%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SWC029-1 : 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 : n003.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 01:04:21 PM UTC 2026
% Result : Unsatisfiable 0.18s 0.48s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 28
% Syntax : Number of formulae : 102 ( 11 unt; 12 def)
% Number of atoms : 278 ( 65 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 329 ( 153 ~; 164 |; 0 &)
% ( 12 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 17 ( 15 usr; 13 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 19 ( 0 sgn 19 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause8) ).
fof(f86,axiom,
! [X0,X1] :
( ssList(cons(X0,X1))
| ~ ssList(X1)
| ~ ssItem(X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause86) ).
fof(f101,axiom,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| neq(X1,X0)
| X1 = X0 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause100) ).
fof(f102,plain,
! [X0,X1] :
( neq(X1,X0)
| ~ ssList(X1)
| ~ ssList(X0)
| X0 = X1 ),
inference(reorient_equations,[],[f101]) ).
fof(f121,axiom,
! [X0,X1] :
( app(X0,X1) != nil
| ~ ssList(X1)
| ~ ssList(X0)
| nil = X0 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause118) ).
fof(f122,plain,
! [X0,X1] :
( nil != app(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0)
| nil = X0 ),
inference(reorient_equations,[],[f121]) ).
fof(f123,axiom,
! [X0,X1] :
( app(X0,X1) != nil
| ~ ssList(X1)
| ~ ssList(X0)
| nil = X1 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause119) ).
fof(f124,plain,
! [X0,X1] :
( nil != app(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0)
| nil = X1 ),
inference(reorient_equations,[],[f123]) ).
fof(f156,axiom,
! [X0,X1] :
( nil != X0
| nil != X1
| ~ ssList(X1)
| ~ ssList(X0)
| app(X0,X1) = nil ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause145) ).
fof(f157,plain,
! [X0,X1] :
( nil != X0
| nil != X1
| ~ ssList(X1)
| ~ ssList(X0)
| nil = app(X0,X1) ),
inference(reorient_equations,[],[f156]) ).
fof(f203,negated_conjecture,
ssList(sk4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_4) ).
fof(f204,negated_conjecture,
sk2 = sk4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_5) ).
fof(f205,negated_conjecture,
sk1 = sk3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_6) ).
fof(f206,negated_conjecture,
( nil = sk3
| nil != sk4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_7) ).
fof(f207,negated_conjecture,
( ssItem(sk5)
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_8) ).
fof(f208,negated_conjecture,
( ssList(sk6)
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_9) ).
fof(f209,negated_conjecture,
( app(cons(sk5,nil),sk6) = sk4
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_10) ).
fof(f210,plain,
( sk4 = app(cons(sk5,nil),sk6)
| ~ neq(sk4,nil) ),
inference(reorient_equations,[],[f209]) ).
fof(f211,negated_conjecture,
( app(sk6,cons(sk5,nil)) = sk3
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_11) ).
fof(f212,plain,
( sk3 = app(sk6,cons(sk5,nil))
| ~ neq(sk4,nil) ),
inference(reorient_equations,[],[f211]) ).
fof(f213,negated_conjecture,
( nil = sk2
| nil = sk1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_12) ).
fof(f216,negated_conjecture,
( nil != sk1
| nil != sk2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_15) ).
fof(f219,plain,
( nil = sk4
| nil = sk3 ),
inference(definition_unfolding,[],[f213,f204,f205]) ).
fof(f222,plain,
( nil != sk3
| nil != sk4 ),
inference(definition_unfolding,[],[f216,f205,f204]) ).
fof(f235,plain,
! [X1] :
( nil != X1
| ~ ssList(X1)
| ~ ssList(nil)
| nil = app(nil,X1) ),
inference(equality_resolution,[],[f157]) ).
fof(f236,plain,
( ~ ssList(nil)
| ~ ssList(nil)
| nil = app(nil,nil) ),
inference(equality_resolution,[],[f235]) ).
fof(f248,plain,
( ~ ssList(nil)
| nil = app(nil,nil) ),
inference(duplicate_literal_removal,[],[f236]) ).
fof(f254,definition,
( spl0_1
<=> nil = sk4 ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f256,plain,
( nil != sk4
| spl0_1 ),
inference(avatar_component_clause,[],[f254]) ).
