%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET928+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 : n007.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 0.10s 0.44s
% Output : Refutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 8
% Syntax : Number of formulae : 55 ( 7 unt; 3 def)
% Number of atoms : 135 ( 27 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 141 ( 61 ~; 60 |; 13 &)
% ( 6 <=>; 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 : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 52 ( 0 sgn 43 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(f6,axiom,
! [X0,X1,X2] :
~ ( disjoint(unordered_pair(X0,X1),X2)
& in(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t55_zfmisc_1) ).
fof(f7,axiom,
! [X0,X1,X2] :
~ ( ~ in(X0,X1)
& ~ in(X2,X1)
& ~ disjoint(unordered_pair(X0,X2),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t57_zfmisc_1) ).
fof(f8,conjecture,
! [X0,X1,X2] :
( set_difference(unordered_pair(X0,X1),X2) = unordered_pair(X0,X1)
<=> ( ~ in(X0,X2)
& ~ in(X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t72_zfmisc_1) ).
fof(f9,negated_conjecture,
~ ! [X0,X1,X2] :
( set_difference(unordered_pair(X0,X1),X2) = unordered_pair(X0,X1)
<=> ( ~ in(X0,X2)
& ~ in(X1,X2) ) ),
inference(negated_conjecture,[status(cth)],[f8]) ).
fof(f10,axiom,
! [X0,X1] :
( disjoint(X0,X1)
<=> set_difference(X0,X1) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t83_xboole_1) ).
fof(f13,plain,
! [X0,X1,X2] :
( ~ disjoint(unordered_pair(X0,X1),X2)
| ~ in(X0,X2) ),
inference(ennf_transformation,[],[f6]) ).
fof(f14,plain,
! [X0,X1,X2] :
( in(X0,X1)
| in(X2,X1)
| disjoint(unordered_pair(X0,X2),X1) ),
inference(ennf_transformation,[],[f7]) ).
fof(f15,plain,
? [X0,X1,X2] :
( set_difference(unordered_pair(X0,X1),X2) = unordered_pair(X0,X1)
<~> ( ~ in(X0,X2)
& ~ in(X1,X2) ) ),
inference(ennf_transformation,[],[f9]) ).
fof(f18,plain,
? [X0,X1,X2] :
( ( in(X0,X2)
| in(X1,X2)
| unordered_pair(X0,X1) != set_difference(unordered_pair(X0,X1),X2) )
& ( ( ~ in(X0,X2)
& ~ in(X1,X2) )
| set_difference(unordered_pair(X0,X1),X2) = unordered_pair(X0,X1) ) ),
inference(nnf_transformation,[],[f15]) ).
fof(f19,plain,
? [X0,X1,X2] :
( ( in(X0,X2)
| in(X1,X2)
| unordered_pair(X0,X1) != set_difference(unordered_pair(X0,X1),X2) )
& ( ( ~ in(X0,X2)
& ~ in(X1,X2) )
| set_difference(unordered_pair(X0,X1),X2) = unordered_pair(X0,X1) ) ),
inference(flattening,[],[f18]) ).
fof(f20,plain,
( ( in(sK2,sK4)
| in(sK3,sK4)
| unordered_pair(sK2,sK3) != set_difference(unordered_pair(sK2,sK3),sK4) )
& ( ( ~ in(sK2,sK4)
& ~ in(sK3,sK4) )
| unordered_pair(sK2,sK3) = 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)],[f19]) ).
fof(f21,plain,
! [X0,X1] :
( ( disjoint(X0,X1)
| set_difference(X0,X1) != X0 )
& ( set_difference(X0,X1) = X0
| ~ disjoint(X0,X1) ) ),
inference(nnf_transformation,[],[f10]) ).
fof(f23,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f2]) ).
fof(f27,plain,
! [X2,X0,X1] :
( ~ disjoint(unordered_pair(X0,X1),X2)
| ~ in(X0,X2) ),
inference(cnf_transformation,[],[f13]) ).
