%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET621+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 : n002.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 0.09s 0.40s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% 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 : 8 ( 8 ~; 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 : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 25 ( 22 !; 3 ?)
% 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,C,D] : difference(difference(B,C),D) = difference(B,union(C,D)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [B,C,D] : difference(union(B,C),D) = union(difference(B,D),difference(C,D)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,conjecture,
! [B,C,D] : difference(symmetric_difference(B,C),D) = union(difference(B,union(C,D)),difference(C,union(B,D))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
~ ! [B,C,D] : difference(symmetric_difference(B,C),D) = union(difference(B,union(C,D)),difference(C,union(B,D))),
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,X1,X2] : difference(difference(X0,X1),X2) = difference(X0,union(X1,X2)),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f16,plain,
! [X0,X1,X2] : difference(union(X0,X1),X2) = union(difference(X0,X2),difference(X1,X2)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f49,plain,
? [B,C,D] : difference(symmetric_difference(B,C),D) != union(difference(B,union(C,D)),difference(C,union(B,D))),
inference(pre_NNF_transformation,[status(thm)],[f13]) ).
fof(f50,plain,
difference(symmetric_difference(sK2_skl,sK3_skl),sK4_skl) != union(difference(sK2_skl,union(sK3_skl,sK4_skl)),difference(sK3_skl,union(sK2_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)],[f49]) ).
fof(f51,plain,
difference(symmetric_difference(sK2_skl,sK3_skl),sK4_skl) != union(difference(sK2_skl,union(sK3_skl,sK4_skl)),difference(sK3_skl,union(sK2_skl,sK4_skl))),
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f81,plain,
difference(symmetric_difference(sK2_skl,sK3_skl),sK4_skl) != union(difference(sK2_skl,union(sK3_skl,sK4_skl)),difference(difference(sK3_skl,sK2_skl),sK4_skl)),
inference(paramodulation,[status(thm)],[f15,f51]) ).
fof(f119,plain,
difference(symmetric_difference(sK2_skl,sK3_skl),sK4_skl) != union(difference(difference(sK2_skl,sK3_skl),sK4_skl),difference(difference(sK3_skl,sK2_skl),sK4_skl)),
inference(paramodulation,[status(thm)],[f15,f81]) ).
fof(f120,plain,
difference(symmetric_difference(sK2_skl,sK3_skl),sK4_skl) != difference(union(difference(sK2_skl,sK3_skl),difference(sK3_skl,sK2_skl)),sK4_skl),
inference(forward_demodulation,[status(thm)],[f16,f119]) ).
fof(f121,plain,
difference(symmetric_difference(sK2_skl,sK3_skl),sK4_skl) != difference(symmetric_difference(sK2_skl,sK3_skl),sK4_skl),
inference(forward_demodulation,[status(thm)],[f14,f120]) ).
fof(f122,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f121]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET621+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n002.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 21 05:32:17 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.38 % Drodi V4.1.1
% 0.09/0.40 % Refutation found
% 0.09/0.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.09/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.09/0.42 % Elapsed time: 0.045829 seconds
% 0.09/0.42 % CPU time: 0.136939 seconds
% 0.09/0.42 % Total memory used: 70.294 MB
% 0.09/0.42 % Net memory used: 70.070 MB
%------------------------------------------------------------------------------