%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC190-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n017.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 01:02:52 PM UTC 2026
% Result : Unsatisfiable 1.70s 1.13s
% Output : Refutation 2.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 22
% Syntax : Number of formulae : 87 ( 21 unt; 7 def)
% Number of atoms : 251 ( 13 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 323 ( 159 ~; 157 |; 0 &)
% ( 7 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 8 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 37 ( 0 sgn 37 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause8) ).
fof(f85,axiom,
! [X0,X1] :
( ssList(app(X1,X0))
| ~ ssList(X1)
| ~ ssList(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause85) ).
fof(f86,axiom,
! [X0,X1] :
( ssList(cons(X0,X1))
| ~ ssList(X1)
| ~ ssItem(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause86) ).
fof(f149,axiom,
! [X2,X0,X1] :
( X0 != X1
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0)
| memberP(cons(X1,X2),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause138) ).
fof(f151,axiom,
! [X2,X0,X1] :
( memberP(app(X0,X2),X1)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ memberP(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause140) ).
fof(f152,axiom,
! [X2,X0,X1] :
( memberP(app(X2,X0),X1)
| ~ ssList(X0)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ memberP(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause141) ).
fof(f189,axiom,
! [X2,X3,X0,X1] :
( app(X0,cons(X1,X2)) != X3
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ ssList(X3)
| memberP(X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause175) ).
fof(f205,negated_conjecture,
sk1 = sk3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_6) ).
fof(f206,negated_conjecture,
ssItem(sk5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_7) ).
fof(f207,negated_conjecture,
ssItem(sk6),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_8) ).
fof(f208,negated_conjecture,
ssList(sk7),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_9) ).
fof(f209,negated_conjecture,
ssList(sk8),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_10) ).
fof(f210,negated_conjecture,
app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8) = sk1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_11) ).
fof(f211,plain,
sk1 = app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8),
inference(reorient_equations,[],[f210]) ).
fof(f212,negated_conjecture,
sk5 != sk6,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_12) ).
fof(f214,negated_conjecture,
! [X0] :
( ~ memberP(sk3,X0)
| sk9 = X0
| ~ ssItem(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_14) ).
fof(f217,plain,
sk3 = app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8),
inference(definition_unfolding,[],[f211,f205]) ).
fof(f220,plain,
! [X2,X0,X1] :
( memberP(app(X0,cons(X1,X2)),X1)
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ ssList(app(X0,cons(X1,X2)))
| ~ ssList(X2) ),
inference(equality_resolution,[],[f189]) ).
fof(f221,plain,
! [X2,X1] :
( ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X1)
| memberP(cons(X1,X2),X1) ),
inference(equality_resolution,[],[f149]) ).
fof(f222,plain,
! [X2,X1] :
( memberP(cons(X1,X2),X1)
| ~ ssItem(X1)
| ~ ssList(X2) ),
inference(duplicate_literal_removal,[],[f221]) ).
fof(f248,definition,
( spl0_4
<=> ssList(app(app(sk7,cons(sk5,nil)),cons(sk6,nil))) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f249,plain,
( ~ ssList(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)))
| spl0_4 ),
inference(avatar_component_clause,[],[f248]) ).
fof(f254,plain,
( ~ ssList(app(sk7,cons(sk5,nil)))
| ~ ssList(cons(sk6,nil))
| spl0_4 ),
inference(resolution,[],[f249,f85]) ).
fof(f256,definition,
( spl0_6
<=> ssList(cons(sk6,nil)) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f257,plain,
( ~ ssList(cons(sk6,nil))
| spl0_6 ),
inference(avatar_component_clause,[],[f256]) ).
fof(f259,definition,
( spl0_7
<=> ssList(app(sk7,cons(sk5,nil))) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f260,plain,
( ~ ssList(app(sk7,cons(sk5,nil)))
| spl0_7 ),
inference(avatar_component_clause,[],[f259]) ).
fof(f261,plain,
( ~ spl0_6
| ~ spl0_7
| spl0_4 ),
inference(avatar_split_clause,[],[f254,f248,f259,f256]) ).
fof(f265,plain,
( ~ ssList(nil)
| ~ ssItem(sk6)
| spl0_6 ),
inference(resolution,[],[f257,f86]) ).
fof(f266,plain,
( ~ ssItem(sk6)
| spl0_6 ),
inference(forward_subsumption_resolution,[],[f265,f8]) ).
