%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SWC419+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 0.08s 0.26s
% Output : Refutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 13
% Syntax : Number of formulae : 77 ( 21 unt; 8 def)
% Number of atoms : 230 ( 58 equ)
% Maximal formula atoms : 19 ( 2 avg)
% Number of connectives : 272 ( 119 ~; 109 |; 24 &)
% ( 8 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 9 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 51 ( 0 sgn 39 !; 12 ?)
% 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 ) ) )
| ( nil != X2
& nil = X3 )
| ( ! [X7] :
( ssItem(X7)
=> ! [X8] :
( ~ ssList(X8)
| app(cons(X7,nil),X8) != X3
| app(X8,cons(X7,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
| ~ 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 ) ) )
| ( nil != X2
& nil = X3 )
| ( ! [X7] :
( ssItem(X7)
=> ! [X8] :
( ~ ssList(X8)
| app(cons(X7,nil),X8) != X3
| app(X8,cons(X7,nil)) != X2 ) )
& 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] :
( 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 ) ) )
& ( nil = X2
| nil != X3 )
& ( ? [X7] :
( ? [X8] :
( ssList(X8)
& app(cons(X7,nil),X8) = X3
& app(X8,cons(X7,nil)) = X2 )
& ssItem(X7) )
| ~ neq(X3,nil) ) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(ennf_transformation,[],[f97]) ).
fof(f304,plain,
! [X0,X1] :
( ~ ssItem(X1)
| ~ ssList(X0)
| ssList(cons(X1,X0)) ),
inference(cnf_transformation,[],[f119]) ).
fof(f305,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f319,plain,
! [X0] :
( ~ ssList(X0)
| app(nil,X0) = X0 ),
inference(cnf_transformation,[],[f134]) ).
fof(f396,plain,
! [X0] :
( ~ ssList(X0)
| app(X0,nil) = X0 ),
inference(cnf_transformation,[],[f201]) ).
fof(f410,plain,
! [X6,X4,X5] :
( 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,[],[f221]) ).
fof(f411,plain,
( ~ neq(sK50,nil)
| sK49 = app(sK52,cons(sK51,nil)) ),
inference(cnf_transformation,[],[f221]) ).
fof(f412,plain,
( ~ neq(sK50,nil)
| sK50 = app(cons(sK51,nil),sK52) ),
inference(cnf_transformation,[],[f221]) ).
fof(f413,plain,
( ~ neq(sK50,nil)
| ssList(sK52) ),
inference(cnf_transformation,[],[f221]) ).
fof(f414,plain,
( ~ neq(sK50,nil)
| ssItem(sK51) ),
inference(cnf_transformation,[],[f221]) ).
fof(f416,plain,
neq(sK48,nil),
inference(cnf_transformation,[],[f221]) ).
fof(f417,plain,
sK47 = sK49,
inference(cnf_transformation,[],[f221]) ).
fof(f418,plain,
sK48 = sK50,
inference(cnf_transformation,[],[f221]) ).
fof(f420,plain,
ssList(sK49),
inference(cnf_transformation,[],[f221]) ).
fof(f425,plain,
neq(sK50,nil),
inference(definition_unfolding,[],[f416,f418]) ).
fof(f426,plain,
! [X6,X4,X5] :
( ~ ssItem(X4)
| app(app(X5,cons(X4,nil)),X6) != sK50
| ~ ssList(X6)
| ~ ssList(X5)
| app(app(X6,cons(X4,nil)),X5) != sK49 ),
inference(definition_unfolding,[],[f410,f417,f418]) ).
fof(f460,definition,
( spl53_1
<=> sK49 = app(sK52,cons(sK51,nil)) ),
introduced(definition,[new_symbols(definition,[spl53_1])],[avatar_definition]) ).
fof(f462,plain,
( sK49 = app(sK52,cons(sK51,nil))
| ~ spl53_1 ),
inference(avatar_component_clause,[],[f460]) ).
fof(f464,definition,
( spl53_2
<=> neq(sK50,nil) ),
introduced(definition,[new_symbols(definition,[spl53_2])],[avatar_definition]) ).
fof(f467,plain,
( spl53_1
| ~ spl53_2 ),
inference(avatar_split_clause,[],[f411,f464,f460]) ).
fof(f469,definition,
( spl53_3
<=> sK50 = app(cons(sK51,nil),sK52) ),
introduced(definition,[new_symbols(definition,[spl53_3])],[avatar_definition]) ).
fof(f471,plain,
( sK50 = app(cons(sK51,nil),sK52)
| ~ spl53_3 ),
inference(avatar_component_clause,[],[f469]) ).
fof(f472,plain,
( spl53_3
| ~ spl53_2 ),
inference(avatar_split_clause,[],[f412,f464,f469]) ).
fof(f474,definition,
( spl53_4
<=> ssList(sK52) ),
introduced(definition,[new_symbols(definition,[spl53_4])],[avatar_definition]) ).
