%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET877+1 : 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 : n018.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 0.11s 0.44s
% Output : Refutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of formulae : 22 ( 7 unt; 0 def)
% Number of atoms : 63 ( 41 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 67 ( 26 ~; 25 |; 11 &)
% ( 2 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 37 ( 33 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
fof(f3,axiom,
! [X0,X1] :
( X1 = singleton(X0)
<=> ! [X2] :
( in(X2,X1)
<=> X2 = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).
fof(f5,axiom,
! [X0,X1] :
( set_intersection2(X0,singleton(X1)) = singleton(X1)
=> in(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l30_zfmisc_1) ).
fof(f8,conjecture,
! [X0,X1] :
( set_intersection2(singleton(X0),singleton(X1)) = singleton(X0)
=> X0 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t18_zfmisc_1) ).
fof(f9,negated_conjecture,
~ ! [X0,X1] :
( set_intersection2(singleton(X0),singleton(X1)) = singleton(X0)
=> X0 = X1 ),
inference(negated_conjecture,[status(cth)],[f8]) ).
fof(f12,plain,
! [X0,X1] :
( in(X1,X0)
| singleton(X1) != set_intersection2(X0,singleton(X1)) ),
inference(ennf_transformation,[],[f5]) ).
fof(f13,plain,
? [X0,X1] :
( X0 != X1
& set_intersection2(singleton(X0),singleton(X1)) = singleton(X0) ),
inference(ennf_transformation,[],[f9]) ).
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,[],[f3]) ).
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(f19,plain,
( sK3 != sK4
& singleton(sK3) = set_intersection2(singleton(sK3),singleton(sK4)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4]),skolemize(X0,sK3),skolemize(X1,sK4)],[f13]) ).
fof(f21,plain,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
inference(cnf_transformation,[],[f2]) ).
fof(f22,plain,
! [X3,X0,X1] :
( X0 = X3
| ~ in(X3,X1)
| singleton(X0) != X1 ),
inference(cnf_transformation,[],[f16]) ).
fof(f27,plain,
! [X0,X1] :
( singleton(X1) != set_intersection2(X0,singleton(X1))
| in(X1,X0) ),
inference(cnf_transformation,[],[f12]) ).
fof(f30,plain,
singleton(sK3) = set_intersection2(singleton(sK3),singleton(sK4)),
inference(cnf_transformation,[],[f19]) ).
fof(f31,plain,
sK3 != sK4,
inference(cnf_transformation,[],[f19]) ).
fof(f34,plain,
! [X3,X0] :
( ~ in(X3,singleton(X0))
| X0 = X3 ),
inference(equality_resolution,[],[f22]) ).
fof(f104,plain,
! [X0,X1] :
( singleton(X0) != set_intersection2(singleton(X0),X1)
| in(X0,X1) ),
inference(superposition,[],[f27,f21]) ).
fof(f137,plain,
( singleton(sK3) != singleton(sK3)
| in(sK3,singleton(sK4)) ),
inference(superposition,[],[f104,f30]) ).
fof(f142,plain,
in(sK3,singleton(sK4)),
inference(trivial_inequality_removal,[],[f137]) ).
fof(f151,plain,
sK3 = sK4,
inference(resolution,[],[f142,f34]) ).
fof(f153,plain,
$false,
inference(forward_subsumption_resolution,[],[f151,f31]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET877+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.37 % Computer : n018.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 28 03:07:55 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.39 Running first-order model finding
% 0.11/0.39 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
% 0.11/0.44 % (2956407)Will run a generic schedule for satisfiability detection.
% 0.11/0.44 % (2956414)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2628703473:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.11/0.44 % (2956414) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2956407-2956414"...
% 0.11/0.44 % (2956414)...printing done.
% 0.11/0.44 % (2956414)Refutation found. Thanks to Tanya!
% 0.11/0.44 % SZS status Theorem for theBenchmark
% 0.11/0.44 % SZS output start Proof for theBenchmark
% See solution above
% 0.11/0.44 % (2956414)------------------------------
% 0.11/0.44 % (2956414)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.11/0.44 % (2956414)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.11/0.44 % (2956414)CaDiCaL version: 2.1.3
% 0.11/0.44 % (2956414)Termination reason: Refutation
% 0.11/0.44 % (2956414)Time elapsed: 0.002 s
% 0.11/0.44 % (2956414)Peak memory usage: 12 MB
% 0.11/0.44 % (2956414)Instructions burned: 3 (million)
% 0.11/0.44 % (2956407)Success in time 0.032 s
% 0.11/0.44 % Vampire exiting
%------------------------------------------------------------------------------