%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU148+3 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n014.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 12:52:06 PM UTC 2026
% Result : Theorem 0.13s 0.43s
% Output : Refutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 4
% Syntax : Number of formulae : 26 ( 8 unt; 0 def)
% Number of atoms : 81 ( 51 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 90 ( 35 ~; 35 |; 15 &)
% ( 3 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 40 ( 36 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1] :
( X1 = singleton(X0)
<=> ! [X2] :
( in(X2,X1)
<=> X2 = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).
fof(f4,axiom,
! [X0] : singleton(X0) != empty_set,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l1_zfmisc_1) ).
fof(f5,axiom,
! [X0,X1] :
( subset(X0,singleton(X1))
<=> ( X0 = empty_set
| X0 = singleton(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l4_zfmisc_1) ).
fof(f9,conjecture,
! [X0,X1] :
( subset(singleton(X0),singleton(X1))
=> X0 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_zfmisc_1) ).
fof(f10,negated_conjecture,
~ ! [X0,X1] :
( subset(singleton(X0),singleton(X1))
=> X0 = X1 ),
inference(negated_conjecture,[status(cth)],[f9]) ).
fof(f13,plain,
? [X0,X1] :
( X0 != X1
& subset(singleton(X0),singleton(X1)) ),
inference(ennf_transformation,[],[f10]) ).
fof(f14,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(f15,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,[],[f14]) ).
fof(f16,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))],[f15]) ).
fof(f17,plain,
! [X0,X1] :
( ( subset(X0,singleton(X1))
| ( empty_set != X0
& singleton(X1) != X0 ) )
& ( X0 = empty_set
| X0 = singleton(X1)
| ~ subset(X0,singleton(X1)) ) ),
inference(nnf_transformation,[],[f5]) ).
fof(f18,plain,
! [X0,X1] :
( ( subset(X0,singleton(X1))
| ( empty_set != X0
& singleton(X1) != X0 ) )
& ( X0 = empty_set
| X0 = singleton(X1)
| ~ subset(X0,singleton(X1)) ) ),
inference(flattening,[],[f17]) ).
fof(f21,plain,
( sK3 != sK4
& subset(singleton(sK3),singleton(sK4)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4]),skolemize(X0,sK3),skolemize(X1,sK4)],[f13]) ).
fof(f23,plain,
! [X3,X0,X1] :
( ~ in(X3,X1)
| X0 = X3
| singleton(X0) != X1 ),
inference(cnf_transformation,[],[f16]) ).
fof(f24,plain,
! [X3,X0,X1] :
( X0 != X3
| in(X3,X1)
| singleton(X0) != X1 ),
inference(cnf_transformation,[],[f16]) ).
fof(f28,plain,
! [X0] : singleton(X0) != empty_set,
inference(cnf_transformation,[],[f4]) ).
fof(f29,plain,
! [X0,X1] :
( ~ subset(X0,singleton(X1))
| singleton(X1) = X0
| empty_set = X0 ),
inference(cnf_transformation,[],[f18]) ).
fof(f35,plain,
subset(singleton(sK3),singleton(sK4)),
inference(cnf_transformation,[],[f21]) ).
fof(f36,plain,
sK3 != sK4,
inference(cnf_transformation,[],[f21]) ).
fof(f39,plain,
! [X0,X1] :
( singleton(X0) != X1
| in(X0,X1) ),
inference(equality_resolution,[],[f24]) ).
fof(f40,plain,
( singleton(sK3) = singleton(sK4)
| empty_set = singleton(sK3) ),
inference(resolution,[],[f29,f35]) ).
fof(f43,plain,
singleton(sK3) = singleton(sK4),
inference(forward_subsumption_resolution,[],[f40,f28]) ).
fof(f51,plain,
! [X0] :
( singleton(sK3) != X0
| in(sK4,X0) ),
inference(superposition,[],[f39,f43]) ).
fof(f55,plain,
in(sK4,singleton(sK3)),
inference(equality_resolution,[],[f51]) ).
fof(f56,plain,
! [X0] :
( singleton(X0) != singleton(sK3)
| sK4 = X0 ),
inference(resolution,[],[f55,f23]) ).
fof(f61,plain,
sK3 = sK4,
inference(equality_resolution,[],[f56]) ).
fof(f62,plain,
$false,
inference(forward_subsumption_resolution,[],[f61,f36]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU148+3 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.36 % Computer : n014.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 28 03:44:46 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.13/0.39 Running first-order model finding
% 0.13/0.39 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.43 % (1414129)Will run a generic schedule for satisfiability detection.
% 0.13/0.43 % (1414139)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2626045757:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.13/0.43 % (1414139) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1414129-1414139"...
% 0.13/0.43 % (1414139)...printing done.
% 0.13/0.43 % (1414139)Refutation found. Thanks to Tanya!
% 0.13/0.43 % SZS status Theorem for theBenchmark
% 0.13/0.43 % SZS output start Proof for theBenchmark
% See solution above
% 0.13/0.43 % (1414139)------------------------------
% 0.13/0.43 % (1414139)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.13/0.43 % (1414139)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.13/0.43 % (1414139)CaDiCaL version: 2.1.3
% 0.13/0.43 % (1414139)Termination reason: Refutation
% 0.13/0.43 % (1414139)Time elapsed: 0.001 s
% 0.13/0.43 % (1414139)Peak memory usage: 11 MB
% 0.13/0.43 % (1414139)Instructions burned: 2 (million)
% 0.13/0.43 % (1414129)Success in time 0.03 s
% 0.13/0.43 % Vampire exiting
%------------------------------------------------------------------------------