fof(f258,definition,
( spl0_2
<=> nil = sk3 ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f259,plain,
( nil = sk3
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f258]) ).
fof(f261,plain,
( ~ spl0_1
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f222,f258,f254]) ).
fof(f262,plain,
( spl0_2
| spl0_1 ),
inference(avatar_split_clause,[],[f219,f254,f258]) ).
fof(f264,definition,
( spl0_3
<=> neq(sk4,nil) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f266,plain,
( ~ neq(sk4,nil)
| spl0_3 ),
inference(avatar_component_clause,[],[f264]) ).
fof(f268,definition,
( spl0_4
<=> sk3 = app(sk6,cons(sk5,nil)) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f270,plain,
( sk3 = app(sk6,cons(sk5,nil))
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f268]) ).
fof(f271,plain,
( ~ spl0_3
| spl0_4 ),
inference(avatar_split_clause,[],[f212,f268,f264]) ).
fof(f273,definition,
( spl0_5
<=> sk4 = app(cons(sk5,nil),sk6) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f275,plain,
( sk4 = app(cons(sk5,nil),sk6)
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f273]) ).
fof(f276,plain,
( ~ spl0_3
| spl0_5 ),
inference(avatar_split_clause,[],[f210,f273,f264]) ).
fof(f278,definition,
( spl0_6
<=> ssList(sk6) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f280,plain,
( ssList(sk6)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f278]) ).
fof(f281,plain,
( ~ spl0_3
| spl0_6 ),
inference(avatar_split_clause,[],[f208,f278,f264]) ).
fof(f283,definition,
( spl0_7
<=> ssItem(sk5) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f285,plain,
( ssItem(sk5)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f283]) ).
fof(f286,plain,
( ~ spl0_3
| spl0_7 ),
inference(avatar_split_clause,[],[f207,f283,f264]) ).
fof(f287,plain,
( ~ spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f206,f258,f254]) ).
fof(f289,definition,
( spl0_8
<=> nil = app(nil,nil) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f291,plain,
( nil = app(nil,nil)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f289]) ).
fof(f293,definition,
( spl0_9
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f294,plain,
( ssList(nil)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f293]) ).
fof(f296,plain,
( spl0_8
| ~ spl0_9 ),
inference(avatar_split_clause,[],[f248,f293,f289]) ).
fof(f329,plain,
spl0_9,
inference(avatar_split_clause,[],[f8,f293]) ).
fof(f524,plain,
( ~ ssList(sk4)
| ~ ssList(nil)
| nil = sk4
| spl0_3 ),
inference(resolution,[],[f102,f266]) ).
fof(f527,plain,
( ~ ssList(nil)
| nil = sk4
| spl0_3 ),
inference(forward_subsumption_resolution,[],[f524,f203]) ).
fof(f528,plain,
( nil = sk4
| spl0_3
| ~ spl0_9 ),
inference(forward_subsumption_resolution,[],[f527,f294]) ).
fof(f529,plain,
( $false
| spl0_1
| spl0_3
| ~ spl0_9 ),
inference(forward_subsumption_resolution,[],[f528,f256]) ).
fof(f530,plain,
( spl0_1
| spl0_3
| ~ spl0_9 ),
inference(avatar_contradiction_clause,[],[f529]) ).
fof(f531,plain,
( nil = app(sk6,cons(sk5,nil))
| ~ spl0_2
| ~ spl0_4 ),
inference(forward_demodulation,[],[f270,f259]) ).
fof(f601,definition,
( spl0_17
<=> nil = sk6 ),
introduced(definition,[new_symbols(definition,[spl0_17])],[avatar_definition]) ).
fof(f603,plain,
( nil = sk6
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f601]) ).
fof(f691,plain,
( nil != nil
| ~ ssList(cons(sk5,nil))
| ~ ssList(sk6)
| nil = sk6
| ~ spl0_2
| ~ spl0_4 ),
inference(superposition,[],[f122,f531]) ).
fof(f693,plain,
( ~ ssList(cons(sk5,nil))
| ~ ssList(sk6)
| nil = sk6
| ~ spl0_2
| ~ spl0_4 ),
inference(trivial_inequality_removal,[],[f691]) ).
