%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET618+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n026.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 : Thu Sep 24 02:10:15 PM UTC 2026
% Result : Theorem 0.14s 0.39s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of formulae : 16 ( 16 unt; 0 def)
% Number of atoms : 16 ( 15 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 6 ( 6 ~; 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 : 13 ( 12 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [B,C] : symmetric_difference(B,C) = union(difference(B,C),difference(C,B)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [B] : union(B,B) = B,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [B] : difference(B,B) = empty_set,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,conjecture,
! [B] : symmetric_difference(B,B) = empty_set,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
~ ! [B] : symmetric_difference(B,B) = empty_set,
inference(negated_conjecture,[status(cth)],[f12]) ).
fof(f14,plain,
! [X0,X1] : symmetric_difference(X0,X1) = union(difference(X0,X1),difference(X1,X0)),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f15,plain,
! [X0] : union(X0,X0) = X0,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f16,plain,
! [X0] : difference(X0,X0) = empty_set,
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f45,plain,
? [B] : symmetric_difference(B,B) != empty_set,
inference(pre_NNF_transformation,[status(thm)],[f13]) ).
fof(f46,plain,
symmetric_difference(sK3_skl,sK3_skl) != empty_set,
inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl]),skolemize(B,sK3_skl)],[f45]) ).
fof(f47,plain,
symmetric_difference(sK3_skl,sK3_skl) != empty_set,
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f54,plain,
! [X0] : symmetric_difference(X0,X0) = union(empty_set,difference(X0,X0)),
inference(paramodulation,[status(thm)],[f16,f14]) ).
fof(f56,plain,
! [X0] : symmetric_difference(X0,X0) = union(empty_set,empty_set),
inference(forward_demodulation,[status(thm)],[f16,f54]) ).
fof(f58,plain,
union(empty_set,empty_set) != empty_set,
inference(backward_demodulation,[status(thm)],[f56,f47]) ).
fof(f59,plain,
empty_set != empty_set,
inference(backward_demodulation,[status(thm)],[f15,f58]) ).
fof(f63,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f59]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET618+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n026.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
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 05:32:22 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 0.14/0.39 % Refutation found
% 0.14/0.39 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.42 % Elapsed time: 0.055984 seconds
% 0.14/0.42 % CPU time: 0.160869 seconds
% 0.14/0.42 % Total memory used: 101.462 MB
% 0.14/0.42 % Net memory used: 101.052 MB
%------------------------------------------------------------------------------