%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET118-7 : TPTP v9.3.1. Bugfixed v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n020.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 12:40:12 PM UTC 2026
% Result : Unsatisfiable 3.62s 1.45s
% Output : Refutation 3.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 6
% Syntax : Number of formulae : 20 ( 8 unt; 2 def)
% Number of atoms : 36 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 35 ( 19 ~; 14 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 3 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 20 ( 0 sgn 20 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f16,axiom,
! [X2,X3,X0,X1] :
( member(ordered_pair(X0,X2),cross_product(X1,X3))
| ~ member(X2,X3)
| ~ member(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartesian_product3) ).
fof(f104,axiom,
! [X2,X3,X0,X1] :
( ~ member(ordered_pair(X0,X1),cross_product(X2,X3))
| member(X1,universal_class) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',corollary_2_to_cartesian_product) ).
fof(f185,negated_conjecture,
member(x,cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_corollary_2_to_ordered_pairs_are_sets_1) ).
fof(f186,negated_conjecture,
~ member(x,universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_corollary_2_to_ordered_pairs_are_sets_2) ).
fof(f187,plain,
! [X2,X3,X0,X1] :
( ~ member(X0,X1)
| ~ member(X2,X3)
| member(X0,universal_class) ),
inference(resolution,[],[f16,f104]) ).
fof(f192,definition,
( spl0_1
<=> ! [X2,X3] :
( ~ member(X2,X3)
| member(X2,universal_class) ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f193,plain,
( ! [X2,X3] :
( ~ member(X2,X3)
| member(X2,universal_class) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f192]) ).
fof(f195,definition,
( spl0_2
<=> ! [X0,X1] : ~ member(X0,X1) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f196,plain,
( ! [X0,X1] : ~ member(X0,X1)
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f195]) ).
fof(f198,plain,
( spl0_2
| spl0_1 ),
inference(avatar_split_clause,[],[f187,f192,f195]) ).
fof(f199,plain,
( $false
| ~ spl0_2 ),
inference(resolution,[],[f196,f185]) ).
fof(f203,plain,
~ spl0_2,
inference(avatar_contradiction_clause,[],[f199]) ).
fof(f205,plain,
( member(x,universal_class)
| ~ spl0_1 ),
inference(resolution,[],[f193,f185]) ).
fof(f208,plain,
( $false
| ~ spl0_1 ),
inference(forward_subsumption_resolution,[],[f205,f186]) ).
fof(f209,plain,
~ spl0_1,
inference(avatar_contradiction_clause,[],[f208]) ).
cnf(s2,plain,
( spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f198]) ).
cnf(s4,plain,
~ spl0_2,
inference(sat_conversion,[],[f203]) ).
cnf(s5,plain,
~ spl0_1,
inference(sat_conversion,[],[f209]) ).
cnf(s6,plain,
$false,
inference(rat,[],[s2,s4,s5]) ).
fof(f210,plain,
$false,
inference(avatar_sat_refutation,[],[s6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET118-7 : TPTP v9.3.1. Bugfixed v7.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.39 % Computer : n020.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Mon Sep 28 00:49:35 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.43 Running first-order theorem proving
% 0.12/0.43 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.62/1.45 % (3929530)Input is clausal, will run a generic CNF schedule.
% 3.62/1.45 % (3929535)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=3566563963:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.62/1.45 % (3929537)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=247355408:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.62/1.45 % (3929540)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1321030410:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.62/1.45 % (3929541)dis-21_1_sil=8000:lcm=predicate:random_seed=4264970548: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)
% 3.62/1.45 % (3929539)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=2441285281:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.62/1.45 % (3929536)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=3949346114:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.62/1.45 % (3929538)lrs+10_1_sil=8000:sp=occurrence:random_seed=1927635781:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.62/1.45 % (3929538)First to succeed.
% 3.62/1.45 % (3929538)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3929530"
% 3.62/1.45 % (3929539)Also succeeded, but the first one will report.
% 3.62/1.45 % (3929541)Also succeeded, but the first one will report.
% 3.62/1.45 % (3929540)Also succeeded, but the first one will report.
% 3.62/1.45 % (3929538)Refutation found. Thanks to Tanya!
% 3.62/1.45 % SZS status Unsatisfiable for theBenchmark
% 3.62/1.45 % SZS output start Proof for theBenchmark
% See solution above
% 3.62/1.45 % (3929538)------------------------------
% 3.62/1.45 % (3929538)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.62/1.45 % (3929538)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.62/1.45 % (3929538)CaDiCaL version: 2.1.3
% 3.62/1.45 % (3929538)Termination reason: Refutation
% 3.62/1.45 % (3929538)Time elapsed: 0.003 s
% 3.62/1.45 % (3929538)Peak memory usage: 89 MB
% 3.62/1.45 % (3929538)Instructions burned: 1 (million)
% 3.62/1.45 % (3929538)------------------------------
% 3.62/1.45 % (3929538)------------------------------
% 3.62/1.45 % (3929530)Success in time 0.439 s
% 3.62/1.45 % Vampire exiting
%------------------------------------------------------------------------------