%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU148+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n026.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 0.16s 0.46s
% Output : Refutation 0.16s
% 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/sandbox2/benchmark/theBenchmark.p',d1_tarski) ).
fof(f6,axiom,
! [X0] : singleton(X0) != empty_set,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l1_zfmisc_1) ).
fof(f7,axiom,
! [X0,X1] :
( subset(X0,singleton(X1))
<=> ( X0 = empty_set
| X0 = singleton(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l4_zfmisc_1) ).
fof(f11,conjecture,
! [X0,X1] :
( subset(singleton(X0),singleton(X1))
=> X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_zfmisc_1) ).
fof(f12,negated_conjecture,
~ ! [X0,X1] :
( subset(singleton(X0),singleton(X1))
=> X0 = X1 ),
inference(negated_conjecture,[status(cth)],[f11]) ).
fof(f15,plain,
? [X0,X1] :
( X0 != X1
& subset(singleton(X0),singleton(X1)) ),
inference(ennf_transformation,[],[f12]) ).
fof(f16,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(f17,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,[],[f16]) ).
fof(f18,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))],[f17]) ).
fof(f19,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,[],[f7]) ).
fof(f20,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,[],[f19]) ).
fof(f23,plain,
( sK3 != sK4
& subset(singleton(sK3),singleton(sK4)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4]),skolemize(X0,sK3),skolemize(X1,sK4)],[f15]) ).
fof(f25,plain,
! [X3,X0,X1] :
( ~ in(X3,X1)
| X0 = X3
| singleton(X0) != X1 ),
inference(cnf_transformation,[],[f18]) ).
fof(f26,plain,
! [X3,X0,X1] :
( X0 != X3
| in(X3,X1)
| singleton(X0) != X1 ),
inference(cnf_transformation,[],[f18]) ).
fof(f30,plain,
! [X0] : singleton(X0) != empty_set,
inference(cnf_transformation,[],[f6]) ).
fof(f31,plain,
! [X0,X1] :
( ~ subset(X0,singleton(X1))
| singleton(X1) = X0
| empty_set = X0 ),
inference(cnf_transformation,[],[f20]) ).
fof(f37,plain,
subset(singleton(sK3),singleton(sK4)),
inference(cnf_transformation,[],[f23]) ).
fof(f38,plain,
sK3 != sK4,
inference(cnf_transformation,[],[f23]) ).
fof(f41,plain,
! [X0,X1] :
( singleton(X0) != X1
| in(X0,X1) ),
inference(equality_resolution,[],[f26]) ).
fof(f42,plain,
( singleton(sK3) = singleton(sK4)
| empty_set = singleton(sK3) ),
inference(resolution,[],[f31,f37]) ).
fof(f45,plain,
singleton(sK3) = singleton(sK4),
inference(forward_subsumption_resolution,[],[f42,f30]) ).
fof(f53,plain,
! [X0] :
( singleton(sK3) != X0
| in(sK4,X0) ),
inference(superposition,[],[f41,f45]) ).
fof(f57,plain,
in(sK4,singleton(sK3)),
inference(equality_resolution,[],[f53]) ).
fof(f58,plain,
! [X0] :
( singleton(X0) != singleton(sK3)
| sK4 = X0 ),
inference(resolution,[],[f57,f25]) ).
fof(f63,plain,
sK3 = sK4,
inference(equality_resolution,[],[f58]) ).
fof(f64,plain,
$false,
inference(forward_subsumption_resolution,[],[f63,f38]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU148+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.38 % Computer : n026.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Mon Sep 28 03:47:27 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.41 Running first-order model finding
% 0.10/0.41 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
% 0.16/0.46 % (3442635)Will run a generic schedule for satisfiability detection.
% 0.16/0.46 % (3442645)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1317146386:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.16/0.46 % (3442645) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3442635-3442645"...
% 0.16/0.46 % (3442645)...printing done.
% 0.16/0.46 % (3442645)Refutation found. Thanks to Tanya!
% 0.16/0.46 % SZS status Theorem for theBenchmark
% 0.16/0.46 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.46 % (3442645)------------------------------
% 0.16/0.46 % (3442645)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.16/0.46 % (3442645)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/0.46 % (3442645)CaDiCaL version: 2.1.3
% 0.16/0.46 % (3442645)Termination reason: Refutation
% 0.16/0.46 % (3442645)Time elapsed: 0.001 s
% 0.16/0.46 % (3442645)Peak memory usage: 11 MB
% 0.16/0.46 % (3442645)Instructions burned: 2 (million)
% 0.16/0.46 % (3442635)Success in time 0.036 s
% 0.16/0.46 % Vampire exiting
%------------------------------------------------------------------------------