%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET506-6 : 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 : 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 12:43:53 PM UTC 2026
% Result : Unsatisfiable 0.15s 0.49s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 19
% Syntax : Number of formulae : 46 ( 26 unt; 0 def)
% Number of atoms : 69 ( 23 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 42 ( 19 ~; 23 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 11 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 19 ( 19 usr; 5 con; 0-3 aty)
% Number of variables : 53 ( 53 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1] :
( member(not_subclass_element(X0,X1),X0)
| subclass(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',not_subclass_members1) ).
fof(f4,axiom,
! [X0] : subclass(X0,universal_class),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',class_elements_are_sets) ).
fof(f7,axiom,
! [X0,X1] :
( ~ subclass(X0,X1)
| ~ subclass(X1,X0)
| X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',subclass_implies_equal) ).
fof(f11,axiom,
! [X0,X1] : member(unordered_pair(X0,X1),universal_class),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',unordered_pairs_in_universal) ).
fof(f21,axiom,
! [X2,X0,X1] :
( ~ member(X0,intersection(X1,X2))
| member(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',intersection1) ).
fof(f24,axiom,
! [X0,X1] :
( ~ member(X0,complement(X1))
| ~ member(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',complement1) ).
fof(f28,axiom,
! [X2,X0,X1] : intersection(X0,cross_product(X1,X2)) = restrict(X0,X1,X2),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',restriction1) ).
fof(f39,axiom,
! [X0] : domain_of(flip(cross_product(X0,universal_class))) = inverse(X0),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',inverse) ).
fof(f40,axiom,
! [X0] : domain_of(inverse(X0)) = range_of(X0),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/SET004-0.ax',image) ).
fof(f53,axiom,
member(omega,universal_class),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',omega_in_universal) ).
fof(f54,axiom,
! [X0] : domain_of(restrict(element_relation,universal_class,X0)) = sum_class(X0),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',sum_class_definition) ).
fof(f55,axiom,
! [X0] :
( ~ member(X0,universal_class)
| member(sum_class(X0),universal_class) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',sum_class2) ).
fof(f56,axiom,
! [X0] : complement(image(element_relation,complement(X0))) = power_class(X0),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',power_class_definition) ).
fof(f57,axiom,
! [X0] :
( ~ member(X0,universal_class)
| member(power_class(X0),universal_class) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',power_class2) ).
fof(f66,axiom,
! [X0,X1] :
( ~ function(X0)
| ~ member(X1,universal_class)
| member(image(X0,X1),universal_class) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',replacement) ).
fof(f69,axiom,
! [X0] :
( X0 = null_class
| intersection(X0,regular(X0)) = null_class ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',regularity2) ).
fof(f70,plain,
! [X0] :
( null_class = intersection(X0,regular(X0))
| null_class = X0 ),
inference(reorient_equations,[],[f69]) ).
fof(f72,axiom,
function(choice),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',choice1) ).
fof(f122,negated_conjecture,
universal_class = null_class,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_universal_class_not_null_class_1) ).
fof(f123,plain,
! [X0] : sum_class(X0) = domain_of(intersection(element_relation,cross_product(null_class,X0))),
inference(definition_unfolding,[],[f54,f28,f122]) ).
fof(f124,plain,
! [X0] : inverse(X0) = domain_of(flip(cross_product(X0,null_class))),
inference(definition_unfolding,[],[f39,f122]) ).
fof(f125,plain,
! [X0] : range_of(X0) = domain_of(domain_of(flip(cross_product(X0,null_class)))),
inference(definition_unfolding,[],[f40,f124]) ).
fof(f126,plain,
! [X0,X1] : image(X0,X1) = domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(X1,null_class)),null_class)))),
inference(definition_unfolding,[],[f43,f125,f28,f122]) ).
fof(f135,plain,
! [X0] : power_class(X0) = complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X0),null_class)),null_class))))),
inference(definition_unfolding,[],[f56,f126]) ).
fof(f137,plain,
! [X0] : subclass(X0,null_class),
inference(definition_unfolding,[],[f4,f122]) ).
fof(f140,plain,
! [X0,X1] : member(unordered_pair(X0,X1),null_class),
inference(definition_unfolding,[],[f11,f122]) ).
fof(f163,plain,
member(omega,null_class),
inference(definition_unfolding,[],[f53,f122]) ).
fof(f164,plain,
! [X0] :
( ~ member(X0,null_class)
| member(domain_of(intersection(element_relation,cross_product(null_class,X0))),null_class) ),
inference(definition_unfolding,[],[f55,f122,f123,f122]) ).
