%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM139-1 : 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 : n018.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 12:18:00 PM UTC 2026
% Result : Unsatisfiable 0.14s 0.44s
% Output : Refutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 9
% Syntax : Number of formulae : 17 ( 15 unt; 0 def)
% Number of atoms : 19 ( 8 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 7 ( 5 ~; 2 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 11 ( 3 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 4 con; 0-3 aty)
% Number of variables : 17 ( 17 !; 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(f22,axiom,
! [X2,X0,X1] :
( ~ member(X0,intersection(X1,X2))
| member(X0,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',intersection2) ).
fof(f28,axiom,
! [X2,X0,X1] : intersection(X0,cross_product(X1,X2)) = restrict(X0,X1,X2),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',restriction1) ).
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(f40,axiom,
! [X0] : domain_of(inverse(X0)) = range_of(X0),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',range_of) ).
fof(f43,axiom,
! [X0,X1] : range_of(restrict(X0,X1,universal_class)) = image(X0,X1),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',image) ).
fof(f56,axiom,
! [X0] : complement(image(element_relation,complement(X0))) = power_class(X0),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',power_class_definition) ).
fof(f176,negated_conjecture,
~ member(not_subclass_element(intersection(power_class(x),z),x),z),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_complete_induction3_1) ).
fof(f177,negated_conjecture,
~ subclass(intersection(power_class(x),z),x),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_complete_induction3_2) ).
fof(f179,plain,
! [X0] : range_of(X0) = domain_of(domain_of(flip(cross_product(X0,universal_class)))),
inference(definition_unfolding,[],[f40,f39]) ).
fof(f182,plain,
! [X0,X1] : image(X0,X1) = domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(X1,universal_class)),universal_class)))),
inference(definition_unfolding,[],[f43,f179,f28]) ).
fof(f185,plain,
! [X0] : power_class(X0) = complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X0),universal_class)),universal_class))))),
inference(definition_unfolding,[],[f56,f182]) ).
fof(f268,plain,
~ member(not_subclass_element(intersection(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(x),universal_class)),universal_class))))),z),x),z),
inference(definition_unfolding,[],[f176,f185]) ).
fof(f269,plain,
~ subclass(intersection(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(x),universal_class)),universal_class))))),z),x),
inference(definition_unfolding,[],[f177,f185]) ).
fof(f294,plain,
member(not_subclass_element(intersection(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(x),universal_class)),universal_class))))),z),x),intersection(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(x),universal_class)),universal_class))))),z)),
inference(resolution,[],[f2,f269]) ).
fof(f299,plain,
member(not_subclass_element(intersection(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(x),universal_class)),universal_class))))),z),x),z),
inference(resolution,[],[f22,f294]) ).
fof(f302,plain,
$false,
inference(forward_subsumption_resolution,[],[f299,f268]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM139-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.35 % Computer : n018.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Sun Sep 27 19:01:24 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.14/0.39 Running first-order model finding
% 0.14/0.39 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
% 0.14/0.44 % (2670764)Will run a generic schedule for satisfiability detection.
% 0.14/0.44 % (2670773)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=323863581:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.14/0.44 % (2670773) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2670764-2670773"...
% 0.14/0.44 % (2670770)% WARNING: option uhcvi not known.
% 0.14/0.44 % (2670773)...printing done.
% 0.14/0.44 % (2670771)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=4058288990:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.14/0.44 % (2670769)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2561750759_2999 on theBenchmark for (2999ds/0Mi)
% 0.14/0.44 % (2670772)dis+10_1_sil=32000:sp=arity:random_seed=2610418942:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.14/0.44 % (2670773)Refutation found. Thanks to Tanya!
% 0.14/0.44 % SZS status Unsatisfiable for theBenchmark
% 0.14/0.44 % SZS output start Proof for theBenchmark
% See solution above
% 0.14/0.44 % (2670773)------------------------------
% 0.14/0.44 % (2670773)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.14/0.44 % (2670773)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.14/0.44 % (2670773)CaDiCaL version: 2.1.3
% 0.14/0.44 % (2670773)Termination reason: Refutation
% 0.14/0.44 % (2670773)Time elapsed: 0.005 s
% 0.14/0.44 % (2670773)Peak memory usage: 12 MB
% 0.14/0.44 % (2670773)Instructions burned: 16 (million)
% 0.14/0.44 % (2670764)Success in time 0.037 s
% 0.14/0.44 % Vampire exiting
%------------------------------------------------------------------------------