%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET047+1 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n010.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 12:42:48 PM UTC 2026
% Result : Theorem 0.13s 0.42s
% Output : Refutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 4
% Syntax : Number of formulae : 61 ( 5 unt; 2 def)
% Number of atoms : 202 ( 0 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 235 ( 94 ~; 123 |; 11 &)
% ( 6 <=>; 0 =>; 0 <=; 1 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 70 ( 0 sgn 64 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( set_equal(X0,X1)
<=> ! [X2] :
( element(X2,X0)
<=> element(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel43_1) ).
fof(f2,conjecture,
! [X0,X1] :
( set_equal(X0,X1)
<=> set_equal(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel43) ).
fof(f3,negated_conjecture,
~ ! [X0,X1] :
( set_equal(X0,X1)
<=> set_equal(X1,X0) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
fof(f4,plain,
? [X0,X1] :
( set_equal(X0,X1)
<~> set_equal(X1,X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f5,plain,
! [X0,X1] :
( ( set_equal(X0,X1)
| ? [X2] :
( ( ~ element(X2,X1)
| ~ element(X2,X0) )
& ( element(X2,X1)
| element(X2,X0) ) ) )
& ( ! [X2] :
( ( element(X2,X0)
| ~ element(X2,X1) )
& ( element(X2,X1)
| ~ element(X2,X0) ) )
| ~ set_equal(X0,X1) ) ),
inference(nnf_transformation,[],[f1]) ).
fof(f6,plain,
! [X0,X1] :
( ( set_equal(X0,X1)
| ? [X2] :
( ( ~ element(X2,X1)
| ~ element(X2,X0) )
& ( element(X2,X1)
| element(X2,X0) ) ) )
& ( ! [X3] :
( ( element(X3,X0)
| ~ element(X3,X1) )
& ( element(X3,X1)
| ~ element(X3,X0) ) )
| ~ set_equal(X0,X1) ) ),
inference(rectify,[],[f5]) ).
fof(f7,plain,
! [X0,X1] :
( ( set_equal(X0,X1)
| ( ( ~ element(sK0(X0,X1),X1)
| ~ element(sK0(X0,X1),X0) )
& ( element(sK0(X0,X1),X1)
| element(sK0(X0,X1),X0) ) ) )
& ( ! [X3] :
( ( element(X3,X0)
| ~ element(X3,X1) )
& ( element(X3,X1)
| ~ element(X3,X0) ) )
| ~ set_equal(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0,X1))],[f6]) ).
fof(f8,plain,
? [X0,X1] :
( ( ~ set_equal(X1,X0)
| ~ set_equal(X0,X1) )
& ( set_equal(X1,X0)
| set_equal(X0,X1) ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f9,plain,
( ( ~ set_equal(sK2,sK1)
| ~ set_equal(sK1,sK2) )
& ( set_equal(sK2,sK1)
| set_equal(sK1,sK2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2]),skolemize(X0,sK1),skolemize(X1,sK2)],[f8]) ).
fof(f10,plain,
! [X3,X0,X1] :
( ~ element(X3,X0)
| element(X3,X1)
| ~ set_equal(X0,X1) ),
inference(cnf_transformation,[],[f7]) ).
fof(f11,plain,
! [X3,X0,X1] :
( ~ element(X3,X1)
| element(X3,X0)
| ~ set_equal(X0,X1) ),
inference(cnf_transformation,[],[f7]) ).
fof(f12,plain,
! [X0,X1] :
( element(sK0(X0,X1),X1)
| element(sK0(X0,X1),X0)
| set_equal(X0,X1) ),
inference(cnf_transformation,[],[f7]) ).
fof(f13,plain,
! [X0,X1] :
( ~ element(sK0(X0,X1),X1)
| set_equal(X0,X1)
| ~ element(sK0(X0,X1),X0) ),
inference(cnf_transformation,[],[f7]) ).
fof(f14,plain,
( set_equal(sK2,sK1)
| set_equal(sK1,sK2) ),
inference(cnf_transformation,[],[f9]) ).
fof(f15,plain,
( ~ set_equal(sK2,sK1)
| ~ set_equal(sK1,sK2) ),
inference(cnf_transformation,[],[f9]) ).
fof(f17,definition,
( spl3_1
<=> set_equal(sK1,sK2) ),
introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition]) ).
fof(f18,plain,
( ~ set_equal(sK1,sK2)
| spl3_1 ),
inference(avatar_component_clause,[],[f17]) ).
fof(f19,plain,
( set_equal(sK1,sK2)
| ~ spl3_1 ),
inference(avatar_component_clause,[],[f17]) ).
fof(f21,definition,
( spl3_2
<=> set_equal(sK2,sK1) ),
introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition]) ).
fof(f22,plain,
( ~ set_equal(sK2,sK1)
| spl3_2 ),
inference(avatar_component_clause,[],[f21]) ).
