%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET875+1 : TPTP v9.3.1. Released v3.2.0.
% 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 12:44:54 PM UTC 2026
% Result : Theorem 0.07s 0.34s
% Output : Refutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 3
% Syntax : Number of formulae : 19 ( 6 unt; 0 def)
% Number of atoms : 58 ( 28 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 66 ( 27 ~; 23 |; 14 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 32 ( 28 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1] :
( X1 = singleton(X0)
<=> ! [X2] :
( in(X2,X1)
<=> X2 = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tarski) ).
fof(f3,axiom,
! [X0,X1] :
~ ( disjoint(singleton(X0),X1)
& in(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l25_zfmisc_1) ).
fof(f7,conjecture,
! [X0,X1] :
~ ( disjoint(singleton(X0),singleton(X1))
& X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_zfmisc_1) ).
fof(f8,negated_conjecture,
~ ! [X0,X1] :
~ ( disjoint(singleton(X0),singleton(X1))
& X0 = X1 ),
inference(negated_conjecture,[status(cth)],[f7]) ).
fof(f10,plain,
! [X0,X1] :
( ~ disjoint(singleton(X0),X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f3]) ).
fof(f12,plain,
? [X0,X1] :
( disjoint(singleton(X0),singleton(X1))
& X0 = X1 ),
inference(ennf_transformation,[],[f8]) ).
fof(f13,plain,
! [X0,X1] :
( ( X1 = singleton(X0)
| ? [X2] :
( ( X0 != X2
| ~ in(X2,X1) )
& ( X2 = X0
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| X0 != X2 )
& ( X2 = X0
| ~ in(X2,X1) ) )
| singleton(X0) != X1 ) ),
inference(nnf_transformation,[],[f2]) ).
fof(f14,plain,
! [X0,X1] :
( ( X1 = singleton(X0)
| ? [X2] :
( ( X0 != X2
| ~ in(X2,X1) )
& ( X2 = X0
| in(X2,X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| X0 != X3 )
& ( X0 = X3
| ~ in(X3,X1) ) )
| singleton(X0) != X1 ) ),
inference(rectify,[],[f13]) ).
fof(f15,plain,
! [X0,X1] :
( ( X1 = singleton(X0)
| ( ( sK0(X0,X1) != X0
| ~ in(sK0(X0,X1),X1) )
& ( sK0(X0,X1) = X0
| in(sK0(X0,X1),X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| X0 != X3 )
& ( X0 = X3
| ~ in(X3,X1) ) )
| singleton(X0) != X1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0,X1))],[f14]) ).
fof(f18,plain,
( disjoint(singleton(sK3),singleton(sK4))
& sK3 = sK4 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4]),skolemize(X0,sK3),skolemize(X1,sK4)],[f12]) ).
fof(f21,plain,
! [X3,X0,X1] :
( in(X3,X1)
| X0 != X3
| singleton(X0) != X1 ),
inference(cnf_transformation,[],[f15]) ).
fof(f24,plain,
! [X0,X1] :
( ~ disjoint(singleton(X0),X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f10]) ).
fof(f28,plain,
sK3 = sK4,
inference(cnf_transformation,[],[f18]) ).
fof(f29,plain,
disjoint(singleton(sK3),singleton(sK4)),
inference(cnf_transformation,[],[f18]) ).
fof(f30,plain,
disjoint(singleton(sK4),singleton(sK4)),
inference(definition_unfolding,[],[f29,f28]) ).
fof(f31,plain,
! [X3,X1] :
( in(X3,X1)
| singleton(X3) != X1 ),
inference(equality_resolution,[],[f21]) ).
fof(f32,plain,
! [X3] : in(X3,singleton(X3)),
inference(equality_resolution,[],[f31]) ).
fof(f36,plain,
~ in(sK4,singleton(sK4)),
inference(resolution,[],[f24,f30]) ).
fof(f37,plain,
$false,
inference(forward_subsumption_resolution,[],[f36,f32]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SET875+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.05/0.30 % Computer : n012.cluster.edu
% 0.05/0.30 % Model : x86_64 x86_64
% 0.05/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.05/0.30 % Memory : 8046.5625MB
% 0.05/0.30 % OS : Linux 6.8.0-71-generic
% 0.05/0.30 % CPULimit : 300
% 0.05/0.30 % WCLimit : 300
% 0.05/0.30 % DateTime : Mon Sep 28 03:05:44 UTC 2026
% 0.05/0.30 % CPUTime :
% 0.05/0.30 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.05/0.32 Running first-order model finding
% 0.05/0.32 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
% 0.07/0.34 % (2978910)Will run a generic schedule for satisfiability detection.
% 0.07/0.34 % (2978916)% WARNING: option uhcvi not known.
% 0.07/0.34 % (2978915)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1920379013_3000 on theBenchmark for (3000ds/0Mi)
% 0.07/0.34 % (2978918)dis+10_1_sil=32000:sp=arity:random_seed=3013655182:i=103:fgj=on_3000 on theBenchmark for (3000ds/103Mi)
% 0.07/0.34 % (2978920)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=4139955743:i=131_3000 on theBenchmark for (3000ds/131Mi)
% 0.07/0.34 % (2978916)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=4050845664:i=135531:add=off:rawr=on_3000 on theBenchmark for (3000ds/135531Mi)
% 0.07/0.34 % (2978917)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3734215489:i=88024:add=on:rawr=on_3000 on theBenchmark for (3000ds/88024Mi)
% 0.07/0.34 % (2978921)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1266752151:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_3000 on theBenchmark for (3000ds/159Mi)
% 0.07/0.34 % (2978919)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1518376235:i=116_3000 on theBenchmark for (3000ds/116Mi)
% 0.07/0.34 % TRYING [1]
% 0.07/0.34 % (2978918) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2978910-2978918"...
% 0.07/0.34 % TRYING [2]
% 0.07/0.34 % (2978920) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2978910-2978920"...
% 0.07/0.34 % TRYING [3]
% 0.07/0.34 % (2978916) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2978910-2978916"...
% 0.07/0.34 % (2978921) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2978910-2978921"...
% 0.07/0.34 % (2978919) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2978910-2978919"...
% 0.07/0.34 % TRYING [4]
% 0.07/0.34 % (2978917) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2978910-2978917"...
% 0.07/0.34 % TRYING [5]
% 0.07/0.34 % (2978918)...printing done.
% 0.07/0.34 % (2978920)...printing done.
% 0.07/0.34 % (2978916)...printing done.
% 0.07/0.34 % (2978921)...printing done.
% 0.07/0.34 % (2978919)...printing done.
% 0.07/0.34 % (2978917)...printing done.
% 0.07/0.34 % TRYING [6]
% 0.07/0.34 % (2978918)Refutation found. Thanks to Tanya!
% 0.07/0.34 % SZS status Theorem for theBenchmark
% 0.07/0.34 % SZS output start Proof for theBenchmark
% See solution above
% 0.07/0.34 % (2978918)------------------------------
% 0.07/0.34 % (2978918)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.07/0.34 % (2978918)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.07/0.34 % (2978918)CaDiCaL version: 2.1.3
% 0.07/0.34 % (2978918)Termination reason: Refutation
% 0.07/0.34 % (2978918)Time elapsed: 0.001 s
% 0.07/0.34 % (2978918)Peak memory usage: 11 MB
% 0.07/0.34 % (2978918)Instructions burned: 1 (million)
% 0.07/0.34 % (2978910)Success in time 0.014 s
% 0.07/0.34 % Vampire exiting
%------------------------------------------------------------------------------