%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET233-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 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 12:43:30 PM UTC 2026
% Result : Unsatisfiable 0.18s 0.48s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 7
% Syntax : Number of formulae : 15 ( 9 unt; 0 def)
% Number of atoms : 21 ( 6 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 13 ( 7 ~; 6 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 3 con; 0-2 aty)
% Number of variables : 23 ( 23 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1] :
( subclass(X0,X1)
| member(not_subclass_element(X0,X1),X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',not_subclass_members1) ).
fof(f12,axiom,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/SET004-0.ax',ordered_pair) ).
fof(f15,axiom,
! [X2,X3,X0,X1] :
( ~ member(ordered_pair(X0,X1),cross_product(X2,X3))
| member(X1,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',cartesian_product2) ).
fof(f17,axiom,
! [X2,X0,X1] :
( ~ member(X0,cross_product(X1,X2))
| ordered_pair(first(X0),second(X0)) = X0 ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',cartesian_product4) ).
fof(f122,negated_conjecture,
~ subclass(cross_product(x,y),z),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_cross_product_property8_1) ).
fof(f123,negated_conjecture,
~ member(second(not_subclass_element(cross_product(x,y),z)),y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_cross_product_property8_2) ).
fof(f128,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(f138,plain,
! [X2,X3,X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(X2,X3))
| member(X1,X3) ),
inference(definition_unfolding,[],[f15,f128]) ).
fof(f140,plain,
! [X2,X0,X1] :
( ~ member(X0,cross_product(X1,X2))
| unordered_pair(unordered_pair(first(X0),first(X0)),unordered_pair(first(X0),unordered_pair(second(X0),second(X0)))) = X0 ),
inference(definition_unfolding,[],[f17,f128]) ).
fof(f194,plain,
member(not_subclass_element(cross_product(x,y),z),cross_product(x,y)),
inference(resolution,[],[f2,f122]) ).
fof(f432,plain,
not_subclass_element(cross_product(x,y),z) = unordered_pair(unordered_pair(first(not_subclass_element(cross_product(x,y),z)),first(not_subclass_element(cross_product(x,y),z))),unordered_pair(first(not_subclass_element(cross_product(x,y),z)),unordered_pair(second(not_subclass_element(cross_product(x,y),z)),second(not_subclass_element(cross_product(x,y),z))))),
inference(resolution,[],[f140,f194]) ).
fof(f441,plain,
! [X0,X1] :
( ~ member(not_subclass_element(cross_product(x,y),z),cross_product(X0,X1))
| member(second(not_subclass_element(cross_product(x,y),z)),X1) ),
inference(superposition,[],[f138,f432]) ).
fof(f498,plain,
member(second(not_subclass_element(cross_product(x,y),z)),y),
inference(resolution,[],[f441,f194]) ).
fof(f512,plain,
$false,
inference(forward_subsumption_resolution,[],[f498,f123]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET233-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 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
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Mon Sep 28 01:11:07 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.41 Running first-order model finding
% 0.11/0.41 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.48 % (4055501)Will run a generic schedule for satisfiability detection.
% 0.18/0.48 % (4055508)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=747097450:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.18/0.48 % (4055507)% WARNING: option uhcvi not known.
% 0.18/0.48 % (4055507)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1240672215:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.18/0.48 % (4055506)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2694859268_2999 on theBenchmark for (2999ds/0Mi)
% 0.18/0.48 % (4055509)dis+10_1_sil=32000:sp=arity:random_seed=1123707440:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.18/0.48 % (4055510)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3580780755:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.18/0.48 % (4055511)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2933712906:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.18/0.48 % (4055512)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3785061722:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.18/0.48 % (4055510) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-4055501-4055510"...
% 0.18/0.48 % (4055510)...printing done.
% 0.18/0.48 % (4055510)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 % (4055510)------------------------------
% 0.18/0.48 % (4055510)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.48 % (4055510)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.48 % (4055510)CaDiCaL version: 2.1.3
% 0.18/0.48 % (4055510)Termination reason: Refutation
% 0.18/0.48 % (4055510)Time elapsed: 0.015 s
% 0.18/0.48 % (4055510)Peak memory usage: 12 MB
% 0.18/0.48 % (4055510)Instructions burned: 22 (million)
% 0.18/0.48 % (4055501)Success in time 0.063 s
% 0.18/0.49 % Vampire exiting
%------------------------------------------------------------------------------