%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET211-6 : 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 12:43:28 PM UTC 2026
% Result : Unsatisfiable 0.17s 0.47s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 15
% Syntax : Number of formulae : 38 ( 18 unt; 0 def)
% Number of atoms : 63 ( 7 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 55 ( 30 ~; 25 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 4 con; 0-2 aty)
% Number of variables : 60 ( 60 !; 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(f2,axiom,
! [X0,X1] :
( subclass(X0,X1)
| member(not_subclass_element(X0,X1),X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',not_subclass_members1) ).
fof(f3,axiom,
! [X0,X1] :
( subclass(X0,X1)
| ~ member(not_subclass_element(X0,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',not_subclass_members2) ).
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(f14,axiom,
! [X2,X3,X0,X1] :
( ~ member(ordered_pair(X0,X1),cross_product(X2,X3))
| member(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',cartesian_product1) ).
fof(f15,axiom,
! [X2,X3,X0,X1] :
( ~ member(ordered_pair(X0,X1),cross_product(X2,X3))
| member(X1,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',cartesian_product2) ).
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(f17,axiom,
! [X2,X0,X1] :
( ~ member(X0,cross_product(X1,X2))
| ordered_pair(first(X0),second(X0)) = X0 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',cartesian_product4) ).
fof(f22,axiom,
! [X2,X0,X1] :
( ~ member(X0,intersection(X1,X2))
| member(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',intersection2) ).
fof(f24,axiom,
! [X0,X1] :
( ~ member(X0,complement(X1))
| ~ member(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',complement1) ).
fof(f25,axiom,
! [X0,X1] :
( member(X0,complement(X1))
| ~ member(X0,universal_class)
| member(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',complement2) ).
fof(f26,axiom,
! [X0,X1] : complement(intersection(complement(X0),complement(X1))) = union(X0,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',union) ).
fof(f122,negated_conjecture,
~ subclass(cross_product(y,z),cross_product(union(x,y),z)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_corollary_2_to_X_product_monotonicity_1) ).
fof(f127,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(f136,plain,
! [X2,X3,X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(X2,X3))
| member(X0,X2) ),
inference(definition_unfolding,[],[f14,f127]) ).
fof(f137,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,f127]) ).
fof(f138,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(definition_unfolding,[],[f16,f127]) ).
fof(f139,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,f127]) ).
fof(f185,plain,
~ subclass(cross_product(y,z),cross_product(complement(intersection(complement(x),complement(y))),z)),
inference(definition_unfolding,[],[f122,f26]) ).
fof(f194,plain,
member(not_subclass_element(cross_product(y,z),cross_product(complement(intersection(complement(x),complement(y))),z)),cross_product(y,z)),
inference(resolution,[],[f2,f185]) ).
fof(f195,plain,
~ member(not_subclass_element(cross_product(y,z),cross_product(complement(intersection(complement(x),complement(y))),z)),cross_product(complement(intersection(complement(x),complement(y))),z)),
inference(resolution,[],[f3,f185]) ).
fof(f198,plain,
! [X0,X1] :
( ~ member(X0,X1)
| member(X0,universal_class) ),
inference(resolution,[],[f1,f4]) ).
fof(f432,plain,
not_subclass_element(cross_product(y,z),cross_product(complement(intersection(complement(x),complement(y))),z)) = unordered_pair(unordered_pair(first(not_subclass_element(cross_product(y,z),cross_product(complement(intersection(complement(x),complement(y))),z))),first(not_subclass_element(cross_product(y,z),cross_product(complement(intersection(complement(x),complement(y))),z)))),unordered_pair(first(not_subclass_element(cross_product(y,z),cross_product(complement(intersection(complement(x),complement(y))),z))),unordered_pair(second(not_subclass_element(cross_product(y,z),cross_product(complement(intersection(complement(x),complement(y))),z))),second(not_subclass_element(cross_product(y,z),cross_product(complement(intersection(complement(x),complement(y))),z)))))),
inference(resolution,[],[f139,f194]) ).
fof(f513,plain,
! [X0,X1] :
( ~ member(not_subclass_element(cross_product(y,z),cross_product(complement(intersection(complement(x),complement(y))),z)),cross_product(X0,X1))
| member(first(not_subclass_element(cross_product(y,z),cross_product(complement(intersection(complement(x),complement(y))),z))),X0) ),
inference(superposition,[],[f136,f432]) ).
fof(f514,plain,
! [X0,X1] :
( ~ member(not_subclass_element(cross_product(y,z),cross_product(complement(intersection(complement(x),complement(y))),z)),cross_product(X0,X1))
| member(second(not_subclass_element(cross_product(y,z),cross_product(complement(intersection(complement(x),complement(y))),z))),X1) ),
inference(superposition,[],[f137,f432]) ).
