%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET619+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 : n015.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 0.09s 0.44s
% Output : Refutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 7
% Syntax : Number of formulae : 28 ( 28 unt; 0 def)
% Number of atoms : 28 ( 27 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 10 ( 10 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 41 ( 39 !; 2 ?)
% 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,X1,X2] : union(union(X0,X1),X2) = union(X0,union(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_union) ).
fof(f3,axiom,
! [X0,X1] : union(X0,intersection(X0,X1)) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union_intersection) ).
fof(f4,axiom,
! [X0,X1] : union(intersection(X0,X1),difference(X0,X1)) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union_intersection_difference) ).
fof(f8,axiom,
! [X0,X1] : union(X0,X1) = union(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_union) ).
fof(f9,axiom,
! [X0,X1] : intersection(X0,X1) = intersection(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_intersection) ).
fof(f14,conjecture,
! [X0,X1] : union(X0,X1) = union(symmetric_difference(X0,X1),intersection(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th95) ).
fof(f15,negated_conjecture,
~ ! [X0,X1] : union(X0,X1) = union(symmetric_difference(X0,X1),intersection(X0,X1)),
inference(negated_conjecture,[status(cth)],[f14]) ).
fof(f17,plain,
? [X0,X1] : union(X0,X1) != union(symmetric_difference(X0,X1),intersection(X0,X1)),
inference(ennf_transformation,[],[f15]) ).
fof(f30,plain,
union(sK2,sK3) != union(symmetric_difference(sK2,sK3),intersection(sK2,sK3)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3]),skolemize(X0,sK2),skolemize(X1,sK3)],[f17]) ).
fof(f31,plain,
! [X0,X1] : symmetric_difference(X0,X1) = union(difference(X0,X1),difference(X1,X0)),
inference(cnf_transformation,[],[f1]) ).
fof(f32,plain,
! [X2,X0,X1] : union(union(X0,X1),X2) = union(X0,union(X1,X2)),
inference(cnf_transformation,[],[f2]) ).
fof(f33,plain,
! [X0,X1] : union(X0,intersection(X0,X1)) = X0,
inference(cnf_transformation,[],[f3]) ).
fof(f34,plain,
! [X0,X1] : union(intersection(X0,X1),difference(X0,X1)) = X0,
inference(cnf_transformation,[],[f4]) ).
fof(f44,plain,
! [X0,X1] : union(X0,X1) = union(X1,X0),
inference(cnf_transformation,[],[f8]) ).
fof(f45,plain,
! [X0,X1] : intersection(X0,X1) = intersection(X1,X0),
inference(cnf_transformation,[],[f9]) ).
fof(f55,plain,
union(sK2,sK3) != union(symmetric_difference(sK2,sK3),intersection(sK2,sK3)),
inference(cnf_transformation,[],[f30]) ).
fof(f57,plain,
union(sK2,sK3) != union(union(difference(sK2,sK3),difference(sK3,sK2)),intersection(sK2,sK3)),
inference(definition_unfolding,[],[f55,f31]) ).
fof(f98,plain,
! [X0,X1] : union(intersection(X0,X1),difference(X1,X0)) = X1,
inference(superposition,[],[f34,f45]) ).
fof(f116,plain,
! [X0,X1] : union(difference(X0,X1),intersection(X1,X0)) = X0,
inference(superposition,[],[f44,f98]) ).
fof(f121,plain,
! [X2,X0,X1] : union(X0,union(intersection(X0,X1),X2)) = union(X0,X2),
inference(superposition,[],[f32,f33]) ).
fof(f133,plain,
union(sK2,sK3) != union(difference(sK2,sK3),union(difference(sK3,sK2),intersection(sK2,sK3))),
inference(superposition,[],[f57,f32]) ).
fof(f142,plain,
union(sK2,sK3) != union(difference(sK2,sK3),sK3),
inference(superposition,[],[f133,f116]) ).
fof(f147,plain,
union(sK2,sK3) != union(sK3,difference(sK2,sK3)),
inference(superposition,[],[f142,f44]) ).
fof(f255,plain,
! [X0,X1] : union(X1,X0) = union(X1,difference(X0,X1)),
inference(superposition,[],[f121,f98]) ).
fof(f301,plain,
union(sK2,sK3) != union(sK3,sK2),
inference(superposition,[],[f147,f255]) ).
fof(f303,plain,
union(sK2,sK3) != union(sK2,sK3),
inference(superposition,[],[f301,f44]) ).
fof(f304,plain,
$false,
inference(trivial_inequality_removal,[],[f303]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET619+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.37 % Computer : n015.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Mon Sep 28 02:25:31 UTC 2026
% 0.09/0.38 % CPUTime :
% 0.09/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.41 Running first-order model finding
% 0.09/0.41 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
% 0.09/0.44 % (2198889)Will run a generic schedule for satisfiability detection.
% 0.09/0.44 % (2198900)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1455933706:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.09/0.44 % (2198900) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2198889-2198900"...
% 0.09/0.44 % (2198900)...printing done.
% 0.09/0.44 % (2198900)Refutation found. Thanks to Tanya!
% 0.09/0.44 % SZS status Theorem for theBenchmark
% 0.09/0.44 % SZS output start Proof for theBenchmark
% See solution above
% 0.09/0.44 % (2198900)------------------------------
% 0.09/0.44 % (2198900)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.09/0.44 % (2198900)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.09/0.44 % (2198900)CaDiCaL version: 2.1.3
% 0.09/0.44 % (2198900)Termination reason: Refutation
% 0.09/0.44 % (2198900)Time elapsed: 0.005 s
% 0.09/0.44 % (2198900)Peak memory usage: 11 MB
% 0.09/0.44 % (2198900)Instructions burned: 11 (million)
% 0.09/0.44 % (2198889)Success in time 0.021 s
% 0.09/0.44 % Vampire exiting
%------------------------------------------------------------------------------