%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET047-5 : TPTP v9.3.1. Released v1.0.0.
% 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 12:42:49 PM UTC 2026
% Result : Unsatisfiable 0.09s 0.44s
% Output : Refutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 8
% Syntax : Number of formulae : 35 ( 4 unt; 2 def)
% Number of atoms : 81 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 79 ( 33 ~; 44 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 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 : 26 ( 0 sgn 26 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] :
( ~ element(X2,X0)
| element(X2,X1)
| ~ set_equal(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_substitution1) ).
fof(f2,axiom,
! [X2,X0,X1] :
( ~ element(X2,X1)
| element(X2,X0)
| ~ set_equal(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_substitution2) ).
fof(f3,axiom,
! [X0,X1] :
( element(f(X0,X1),X0)
| element(f(X0,X1),X1)
| set_equal(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_3) ).
fof(f4,axiom,
! [X0,X1] :
( ~ element(f(X0,X1),X1)
| ~ element(f(X0,X1),X0)
| set_equal(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_4) ).
fof(f5,negated_conjecture,
( set_equal(a,b)
| set_equal(b,a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_symmetry1) ).
fof(f6,negated_conjecture,
( ~ set_equal(b,a)
| ~ set_equal(a,b) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_symmetry2) ).
fof(f8,definition,
( spl0_1
<=> set_equal(a,b) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f9,plain,
( set_equal(a,b)
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f8]) ).
fof(f10,plain,
( ~ set_equal(a,b)
| spl0_1 ),
inference(avatar_component_clause,[],[f8]) ).
fof(f12,definition,
( spl0_2
<=> set_equal(b,a) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f13,plain,
( set_equal(b,a)
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f12]) ).
fof(f14,plain,
( ~ set_equal(b,a)
| spl0_2 ),
inference(avatar_component_clause,[],[f12]) ).
fof(f15,plain,
( ~ spl0_1
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f6,f12,f8]) ).
fof(f16,plain,
( spl0_2
| spl0_1 ),
inference(avatar_split_clause,[],[f5,f8,f12]) ).
fof(f30,plain,
! [X2,X0,X1] :
( element(f(X0,X1),X1)
| element(f(X0,X1),X2)
| set_equal(X0,X1)
| ~ set_equal(X2,X0) ),
inference(resolution,[],[f3,f2]) ).
fof(f34,plain,
! [X2,X0,X1] :
( element(f(X0,X1),X0)
| element(f(X0,X1),X2)
| set_equal(X0,X1)
| ~ set_equal(X1,X2) ),
inference(resolution,[],[f3,f1]) ).
fof(f145,plain,
! [X0,X1] :
( element(f(X0,X1),X1)
| set_equal(X0,X1)
| ~ set_equal(X1,X0) ),
inference(factoring,[],[f30]) ).
fof(f149,plain,
! [X0,X1] :
( set_equal(X0,X1)
| ~ set_equal(X1,X0)
| ~ element(f(X0,X1),X0)
| set_equal(X0,X1) ),
inference(resolution,[],[f145,f4]) ).
fof(f158,plain,
! [X0,X1] :
( ~ element(f(X0,X1),X0)
| ~ set_equal(X1,X0)
| set_equal(X0,X1) ),
inference(duplicate_literal_removal,[],[f149]) ).
fof(f253,plain,
! [X0,X1] :
( element(f(X0,X1),X0)
| set_equal(X0,X1)
| ~ set_equal(X1,X0) ),
inference(factoring,[],[f34]) ).
fof(f258,plain,
! [X0,X1] :
( set_equal(X0,X1)
| ~ set_equal(X1,X0) ),
inference(forward_subsumption_resolution,[],[f253,f158]) ).
fof(f260,plain,
( set_equal(a,b)
| ~ spl0_2 ),
inference(resolution,[],[f258,f13]) ).
fof(f262,plain,
( $false
| spl0_1
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f260,f10]) ).
fof(f263,plain,
( spl0_1
| ~ spl0_2 ),
inference(avatar_contradiction_clause,[],[f262]) ).
fof(f264,plain,
( ~ set_equal(a,b)
| spl0_2 ),
inference(resolution,[],[f14,f258]) ).
fof(f265,plain,
( $false
| ~ spl0_1
| spl0_2 ),
inference(forward_subsumption_resolution,[],[f264,f9]) ).
fof(f266,plain,
( ~ spl0_1
| spl0_2 ),
inference(avatar_contradiction_clause,[],[f265]) ).
cnf(s1,plain,
( ~ spl0_1
| ~ spl0_2 ),
inference(sat_conversion,[],[f15]) ).
cnf(s2,plain,
( spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f16]) ).
cnf(s3,plain,
( spl0_1
| ~ spl0_2 ),
inference(sat_conversion,[],[f263]) ).
cnf(s4,plain,
( ~ spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f266]) ).
cnf(s5,plain,
spl0_1,
inference(rat,[],[s2,s3]) ).
cnf(s6,plain,
spl0_2,
inference(rat,[],[s4,s5]) ).
cnf(s7,plain,
$false,
inference(rat,[],[s1,s6,s5]) ).
fof(f267,plain,
$false,
inference(avatar_sat_refutation,[],[s7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET047-5 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.36 % Computer : n010.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 28 00:22:47 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.39 Running first-order model finding
% 0.09/0.39 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
% 0.09/0.44 % (1456599)Will run a generic schedule for satisfiability detection.
% 0.09/0.44 % (1456608)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=951176735:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.09/0.44 % (1456608) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1456599-1456608"...
% 0.09/0.44 % (1456608)...printing done.
% 0.09/0.44 % (1456608)Refutation found. Thanks to Tanya!
% 0.09/0.44 % SZS status Unsatisfiable for theBenchmark
% 0.09/0.44 % SZS output start Proof for theBenchmark
% See solution above
% 0.09/0.44 % (1456608)------------------------------
% 0.09/0.44 % (1456608)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.09/0.44 % (1456608)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.09/0.44 % (1456608)CaDiCaL version: 2.1.3
% 0.09/0.44 % (1456608)Termination reason: Refutation
% 0.09/0.44 % (1456608)Time elapsed: 0.005 s
% 0.09/0.44 % (1456608)Peak memory usage: 12 MB
% 0.09/0.44 % (1456608)Instructions burned: 17 (million)
% 0.09/0.44 % (1456599)Success in time 0.033 s
% 0.09/0.44 % Vampire exiting
%------------------------------------------------------------------------------