(f804,plain,
( sK50 != app(cons(sK51,nil),sK52)
| ~ ssList(sK52)
| ~ ssList(cons(sK51,nil))
| ~ spl53_3 ),
inference(trivial_inequality_removal,[],[f803]) ).
fof(f805,plain,
( ~ ssList(sK52)
| ~ ssList(cons(sK51,nil))
| ~ spl53_3
| ~ spl53_4 ),
inference(forward_subsumption_resolution,[],[f804,f590]) ).
fof(f806,plain,
( ~ ssList(cons(sK51,nil))
| ~ spl53_1
| ~ spl53_3
| ~ spl53_4 ),
inference(forward_subsumption_resolution,[],[f805,f576]) ).
fof(f807,plain,
( ssItem(sK51)
| ~ ssList(nil)
| ~ spl53_1
| ~ spl53_3
| ~ spl53_4 ),
inference(resolution,[],[f806,f498]) ).
fof(f808,plain,
( ~ ssList(nil)
| ~ spl53_1
| ~ spl53_3
| ~ spl53_4
| spl53_5 ),
inference(forward_subsumption_resolution,[],[f807,f595]) ).
fof(f809,plain,
( $false
| ~ spl53_1
| ~ spl53_3
| ~ spl53_4
| spl53_5
| ~ spl53_9 ),
inference(forward_subsumption_resolution,[],[f808,f612]) ).
fof(f810,plain,
( ~ spl53_1
| ~ spl53_3
| ~ spl53_4
| spl53_5
| ~ spl53_9 ),
inference(avatar_contradiction_clause,[],[f809]) ).
cnf(s1,plain,
( spl53_1
| ~ spl53_2 ),
inference(sat_conversion,[],[f581]) ).
cnf(s2,plain,
( ~ spl53_2
| spl53_3 ),
inference(sat_conversion,[],[f586]) ).
cnf(s3,plain,
( ~ spl53_2
| spl53_4 ),
inference(sat_conversion,[],[f591]) ).
cnf(s4,plain,
( ~ spl53_2
| ~ spl53_5 ),
inference(sat_conversion,[],[f596]) ).
cnf(s5,plain,
( spl53_6
| ~ spl53_7 ),
inference(sat_conversion,[],[f605]) ).
cnf(s6,plain,
( spl53_8
| ~ spl53_9 ),
inference(sat_conversion,[],[f614]) ).
cnf(s14,plain,
spl53_9,
inference(sat_conversion,[],[f640]) ).
cnf(s17,plain,
( spl53_2
| spl53_7
| ~ spl53_9 ),
inference(sat_conversion,[],[f737]) ).
cnf(s19,plain,
( ~ spl53_6
| ~ spl53_7
| ~ spl53_8
| ~ spl53_9 ),
inference(sat_conversion,[],[f749]) ).
cnf(s24,plain,
( ~ spl53_1
| ~ spl53_3
| ~ spl53_4
| spl53_5
| ~ spl53_9 ),
inference(sat_conversion,[],[f810]) ).
cnf(s28,plain,
spl53_8,
inference(rat,[],[s6,s14]) ).
cnf(s29,plain,
~ spl53_7,
inference(rat,[],[s5,s19,s28,s14]) ).
cnf(s30,plain,
spl53_2,
inference(rat,[],[s17,s14,s29]) ).
cnf(s31,plain,
~ spl53_5,
inference(rat,[],[s4,s30]) ).
cnf(s32,plain,
spl53_4,
inference(rat,[],[s3,s30]) ).
cnf(s33,plain,
spl53_3,
inference(rat,[],[s2,s30]) ).
cnf(s34,plain,
spl53_1,
inference(rat,[],[s1,s30]) ).
cnf(s35,plain,
$false,
inference(rat,[],[s24,s14,s31,s34,s32,s33]) ).
fof(f811,plain,
$false,
inference(avatar_sat_refutation,[],[s35]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC323+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.18 % Computer : n010.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Mon Sep 28 09:06:17 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.21 Running first-order model finding
% 0.08/0.21 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
% 0.08/0.27 % (1788917)Will run a generic schedule for satisfiability detection.
% 0.08/0.27 % (1788927)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=4203100201:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.08/0.27 % (1788923)% WARNING: option uhcvi not known.
% 0.08/0.27 % (1788922)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2612999131_2999 on theBenchmark for (2999ds/0Mi)
% 0.08/0.27 % (1788924)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2940139567:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.08/0.27 % (1788923)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3180724980:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.08/0.27 % (1788925)dis+10_1_sil=32000:sp=arity:random_seed=1975720387:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.08/0.27 % (1788928)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3991357022:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.08/0.27 % (1788926)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3979727436:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.08/0.27 % (1788923) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1788917-1788923"...
% 0.08/0.27 % TRYING [1]
% 0.08/0.27 % (1788923)...printing done.
% 0.08/0.27 % TRYING [2]
% 0.08/0.27 % (1788923)Refutation found. Thanks to Tanya!
% 0.08/0.27 % SZS status Theorem for theBenchmark
% 0.08/0.27 % SZS output start Proof for theBenchmark
% See solution above
% 0.08/0.27 % (1788923)------------------------------
% 0.08/0.27 % (1788923)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.08/0.27 % (1788923)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/0.27 % (1788923)CaDiCaL version: 2.1.3
% 0.08/0.27 % (1788923)Termination reason: Refutation
% 0.08/0.27 % (1788923)Time elapsed: 0.014 s
% 0.08/0.27 % (1788923)Peak memory usage: 13 MB
% 0.08/0.27 % (1788923)Instructions burned: 20 (million)
% 0.08/0.27 % (1788917)Success in time 0.05 s
% 0.08/0.27 % Vampire exiting
%------------------------------------------------------------------------------