%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET618+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 : n018.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 0.12s 0.47s
% Output : Refutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of formulae : 15 ( 15 unt; 0 def)
% Number of atoms : 15 ( 14 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 7 ( 7 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 11 ( 10 !; 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,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotency_of_union) ).
fof(f3,axiom,
! [X0] : difference(X0,X0) = empty_set,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',self_difference_is_empty_set) ).
fof(f12,conjecture,
! [X0] : symmetric_difference(X0,X0) = empty_set,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th93) ).
fof(f13,negated_conjecture,
~ ! [X0] : symmetric_difference(X0,X0) = empty_set,
inference(negated_conjecture,[status(cth)],[f12]) ).
fof(f15,plain,
? [X0] : empty_set != symmetric_difference(X0,X0),
inference(ennf_transformation,[],[f13]) ).
fof(f24,plain,
empty_set != symmetric_difference(sK2,sK2),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X0,sK2)],[f15]) ).
fof(f25,plain,
! [X0,X1] : symmetric_difference(X0,X1) = union(difference(X0,X1),difference(X1,X0)),
inference(cnf_transformation,[],[f1]) ).
fof(f26,plain,
! [X0] : union(X0,X0) = X0,
inference(cnf_transformation,[],[f2]) ).
fof(f27,plain,
! [X0] : difference(X0,X0) = empty_set,
inference(cnf_transformation,[],[f3]) ).
fof(f42,plain,
empty_set != symmetric_difference(sK2,sK2),
inference(cnf_transformation,[],[f24]) ).
fof(f44,plain,
empty_set != union(difference(sK2,sK2),difference(sK2,sK2)),
inference(definition_unfolding,[],[f42,f25]) ).
fof(f49,plain,
empty_set != difference(sK2,sK2),
inference(superposition,[],[f44,f26]) ).
fof(f50,plain,
empty_set != empty_set,
inference(superposition,[],[f49,f27]) ).
fof(f52,plain,
$false,
inference(trivial_inequality_removal,[],[f50]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET618+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.40 % Computer : n018.cluster.edu
% 0.12/0.40 % Model : x86_64 x86_64
% 0.12/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.40 % Memory : 8046.5625MB
% 0.12/0.40 % OS : Linux 6.8.0-71-generic
% 0.12/0.40 % CPULimit : 300
% 0.12/0.40 % WCLimit : 300
% 0.12/0.40 % DateTime : Mon Sep 28 02:22:09 UTC 2026
% 0.12/0.40 % CPUTime :
% 0.12/0.40 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.43 Running first-order model finding
% 0.12/0.43 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
% 0.12/0.47 % (2931157)Will run a generic schedule for satisfiability detection.
% 0.12/0.47 % (2931165)dis+10_1_sil=32000:sp=arity:random_seed=3175584387:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.12/0.47 % (2931165) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2931157-2931165"...
% 0.12/0.47 % (2931165)...printing done.
% 0.12/0.47 % (2931165)Refutation found. Thanks to Tanya!
% 0.12/0.47 % SZS status Theorem for theBenchmark
% 0.12/0.47 % SZS output start Proof for theBenchmark
% See solution above
% 0.12/0.47 % (2931165)------------------------------
% 0.12/0.47 % (2931165)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.12/0.47 % (2931165)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.12/0.47 % (2931165)CaDiCaL version: 2.1.3
% 0.12/0.47 % (2931165)Termination reason: Refutation
% 0.12/0.47 % (2931165)Time elapsed: 0.001 s
% 0.12/0.47 % (2931165)Peak memory usage: 12 MB
% 0.12/0.47 % (2931165)Instructions burned: 1 (million)
% 0.12/0.47 % (2931157)Success in time 0.029 s
% 0.12/0.47 % Vampire exiting
%------------------------------------------------------------------------------