%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET929+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 : n011.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 12:45:01 PM UTC 2026
% Result : Theorem 0.13s 0.45s
% Output : Refutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 6
% Syntax : Number of formulae : 51 ( 5 unt; 3 def)
% Number of atoms : 135 ( 24 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 142 ( 58 ~; 61 |; 15 &)
% ( 7 <=>; 0 =>; 0 <=; 1 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 4 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 45 ( 0 sgn 36 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
! [X0,X1] :
( set_difference(X0,X1) = empty_set
<=> subset(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_xboole_1) ).
fof(f8,axiom,
! [X0,X1,X2] :
( subset(unordered_pair(X0,X1),X2)
<=> ( in(X0,X2)
& in(X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t38_zfmisc_1) ).
fof(f9,conjecture,
! [X0,X1,X2] :
( set_difference(unordered_pair(X0,X1),X2) = empty_set
<=> ( in(X0,X2)
& in(X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t73_zfmisc_1) ).
fof(f10,negated_conjecture,
~ ! [X0,X1,X2] :
( set_difference(unordered_pair(X0,X1),X2) = empty_set
<=> ( in(X0,X2)
& in(X1,X2) ) ),
inference(negated_conjecture,[status(cth)],[f9]) ).
fof(f13,plain,
? [X0,X1,X2] :
( set_difference(unordered_pair(X0,X1),X2) = empty_set
<~> ( in(X0,X2)
& in(X1,X2) ) ),
inference(ennf_transformation,[],[f10]) ).
fof(f16,plain,
! [X0,X1] :
( ( set_difference(X0,X1) = empty_set
| ~ subset(X0,X1) )
& ( subset(X0,X1)
| empty_set != set_difference(X0,X1) ) ),
inference(nnf_transformation,[],[f7]) ).
fof(f17,plain,
! [X0,X1,X2] :
( ( subset(unordered_pair(X0,X1),X2)
| ~ in(X0,X2)
| ~ in(X1,X2) )
& ( ( in(X0,X2)
& in(X1,X2) )
| ~ subset(unordered_pair(X0,X1),X2) ) ),
inference(nnf_transformation,[],[f8]) ).
fof(f18,plain,
! [X0,X1,X2] :
( ( subset(unordered_pair(X0,X1),X2)
| ~ in(X0,X2)
| ~ in(X1,X2) )
& ( ( in(X0,X2)
& in(X1,X2) )
| ~ subset(unordered_pair(X0,X1),X2) ) ),
inference(flattening,[],[f17]) ).
fof(f19,plain,
? [X0,X1,X2] :
( ( ~ in(X0,X2)
| ~ in(X1,X2)
| empty_set != set_difference(unordered_pair(X0,X1),X2) )
& ( ( in(X0,X2)
& in(X1,X2) )
| set_difference(unordered_pair(X0,X1),X2) = empty_set ) ),
inference(nnf_transformation,[],[f13]) ).
fof(f20,plain,
? [X0,X1,X2] :
( ( ~ in(X0,X2)
| ~ in(X1,X2)
| empty_set != set_difference(unordered_pair(X0,X1),X2) )
& ( ( in(X0,X2)
& in(X1,X2) )
| set_difference(unordered_pair(X0,X1),X2) = empty_set ) ),
inference(flattening,[],[f19]) ).
fof(f21,plain,
( ( ~ in(sK2,sK4)
| ~ in(sK3,sK4)
| empty_set != set_difference(unordered_pair(sK2,sK3),sK4) )
& ( ( in(sK2,sK4)
& in(sK3,sK4) )
| empty_set = set_difference(unordered_pair(sK2,sK3),sK4) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4]),skolemize(X0,sK2),skolemize(X1,sK3),skolemize(X2,sK4)],[f20]) ).
fof(f28,plain,
! [X0,X1] :
( empty_set != set_difference(X0,X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f16]) ).
fof(f29,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| empty_set = set_difference(X0,X1) ),
inference(cnf_transformation,[],[f16]) ).
