%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET925+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 : n017.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 0.19s 0.46s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 4
% Syntax : Number of formulae : 34 ( 4 unt; 2 def)
% Number of atoms : 73 ( 19 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 68 ( 29 ~; 30 |; 3 &)
% ( 5 <=>; 0 =>; 0 <=; 1 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 3 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 16 ( 0 sgn 12 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,conjecture,
! [X0,X1] :
( set_difference(singleton(X0),X1) = empty_set
<=> in(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t68_zfmisc_1) ).
fof(f6,negated_conjecture,
~ ! [X0,X1] :
( set_difference(singleton(X0),X1) = empty_set
<=> in(X0,X1) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
fof(f7,axiom,
! [X0,X1] :
( set_difference(singleton(X0),X1) = empty_set
<=> in(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l36_zfmisc_1) ).
fof(f9,plain,
? [X0,X1] :
( set_difference(singleton(X0),X1) = empty_set
<~> in(X0,X1) ),
inference(ennf_transformation,[],[f6]) ).
fof(f12,plain,
? [X0,X1] :
( ( ~ in(X0,X1)
| empty_set != set_difference(singleton(X0),X1) )
& ( in(X0,X1)
| set_difference(singleton(X0),X1) = empty_set ) ),
inference(nnf_transformation,[],[f9]) ).
fof(f13,plain,
( ( ~ in(sK2,sK3)
| empty_set != set_difference(singleton(sK2),sK3) )
& ( in(sK2,sK3)
| empty_set = set_difference(singleton(sK2),sK3) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3]),skolemize(X0,sK2),skolemize(X1,sK3)],[f12]) ).
fof(f14,plain,
! [X0,X1] :
( ( set_difference(singleton(X0),X1) = empty_set
| ~ in(X0,X1) )
& ( in(X0,X1)
| empty_set != set_difference(singleton(X0),X1) ) ),
inference(nnf_transformation,[],[f7]) ).
fof(f19,plain,
( in(sK2,sK3)
| empty_set = set_difference(singleton(sK2),sK3) ),
inference(cnf_transformation,[],[f13]) ).
fof(f20,plain,
( ~ in(sK2,sK3)
| empty_set != set_difference(singleton(sK2),sK3) ),
inference(cnf_transformation,[],[f13]) ).
fof(f21,plain,
! [X0,X1] :
( empty_set != set_difference(singleton(X0),X1)
| in(X0,X1) ),
inference(cnf_transformation,[],[f14]) ).
fof(f22,plain,
! [X0,X1] :
( ~ in(X0,X1)
| empty_set = set_difference(singleton(X0),X1) ),
inference(cnf_transformation,[],[f14]) ).
fof(f24,definition,
( spl4_1
<=> empty_set = set_difference(singleton(sK2),sK3) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
fof(f25,plain,
( empty_set != set_difference(singleton(sK2),sK3)
| spl4_1 ),
inference(avatar_component_clause,[],[f24]) ).
fof(f26,plain,
( empty_set = set_difference(singleton(sK2),sK3)
| ~ spl4_1 ),
inference(avatar_component_clause,[],[f24]) ).
fof(f28,definition,
( spl4_2
<=> in(sK2,sK3) ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
fof(f29,plain,
( ~ in(sK2,sK3)
| spl4_2 ),
inference(avatar_component_clause,[],[f28]) ).
fof(f30,plain,
( in(sK2,sK3)
| ~ spl4_2 ),
inference(avatar_component_clause,[],[f28]) ).
fof(f31,plain,
( spl4_1
| spl4_2 ),
inference(avatar_split_clause,[],[f19,f28,f24]) ).
fof(f32,plain,
( ~ spl4_1
| ~ spl4_2 ),
inference(avatar_split_clause,[],[f20,f28,f24]) ).
fof(f34,plain,
( empty_set = set_difference(singleton(sK2),sK3)
| ~ spl4_2 ),
inference(resolution,[],[f22,f30]) ).
fof(f35,plain,
( $false
| spl4_1
| ~ spl4_2 ),
inference(forward_subsumption_resolution,[],[f34,f25]) ).
fof(f36,plain,
( spl4_1
| ~ spl4_2 ),
inference(avatar_contradiction_clause,[],[f35]) ).
fof(f37,plain,
( empty_set != empty_set
| in(sK2,sK3)
| ~ spl4_1 ),
inference(superposition,[],[f21,f26]) ).
fof(f38,plain,
( in(sK2,sK3)
| ~ spl4_1 ),
inference(trivial_inequality_removal,[],[f37]) ).
fof(f39,plain,
( $false
| ~ spl4_1
| spl4_2 ),
inference(forward_subsumption_resolution,[],[f38,f29]) ).
fof(f40,plain,
( ~ spl4_1
| spl4_2 ),
inference(avatar_contradiction_clause,[],[f39]) ).
cnf(s1,plain,
( spl4_1
| spl4_2 ),
inference(sat_conversion,[],[f31]) ).
cnf(s2,plain,
( ~ spl4_1
| ~ spl4_2 ),
inference(sat_conversion,[],[f32]) ).
cnf(s3,plain,
( spl4_1
| ~ spl4_2 ),
inference(sat_conversion,[],[f36]) ).
cnf(s4,plain,
( ~ spl4_1
| spl4_2 ),
inference(sat_conversion,[],[f40]) ).
cnf(s5,plain,
spl4_1,
inference(rat,[],[s1,s3]) ).
cnf(s6,plain,
spl4_2,
inference(rat,[],[s4,s5]) ).
cnf(s7,plain,
$false,
inference(rat,[],[s2,s6,s5]) ).
fof(f41,plain,
$false,
inference(avatar_sat_refutation,[],[s7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET925+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.39 % Computer : n017.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 03:06:21 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.43 Running first-order model finding
% 0.12/0.43 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
% 0.19/0.46 % (3171890)Will run a generic schedule for satisfiability detection.
% 0.19/0.46 % (3171898)dis+10_1_sil=32000:sp=arity:random_seed=452793728:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.19/0.46 % (3171898) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3171890-3171898"...
% 0.19/0.46 % (3171898)...printing done.
% 0.19/0.46 % (3171896)% WARNING: option uhcvi not known.
% 0.19/0.46 % (3171898)Refutation found. Thanks to Tanya!
% 0.19/0.46 % SZS status Theorem for theBenchmark
% 0.19/0.46 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.46 % (3171898)------------------------------
% 0.19/0.46 % (3171898)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.46 % (3171898)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.46 % (3171898)CaDiCaL version: 2.1.3
% 0.19/0.46 % (3171898)Termination reason: Refutation
% 0.19/0.46 % (3171898)Time elapsed: 0.001 s
% 0.19/0.46 % (3171898)Peak memory usage: 12 MB
% 0.19/0.46 % (3171898)Instructions burned: 1 (million)
% 0.19/0.46 % (3171890)Success in time 0.025 s
% 0.19/0.46 % Vampire exiting
%------------------------------------------------------------------------------