%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET617+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n016.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 12:44:11 PM UTC 2026
% Result : Theorem 0.10s 0.45s
% Output : Refutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 9
% Syntax : Number of formulae : 39 ( 19 unt; 2 def)
% Number of atoms : 59 ( 34 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 40 ( 20 ~; 16 |; 2 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 3 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 23 ( 0 sgn 22 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : symmetric_difference(X0,X1) = union(difference(X0,X1),difference(X1,X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetric_difference_defn) ).
fof(f2,axiom,
! [X0] : union(X0,empty_set) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union_empty_set) ).
fof(f3,axiom,
! [X0] : difference(X0,empty_set) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',no_difference_with_empty_set1) ).
fof(f4,axiom,
! [X0] : difference(empty_set,X0) = empty_set,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',no_difference_with_empty_set2) ).
fof(f7,axiom,
! [X0,X1] : union(X0,X1) = union(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_union) ).
fof(f8,axiom,
! [X0,X1] : symmetric_difference(X0,X1) = symmetric_difference(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_symmetric_difference) ).
fof(f13,conjecture,
! [X0] :
( symmetric_difference(X0,empty_set) = X0
& symmetric_difference(empty_set,X0) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th92) ).
fof(f14,negated_conjecture,
~ ! [X0] :
( symmetric_difference(X0,empty_set) = X0
& symmetric_difference(empty_set,X0) = X0 ),
inference(negated_conjecture,[status(cth)],[f13]) ).
fof(f16,plain,
? [X0] :
( symmetric_difference(X0,empty_set) != X0
| symmetric_difference(empty_set,X0) != X0 ),
inference(ennf_transformation,[],[f14]) ).
fof(f17,plain,
! [X0,X1] : symmetric_difference(X0,X1) = union(difference(X0,X1),difference(X1,X0)),
inference(cnf_transformation,[],[f1]) ).
fof(f18,plain,
! [X0] : union(X0,empty_set) = X0,
inference(cnf_transformation,[],[f2]) ).
fof(f19,plain,
! [X0] : difference(X0,empty_set) = X0,
inference(cnf_transformation,[],[f3]) ).
fof(f20,plain,
! [X0] : empty_set = difference(empty_set,X0),
inference(cnf_transformation,[],[f4]) ).
fof(f25,plain,
! [X0,X1] : union(X0,X1) = union(X1,X0),
inference(cnf_transformation,[],[f7]) ).
fof(f26,plain,
! [X0,X1] : symmetric_difference(X0,X1) = symmetric_difference(X1,X0),
inference(cnf_transformation,[],[f8]) ).
fof(f35,plain,
( sK2 != symmetric_difference(empty_set,sK2)
| sK2 != symmetric_difference(sK2,empty_set) ),
inference(cnf_transformation,[],[f16]) ).
fof(f36,plain,
! [X0,X1] : union(difference(X0,X1),difference(X1,X0)) = union(difference(X1,X0),difference(X0,X1)),
inference(definition_unfolding,[],[f26,f17,f17]) ).
fof(f37,plain,
( sK2 != union(difference(empty_set,sK2),difference(sK2,empty_set))
| sK2 != union(difference(sK2,empty_set),difference(empty_set,sK2)) ),
inference(definition_unfolding,[],[f35,f17,f17]) ).
fof(f43,definition,
( spl3_1
<=> sK2 = union(difference(sK2,empty_set),difference(empty_set,sK2)) ),
introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition]) ).
fof(f45,plain,
( sK2 != union(difference(sK2,empty_set),difference(empty_set,sK2))
| spl3_1 ),
inference(avatar_component_clause,[],[f43]) ).
fof(f47,definition,
( spl3_2
<=> sK2 = union(difference(empty_set,sK2),difference(sK2,empty_set)) ),
introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition]) ).
fof(f49,plain,
( sK2 != union(difference(empty_set,sK2),difference(sK2,empty_set))
| spl3_2 ),
inference(avatar_component_clause,[],[f47]) ).
fof(f50,plain,
( ~ spl3_1
| ~ spl3_2 ),
inference(avatar_split_clause,[],[f37,f47,f43]) ).
fof(f51,plain,
( sK2 != union(difference(empty_set,sK2),difference(sK2,empty_set))
| spl3_1 ),
inference(forward_demodulation,[],[f45,f36]) ).
fof(f52,plain,
( sK2 != union(difference(empty_set,sK2),sK2)
| spl3_1 ),
inference(forward_demodulation,[],[f51,f19]) ).
fof(f53,plain,
( sK2 != union(sK2,difference(empty_set,sK2))
| spl3_1 ),
inference(forward_demodulation,[],[f52,f25]) ).
fof(f54,plain,
( sK2 != union(sK2,empty_set)
| spl3_1 ),
inference(forward_demodulation,[],[f53,f20]) ).
fof(f55,plain,
( $false
| spl3_1 ),
inference(forward_subsumption_resolution,[],[f54,f18]) ).
fof(f56,plain,
spl3_1,
inference(avatar_contradiction_clause,[],[f55]) ).
fof(f58,plain,
( sK2 != union(difference(empty_set,sK2),sK2)
| spl3_2 ),
inference(forward_demodulation,[],[f49,f19]) ).
fof(f60,plain,
( sK2 != union(sK2,difference(empty_set,sK2))
| spl3_2 ),
inference(forward_demodulation,[],[f58,f25]) ).
fof(f62,plain,
( sK2 != union(sK2,empty_set)
| spl3_2 ),
inference(forward_demodulation,[],[f60,f20]) ).
fof(f64,plain,
( $false
| spl3_2 ),
inference(forward_subsumption_resolution,[],[f62,f18]) ).
fof(f65,plain,
spl3_2,
inference(avatar_contradiction_clause,[],[f64]) ).
cnf(s1,plain,
( ~ spl3_1
| ~ spl3_2 ),
inference(sat_conversion,[],[f50]) ).
cnf(s2,plain,
spl3_1,
inference(sat_conversion,[],[f56]) ).
cnf(s3,plain,
spl3_2,
inference(sat_conversion,[],[f65]) ).
cnf(s4,plain,
$false,
inference(rat,[],[s1,s3,s2]) ).
fof(f66,plain,
$false,
inference(avatar_sat_refutation,[],[s4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET617+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.37 % Computer : n016.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 02:24:03 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.41 Running first-order model finding
% 0.10/0.41 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
% 0.10/0.45 % (3194845)Will run a generic schedule for satisfiability detection.
% 0.10/0.45 % (3194854)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2776418984:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.10/0.45 % (3194854) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3194845-3194854"...
% 0.10/0.45 % (3194854)...printing done.
% 0.10/0.45 % (3194851)% WARNING: option uhcvi not known.
% 0.10/0.45 % (3194854)Refutation found. Thanks to Tanya!
% 0.10/0.45 % SZS status Theorem for theBenchmark
% 0.10/0.45 % SZS output start Proof for theBenchmark
% See solution above
% 0.10/0.45 % (3194854)------------------------------
% 0.10/0.45 % (3194854)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.10/0.45 % (3194854)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.10/0.45 % (3194854)CaDiCaL version: 2.1.3
% 0.10/0.45 % (3194854)Termination reason: Refutation
% 0.10/0.45 % (3194854)Time elapsed: 0.001 s
% 0.10/0.45 % (3194854)Peak memory usage: 12 MB
% 0.10/0.45 % (3194854)Instructions burned: 2 (million)
% 0.10/0.45 % (3194845)Success in time 0.034 s
% 0.10/0.45 % Vampire exiting
%------------------------------------------------------------------------------