fof(f30,plain,
! [X2,X0,X1] :
( ~ subset(unordered_pair(X0,X1),X2)
| in(X1,X2) ),
inference(cnf_transformation,[],[f18]) ).
fof(f31,plain,
! [X2,X0,X1] :
( ~ subset(unordered_pair(X0,X1),X2)
| in(X0,X2) ),
inference(cnf_transformation,[],[f18]) ).
fof(f32,plain,
! [X2,X0,X1] :
( subset(unordered_pair(X0,X1),X2)
| ~ in(X0,X2)
| ~ in(X1,X2) ),
inference(cnf_transformation,[],[f18]) ).
fof(f33,plain,
( in(sK3,sK4)
| empty_set = set_difference(unordered_pair(sK2,sK3),sK4) ),
inference(cnf_transformation,[],[f21]) ).
fof(f34,plain,
( in(sK2,sK4)
| empty_set = set_difference(unordered_pair(sK2,sK3),sK4) ),
inference(cnf_transformation,[],[f21]) ).
fof(f35,plain,
( ~ in(sK2,sK4)
| ~ in(sK3,sK4)
| empty_set != set_difference(unordered_pair(sK2,sK3),sK4) ),
inference(cnf_transformation,[],[f21]) ).
fof(f37,definition,
( spl5_1
<=> empty_set = set_difference(unordered_pair(sK2,sK3),sK4) ),
introduced(definition,[new_symbols(definition,[spl5_1])],[avatar_definition]) ).
fof(f38,plain,
( empty_set != set_difference(unordered_pair(sK2,sK3),sK4)
| spl5_1 ),
inference(avatar_component_clause,[],[f37]) ).
fof(f39,plain,
( empty_set = set_difference(unordered_pair(sK2,sK3),sK4)
| ~ spl5_1 ),
inference(avatar_component_clause,[],[f37]) ).
fof(f41,definition,
( spl5_2
<=> in(sK3,sK4) ),
introduced(definition,[new_symbols(definition,[spl5_2])],[avatar_definition]) ).
fof(f43,plain,
( in(sK3,sK4)
| ~ spl5_2 ),
inference(avatar_component_clause,[],[f41]) ).
fof(f44,plain,
( spl5_1
| spl5_2 ),
inference(avatar_split_clause,[],[f33,f41,f37]) ).
fof(f46,definition,
( spl5_3
<=> in(sK2,sK4) ),
introduced(definition,[new_symbols(definition,[spl5_3])],[avatar_definition]) ).
fof(f48,plain,
( in(sK2,sK4)
| ~ spl5_3 ),
inference(avatar_component_clause,[],[f46]) ).
fof(f49,plain,
( spl5_1
| spl5_3 ),
inference(avatar_split_clause,[],[f34,f46,f37]) ).
fof(f50,plain,
( ~ spl5_1
| ~ spl5_2
| ~ spl5_3 ),
inference(avatar_split_clause,[],[f35,f46,f41,f37]) ).
fof(f67,plain,
! [X2,X0,X1] :
( ~ in(X2,X1)
| ~ in(X0,X1)
| empty_set = set_difference(unordered_pair(X0,X2),X1) ),
inference(resolution,[],[f32,f29]) ).
fof(f75,plain,
( ! [X0] :
( ~ in(X0,sK4)
| empty_set = set_difference(unordered_pair(X0,sK3),sK4) )
| ~ spl5_2 ),
inference(resolution,[],[f67,f43]) ).
fof(f80,plain,
( empty_set = set_difference(unordered_pair(sK2,sK3),sK4)
| ~ spl5_2
| ~ spl5_3 ),
inference(resolution,[],[f75,f48]) ).
fof(f81,plain,
( $false
| spl5_1
| ~ spl5_2
| ~ spl5_3 ),
inference(forward_subsumption_resolution,[],[f80,f38]) ).
fof(f82,plain,
( spl5_1
| ~ spl5_2
| ~ spl5_3 ),
inference(avatar_contradiction_clause,[],[f81]) ).
