%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET918+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 : n002.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 12:44:59 PM UTC 2026
% Result : Theorem 0.10s 0.45s
% Output : Refutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 24 ( 10 unt; 0 def)
% Number of atoms : 52 ( 25 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 49 ( 21 ~; 15 |; 7 &)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 46 ( 43 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
fof(f4,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,X2] :
( X2 = unordered_pair(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( X3 = X0
| X3 = X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_tarski) ).
fof(f6,axiom,
! [X0,X1,X2] :
( X2 = set_intersection2(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X0)
& in(X3,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_xboole_0) ).
fof(f10,conjecture,
! [X0,X1,X2] :
~ ( set_intersection2(unordered_pair(X0,X1),X2) = singleton(X0)
& in(X1,X2)
& X0 != X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t59_zfmisc_1) ).
fof(f11,negated_conjecture,
~ ! [X0,X1,X2] :
~ ( set_intersection2(unordered_pair(X0,X1),X2) = singleton(X0)
& in(X1,X2)
& X0 != X1 ),
inference(negated_conjecture,[status(cth)],[f10]) ).
fof(f14,plain,
? [X0,X1,X2] :
( set_intersection2(unordered_pair(X0,X1),X2) = singleton(X0)
& in(X1,X2)
& X0 != X1 ),
inference(ennf_transformation,[],[f11]) ).
fof(f17,plain,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
inference(cnf_transformation,[],[f3]) ).
fof(f19,plain,
! [X2,X0,X1] :
( X0 = X2
| ~ in(X2,X1)
| singleton(X0) != X1 ),
inference(cnf_transformation,[],[f4]) ).
fof(f26,plain,
! [X2,X3,X0,X1] :
( X1 != X3
| in(X3,X2)
| unordered_pair(X0,X1) != X2 ),
inference(cnf_transformation,[],[f5]) ).
fof(f33,plain,
! [X2,X3,X0,X1] :
( ~ in(X3,X1)
| ~ in(X3,X0)
| in(X3,X2)
| set_intersection2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f6]) ).
fof(f37,plain,
sK5 != sK6,
inference(cnf_transformation,[],[f14]) ).
fof(f38,plain,
in(sK6,sK7),
inference(cnf_transformation,[],[f14]) ).
fof(f39,plain,
singleton(sK5) = set_intersection2(unordered_pair(sK5,sK6),sK7),
inference(cnf_transformation,[],[f14]) ).
fof(f40,plain,
! [X2,X0] :
( ~ in(X2,singleton(X0))
| X0 = X2 ),
inference(equality_resolution,[],[f19]) ).
fof(f45,plain,
! [X2,X3,X0] :
( in(X3,X2)
| unordered_pair(X0,X3) != X2 ),
inference(equality_resolution,[],[f26]) ).
fof(f46,plain,
! [X3,X0] : in(X3,unordered_pair(X0,X3)),
inference(equality_resolution,[],[f45]) ).
fof(f48,plain,
! [X3,X0,X1] :
( in(X3,set_intersection2(X0,X1))
| ~ in(X3,X0)
| ~ in(X3,X1) ),
inference(equality_resolution,[],[f33]) ).
fof(f58,plain,
singleton(sK5) = set_intersection2(sK7,unordered_pair(sK5,sK6)),
inference(superposition,[],[f39,f17]) ).
fof(f83,plain,
! [X0] :
( ~ in(X0,unordered_pair(sK5,sK6))
| ~ in(X0,sK7)
| in(X0,singleton(sK5)) ),
inference(superposition,[],[f48,f58]) ).
fof(f145,plain,
( ~ in(sK6,sK7)
| in(sK6,singleton(sK5)) ),
inference(resolution,[],[f83,f46]) ).
fof(f151,plain,
in(sK6,singleton(sK5)),
inference(forward_subsumption_resolution,[],[f145,f38]) ).
fof(f165,plain,
sK5 = sK6,
inference(resolution,[],[f151,f40]) ).
fof(f166,plain,
$false,
inference(forward_subsumption_resolution,[],[f165,f37]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET918+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.38 % Computer : n002.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 03:13:07 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.41 Running first-order model finding
% 0.10/0.41 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
% 0.10/0.45 % (4117851)Will run a generic schedule for satisfiability detection.
% 0.10/0.45 % (4117860)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3573955909:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.10/0.45 % (4117857)% WARNING: option uhcvi not known.
% 0.10/0.45 % (4117860) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-4117851-4117860"...
% 0.10/0.45 % (4117860)...printing done.
% 0.10/0.45 % (4117860)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 % (4117860)------------------------------
% 0.10/0.45 % (4117860)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.10/0.45 % (4117860)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.10/0.45 % (4117860)CaDiCaL version: 2.1.3
% 0.10/0.45 % (4117860)Termination reason: Refutation
% 0.10/0.45 % (4117860)Time elapsed: 0.004 s
% 0.10/0.45 % (4117860)Peak memory usage: 12 MB
% 0.10/0.45 % (4117860)Instructions burned: 9 (million)
% 0.10/0.45 % (4117851)Success in time 0.029 s
% 0.10/0.45 % Vampire exiting
%------------------------------------------------------------------------------