fof(f267,plain,
( $false
| spl0_6 ),
inference(forward_subsumption_resolution,[],[f266,f207]) ).
fof(f268,plain,
spl0_6,
inference(avatar_contradiction_clause,[],[f267]) ).
fof(f283,plain,
( ~ ssList(sk7)
| ~ ssList(cons(sk5,nil))
| spl0_7 ),
inference(resolution,[],[f260,f85]) ).
fof(f284,plain,
( ~ ssList(cons(sk5,nil))
| spl0_7 ),
inference(forward_subsumption_resolution,[],[f283,f208]) ).
fof(f287,plain,
( ~ ssList(nil)
| ~ ssItem(sk5)
| spl0_7 ),
inference(resolution,[],[f284,f86]) ).
fof(f288,plain,
( ~ ssItem(sk5)
| spl0_7 ),
inference(forward_subsumption_resolution,[],[f287,f8]) ).
fof(f289,plain,
( $false
| spl0_7 ),
inference(forward_subsumption_resolution,[],[f288,f206]) ).
fof(f290,plain,
spl0_7,
inference(avatar_contradiction_clause,[],[f289]) ).
fof(f300,plain,
! [X0] :
( memberP(sk3,X0)
| ~ ssList(sk8)
| ~ ssList(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)))
| ~ ssItem(X0)
| ~ memberP(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),X0) ),
inference(superposition,[],[f151,f217]) ).
fof(f305,plain,
! [X0] :
( memberP(sk3,X0)
| ~ ssList(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)))
| ~ ssItem(X0)
| ~ memberP(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),X0) ),
inference(forward_subsumption_resolution,[],[f300,f209]) ).
fof(f307,definition,
( spl0_9
<=> ! [X0] :
( memberP(sk3,X0)
| ~ memberP(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f308,plain,
( ! [X0] :
( ~ memberP(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),X0)
| memberP(sk3,X0)
| ~ ssItem(X0) )
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f307]) ).
fof(f309,plain,
( ~ spl0_4
| spl0_9 ),
inference(avatar_split_clause,[],[f305,f307,f248]) ).
fof(f392,plain,
( ! [X0] :
( memberP(sk3,X0)
| ~ ssItem(X0)
| ~ ssList(cons(sk6,nil))
| ~ ssList(app(sk7,cons(sk5,nil)))
| ~ ssItem(X0)
| ~ memberP(cons(sk6,nil),X0) )
| ~ spl0_9 ),
inference(resolution,[],[f308,f152]) ).
fof(f393,plain,
( ! [X0] :
( memberP(sk3,X0)
| ~ ssItem(X0)
| ~ ssList(cons(sk6,nil))
| ~ ssList(app(sk7,cons(sk5,nil)))
| ~ ssItem(X0)
| ~ memberP(app(sk7,cons(sk5,nil)),X0) )
| ~ spl0_9 ),
inference(resolution,[],[f308,f151]) ).
fof(f394,plain,
( ! [X0] :
( memberP(sk3,X0)
| ~ ssItem(X0)
| ~ ssList(cons(sk6,nil))
| ~ ssList(app(sk7,cons(sk5,nil)))
| ~ memberP(app(sk7,cons(sk5,nil)),X0) )
| ~ spl0_9 ),
inference(duplicate_literal_removal,[],[f393]) ).
fof(f395,plain,
( ! [X0] :
( memberP(sk3,X0)
| ~ ssItem(X0)
| ~ ssList(cons(sk6,nil))
| ~ ssList(app(sk7,cons(sk5,nil)))
| ~ memberP(cons(sk6,nil),X0) )
| ~ spl0_9 ),
inference(duplicate_literal_removal,[],[f392]) ).
fof(f397,definition,
( spl0_13
<=> ! [X0] :
( memberP(sk3,X0)
| ~ memberP(app(sk7,cons(sk5,nil)),X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f398,plain,
( ! [X0] :
( ~ memberP(app(sk7,cons(sk5,nil)),X0)
| memberP(sk3,X0)
| ~ ssItem(X0) )
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f397]) ).
fof(f399,plain,
( ~ spl0_7
| ~ spl0_6
| spl0_13
| ~ spl0_9 ),
inference(avatar_split_clause,[],[f394,f307,f397,f256,f259]) ).