fof(f83,plain,
( empty_set != empty_set
| subset(unordered_pair(sK2,sK3),sK4)
| ~ spl5_1 ),
inference(superposition,[],[f28,f39]) ).
fof(f84,plain,
( subset(unordered_pair(sK2,sK3),sK4)
| ~ spl5_1 ),
inference(trivial_inequality_removal,[],[f83]) ).
fof(f85,plain,
( in(sK2,sK4)
| ~ spl5_1 ),
inference(resolution,[],[f84,f31]) ).
fof(f86,plain,
( in(sK3,sK4)
| ~ spl5_1 ),
inference(resolution,[],[f84,f30]) ).
fof(f90,plain,
( spl5_3
| ~ spl5_1 ),
inference(avatar_split_clause,[],[f85,f37,f46]) ).
fof(f91,plain,
( spl5_2
| ~ spl5_1 ),
inference(avatar_split_clause,[],[f86,f37,f41]) ).
cnf(s1,plain,
( spl5_1
| spl5_2 ),
inference(sat_conversion,[],[f44]) ).
cnf(s2,plain,
( spl5_1
| spl5_3 ),
inference(sat_conversion,[],[f49]) ).
cnf(s3,plain,
( ~ spl5_1
| ~ spl5_2
| ~ spl5_3 ),
inference(sat_conversion,[],[f50]) ).
cnf(s4,plain,
( spl5_1
| ~ spl5_2
| ~ spl5_3 ),
inference(sat_conversion,[],[f82]) ).
cnf(s6,plain,
( ~ spl5_1
| spl5_3 ),
inference(sat_conversion,[],[f90]) ).
cnf(s7,plain,
( ~ spl5_1
| spl5_2 ),
inference(sat_conversion,[],[f91]) ).
cnf(s8,plain,
spl5_1,
inference(rat,[],[s4,s1,s2]) ).
cnf(s9,plain,
spl5_2,
inference(rat,[],[s7,s8]) ).
cnf(s10,plain,
spl5_3,
inference(rat,[],[s6,s8]) ).
cnf(s11,plain,
$false,
inference(rat,[],[s3,s9,s10,s8]) ).
fof(f92,plain,
$false,
inference(avatar_sat_refutation,[],[s11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET929+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.13/0.37 % Computer : n011.cluster.edu
% 0.13/0.37 % Model : x86_64 x86_64
% 0.13/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.37 % Memory : 8046.5625MB
% 0.13/0.37 % OS : Linux 6.8.0-71-generic
% 0.13/0.37 % CPULimit : 300
% 0.13/0.37 % WCLimit : 300
% 0.13/0.37 % DateTime : Mon Sep 28 03:11:30 UTC 2026
% 0.13/0.38 % CPUTime :
% 0.13/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.13/0.41 Running first-order model finding
% 0.13/0.41 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
% 0.13/0.45 % (2981263)Will run a generic schedule for satisfiability detection.
% 0.13/0.45 % (2981271)dis+10_1_sil=32000:sp=arity:random_seed=1833406218:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.13/0.45 % (2981271) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2981263-2981271"...
% 0.13/0.45 % (2981271)...printing done.
% 0.13/0.45 % (2981271)Refutation found. Thanks to Tanya!
% 0.13/0.45 % SZS status Theorem for theBenchmark
% 0.13/0.45 % SZS output start Proof for theBenchmark
% See solution above
% 0.13/0.45 % (2981271)------------------------------
% 0.13/0.45 % (2981271)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.13/0.45 % (2981271)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.13/0.45 % (2981271)CaDiCaL version: 2.1.3
% 0.13/0.45 % (2981271)Termination reason: Refutation
% 0.13/0.45 % (2981271)Time elapsed: 0.002 s
% 0.13/0.45 % (2981271)Peak memory usage: 12 MB
% 0.13/0.45 % (2981271)Instructions burned: 3 (million)
% 0.13/0.45 % (2981263)Success in time 0.037 s
% 0.13/0.45 % Vampire exiting
%------------------------------------------------------------------------------