fof(f23,plain,
( set_equal(sK2,sK1)
| ~ spl3_2 ),
inference(avatar_component_clause,[],[f21]) ).
fof(f24,plain,
( spl3_1
| spl3_2 ),
inference(avatar_split_clause,[],[f14,f21,f17]) ).
fof(f25,plain,
( ~ spl3_1
| ~ spl3_2 ),
inference(avatar_split_clause,[],[f15,f21,f17]) ).
fof(f26,plain,
! [X2,X0,X1] :
( element(sK0(X0,X1),X2)
| element(sK0(X0,X1),X0)
| set_equal(X0,X1)
| ~ set_equal(X2,X1) ),
inference(resolution,[],[f12,f11]) ).
fof(f27,plain,
! [X2,X0,X1] :
( element(sK0(X0,X1),X2)
| element(sK0(X0,X1),X0)
| set_equal(X0,X1)
| ~ set_equal(X1,X2) ),
inference(resolution,[],[f12,f10]) ).
fof(f28,plain,
! [X2,X0,X1] :
( element(sK0(X0,X1),X2)
| element(sK0(X0,X1),X1)
| set_equal(X0,X1)
| ~ set_equal(X2,X0) ),
inference(resolution,[],[f12,f11]) ).
fof(f30,plain,
! [X0] :
( element(sK0(X0,X0),X0)
| set_equal(X0,X0) ),
inference(factoring,[],[f12]) ).
fof(f33,plain,
! [X0] :
( set_equal(X0,X0)
| set_equal(X0,X0)
| ~ element(sK0(X0,X0),X0) ),
inference(resolution,[],[f30,f13]) ).
fof(f36,plain,
! [X0] :
( set_equal(X0,X0)
| ~ element(sK0(X0,X0),X0) ),
inference(duplicate_literal_removal,[],[f33]) ).
fof(f37,plain,
! [X0] : set_equal(X0,X0),
inference(forward_subsumption_resolution,[],[f36,f30]) ).
fof(f40,plain,
! [X2,X3,X0,X1] :
( ~ set_equal(X2,X3)
| set_equal(X0,X1)
| ~ set_equal(X2,X1)
| element(sK0(X0,X1),X3)
| element(sK0(X0,X1),X0) ),
inference(resolution,[],[f26,f10]) ).
fof(f54,plain,
! [X0,X1] :
( element(sK0(X0,X1),X0)
| set_equal(X0,X1)
| ~ set_equal(X1,X0) ),
inference(factoring,[],[f27]) ).
fof(f58,plain,
! [X2,X3,X0,X1] :
( ~ set_equal(X3,X2)
| set_equal(X0,X1)
| ~ set_equal(X2,X0)
| element(sK0(X0,X1),X3)
| element(sK0(X0,X1),X1) ),
inference(resolution,[],[f28,f11]) ).
fof(f93,plain,
( ! [X0,X1] :
( element(sK0(X0,X1),sK1)
| element(sK0(X0,X1),X0)
| ~ set_equal(sK2,X1)
| set_equal(X0,X1) )
| ~ spl3_2 ),
inference(resolution,[],[f40,f23]) ).
fof(f138,plain,
( ! [X0] :
( element(sK0(sK1,X0),sK1)
| ~ set_equal(sK2,X0)
| set_equal(sK1,X0) )
| ~ spl3_2 ),
inference(factoring,[],[f93]) ).
fof(f153,plain,
( ! [X0,X1] :
( element(sK0(sK1,X0),X1)
| set_equal(sK1,X0)
| ~ set_equal(sK2,X0)
| ~ set_equal(X1,sK1) )
| ~ spl3_2 ),
inference(resolution,[],[f138,f11]) ).
fof(f165,plain,
( ! [X0] :
( set_equal(sK1,X0)
| ~ set_equal(sK2,X0)
| ~ set_equal(X0,sK1)
| set_equal(sK1,X0)
| ~ element(sK0(sK1,X0),sK1) )
| ~ spl3_2 ),
inference(resolution,[],[f153,f13]) ).
fof(f168,plain,
( ! [X0] :
( set_equal(sK1,X0)
| ~ set_equal(sK2,X0)
| ~ set_equal(X0,sK1)
| ~ element(sK0(sK1,X0),sK1) )
| ~ spl3_2 ),
inference(duplicate_literal_removal,[],[f165]) ).
fof(f169,plain,
( ! [X0] :
( ~ set_equal(sK2,X0)
| set_equal(sK1,X0)
| ~ set_equal(X0,sK1) )
| ~ spl3_2 ),
inference(forward_subsumption_resolution,[],[f168,f54]) ).
fof(f173,plain,
( set_equal(sK1,sK2)
| ~ set_equal(sK2,sK1)
| ~ spl3_2 ),
inference(resolution,[],[f169,f37]) ).
fof(f174,plain,
( ~ set_equal(sK2,sK1)
| spl3_1
| ~ spl3_2 ),
inference(forward_subsumption_resolution,[],[f173,f18]) ).
