%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET203-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/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 12:43:27 PM UTC 2026
% Result : Unsatisfiable 0.11s 0.46s
% Output : Refutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 10
% Syntax : Number of formulae : 36 ( 18 unt; 2 def)
% Number of atoms : 61 ( 3 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 50 ( 25 ~; 23 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 29 ( 0 sgn 29 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] :
( ~ subclass(X0,X1)
| ~ member(X2,X0)
| member(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',subclass_members) ).
fof(f4,axiom,
! [X0] : subclass(X0,universal_class),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',class_elements_are_sets) ).
fof(f12,axiom,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',singleton_set) ).
fof(f13,axiom,
! [X0,X1] : unordered_pair(singleton(X0),unordered_pair(X0,singleton(X1))) = ordered_pair(X0,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',ordered_pair) ).
fof(f16,axiom,
! [X2,X3,X0,X1] :
( ~ member(X0,X1)
| ~ member(X2,X3)
| member(ordered_pair(X0,X2),cross_product(X1,X3)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',cartesian_product3) ).
fof(f122,negated_conjecture,
member(u,x),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_corollary_to_X_product_property1_1) ).
fof(f123,negated_conjecture,
member(v,y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_corollary_to_X_product_property1_2) ).
fof(f124,negated_conjecture,
~ member(ordered_pair(u,v),cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_corollary_to_X_product_property1_3) ).
fof(f129,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),
inference(definition_unfolding,[],[f13,f12,f12]) ).
fof(f140,plain,
! [X2,X3,X0,X1] :
( ~ member(X0,X1)
| ~ member(X2,X3)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X2,X2))),cross_product(X1,X3)) ),
inference(definition_unfolding,[],[f16,f129]) ).
fof(f187,plain,
~ member(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v))),cross_product(universal_class,universal_class)),
inference(definition_unfolding,[],[f124,f129]) ).
fof(f192,plain,
! [X2,X0,X1] :
( ~ member(X2,X1)
| member(X2,X0)
| subclass(X0,X1) ),
inference(consistent_polarity_flipping,[],[f1]) ).
fof(f195,plain,
! [X0] : ~ subclass(X0,universal_class),
inference(consistent_polarity_flipping,[],[f4]) ).
fof(f205,plain,
! [X2,X3,X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X2,X2))),cross_product(X1,X3))
| member(X2,X3)
| member(X0,X1) ),
inference(consistent_polarity_flipping,[],[f140]) ).
fof(f278,plain,
~ member(u,x),
inference(consistent_polarity_flipping,[],[f122]) ).
fof(f279,plain,
~ member(v,y),
inference(consistent_polarity_flipping,[],[f123]) ).
fof(f280,plain,
member(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v))),cross_product(universal_class,universal_class)),
inference(consistent_polarity_flipping,[],[f187]) ).
fof(f484,plain,
( member(v,universal_class)
| member(u,universal_class) ),
inference(resolution,[],[f205,f280]) ).
fof(f489,definition,
( spl0_17
<=> member(u,universal_class) ),
introduced(definition,[new_symbols(definition,[spl0_17])],[avatar_definition]) ).
fof(f491,plain,
( member(u,universal_class)
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f489]) ).
fof(f493,definition,
( spl0_18
<=> member(v,universal_class) ),
introduced(definition,[new_symbols(definition,[spl0_18])],[avatar_definition]) ).
fof(f495,plain,
( member(v,universal_class)
| ~ spl0_18 ),
inference(avatar_component_clause,[],[f493]) ).
fof(f496,plain,
( spl0_17
| spl0_18 ),
inference(avatar_split_clause,[],[f484,f493,f489]) ).
fof(f518,plain,
( ! [X0] :
( member(u,X0)
| subclass(X0,universal_class) )
| ~ spl0_17 ),
inference(resolution,[],[f491,f192]) ).
fof(f519,plain,
( ! [X0] : member(u,X0)
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f518,f195]) ).
fof(f520,plain,
( $false
| ~ spl0_17 ),
inference(backward_subsumption_resolution,[],[f278,f519]) ).
fof(f528,plain,
~ spl0_17,
inference(avatar_contradiction_clause,[],[f520]) ).
fof(f552,plain,
( ! [X0] :
( member(v,X0)
| subclass(X0,universal_class) )
| ~ spl0_18 ),
inference(resolution,[],[f495,f192]) ).
fof(f553,plain,
( ! [X0] : member(v,X0)
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[],[f552,f195]) ).
fof(f554,plain,
( $false
| ~ spl0_18 ),
inference(backward_subsumption_resolution,[],[f279,f553]) ).
fof(f561,plain,
~ spl0_18,
inference(avatar_contradiction_clause,[],[f554]) ).
cnf(s9,plain,
( spl0_17
| spl0_18 ),
inference(sat_conversion,[],[f496]) ).
cnf(s12,plain,
~ spl0_17,
inference(sat_conversion,[],[f528]) ).
cnf(s15,plain,
~ spl0_18,
inference(sat_conversion,[],[f561]) ).
cnf(s16,plain,
$false,
inference(rat,[],[s9,s15,s12]) ).
fof(f562,plain,
$false,
inference(avatar_sat_refutation,[],[s16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET203-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.36 % Computer : n010.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Mon Sep 28 01:06:47 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.36 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.39 Running first-order model finding
% 0.11/0.39 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
% 0.11/0.46 % (1473770)Will run a generic schedule for satisfiability detection.
% 0.11/0.46 % (1473775)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1595614167_2999 on theBenchmark for (2999ds/0Mi)
% 0.11/0.46 % (1473778)dis+10_1_sil=32000:sp=arity:random_seed=3696680015:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.11/0.46 % (1473777)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1860433869:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.11/0.46 % (1473779)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=330851249:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.11/0.46 % (1473780)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1722831706:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.11/0.46 % (1473781)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2831239424:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.11/0.46 % (1473776)% WARNING: option uhcvi not known.
% 0.11/0.46 % (1473776)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=623391692:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.11/0.46 % (1473779) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1473770-1473779"...
% 0.11/0.46 % (1473778) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1473770-1473778"...
% 0.11/0.46 % (1473776) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1473770-1473776"...
% 0.11/0.46 % (1473778)...printing done.
% 0.11/0.46 % (1473779)...printing done.
% 0.11/0.46 % (1473776)...printing done.
% 0.11/0.46 % (1473776)Refutation found. Thanks to Tanya!
% 0.11/0.46 % SZS status Unsatisfiable for theBenchmark
% 0.11/0.46 % SZS output start Proof for theBenchmark
% See solution above
% 0.11/0.46 % (1473776)------------------------------
% 0.11/0.46 % (1473776)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.11/0.46 % (1473776)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.11/0.46 % (1473776)CaDiCaL version: 2.1.3
% 0.11/0.46 % (1473776)Termination reason: Refutation
% 0.11/0.46 % (1473776)Time elapsed: 0.009 s
% 0.11/0.46 % (1473776)Peak memory usage: 13 MB
% 0.11/0.46 % (1473776)Instructions burned: 20 (million)
% 0.11/0.46 % (1473770)Success in time 0.054 s
% 0.11/0.46 % Vampire exiting
%------------------------------------------------------------------------------