fof(f698,plain,
( nil != nil
| ~ ssList(cons(sk5,nil))
| ~ ssList(sk6)
| nil = cons(sk5,nil)
| ~ spl0_2
| ~ spl0_4 ),
inference(superposition,[],[f124,f531]) ).
fof(f702,plain,
( ~ ssList(cons(sk5,nil))
| ~ ssList(sk6)
| nil = cons(sk5,nil)
| ~ spl0_2
| ~ spl0_4 ),
inference(trivial_inequality_removal,[],[f698]) ).
fof(f703,plain,
( ~ ssList(cons(sk5,nil))
| nil = cons(sk5,nil)
| ~ spl0_2
| ~ spl0_4
| ~ spl0_6 ),
inference(forward_subsumption_resolution,[],[f702,f280]) ).
fof(f705,definition,
( spl0_22
<=> nil = cons(sk5,nil) ),
introduced(definition,[new_symbols(definition,[spl0_22])],[avatar_definition]) ).
fof(f707,plain,
( nil = cons(sk5,nil)
| ~ spl0_22 ),
inference(avatar_component_clause,[],[f705]) ).
fof(f709,definition,
( spl0_23
<=> ssList(cons(sk5,nil)) ),
introduced(definition,[new_symbols(definition,[spl0_23])],[avatar_definition]) ).
fof(f711,plain,
( ~ ssList(cons(sk5,nil))
| spl0_23 ),
inference(avatar_component_clause,[],[f709]) ).
fof(f712,plain,
( spl0_22
| ~ spl0_23
| ~ spl0_2
| ~ spl0_4
| ~ spl0_6 ),
inference(avatar_split_clause,[],[f703,f278,f268,f258,f709,f705]) ).
fof(f800,plain,
( sk4 = app(nil,sk6)
| ~ spl0_5
| ~ spl0_22 ),
inference(superposition,[],[f275,f707]) ).
fof(f826,plain,
( sk4 = app(nil,nil)
| ~ spl0_5
| ~ spl0_17
| ~ spl0_22 ),
inference(forward_demodulation,[],[f800,f603]) ).
fof(f832,plain,
( nil = sk4
| ~ spl0_5
| ~ spl0_8
| ~ spl0_17
| ~ spl0_22 ),
inference(forward_demodulation,[],[f826,f291]) ).
fof(f833,plain,
( $false
| spl0_1
| ~ spl0_5
| ~ spl0_8
| ~ spl0_17
| ~ spl0_22 ),
inference(forward_subsumption_resolution,[],[f832,f256]) ).
fof(f834,plain,
( spl0_1
| ~ spl0_5
| ~ spl0_8
| ~ spl0_17
| ~ spl0_22 ),
inference(avatar_contradiction_clause,[],[f833]) ).
fof(f843,plain,
( ~ ssList(cons(sk5,nil))
| nil = sk6
| ~ spl0_2
| ~ spl0_4
| ~ spl0_6 ),
inference(forward_subsumption_resolution,[],[f693,f280]) ).
fof(f844,plain,
( spl0_17
| ~ spl0_23
| ~ spl0_2
| ~ spl0_4
| ~ spl0_6 ),
inference(avatar_split_clause,[],[f843,f278,f268,f258,f709,f601]) ).
fof(f919,plain,
( ~ ssList(nil)
| ~ ssItem(sk5)
| spl0_23 ),
inference(resolution,[],[f86,f711]) ).
fof(f928,plain,
( ~ ssItem(sk5)
| ~ spl0_9
| spl0_23 ),
inference(forward_subsumption_resolution,[],[f919,f294]) ).
fof(f929,plain,
( $false
| ~ spl0_7
| ~ spl0_9
| spl0_23 ),
inference(forward_subsumption_resolution,[],[f928,f285]) ).
fof(f930,plain,
( ~ spl0_7
| ~ spl0_9
| spl0_23 ),
inference(avatar_contradiction_clause,[],[f929]) ).
cnf(s1,plain,
( ~ spl0_1
| ~ spl0_2 ),
inference(sat_conversion,[],[f261]) ).
cnf(s2,plain,
( spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f262]) ).