fof(f28,plain,
! [X2,X0,X1] :
( disjoint(unordered_pair(X0,X2),X1)
| in(X2,X1)
| in(X0,X1) ),
inference(cnf_transformation,[],[f14]) ).
fof(f29,plain,
( ~ in(sK3,sK4)
| unordered_pair(sK2,sK3) = set_difference(unordered_pair(sK2,sK3),sK4) ),
inference(cnf_transformation,[],[f20]) ).
fof(f30,plain,
( ~ in(sK2,sK4)
| unordered_pair(sK2,sK3) = set_difference(unordered_pair(sK2,sK3),sK4) ),
inference(cnf_transformation,[],[f20]) ).
fof(f31,plain,
( in(sK2,sK4)
| in(sK3,sK4)
| unordered_pair(sK2,sK3) != set_difference(unordered_pair(sK2,sK3),sK4) ),
inference(cnf_transformation,[],[f20]) ).
fof(f32,plain,
! [X0,X1] :
( ~ disjoint(X0,X1)
| set_difference(X0,X1) = X0 ),
inference(cnf_transformation,[],[f21]) ).
fof(f33,plain,
! [X0,X1] :
( set_difference(X0,X1) != X0
| disjoint(X0,X1) ),
inference(cnf_transformation,[],[f21]) ).
fof(f35,definition,
( spl5_1
<=> unordered_pair(sK2,sK3) = set_difference(unordered_pair(sK2,sK3),sK4) ),
introduced(definition,[new_symbols(definition,[spl5_1])],[avatar_definition]) ).
fof(f36,plain,
( unordered_pair(sK2,sK3) != set_difference(unordered_pair(sK2,sK3),sK4)
| spl5_1 ),
inference(avatar_component_clause,[],[f35]) ).
fof(f37,plain,
( unordered_pair(sK2,sK3) = set_difference(unordered_pair(sK2,sK3),sK4)
| ~ spl5_1 ),
inference(avatar_component_clause,[],[f35]) ).
fof(f39,definition,
( spl5_2
<=> in(sK3,sK4) ),
introduced(definition,[new_symbols(definition,[spl5_2])],[avatar_definition]) ).
fof(f41,plain,
( ~ in(sK3,sK4)
| spl5_2 ),
inference(avatar_component_clause,[],[f39]) ).
fof(f42,plain,
( spl5_1
| ~ spl5_2 ),
inference(avatar_split_clause,[],[f29,f39,f35]) ).
fof(f44,definition,
( spl5_3
<=> in(sK2,sK4) ),
introduced(definition,[new_symbols(definition,[spl5_3])],[avatar_definition]) ).
fof(f46,plain,
( ~ in(sK2,sK4)
| spl5_3 ),
inference(avatar_component_clause,[],[f44]) ).
fof(f47,plain,
( spl5_1
| ~ spl5_3 ),
inference(avatar_split_clause,[],[f30,f44,f35]) ).
fof(f48,plain,
( ~ spl5_1
| spl5_2
| spl5_3 ),
inference(avatar_split_clause,[],[f31,f44,f39,f35]) ).
fof(f49,plain,
! [X2,X0,X1] :
( ~ disjoint(unordered_pair(X0,X1),X2)
| ~ in(X1,X2) ),
inference(superposition,[],[f27,f23]) ).
fof(f52,plain,
! [X2,X0,X1] :
( in(X2,X1)
| in(X0,X1)
| unordered_pair(X2,X0) = set_difference(unordered_pair(X2,X0),X1) ),
inference(resolution,[],[f28,f32]) ).
fof(f65,plain,
( ! [X0] :
( in(X0,sK4)
| unordered_pair(sK3,X0) = set_difference(unordered_pair(sK3,X0),sK4) )
| spl5_2 ),
inference(resolution,[],[f52,f41]) ).
fof(f73,plain,
( unordered_pair(sK3,sK2) = set_difference(unordered_pair(sK3,sK2),sK4)
| spl5_2
| spl5_3 ),
inference(resolution,[],[f65,f46]) ).