fof(f476,plain,
( ssList(sK52)
| ~ spl53_4 ),
inference(avatar_component_clause,[],[f474]) ).
fof(f477,plain,
( spl53_4
| ~ spl53_2 ),
inference(avatar_split_clause,[],[f413,f464,f474]) ).
fof(f479,definition,
( spl53_5
<=> ssItem(sK51) ),
introduced(definition,[new_symbols(definition,[spl53_5])],[avatar_definition]) ).
fof(f481,plain,
( ssItem(sK51)
| ~ spl53_5 ),
inference(avatar_component_clause,[],[f479]) ).
fof(f482,plain,
( spl53_5
| ~ spl53_2 ),
inference(avatar_split_clause,[],[f414,f464,f479]) ).
fof(f492,plain,
spl53_2,
inference(avatar_split_clause,[],[f425,f464]) ).
fof(f494,definition,
( spl53_8
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[spl53_8])],[avatar_definition]) ).
fof(f495,plain,
( ssList(nil)
| ~ spl53_8 ),
inference(avatar_component_clause,[],[f494]) ).
fof(f522,plain,
spl53_8,
inference(avatar_split_clause,[],[f305,f494]) ).
fof(f525,plain,
( ! [X0,X1] :
( ~ ssList(X1)
| ~ ssList(X0)
| sK50 != app(app(X0,cons(sK51,nil)),X1)
| sK49 != app(app(X1,cons(sK51,nil)),X0) )
| ~ spl53_5 ),
inference(resolution,[],[f426,f481]) ).
fof(f531,plain,
( ! [X0] :
( ~ ssList(X0)
| sK50 != app(app(X0,cons(sK51,nil)),sK52)
| sK49 != app(app(sK52,cons(sK51,nil)),X0) )
| ~ spl53_4
| ~ spl53_5 ),
inference(resolution,[],[f525,f476]) ).
fof(f537,plain,
( ! [X0] :
( ~ ssList(X0)
| sK49 != app(sK49,X0)
| sK50 != app(app(X0,cons(sK51,nil)),sK52) )
| ~ spl53_1
| ~ spl53_4
| ~ spl53_5 ),
inference(forward_demodulation,[],[f531,f462]) ).
fof(f579,plain,
( sK49 != app(sK49,nil)
| sK50 != app(app(nil,cons(sK51,nil)),sK52)
| ~ spl53_1
| ~ spl53_4
| ~ spl53_5
| ~ spl53_8 ),
inference(resolution,[],[f537,f495]) ).
fof(f602,definition,
( spl53_26
<=> sK50 = app(app(nil,cons(sK51,nil)),sK52) ),
introduced(definition,[new_symbols(definition,[spl53_26])],[avatar_definition]) ).
fof(f604,plain,
( sK50 != app(app(nil,cons(sK51,nil)),sK52)
| spl53_26 ),
inference(avatar_component_clause,[],[f602]) ).
fof(f606,definition,
( spl53_27
<=> sK49 = app(sK49,nil) ),
introduced(definition,[new_symbols(definition,[spl53_27])],[avatar_definition]) ).
fof(f608,plain,
( sK49 != app(sK49,nil)
| spl53_27 ),
inference(avatar_component_clause,[],[f606]) ).
fof(f609,plain,
( ~ spl53_26
| ~ spl53_27
| ~ spl53_1
| ~ spl53_4
| ~ spl53_5
| ~ spl53_8 ),
inference(avatar_split_clause,[],[f579,f494,f479,f474,f460,f606,f602]) ).
fof(f996,plain,
sK49 = app(sK49,nil),
inference(resolution,[],[f396,f420]) ).
fof(f999,plain,
( $false
| spl53_27 ),
inference(forward_subsumption_resolution,[],[f996,f608]) ).
fof(f1000,plain,
spl53_27,
inference(avatar_contradiction_clause,[],[f999]) ).
fof(f1001,plain,
( ! [X0] :
( ssList(cons(sK51,X0))
| ~ ssList(X0) )
| ~ spl53_5 ),
inference(resolution,[],[f304,f481]) ).
fof(f1095,plain,
( ! [X0] :
( ~ ssList(X0)
| cons(sK51,X0) = app(nil,cons(sK51,X0)) )
| ~ spl53_5 ),
inference(resolution,[],[f1001,f319]) ).
fof(f1140,plain,
( cons(sK51,nil) = app(nil,cons(sK51,nil))
| ~ spl53_5
| ~ spl53_8 ),
inference(resolution,[],[f1095,f495]) ).
fof(f1175,plain,
( sK50 != app(cons(sK51,nil),sK52)
| ~ spl53_5
| ~ spl53_8
| spl53_26 ),
inference(superposition,[],[f604,f1140]) ).
