%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET622+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 : n020.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 02:10:16 PM UTC 2026
% Result : Theorem 0.14s 10.41s
% Output : CNFRefutation 0.14s
% 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 : 5 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 25 ( 22 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [B,C,D] : intersection(intersection(B,C),D) = intersection(B,intersection(C,D)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [B,C,D] : difference(B,difference(C,D)) = union(difference(B,C),intersection(B,D)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [B,C] : symmetric_difference(B,C) = difference(union(B,C),intersection(B,C)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,conjecture,
! [B,C,D] : difference(B,symmetric_difference(C,D)) = union(difference(B,union(C,D)),intersection(intersection(B,C),D)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
~ ! [B,C,D] : difference(B,symmetric_difference(C,D)) = union(difference(B,union(C,D)),intersection(intersection(B,C),D)),
inference(negated_conjecture,[status(cth)],[f15]) ).
fof(f17,plain,
! [X0,X1,X2] : intersection(intersection(X0,X1),X2) = intersection(X0,intersection(X1,X2)),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f18,plain,
! [X0,X1,X2] : difference(X0,difference(X1,X2)) = union(difference(X0,X1),intersection(X0,X2)),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f19,plain,
! [X0,X1] : symmetric_difference(X0,X1) = difference(union(X0,X1),intersection(X0,X1)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f59,plain,
? [B,C,D] : difference(B,symmetric_difference(C,D)) != union(difference(B,union(C,D)),intersection(intersection(B,C),D)),
inference(pre_NNF_transformation,[status(thm)],[f16]) ).
fof(f60,plain,
difference(sK2_skl,symmetric_difference(sK3_skl,sK4_skl)) != union(difference(sK2_skl,union(sK3_skl,sK4_skl)),intersection(intersection(sK2_skl,sK3_skl),sK4_skl)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl,sK3_skl,sK4_skl]),skolemize(B,sK2_skl),skolemize(C,sK3_skl),skolemize(D,sK4_skl)],[f59]) ).
fof(f61,plain,
difference(sK2_skl,symmetric_difference(sK3_skl,sK4_skl)) != union(difference(sK2_skl,union(sK3_skl,sK4_skl)),intersection(intersection(sK2_skl,sK3_skl),sK4_skl)),
inference(cnf_transformation,[status(thm)],[f60]) ).
fof(f64,plain,
difference(sK2_skl,symmetric_difference(sK3_skl,sK4_skl)) != union(difference(sK2_skl,union(sK3_skl,sK4_skl)),intersection(sK2_skl,intersection(sK3_skl,sK4_skl))),
inference(forward_demodulation,[status(thm)],[f17,f61]) ).
fof(f65,plain,
difference(sK2_skl,symmetric_difference(sK3_skl,sK4_skl)) != difference(sK2_skl,difference(union(sK3_skl,sK4_skl),intersection(sK3_skl,sK4_skl))),
inference(forward_demodulation,[status(thm)],[f18,f64]) ).
fof(f66,plain,
difference(sK2_skl,symmetric_difference(sK3_skl,sK4_skl)) != difference(sK2_skl,symmetric_difference(sK3_skl,sK4_skl)),
inference(forward_demodulation,[status(thm)],[f19,f65]) ).
fof(f67,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f66]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET622+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/10.38 % Computer : n020.cluster.edu
% 0.09/10.38 % Model : x86_64 x86_64
% 0.09/10.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/10.38 % Memory : 8046.5625MB
% 0.09/10.38 % OS : Linux 6.8.0-71-generic
% 0.09/10.38 % CPULimit : 300
% 0.09/10.38 % WCLimit : 300
% 0.09/10.38 % DateTime : Mon Sep 21 05:31:13 UTC 2026
% 0.09/10.38 % CPUTime :
% 0.09/10.39 % Drodi V4.1.1
% 0.14/10.41 % Refutation found
% 0.14/10.41 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/10.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/10.43 % Elapsed time: 0.045642 seconds
% 0.14/10.43 % CPU time: 0.121374 seconds
% 0.14/10.43 % Total memory used: 63.737 MB
% 0.14/10.43 % Net memory used: 63.584 MB
%------------------------------------------------------------------------------