%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM030-1 : 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 : n003.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 12:17:51 PM UTC 2026
% Result : Unsatisfiable 0.18s 0.47s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 12
% Syntax : Number of formulae : 25 ( 14 unt; 0 def)
% Number of atoms : 41 ( 7 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 32 ( 16 ~; 16 |; 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 : 11 ( 11 usr; 2 con; 0-2 aty)
% Number of variables : 26 ( 26 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] :
( ~ subclass(X0,X1)
| ~ member(X2,X0)
| member(X2,X1) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/Axioms/SET004-0.ax',not_subclass_members2) ).
fof(f4,axiom,
! [X0] : subclass(X0,universal_class),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',class_elements_are_sets) ).
fof(f22,axiom,
! [X2,X0,X1] :
( ~ member(X0,intersection(X1,X2))
| member(X0,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',intersection2) ).
fof(f24,axiom,
! [X0,X1] :
( ~ member(X0,complement(X1))
| ~ member(X0,X1) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/SET004-0.ax',complement2) ).
fof(f26,axiom,
! [X0,X1] : complement(intersection(complement(X0),complement(X1))) = union(X0,X1),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',union) ).
fof(f39,axiom,
! [X0] : domain_of(flip(cross_product(X0,universal_class))) = inverse(X0),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',inverse) ).
fof(f122,axiom,
! [X0] : union(X0,inverse(X0)) = symmetrization_of(X0),
file('/export/starexec/sandbox/benchmark/Axioms/NUM004-0.ax',symmetrization) ).
fof(f176,negated_conjecture,
symmetrization_of(x) = x,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_symmetrization_property3_1) ).
fof(f177,plain,
x = symmetrization_of(x),
inference(reorient_equations,[],[f176]) ).
fof(f178,negated_conjecture,
~ subclass(inverse(x),x),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_symmetrization_property3_2) ).
fof(f192,plain,
! [X0] : symmetrization_of(X0) = complement(intersection(complement(X0),complement(domain_of(flip(cross_product(X0,universal_class)))))),
inference(definition_unfolding,[],[f122,f26,f39]) ).
fof(f269,plain,
x = complement(intersection(complement(x),complement(domain_of(flip(cross_product(x,universal_class)))))),
inference(definition_unfolding,[],[f177,f192]) ).
fof(f270,plain,
~ subclass(domain_of(flip(cross_product(x,universal_class))),x),
inference(definition_unfolding,[],[f178,f39]) ).
fof(f311,plain,
member(not_subclass_element(domain_of(flip(cross_product(x,universal_class))),x),domain_of(flip(cross_product(x,universal_class)))),
inference(resolution,[],[f2,f270]) ).
fof(f312,plain,
~ member(not_subclass_element(domain_of(flip(cross_product(x,universal_class))),x),x),
inference(resolution,[],[f3,f270]) ).
fof(f332,plain,
! [X0,X1] :
( ~ member(X0,X1)
| member(X0,universal_class) ),
inference(resolution,[],[f1,f4]) ).
fof(f399,plain,
! [X0] :
( member(X0,intersection(complement(x),complement(domain_of(flip(cross_product(x,universal_class))))))
| ~ member(X0,universal_class)
| member(X0,x) ),
inference(superposition,[],[f25,f269]) ).
fof(f401,plain,
! [X0] :
( member(X0,complement(domain_of(flip(cross_product(x,universal_class)))))
| member(X0,x)
| ~ member(X0,universal_class) ),
inference(resolution,[],[f399,f22]) ).
fof(f405,plain,
! [X0] :
( member(X0,x)
| ~ member(X0,universal_class)
| ~ member(X0,domain_of(flip(cross_product(x,universal_class)))) ),
inference(resolution,[],[f401,f24]) ).
fof(f407,plain,
! [X0] :
( ~ member(X0,domain_of(flip(cross_product(x,universal_class))))
| member(X0,x) ),
inference(forward_subsumption_resolution,[],[f405,f332]) ).
fof(f411,plain,
member(not_subclass_element(domain_of(flip(cross_product(x,universal_class))),x),x),
inference(resolution,[],[f407,f311]) ).
fof(f422,plain,
$false,
inference(forward_subsumption_resolution,[],[f411,f312]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM030-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.13/0.38 % Computer : n003.cluster.edu
% 0.13/0.38 % Model : x86_64 x86_64
% 0.13/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.38 % Memory : 8046.5625MB
% 0.13/0.38 % OS : Linux 6.8.0-71-generic
% 0.13/0.38 % CPULimit : 300
% 0.13/0.38 % WCLimit : 300
% 0.13/0.38 % DateTime : Sun Sep 27 18:43:41 UTC 2026
% 0.13/0.38 % CPUTime :
% 0.13/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.13/0.41 Running first-order model finding
% 0.13/0.41 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
% 0.18/0.47 % (854403)Will run a generic schedule for satisfiability detection.
% 0.18/0.47 % (854411)dis+10_1_sil=32000:sp=arity:random_seed=3014816952:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.18/0.47 % (854409)% WARNING: option uhcvi not known.
% 0.18/0.47 % (854412)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3391491417:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.18/0.47 % (854408)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=619365839_2999 on theBenchmark for (2999ds/0Mi)
% 0.18/0.47 % (854409)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2227160105:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.18/0.47 % (854413)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2871402669:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.18/0.47 % (854410)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3294230725:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.18/0.47 % (854414)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=959450180:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.18/0.47 % (854412) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-854403-854412"...
% 0.18/0.47 % (854412)...printing done.
% 0.18/0.47 % (854412)Refutation found. Thanks to Tanya!
% 0.18/0.47 % SZS status Unsatisfiable for theBenchmark
% 0.18/0.47 % SZS output start Proof for theBenchmark
% See solution above
% 0.18/0.47 % (854412)------------------------------
% 0.18/0.47 % (854412)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.47 % (854412)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.47 % (854412)CaDiCaL version: 2.1.3
% 0.18/0.47 % (854412)Termination reason: Refutation
% 0.18/0.47 % (854412)Time elapsed: 0.013 s
% 0.18/0.47 % (854412)Peak memory usage: 12 MB
% 0.18/0.47 % (854412)Instructions burned: 20 (million)
% 0.18/0.47 % (854403)Success in time 0.05 s
% 0.18/0.47 % Vampire exiting
%------------------------------------------------------------------------------