fof(f1181,plain,
( $false
| ~ spl53_3
| ~ spl53_5
| ~ spl53_8
| spl53_26 ),
inference(forward_subsumption_resolution,[],[f1175,f471]) ).
fof(f1182,plain,
( ~ spl53_3
| ~ spl53_5
| ~ spl53_8
| spl53_26 ),
inference(avatar_contradiction_clause,[],[f1181]) ).
cnf(s1,plain,
( spl53_1
| ~ spl53_2 ),
inference(sat_conversion,[],[f467]) ).
cnf(s2,plain,
( ~ spl53_2
| spl53_3 ),
inference(sat_conversion,[],[f472]) ).
cnf(s3,plain,
( ~ spl53_2
| spl53_4 ),
inference(sat_conversion,[],[f477]) ).
cnf(s4,plain,
( ~ spl53_2
| spl53_5 ),
inference(sat_conversion,[],[f482]) ).
cnf(s6,plain,
spl53_2,
inference(sat_conversion,[],[f492]) ).
cnf(s14,plain,
spl53_8,
inference(sat_conversion,[],[f522]) ).
cnf(s21,plain,
( ~ spl53_1
| ~ spl53_4
| ~ spl53_5
| ~ spl53_8
| ~ spl53_26
| ~ spl53_27 ),
inference(sat_conversion,[],[f609]) ).
cnf(s55,plain,
spl53_27,
inference(sat_conversion,[],[f1000]) ).
cnf(s56,plain,
( ~ spl53_3
| ~ spl53_5
| ~ spl53_8
| spl53_26 ),
inference(sat_conversion,[],[f1182]) ).
cnf(s57,plain,
( ~ spl53_1
| ~ spl53_4
| ~ spl53_5
| ~ spl53_8
| ~ spl53_26 ),
inference(rat,[],[s21,s55]) ).
cnf(s61,plain,
spl53_5,
inference(rat,[],[s4,s6]) ).
cnf(s62,plain,
spl53_4,
inference(rat,[],[s3,s6]) ).
cnf(s63,plain,
spl53_3,
inference(rat,[],[s2,s6]) ).
cnf(s64,plain,
spl53_26,
inference(rat,[],[s56,s61,s14,s63]) ).
cnf(s65,plain,
~ spl53_1,
inference(rat,[],[s57,s62,s14,s61,s64]) ).
cnf(s66,plain,
$false,
inference(rat,[],[s1,s6,s65]) ).
fof(f1183,plain,
$false,
inference(avatar_sat_refutation,[],[s66]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC419+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.16 % Computer : n011.cluster.edu
% 0.08/0.16 % Model : x86_64 x86_64
% 0.08/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.16 % Memory : 8046.5625MB
% 0.08/0.16 % OS : Linux 6.8.0-71-generic
% 0.08/0.16 % CPULimit : 300
% 0.08/0.16 % WCLimit : 300
% 0.08/0.16 % DateTime : Mon Sep 28 09:34:50 UTC 2026
% 0.08/0.17 % CPUTime :
% 0.08/0.17 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.19 Running first-order model finding
% 0.08/0.19 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
% 0.08/0.26 % (3273471)Will run a generic schedule for satisfiability detection.
% 0.08/0.26 % (3273477)% WARNING: option uhcvi not known.
% 0.08/0.26 % (3273477)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1228430336:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.08/0.26 % (3273476)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3459232850_2999 on theBenchmark for (2999ds/0Mi)
% 0.08/0.26 % (3273478)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=4142368931:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.08/0.26 % (3273479)dis+10_1_sil=32000:sp=arity:random_seed=3541207392:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.08/0.26 % (3273480)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3072209210:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.08/0.26 % (3273481)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=4129198698:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.08/0.26 % (3273482)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1680437442:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.08/0.26 % TRYING [1]
% 0.08/0.26 % TRYING [2]
% 0.08/0.26 % TRYING [3]
% 0.08/0.26 % (3273480) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3273471-3273480"...
% 0.08/0.26 % (3273480)...printing done.
% 0.08/0.26 % (3273480)Refutation found. Thanks to Tanya!
% 0.08/0.26 % SZS status Theorem for theBenchmark
% 0.08/0.26 % SZS output start Proof for theBenchmark
% See solution above
% 0.08/0.26 % (3273480)------------------------------
% 0.08/0.26 % (3273480)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.08/0.26 % (3273480)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/0.26 % (3273480)CaDiCaL version: 2.1.3
% 0.08/0.26 % (3273480)Termination reason: Refutation
% 0.08/0.26 % (3273480)Time elapsed: 0.026 s
% 0.08/0.26 % (3273480)Peak memory usage: 13 MB
% 0.08/0.26 % (3273480)Instructions burned: 47 (million)
% 0.08/0.26 % (3273471)Success in time 0.062 s
% 0.08/0.26 % Vampire exiting
%------------------------------------------------------------------------------