%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET079+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n008.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 : Theorem 0.10s 0.45s
% Output : Refutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of formulae : 19 ( 9 unt; 0 def)
% Number of atoms : 44 ( 19 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 43 ( 18 ~; 13 |; 9 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 21 ( 20 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0,X1,X2] :
( member(X0,unordered_pair(X1,X2))
<=> ( member(X0,universal_class)
& ( X0 = X1
| X0 = X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET005+0.ax',unordered_pair_defn) ).
fof(f6,axiom,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
file('/export/starexec/sandbox2/benchmark/Axioms/SET005+0.ax',singleton_set_defn) ).
fof(f16,axiom,
! [X0] : ~ member(X0,null_class),
file('/export/starexec/sandbox2/benchmark/Axioms/SET005+0.ax',null_class_defn) ).
fof(f44,conjecture,
! [X0] :
( member(X0,universal_class)
=> singleton(X0) != null_class ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',corollary_to_set_in_its_singleton) ).
fof(f45,negated_conjecture,
~ ! [X0] :
( member(X0,universal_class)
=> singleton(X0) != null_class ),
inference(negated_conjecture,[status(cth)],[f44]) ).
fof(f60,plain,
? [X0] :
( singleton(X0) = null_class
& member(X0,universal_class) ),
inference(ennf_transformation,[],[f45]) ).
fof(f66,plain,
! [X0,X1,X2] :
( ( member(X0,unordered_pair(X1,X2))
| ~ member(X0,universal_class)
| ( X0 != X1
& X0 != X2 ) )
& ( ( member(X0,universal_class)
& ( X0 = X1
| X0 = X2 ) )
| ~ member(X0,unordered_pair(X1,X2)) ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f67,plain,
! [X0,X1,X2] :
( ( member(X0,unordered_pair(X1,X2))
| ~ member(X0,universal_class)
| ( X0 != X1
& X0 != X2 ) )
& ( ( member(X0,universal_class)
& ( X0 = X1
| X0 = X2 ) )
| ~ member(X0,unordered_pair(X1,X2)) ) ),
inference(flattening,[],[f66]) ).
fof(f103,plain,
( null_class = singleton(sK6)
& member(sK6,universal_class) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(X0,sK6)],[f60]) ).
fof(f114,plain,
! [X2,X0,X1] :
( member(X0,unordered_pair(X1,X2))
| ~ member(X0,universal_class)
| X0 != X1 ),
inference(cnf_transformation,[],[f67]) ).
fof(f116,plain,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
inference(cnf_transformation,[],[f6]) ).
fof(f135,plain,
! [X0] : ~ member(X0,null_class),
inference(cnf_transformation,[],[f16]) ).
fof(f191,plain,
member(sK6,universal_class),
inference(cnf_transformation,[],[f103]) ).
fof(f192,plain,
null_class = singleton(sK6),
inference(cnf_transformation,[],[f103]) ).
fof(f230,plain,
null_class = unordered_pair(sK6,sK6),
inference(definition_unfolding,[],[f192,f116]) ).
fof(f233,plain,
! [X2,X1] :
( member(X1,unordered_pair(X1,X2))
| ~ member(X1,universal_class) ),
inference(equality_resolution,[],[f114]) ).
fof(f590,plain,
( member(sK6,null_class)
| ~ member(sK6,universal_class) ),
inference(superposition,[],[f233,f230]) ).
fof(f591,plain,
~ member(sK6,universal_class),
inference(forward_subsumption_resolution,[],[f590,f135]) ).
fof(f592,plain,
$false,
inference(forward_subsumption_resolution,[],[f591,f191]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET079+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.37 % Computer : n008.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 28 00:33:55 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.40 Running first-order model finding
% 0.10/0.40 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
% 0.10/0.45 % (1757064)Will run a generic schedule for satisfiability detection.
% 0.10/0.45 % (1757071)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3035865103:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.10/0.45 % (1757070)% WARNING: option uhcvi not known.
% 0.10/0.45 % (1757071) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1757064-1757071"...
% 0.10/0.45 % (1757071)...printing done.
% 0.10/0.45 % (1757072)dis+10_1_sil=32000:sp=arity:random_seed=3493046962:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.10/0.45 % (1757069)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1959446984_2999 on theBenchmark for (2999ds/0Mi)
% 0.10/0.45 % (1757071)Refutation found. Thanks to Tanya!
% 0.10/0.45 % SZS status Theorem for theBenchmark
% 0.10/0.45 % SZS output start Proof for theBenchmark
% See solution above
% 0.10/0.45 % (1757071)------------------------------
% 0.10/0.45 % (1757071)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.10/0.45 % (1757071)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.10/0.45 % (1757071)CaDiCaL version: 2.1.3
% 0.10/0.45 % (1757071)Termination reason: Refutation
% 0.10/0.45 % (1757071)Time elapsed: 0.006 s
% 0.10/0.45 % (1757071)Peak memory usage: 12 MB
% 0.10/0.45 % (1757071)Instructions burned: 12 (million)
% 0.10/0.45 % (1757064)Success in time 0.038 s
% 0.10/0.45 % Vampire exiting
%------------------------------------------------------------------------------