%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET923+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 : n009.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 12:45:00 PM UTC 2026
% Result : Theorem 0.17s 0.46s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 3
% Syntax : Number of formulae : 19 ( 6 unt; 0 def)
% Number of atoms : 48 ( 35 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 53 ( 24 ~; 14 |; 13 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 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; 3 con; 0-2 aty)
% Number of variables : 20 ( 18 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1] :
( subset(X0,singleton(X1))
<=> ( X0 = empty_set
| X0 = singleton(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l4_zfmisc_1) ).
fof(f6,axiom,
! [X0,X1] :
( set_difference(X0,X1) = empty_set
<=> subset(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_xboole_1) ).
fof(f7,conjecture,
! [X0,X1] :
~ ( set_difference(X0,singleton(X1)) = empty_set
& X0 != empty_set
& X0 != singleton(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t66_zfmisc_1) ).
fof(f8,negated_conjecture,
~ ! [X0,X1] :
~ ( set_difference(X0,singleton(X1)) = empty_set
& X0 != empty_set
& X0 != singleton(X1) ),
inference(negated_conjecture,[status(cth)],[f7]) ).
fof(f10,plain,
? [X0,X1] :
( set_difference(X0,singleton(X1)) = empty_set
& X0 != empty_set
& X0 != singleton(X1) ),
inference(ennf_transformation,[],[f8]) ).
fof(f11,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,[],[f2]) ).
fof(f12,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,[],[f11]) ).
fof(f15,plain,
! [X0,X1] :
( ( set_difference(X0,X1) = empty_set
| ~ subset(X0,X1) )
& ( subset(X0,X1)
| empty_set != set_difference(X0,X1) ) ),
inference(nnf_transformation,[],[f6]) ).
fof(f16,plain,
( empty_set = set_difference(sK2,singleton(sK3))
& empty_set != sK2
& sK2 != singleton(sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3]),skolemize(X0,sK2),skolemize(X1,sK3)],[f10]) ).
fof(f18,plain,
! [X0,X1] :
( ~ subset(X0,singleton(X1))
| singleton(X1) = X0
| empty_set = X0 ),
inference(cnf_transformation,[],[f12]) ).
fof(f24,plain,
! [X0,X1] :
( empty_set != set_difference(X0,X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f15]) ).
fof(f26,plain,
sK2 != singleton(sK3),
inference(cnf_transformation,[],[f16]) ).
fof(f27,plain,
empty_set != sK2,
inference(cnf_transformation,[],[f16]) ).
fof(f28,plain,
empty_set = set_difference(sK2,singleton(sK3)),
inference(cnf_transformation,[],[f16]) ).
fof(f37,plain,
( empty_set != empty_set
| subset(sK2,singleton(sK3)) ),
inference(superposition,[],[f24,f28]) ).
fof(f38,plain,
subset(sK2,singleton(sK3)),
inference(trivial_inequality_removal,[],[f37]) ).
fof(f142,plain,
( sK2 = singleton(sK3)
| empty_set = sK2 ),
inference(resolution,[],[f18,f38]) ).
fof(f143,plain,
empty_set = sK2,
inference(forward_subsumption_resolution,[],[f142,f26]) ).
fof(f144,plain,
$false,
inference(forward_subsumption_resolution,[],[f143,f27]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET923+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.39 % Computer : n009.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Mon Sep 28 03:10:01 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.42 Running first-order model finding
% 0.12/0.42 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
% 0.17/0.46 % (2628107)Will run a generic schedule for satisfiability detection.
% 0.17/0.46 % (2628114)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1863661290:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.17/0.46 % (2628114) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2628107-2628114"...
% 0.17/0.46 % (2628114)...printing done.
% 0.17/0.46 % (2628113)% WARNING: option uhcvi not known.
% 0.17/0.46 % (2628114)Refutation found. Thanks to Tanya!
% 0.17/0.46 % SZS status Theorem for theBenchmark
% 0.17/0.46 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/0.46 % (2628114)------------------------------
% 0.17/0.46 % (2628114)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.17/0.46 % (2628114)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/0.46 % (2628114)CaDiCaL version: 2.1.3
% 0.17/0.46 % (2628114)Termination reason: Refutation
% 0.17/0.46 % (2628114)Time elapsed: 0.002 s
% 0.17/0.46 % (2628114)Peak memory usage: 12 MB
% 0.17/0.46 % (2628114)Instructions burned: 3 (million)
% 0.17/0.46 % (2628107)Success in time 0.029 s
% 0.17/0.46 % Vampire exiting
%------------------------------------------------------------------------------