%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET075-7 : 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 : n012.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 12:42:59 PM UTC 2026
% Result : Unsatisfiable 0.07s 0.38s
% Output : Refutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 9
% Syntax : Number of formulae : 19 ( 13 unt; 0 def)
% Number of atoms : 26 ( 5 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 16 ( 9 ~; 7 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 21 ( 21 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] :
( ~ member(X2,X0)
| ~ subclass(X0,X1)
| member(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',subclass_members) ).
fof(f4,axiom,
! [X0] : subclass(X0,universal_class),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',class_elements_are_sets) ).
fof(f9,axiom,
! [X0,X1] :
( member(X0,unordered_pair(X0,X1))
| ~ member(X0,universal_class) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',unordered_pair2) ).
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(f113,axiom,
! [X0] : ~ member(X0,null_class),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_of_null_class) ).
fof(f128,negated_conjecture,
member(ordered_pair(x,y),cross_product(u,v)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_corollary_to_unordered_pair_axiom3_1) ).
fof(f129,negated_conjecture,
unordered_pair(x,y) = null_class,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_corollary_to_unordered_pair_axiom3_2) ).
fof(f130,plain,
null_class = unordered_pair(x,y),
inference(reorient_equations,[],[f129]) ).
fof(f135,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(f141,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,f135]) ).
fof(f189,plain,
member(unordered_pair(unordered_pair(x,x),unordered_pair(x,unordered_pair(y,y))),cross_product(u,v)),
inference(definition_unfolding,[],[f128,f135]) ).
fof(f239,plain,
( member(x,null_class)
| ~ member(x,universal_class) ),
inference(superposition,[],[f9,f130]) ).
fof(f246,plain,
~ member(x,universal_class),
inference(forward_subsumption_resolution,[],[f239,f113]) ).
fof(f815,plain,
member(x,u),
inference(resolution,[],[f141,f189]) ).
fof(f872,plain,
! [X0] :
( ~ subclass(u,X0)
| member(x,X0) ),
inference(resolution,[],[f815,f1]) ).
fof(f946,plain,
member(x,universal_class),
inference(resolution,[],[f872,f4]) ).
fof(f958,plain,
$false,
inference(forward_subsumption_resolution,[],[f946,f246]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SET075-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.03/0.31 % Computer : n012.cluster.edu
% 0.03/0.31 % Model : x86_64 x86_64
% 0.03/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.31 % Memory : 8046.5625MB
% 0.03/0.31 % OS : Linux 6.8.0-71-generic
% 0.03/0.31 % CPULimit : 300
% 0.03/0.31 % WCLimit : 300
% 0.03/0.31 % DateTime : Mon Sep 28 00:31:49 UTC 2026
% 0.03/0.31 % CPUTime :
% 0.03/0.31 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.07/0.33 Running first-order model finding
% 0.07/0.33 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
% 0.07/0.38 % (2904913)Will run a generic schedule for satisfiability detection.
% 0.07/0.38 % (2904919)% WARNING: option uhcvi not known.
% 0.07/0.38 % (2904924)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1358830526:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.07/0.38 % (2904921)dis+10_1_sil=32000:sp=arity:random_seed=441641094:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.07/0.38 % (2904918)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=771898256_2999 on theBenchmark for (2999ds/0Mi)
% 0.07/0.38 % (2904920)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2665232627:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.07/0.38 % (2904919)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=680081266:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.07/0.38 % (2904922)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=404550099:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.07/0.38 % (2904923)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3464410786:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.07/0.38 % (2904921) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2904913-2904921"...
% 0.07/0.38 % (2904921)...printing done.
% 0.07/0.38 % (2904922) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2904913-2904922"...
% 0.07/0.38 % (2904921)Refutation found. Thanks to Tanya!
% 0.07/0.38 % SZS status Unsatisfiable for theBenchmark
% 0.07/0.38 % SZS output start Proof for theBenchmark
% See solution above
% 0.07/0.38 % (2904921)------------------------------
% 0.07/0.38 % (2904921)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.07/0.38 % (2904921)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.07/0.38 % (2904921)CaDiCaL version: 2.1.3
% 0.07/0.38 % (2904921)Termination reason: Refutation
% 0.07/0.38 % (2904921)Time elapsed: 0.011 s
% 0.07/0.38 % (2904921)Peak memory usage: 11 MB
% 0.07/0.38 % (2904921)Instructions burned: 31 (million)
% 0.07/0.38 % (2904913)Success in time 0.041 s
% 0.07/0.38 % Vampire exiting
%------------------------------------------------------------------------------