fof(f401,definition,
( spl0_14
<=> ! [X0] :
( memberP(sk3,X0)
| ~ memberP(cons(sk6,nil),X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
fof(f402,plain,
( ! [X0] :
( ~ memberP(cons(sk6,nil),X0)
| memberP(sk3,X0)
| ~ ssItem(X0) )
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f401]) ).
fof(f403,plain,
( ~ spl0_7
| ~ spl0_6
| spl0_14
| ~ spl0_9 ),
inference(avatar_split_clause,[],[f395,f307,f401,f256,f259]) ).
fof(f530,plain,
( memberP(sk3,sk6)
| ~ ssItem(sk6)
| ~ ssItem(sk6)
| ~ ssList(nil)
| ~ spl0_14 ),
inference(resolution,[],[f402,f222]) ).
fof(f533,plain,
( memberP(sk3,sk6)
| ~ ssItem(sk6)
| ~ ssList(nil)
| ~ spl0_14 ),
inference(duplicate_literal_removal,[],[f530]) ).
fof(f534,plain,
( memberP(sk3,sk6)
| ~ ssList(nil)
| ~ spl0_14 ),
inference(forward_subsumption_resolution,[],[f533,f207]) ).
fof(f535,plain,
( memberP(sk3,sk6)
| ~ spl0_14 ),
inference(forward_subsumption_resolution,[],[f534,f8]) ).
fof(f557,plain,
( sk6 = sk9
| ~ ssItem(sk6)
| ~ spl0_14 ),
inference(resolution,[],[f535,f214]) ).
fof(f558,plain,
( sk6 = sk9
| ~ spl0_14 ),
inference(forward_subsumption_resolution,[],[f557,f207]) ).
fof(f610,plain,
( ~ ssList(sk7)
| ~ ssItem(sk5)
| ~ ssList(app(sk7,cons(sk5,nil)))
| ~ ssList(nil)
| memberP(sk3,sk5)
| ~ ssItem(sk5)
| ~ spl0_13 ),
inference(resolution,[],[f220,f398]) ).
fof(f621,plain,
( ~ ssList(sk7)
| ~ ssItem(sk5)
| ~ ssList(app(sk7,cons(sk5,nil)))
| ~ ssList(nil)
| memberP(sk3,sk5)
| ~ spl0_13 ),
inference(duplicate_literal_removal,[],[f610]) ).
fof(f626,plain,
( ~ ssItem(sk5)
| ~ ssList(app(sk7,cons(sk5,nil)))
| ~ ssList(nil)
| memberP(sk3,sk5)
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f621,f208]) ).
fof(f629,plain,
( ~ ssList(app(sk7,cons(sk5,nil)))
| ~ ssList(nil)
| memberP(sk3,sk5)
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f626,f206]) ).
fof(f630,plain,
( ~ ssList(app(sk7,cons(sk5,nil)))
| memberP(sk3,sk5)
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f629,f8]) ).
fof(f632,definition,
( spl0_24
<=> memberP(sk3,sk5) ),
introduced(definition,[new_symbols(definition,[spl0_24])],[avatar_definition]) ).
fof(f633,plain,
( memberP(sk3,sk5)
| ~ spl0_24 ),
inference(avatar_component_clause,[],[f632]) ).
fof(f634,plain,
( spl0_24
| ~ spl0_7
| ~ spl0_13 ),
inference(avatar_split_clause,[],[f630,f397,f259,f632]) ).
fof(f635,plain,
( sk5 = sk9
| ~ ssItem(sk5)
| ~ spl0_24 ),
inference(resolution,[],[f633,f214]) ).
fof(f636,plain,
( sk5 = sk9
| ~ spl0_24 ),
inference(forward_subsumption_resolution,[],[f635,f206]) ).
fof(f688,plain,
( sk5 = sk6
| ~ spl0_14
| ~ spl0_24 ),
inference(superposition,[],[f636,f558]) ).
fof(f693,plain,
( $false
| ~ spl0_14
| ~ spl0_24 ),
inference(forward_subsumption_resolution,[],[f688,f212]) ).
fof(f694,plain,
( ~ spl0_14
| ~ spl0_24 ),
inference(avatar_contradiction_clause,[],[f693]) ).
cnf(s4,plain,
( spl0_4
| ~ spl0_6
| ~ spl0_7 ),
inference(sat_conversion,[],[f261]) ).
cnf(s5,plain,
spl0_6,
inference(sat_conversion,[],[f268]) ).
cnf(s6,plain,
spl0_7,
inference(sat_conversion,[],[f290]) ).