cnf(s3,plain,
( ~ spl0_3
| spl0_4 ),
inference(sat_conversion,[],[f271]) ).
cnf(s4,plain,
( ~ spl0_3
| spl0_5 ),
inference(sat_conversion,[],[f276]) ).
cnf(s5,plain,
( ~ spl0_3
| spl0_6 ),
inference(sat_conversion,[],[f281]) ).
cnf(s6,plain,
( ~ spl0_3
| spl0_7 ),
inference(sat_conversion,[],[f286]) ).
cnf(s7,plain,
( ~ spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f287]) ).
cnf(s8,plain,
( spl0_8
| ~ spl0_9 ),
inference(sat_conversion,[],[f296]) ).
cnf(s17,plain,
spl0_9,
inference(sat_conversion,[],[f329]) ).
cnf(s19,plain,
( spl0_1
| spl0_3
| ~ spl0_9 ),
inference(sat_conversion,[],[f530]) ).
cnf(s24,plain,
( ~ spl0_2
| ~ spl0_4
| ~ spl0_6
| spl0_22
| ~ spl0_23 ),
inference(sat_conversion,[],[f712]) ).
cnf(s34,plain,
( spl0_1
| ~ spl0_5
| ~ spl0_8
| ~ spl0_17
| ~ spl0_22 ),
inference(sat_conversion,[],[f834]) ).
cnf(s37,plain,
( ~ spl0_2
| ~ spl0_4
| ~ spl0_6
| spl0_17
| ~ spl0_23 ),
inference(sat_conversion,[],[f844]) ).
cnf(s40,plain,
( ~ spl0_7
| ~ spl0_9
| spl0_23 ),
inference(sat_conversion,[],[f930]) ).
cnf(s44,plain,
spl0_8,
inference(rat,[],[s8,s17]) ).
cnf(s45,plain,
spl0_1,
inference(rat,[],[s34,s24,s37,s40,s3,s4,s5,s6,s2,s19,s44,s17]) ).
cnf(s46,plain,
spl0_2,
inference(rat,[],[s7,s45]) ).
cnf(s47,plain,
$false,
inference(rat,[],[s1,s46,s45]) ).
fof(f931,plain,
$false,
inference(avatar_sat_refutation,[],[s47]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC029-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.38 % Computer : n003.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Mon Sep 28 07:32:57 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.42 Running first-order model finding
% 0.11/0.42 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
% 0.18/0.48 % (1409137)Will run a generic schedule for satisfiability detection.
% 0.18/0.48 % (1409153)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=201033302:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.18/0.48 % (1409147)% WARNING: option uhcvi not known.
% 0.18/0.48 % (1409146)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1052556900_2999 on theBenchmark for (2999ds/0Mi)
% 0.18/0.48 % (1409149)dis+10_1_sil=32000:sp=arity:random_seed=1217690439:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.18/0.48 % (1409151)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=480385412:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.18/0.48 % (1409148)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3300811122:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.18/0.48 % (1409147)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2437257918:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.18/0.48 % (1409152)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=793626562:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.18/0.48 % TRYING [1]
% 0.18/0.48 % TRYING [2]
% 0.18/0.48 % (1409149) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1409137-1409149"...
% 0.18/0.48 % TRYING [3]
% 0.18/0.48 % (1409149)...printing done.
% 0.18/0.48 % (1409149)Refutation found. Thanks to Tanya!
% 0.18/0.48 % SZS status Unsatisfiable for theBenchmark
% 0.18/0.48 % SZS output start Proof for theBenchmark
% See solution above
% 0.18/0.48 % (1409149)------------------------------
% 0.18/0.48 % (1409149)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.48 % (1409149)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.48 % (1409149)CaDiCaL version: 2.1.3
% 0.18/0.48 % (1409149)Termination reason: Refutation
% 0.18/0.48 % (1409149)Time elapsed: 0.019 s
% 0.18/0.48 % (1409149)Peak memory usage: 13 MB
% 0.18/0.48 % (1409149)Instructions burned: 28 (million)
% 0.18/0.48 % (1409137)Success in time 0.047 s
% 0.18/0.48 % Vampire exiting
%------------------------------------------------------------------------------