fof(f515,plain,
! [X0,X1] :
( member(not_subclass_element(cross_product(y,z),cross_product(complement(intersection(complement(x),complement(y))),z)),cross_product(X0,X1))
| ~ member(second(not_subclass_element(cross_product(y,z),cross_product(complement(intersection(complement(x),complement(y))),z))),X1)
| ~ member(first(not_subclass_element(cross_product(y,z),cross_product(complement(intersection(complement(x),complement(y))),z))),X0) ),
inference(superposition,[],[f138,f432]) ).
fof(f724,plain,
member(first(not_subclass_element(cross_product(y,z),cross_product(complement(intersection(complement(x),complement(y))),z))),y),
inference(resolution,[],[f513,f194]) ).
fof(f731,plain,
member(first(not_subclass_element(cross_product(y,z),cross_product(complement(intersection(complement(x),complement(y))),z))),universal_class),
inference(resolution,[],[f724,f198]) ).
fof(f823,plain,
member(second(not_subclass_element(cross_product(y,z),cross_product(complement(intersection(complement(x),complement(y))),z))),z),
inference(resolution,[],[f514,f194]) ).
fof(f931,plain,
( ~ member(second(not_subclass_element(cross_product(y,z),cross_product(complement(intersection(complement(x),complement(y))),z))),z)
| ~ member(first(not_subclass_element(cross_product(y,z),cross_product(complement(intersection(complement(x),complement(y))),z))),complement(intersection(complement(x),complement(y)))) ),
inference(resolution,[],[f515,f195]) ).
fof(f938,plain,
~ member(first(not_subclass_element(cross_product(y,z),cross_product(complement(intersection(complement(x),complement(y))),z))),complement(intersection(complement(x),complement(y)))),
inference(forward_subsumption_resolution,[],[f931,f823]) ).
fof(f976,plain,
( ~ member(first(not_subclass_element(cross_product(y,z),cross_product(complement(intersection(complement(x),complement(y))),z))),universal_class)
| member(first(not_subclass_element(cross_product(y,z),cross_product(complement(intersection(complement(x),complement(y))),z))),intersection(complement(x),complement(y))) ),
inference(resolution,[],[f938,f25]) ).
fof(f978,plain,
member(first(not_subclass_element(cross_product(y,z),cross_product(complement(intersection(complement(x),complement(y))),z))),intersection(complement(x),complement(y))),
inference(forward_subsumption_resolution,[],[f976,f731]) ).
fof(f1011,plain,
member(first(not_subclass_element(cross_product(y,z),cross_product(complement(intersection(complement(x),complement(y))),z))),complement(y)),
inference(resolution,[],[f978,f22]) ).
fof(f1048,plain,
~ member(first(not_subclass_element(cross_product(y,z),cross_product(complement(intersection(complement(x),complement(y))),z))),y),
inference(resolution,[],[f1011,f24]) ).
fof(f1050,plain,
$false,
inference(forward_subsumption_resolution,[],[f1048,f724]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET211-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.37 % Computer : n010.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 28 01:07:17 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.40 Running first-order model finding
% 0.11/0.40 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
% 0.17/0.47 % (1474620)Will run a generic schedule for satisfiability detection.
% 0.17/0.47 % (1474629)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=670105456:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.17/0.47 % (1474626)% WARNING: option uhcvi not known.
% 0.17/0.47 % (1474626)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2220982808:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.17/0.47 % (1474625)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=875335359_2999 on theBenchmark for (2999ds/0Mi)
% 0.17/0.47 % (1474627)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3071858914:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.17/0.47 % (1474628)dis+10_1_sil=32000:sp=arity:random_seed=168666644:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.17/0.47 % (1474630)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1676982890:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.17/0.47 % (1474631)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1696460322:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.17/0.47 % (1474629) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1474620-1474629"...
% 0.17/0.47 % (1474629)...printing done.
% 0.17/0.47 % (1474629)Refutation found. Thanks to Tanya!
% 0.17/0.47 % SZS status Unsatisfiable for theBenchmark
% 0.17/0.47 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/0.47 % (1474629)------------------------------
% 0.17/0.47 % (1474629)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.17/0.47 % (1474629)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/0.47 % (1474629)CaDiCaL version: 2.1.3
% 0.17/0.47 % (1474629)Termination reason: Refutation
% 0.17/0.47 % (1474629)Time elapsed: 0.024 s
% 0.17/0.47 % (1474629)Peak memory usage: 12 MB
% 0.17/0.47 % (1474629)Instructions burned: 72 (million)
% 0.17/0.47 % (1474620)Success in time 0.057 s
% 0.17/0.47 % Vampire exiting
%------------------------------------------------------------------------------