cnf(s8,plain,
( ~ spl0_4
| spl0_9 ),
inference(sat_conversion,[],[f309]) ).
cnf(s14,plain,
( ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| spl0_13 ),
inference(sat_conversion,[],[f399]) ).
cnf(s15,plain,
( ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| spl0_14 ),
inference(sat_conversion,[],[f403]) ).
cnf(s26,plain,
( ~ spl0_7
| ~ spl0_13
| spl0_24 ),
inference(sat_conversion,[],[f634]) ).
cnf(s38,plain,
( ~ spl0_14
| ~ spl0_24 ),
inference(sat_conversion,[],[f694]) ).
cnf(s43,plain,
spl0_4,
inference(rat,[],[s4,s6,s5]) ).
cnf(s50,plain,
spl0_9,
inference(rat,[],[s8,s43]) ).
cnf(s52,plain,
spl0_14,
inference(rat,[],[s15,s5,s6,s50]) ).
cnf(s53,plain,
spl0_13,
inference(rat,[],[s14,s5,s6,s50]) ).
cnf(s54,plain,
~ spl0_24,
inference(rat,[],[s38,s52]) ).
cnf(s55,plain,
$false,
inference(rat,[],[s26,s6,s54,s53]) ).
fof(f695,plain,
$false,
inference(avatar_sat_refutation,[],[s55]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC190-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.37 % Computer : n017.cluster.edu
% 0.13/0.37 % Model : x86_64 x86_64
% 0.13/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.37 % Memory : 8046.5625MB
% 0.13/0.37 % OS : Linux 6.8.0-71-generic
% 0.13/0.37 % CPULimit : 300
% 0.13/0.37 % WCLimit : 300
% 0.13/0.37 % DateTime : Mon Sep 28 08:17:21 UTC 2026
% 0.05/0.37 % CPUTime :
% 0.05/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.05/0.41 Running first-order theorem proving
% 0.05/0.41 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.70/1.13 % (3394045)Input is clausal, will run a generic CNF schedule.
% 1.70/1.13 % (3394054)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=3456119444:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 1.70/1.13 % (3394054)First to succeed.
% 1.70/1.13 % (3394054)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3394045"
% 1.70/1.13 % (3394050)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=3164299572:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 1.70/1.13 % (3394052)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=1856876793:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 1.70/1.13 % (3394051)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=3421975259:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 1.70/1.13 % (3394055)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3479081579:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 1.70/1.13 % (3394053)lrs+10_1_sil=8000:sp=occurrence:random_seed=1444681763:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 1.70/1.13 % (3394056)dis-21_1_sil=8000:lcm=predicate:random_seed=408565763:st=5:avsq=on:i=117:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/117Mi)
% 1.70/1.13 % (3394053)Also succeeded, but the first one will report.
% 1.70/1.13 % (3394056)Instruction limit reached!
% 1.70/1.13 % (3394056)------------------------------
% 1.70/1.13 % (3394056)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.70/1.13 % (3394056)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.70/1.13 % (3394056)CaDiCaL version: 2.1.3
% 1.70/1.13 % (3394056)Termination reason: Instruction limit
% 1.70/1.13 % (3394056)Termination phase: Saturation
% 1.70/1.13 % (3394056)Time elapsed: 0.053 s
% 1.70/1.13 % (3394056)Peak memory usage: 89 MB
% 1.70/1.13 % (3394056)Instructions burned: 117 (million)
% 1.70/1.13 % (3394054)Refutation found. Thanks to Tanya!
% 1.70/1.13 % SZS status Unsatisfiable for theBenchmark
% 1.70/1.13 % SZS output start Proof for theBenchmark
% See solution above
% 2.59/1.33 % (3394054)------------------------------
% 2.59/1.33 % (3394054)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.59/1.33 % (3394054)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.59/1.33 % (3394054)CaDiCaL version: 2.1.3
% 2.59/1.33 % (3394054)Termination reason: Refutation
% 2.59/1.33 % (3394054)Time elapsed: 0.009 s
% 2.59/1.33 % (3394054)Peak memory usage: 90 MB
% 2.59/1.33 % (3394054)Instructions burned: 22 (million)
% 2.59/1.33 % (3394054)------------------------------
% 2.59/1.33 % (3394054)------------------------------
% 2.59/1.33 % (3394045)Success in time 0.278 s
% 2.59/1.33 % Vampire exiting
%------------------------------------------------------------------------------