fof(f165,plain,
! [X0] :
( ~ member(X0,null_class)
| member(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X0),null_class)),null_class))))),null_class) ),
inference(definition_unfolding,[],[f57,f122,f135,f122]) ).
fof(f174,plain,
! [X0,X1] :
( ~ function(X0)
| ~ member(X1,null_class)
| member(domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(X1,null_class)),null_class)))),null_class) ),
inference(definition_unfolding,[],[f66,f122,f126,f122]) ).
fof(f240,plain,
! [X0,X1] : member(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(unordered_pair(X0,X1)),null_class)),null_class))))),null_class),
inference(resolution,[],[f165,f140]) ).
fof(f261,plain,
! [X0] :
( ~ member(X0,null_class)
| member(domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(X0,null_class)),null_class)))),null_class) ),
inference(resolution,[],[f72,f174]) ).
fof(f475,plain,
! [X0] :
( member(domain_of(intersection(element_relation,cross_product(null_class,not_subclass_element(null_class,X0)))),null_class)
| subclass(null_class,X0) ),
inference(resolution,[],[f2,f164]) ).
fof(f544,plain,
! [X0] :
( ~ subclass(null_class,X0)
| null_class = X0 ),
inference(resolution,[],[f7,f137]) ).
fof(f633,plain,
! [X0] :
( member(omega,intersection(X0,regular(X0)))
| null_class = X0 ),
inference(superposition,[],[f163,f70]) ).
fof(f907,plain,
! [X0] :
( member(omega,X0)
| null_class = X0 ),
inference(resolution,[],[f633,f21]) ).
fof(f921,plain,
! [X0] :
( ~ member(omega,X0)
| complement(X0) = null_class ),
inference(resolution,[],[f907,f24]) ).
fof(f963,plain,
null_class = complement(null_class),
inference(resolution,[],[f921,f163]) ).
fof(f974,plain,
! [X0] :
( ~ member(X0,null_class)
| ~ member(X0,null_class) ),
inference(superposition,[],[f24,f963]) ).
fof(f981,plain,
! [X0] : ~ member(X0,null_class),
inference(duplicate_literal_removal,[],[f974]) ).
fof(f991,plain,
! [X0] :
( subclass(null_class,X0)
| member(domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(domain_of(intersection(element_relation,cross_product(null_class,not_subclass_element(null_class,X0)))),null_class)),null_class)))),null_class) ),
inference(resolution,[],[f475,f261]) ).
fof(f996,plain,
! [X0] : subclass(null_class,X0),
inference(forward_subsumption_resolution,[],[f991,f981]) ).
fof(f1001,plain,
! [X0] : null_class = X0,
inference(resolution,[],[f996,f544]) ).
fof(f1390,plain,
member(complement(domain_of(domain_of(null_class))),null_class),
inference(superposition,[],[f240,f1001]) ).
fof(f1490,plain,
$false,
inference(forward_subsumption_resolution,[],[f1390,f981]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET506-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.38 % Computer : n003.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 02:02:12 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.41 Running first-order model finding
% 0.11/0.41 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
% 0.15/0.49 % (1118193)Will run a generic schedule for satisfiability detection.
% 0.15/0.49 % (1118204)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3389142779:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.15/0.49 % (1118199)% WARNING: option uhcvi not known.
% 0.15/0.49 % (1118201)dis+10_1_sil=32000:sp=arity:random_seed=1455373232:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.15/0.49 % (1118198)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1372568323_2999 on theBenchmark for (2999ds/0Mi)
% 0.15/0.49 % (1118199)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1073361843:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.15/0.49 % (1118200)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=541908706:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.15/0.49 % (1118202)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=376000998:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.15/0.49 % (1118203)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=202322481:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.15/0.49 % (1118203) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1118193-1118203"...
% 0.15/0.49 % (1118203)...printing done.
% 0.15/0.49 % (1118203)Refutation found. Thanks to Tanya!
% 0.15/0.49 % SZS status Unsatisfiable for theBenchmark
% 0.15/0.49 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.49 % (1118203)------------------------------
% 0.15/0.49 % (1118203)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.15/0.49 % (1118203)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.15/0.49 % (1118203)CaDiCaL version: 2.1.3
% 0.15/0.49 % (1118203)Termination reason: Refutation
% 0.15/0.49 % (1118203)Time elapsed: 0.036 s
% 0.15/0.49 % (1118203)Peak memory usage: 12 MB
% 0.15/0.49 % (1118203)Instructions burned: 56 (million)
% 0.15/0.49 % (1118193)Success in time 0.076 s
% 0.15/0.49 % Vampire exiting
%------------------------------------------------------------------------------