fof(f175,plain,
( $false
| spl3_1
| ~ spl3_2 ),
inference(forward_subsumption_resolution,[],[f174,f23]) ).
fof(f176,plain,
( spl3_1
| ~ spl3_2 ),
inference(avatar_contradiction_clause,[],[f175]) ).
fof(f177,plain,
( ! [X0,X1] :
( element(sK0(X0,X1),sK1)
| element(sK0(X0,X1),X1)
| ~ set_equal(sK2,X0)
| set_equal(X0,X1) )
| ~ spl3_1 ),
inference(resolution,[],[f19,f58]) ).
fof(f189,plain,
( ! [X0] :
( element(sK0(X0,sK1),sK1)
| ~ set_equal(sK2,X0)
| set_equal(X0,sK1) )
| ~ spl3_1 ),
inference(factoring,[],[f177]) ).
fof(f191,plain,
( ! [X0] :
( ~ set_equal(sK2,X0)
| set_equal(X0,sK1)
| set_equal(X0,sK1)
| ~ element(sK0(X0,sK1),X0) )
| ~ spl3_1 ),
inference(resolution,[],[f189,f13]) ).
fof(f194,plain,
( ! [X0] :
( ~ element(sK0(X0,sK1),X0)
| set_equal(X0,sK1)
| ~ set_equal(sK2,X0) )
| ~ spl3_1 ),
inference(duplicate_literal_removal,[],[f191]) ).
fof(f196,plain,
( ! [X0] :
( set_equal(X0,sK1)
| ~ set_equal(sK2,X0)
| set_equal(X0,sK1)
| ~ set_equal(sK1,X0) )
| ~ spl3_1 ),
inference(resolution,[],[f194,f54]) ).
fof(f231,plain,
( ! [X0] :
( ~ set_equal(sK2,X0)
| set_equal(X0,sK1)
| ~ set_equal(sK1,X0) )
| ~ spl3_1 ),
inference(duplicate_literal_removal,[],[f196]) ).
fof(f239,plain,
( set_equal(sK2,sK1)
| ~ set_equal(sK1,sK2)
| ~ spl3_1 ),
inference(resolution,[],[f231,f37]) ).
fof(f240,plain,
( ~ set_equal(sK1,sK2)
| ~ spl3_1
| spl3_2 ),
inference(forward_subsumption_resolution,[],[f239,f22]) ).
fof(f241,plain,
( $false
| ~ spl3_1
| spl3_2 ),
inference(forward_subsumption_resolution,[],[f240,f19]) ).
fof(f242,plain,
( ~ spl3_1
| spl3_2 ),
inference(avatar_contradiction_clause,[],[f241]) ).
cnf(s1,plain,
( spl3_1
| spl3_2 ),
inference(sat_conversion,[],[f24]) ).
cnf(s2,plain,
( ~ spl3_1
| ~ spl3_2 ),
inference(sat_conversion,[],[f25]) ).
cnf(s3,plain,
( spl3_1
| ~ spl3_2 ),
inference(sat_conversion,[],[f176]) ).
cnf(s4,plain,
( ~ spl3_1
| spl3_2 ),
inference(sat_conversion,[],[f242]) ).
cnf(s5,plain,
spl3_1,
inference(rat,[],[s1,s3]) ).
cnf(s6,plain,
spl3_2,
inference(rat,[],[s4,s5]) ).
cnf(s7,plain,
$false,
inference(rat,[],[s2,s6,s5]) ).
fof(f243,plain,
$false,
inference(avatar_sat_refutation,[],[s7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET047+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.35 % Computer : n010.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Mon Sep 28 00:22:32 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.13/0.38 Running first-order model finding
% 0.13/0.38 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
% 0.13/0.42 % (1456208)Will run a generic schedule for satisfiability detection.
% 0.13/0.42 % (1456216)dis+10_1_sil=32000:sp=arity:random_seed=1703154723:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.13/0.42 % (1456216) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1456208-1456216"...
% 0.13/0.42 % (1456214)% WARNING: option uhcvi not known.
% 0.13/0.42 % (1456216)...printing done.
% 0.13/0.42 % (1456216)Refutation found. Thanks to Tanya!
% 0.13/0.42 % SZS status Theorem for theBenchmark
% 0.13/0.42 % SZS output start Proof for theBenchmark
% See solution above
% 0.13/0.42 % (1456216)------------------------------
% 0.13/0.42 % (1456216)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.13/0.42 % (1456216)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.13/0.42 % (1456216)CaDiCaL version: 2.1.3
% 0.13/0.42 % (1456216)Termination reason: Refutation
% 0.13/0.42 % (1456216)Time elapsed: 0.003 s
% 0.13/0.42 % (1456216)Peak memory usage: 12 MB
% 0.13/0.42 % (1456216)Instructions burned: 9 (million)
% 0.13/0.42 % (1456208)Success in time 0.03 s
% 0.13/0.42 % Vampire exiting
%------------------------------------------------------------------------------