%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET079-6 : 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 : 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 12:43:00 PM UTC 2026
% Result : Unsatisfiable 0.07s 0.39s
% Output : Refutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 7
% Syntax : Number of formulae : 19 ( 9 unt; 0 def)
% Number of atoms : 30 ( 12 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 21 ( 10 ~; 11 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 15 ( 15 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(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(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(f101,negated_conjecture,
member(x,universal_class),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_corollary_to_set_in_its_singleton_1) ).
fof(f102,negated_conjecture,
singleton(x) = null_class,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_corollary_to_set_in_its_singleton_2) ).
fof(f103,plain,
null_class = singleton(x),
inference(reorient_equations,[],[f102]) ).
fof(f152,plain,
null_class = unordered_pair(x,x),
inference(definition_unfolding,[],[f103,f12]) ).
fof(f310,plain,
( member(x,null_class)
| ~ member(x,universal_class) ),
inference(superposition,[],[f9,f152]) ).
fof(f311,plain,
member(x,null_class),
inference(forward_subsumption_resolution,[],[f310,f101]) ).
fof(f1374,plain,
! [X0,X1] :
( ~ member(X0,null_class)
| member(X0,X1)
| null_class = X1 ),
inference(superposition,[],[f21,f70]) ).
fof(f1659,plain,
! [X0] :
( member(x,X0)
| null_class = X0 ),
inference(resolution,[],[f1374,f311]) ).
fof(f1667,plain,
! [X0] :
( ~ member(x,X0)
| complement(X0) = null_class ),
inference(resolution,[],[f1659,f24]) ).
fof(f1675,plain,
null_class = complement(universal_class),
inference(resolution,[],[f1667,f101]) ).
fof(f1696,plain,
! [X0] :
( ~ member(X0,null_class)
| ~ member(X0,universal_class) ),
inference(superposition,[],[f24,f1675]) ).
fof(f1705,plain,
~ member(x,universal_class),
inference(resolution,[],[f1696,f311]) ).
fof(f1711,plain,
$false,
inference(forward_subsumption_resolution,[],[f1705,f101]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SET079-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.04/0.31 % Computer : n012.cluster.edu
% 0.04/0.31 % Model : x86_64 x86_64
% 0.04/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.31 % Memory : 8046.5625MB
% 0.04/0.31 % OS : Linux 6.8.0-71-generic
% 0.04/0.31 % CPULimit : 300
% 0.04/0.31 % WCLimit : 300
% 0.04/0.31 % DateTime : Mon Sep 28 00:33:05 UTC 2026
% 0.04/0.31 % CPUTime :
% 0.04/0.31 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
% 0.07/0.39 % (2906965)Will run a generic schedule for satisfiability detection.
% 0.07/0.39 % (2906971)% WARNING: option uhcvi not known.
% 0.07/0.39 % (2906976)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3948533152:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.07/0.39 % (2906970)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2226557275_2999 on theBenchmark for (2999ds/0Mi)
% 0.07/0.39 % (2906971)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2426677494:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.07/0.39 % (2906973)dis+10_1_sil=32000:sp=arity:random_seed=545025726:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.07/0.39 % (2906972)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1378783674:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.07/0.39 % (2906974)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2645778036:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.07/0.39 % (2906975)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3336415475:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.07/0.39 % (2906972) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2906965-2906972"...
% 0.07/0.39 % (2906972)...printing done.
% 0.07/0.39 % (2906972)Refutation found. Thanks to Tanya!
% 0.07/0.39 % SZS status Unsatisfiable for theBenchmark
% 0.07/0.39 % SZS output start Proof for theBenchmark
% See solution above
% 0.07/0.39 % (2906972)------------------------------
% 0.07/0.39 % (2906972)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.07/0.39 % (2906972)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.07/0.39 % (2906972)CaDiCaL version: 2.1.3
% 0.07/0.39 % (2906972)Termination reason: Refutation
% 0.07/0.39 % (2906972)Time elapsed: 0.021 s
% 0.07/0.39 % (2906972)Peak memory usage: 13 MB
% 0.07/0.39 % (2906972)Instructions burned: 57 (million)
% 0.07/0.39 % (2906965)Success in time 0.051 s
% 0.07/0.39 % Vampire exiting
%------------------------------------------------------------------------------