%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET235-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n004.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 12:40:34 PM UTC 2026
% Result : Unsatisfiable 2.53s 1.32s
% Output : Refutation 2.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 8
% Syntax : Number of formulae : 25 ( 9 unt; 2 def)
% Number of atoms : 44 ( 1 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 42 ( 23 ~; 17 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 21 ( 0 sgn 21 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ subclass(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subclass_members) ).
fof(f2,axiom,
! [X0,X1] :
( member(not_subclass_element(X0,X1),X0)
| subclass(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_subclass_members1) ).
fof(f17,axiom,
! [X2,X0,X1] :
( ordered_pair(first(X0),second(X0)) = X0
| ~ member(X0,cross_product(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartesian_product4) ).
fof(f122,negated_conjecture,
subclass(x,cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_cross_product_property10_1) ).
fof(f123,negated_conjecture,
~ member(ordered_pair(first(not_subclass_element(x,y)),second(not_subclass_element(x,y))),x),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_cross_product_property10_2) ).
fof(f124,negated_conjecture,
~ subclass(x,y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_cross_product_property10_3) ).
fof(f148,plain,
! [X0,X1] :
( ~ member(not_subclass_element(x,y),x)
| ~ member(not_subclass_element(x,y),cross_product(X0,X1)) ),
inference(superposition,[],[f123,f17]) ).
fof(f152,definition,
( spl0_3
<=> ! [X0,X1] : ~ member(not_subclass_element(x,y),cross_product(X0,X1)) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f153,plain,
( ! [X0,X1] : ~ member(not_subclass_element(x,y),cross_product(X0,X1))
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f152]) ).
fof(f155,definition,
( spl0_4
<=> member(not_subclass_element(x,y),x) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f156,plain,
( ~ member(not_subclass_element(x,y),x)
| spl0_4 ),
inference(avatar_component_clause,[],[f155]) ).
fof(f157,plain,
( spl0_3
| ~ spl0_4 ),
inference(avatar_split_clause,[],[f148,f155,f152]) ).
fof(f166,plain,
( ! [X2,X0,X1] :
( ~ member(not_subclass_element(x,y),X0)
| ~ subclass(X0,cross_product(X1,X2)) )
| ~ spl0_3 ),
inference(resolution,[],[f153,f1]) ).
fof(f172,plain,
( ! [X0,X1] :
( ~ subclass(x,cross_product(X0,X1))
| subclass(x,y) )
| ~ spl0_3 ),
inference(resolution,[],[f166,f2]) ).
fof(f174,plain,
( ! [X0,X1] : ~ subclass(x,cross_product(X0,X1))
| ~ spl0_3 ),
inference(forward_subsumption_resolution,[],[f172,f124]) ).
fof(f177,plain,
( $false
| ~ spl0_3 ),
inference(resolution,[],[f174,f122]) ).
fof(f178,plain,
~ spl0_3,
inference(avatar_contradiction_clause,[],[f177]) ).
fof(f179,plain,
( subclass(x,y)
| spl0_4 ),
inference(resolution,[],[f156,f2]) ).
fof(f182,plain,
( $false
| spl0_4 ),
inference(forward_subsumption_resolution,[],[f179,f124]) ).
fof(f183,plain,
spl0_4,
inference(avatar_contradiction_clause,[],[f182]) ).
cnf(s2,plain,
( spl0_3
| ~ spl0_4 ),
inference(sat_conversion,[],[f157]) ).
cnf(s5,plain,
~ spl0_3,
inference(sat_conversion,[],[f178]) ).
cnf(s7,plain,
spl0_4,
inference(sat_conversion,[],[f183]) ).
cnf(s10,plain,
$false,
inference(rat,[],[s2,s7,s5]) ).
fof(f184,plain,
$false,
inference(avatar_sat_refutation,[],[s10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET235-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n004.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
% 0.11/0.39 % WCLimit : 300
% 0.11/0.39 % DateTime : Mon Sep 28 01:10:52 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 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
% 2.53/1.32 % (4054907)Input is clausal, will run a generic CNF schedule.
% 2.53/1.32 % (4054955)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1251999691:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.53/1.32 % (4054955)First to succeed.
% 2.53/1.32 % (4054955)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-4054907"
% 2.53/1.32 % (4054954)lrs+10_1_sil=8000:sp=occurrence:random_seed=1005688166:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.53/1.32 % (4054953)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=2439440244:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.53/1.32 % (4054951)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=2956679561:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.53/1.32 % (4054952)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=3278390544:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.53/1.32 % (4054956)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3972326684:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.53/1.32 % (4054957)dis-21_1_sil=8000:lcm=predicate:random_seed=3460675440: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)
% 2.53/1.32 % (4054954)Instruction limit reached!
% 2.53/1.32 % (4054954)------------------------------
% 2.53/1.32 % (4054954)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.53/1.32 % (4054954)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.53/1.32 % (4054954)CaDiCaL version: 2.1.3
% 2.53/1.32 % (4054954)Termination reason: Instruction limit
% 2.53/1.32 % (4054954)Termination phase: Saturation
% 2.53/1.32 % (4054954)Time elapsed: 0.078 s
% 2.53/1.32 % (4054954)Peak memory usage: 89 MB
% 2.53/1.32 % (4054954)Instructions burned: 108 (million)
% 2.53/1.32 % (4054957)Instruction limit reached!
% 2.53/1.32 % (4054957)------------------------------
% 2.53/1.32 % (4054957)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.53/1.32 % (4054957)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.53/1.32 % (4054957)CaDiCaL version: 2.1.3
% 2.53/1.32 % (4054957)Termination reason: Instruction limit
% 2.53/1.32 % (4054957)Termination phase: Saturation
% 2.53/1.32 % (4054957)Time elapsed: 0.069 s
% 2.53/1.32 % (4054957)Peak memory usage: 89 MB
% 2.53/1.32 % (4054957)Instructions burned: 118 (million)
% 2.53/1.32 % (4054955)Refutation found. Thanks to Tanya!
% 2.53/1.32 % SZS status Unsatisfiable for theBenchmark
% 2.53/1.32 % SZS output start Proof for theBenchmark
% See solution above
% 2.53/1.32 % (4054955)------------------------------
% 2.53/1.32 % (4054955)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.53/1.32 % (4054955)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.53/1.32 % (4054955)CaDiCaL version: 2.1.3
% 2.53/1.32 % (4054955)Termination reason: Refutation
% 2.53/1.32 % (4054955)Time elapsed: 0.002 s
% 2.53/1.32 % (4054955)Peak memory usage: 89 MB
% 2.53/1.32 % (4054955)Instructions burned: 3 (million)
% 2.53/1.32 % (4054955)------------------------------
% 2.53/1.32 % (4054955)------------------------------
% 2.53/1.32 % (4054907)Success in time 0.268 s
% 2.53/1.32 % Vampire exiting
%------------------------------------------------------------------------------