fof(f75,plain,
( unordered_pair(sK2,sK3) = set_difference(unordered_pair(sK2,sK3),sK4)
| spl5_2
| spl5_3 ),
inference(forward_demodulation,[],[f73,f23]) ).
fof(f76,plain,
( $false
| spl5_1
| spl5_2
| spl5_3 ),
inference(forward_subsumption_resolution,[],[f75,f36]) ).
fof(f77,plain,
( spl5_1
| spl5_2
| spl5_3 ),
inference(avatar_contradiction_clause,[],[f76]) ).
fof(f81,plain,
( unordered_pair(sK2,sK3) != unordered_pair(sK2,sK3)
| disjoint(unordered_pair(sK2,sK3),sK4)
| ~ spl5_1 ),
inference(superposition,[],[f33,f37]) ).
fof(f82,plain,
( disjoint(unordered_pair(sK2,sK3),sK4)
| ~ spl5_1 ),
inference(trivial_inequality_removal,[],[f81]) ).
fof(f83,plain,
( ~ in(sK3,sK4)
| ~ spl5_1 ),
inference(resolution,[],[f82,f49]) ).
fof(f84,plain,
( ~ in(sK2,sK4)
| ~ spl5_1 ),
inference(resolution,[],[f82,f27]) ).
fof(f89,plain,
( ~ spl5_3
| ~ spl5_1 ),
inference(avatar_split_clause,[],[f84,f35,f44]) ).
fof(f90,plain,
( ~ spl5_2
| ~ spl5_1 ),
inference(avatar_split_clause,[],[f83,f35,f39]) ).
cnf(s1,plain,
( spl5_1
| ~ spl5_2 ),
inference(sat_conversion,[],[f42]) ).
cnf(s2,plain,
( spl5_1
| ~ spl5_3 ),
inference(sat_conversion,[],[f47]) ).
cnf(s3,plain,
( ~ spl5_1
| spl5_2
| spl5_3 ),
inference(sat_conversion,[],[f48]) ).
cnf(s4,plain,
( spl5_1
| spl5_2
| spl5_3 ),
inference(sat_conversion,[],[f77]) ).
cnf(s6,plain,
( ~ spl5_1
| ~ spl5_3 ),
inference(sat_conversion,[],[f89]) ).
cnf(s7,plain,
( ~ spl5_1
| ~ spl5_2 ),
inference(sat_conversion,[],[f90]) ).
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,s10,s9,s8]) ).
fof(f91,plain,
$false,
inference(avatar_sat_refutation,[],[s11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET928+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.37 % Computer : n007.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 28 03:09:26 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.40 Running first-order model finding
% 0.10/0.40 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
% 0.10/0.44 % (1992512)Will run a generic schedule for satisfiability detection.
% 0.10/0.44 % (1992520)dis+10_1_sil=32000:sp=arity:random_seed=62914598:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.10/0.44 % (1992520) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1992512-1992520"...
% 0.10/0.44 % (1992520)...printing done.
% 0.10/0.44 % (1992520)Refutation found. Thanks to Tanya!
% 0.10/0.44 % SZS status Theorem for theBenchmark
% 0.10/0.44 % SZS output start Proof for theBenchmark
% See solution above
% 0.10/0.44 % (1992520)------------------------------
% 0.10/0.44 % (1992520)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.10/0.44 % (1992520)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.10/0.44 % (1992520)CaDiCaL version: 2.1.3
% 0.10/0.44 % (1992520)Termination reason: Refutation
% 0.10/0.44 % (1992520)Time elapsed: 0.002 s
% 0.10/0.44 % (1992520)Peak memory usage: 12 MB
% 0.10/0.44 % (1992520)Instructions burned: 3 (million)
% 0.10/0.44 % (1992512)Success in time 0.034 s
% 0.10/0.44 % Vampire exiting
%------------------------------------------------------------------------------