%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET619+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n012.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 0.08s 0.55s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 7
% Syntax : Number of formulae : 26 ( 26 unt; 0 def)
% Number of atoms : 26 ( 25 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 6 ( 6 ~; 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 : 46 ( 44 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [B,C] : symmetric_difference(B,C) = union(difference(B,C),difference(C,B)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [B,C,D] : union(union(B,C),D) = union(B,union(C,D)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [B,C] : union(B,intersection(B,C)) = B,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [B,C] : union(intersection(B,C),difference(B,C)) = B,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [B,C] : union(B,C) = union(C,B),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [B,C] : intersection(B,C) = intersection(C,B),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,conjecture,
! [B,C] : union(B,C) = union(symmetric_difference(B,C),intersection(B,C)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
~ ! [B,C] : union(B,C) = union(symmetric_difference(B,C),intersection(B,C)),
inference(negated_conjecture,[status(cth)],[f14]) ).
fof(f16,plain,
! [X0,X1] : symmetric_difference(X0,X1) = union(difference(X0,X1),difference(X1,X0)),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f17,plain,
! [X0,X1,X2] : union(union(X0,X1),X2) = union(X0,union(X1,X2)),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f18,plain,
! [X0,X1] : union(X0,intersection(X0,X1)) = X0,
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f19,plain,
! [X0,X1] : union(intersection(X0,X1),difference(X0,X1)) = X0,
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f35,plain,
! [X0,X1] : union(X0,X1) = union(X1,X0),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f36,plain,
! [X0,X1] : intersection(X0,X1) = intersection(X1,X0),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f53,plain,
? [B,C] : union(B,C) != union(symmetric_difference(B,C),intersection(B,C)),
inference(pre_NNF_transformation,[status(thm)],[f15]) ).
fof(f54,plain,
union(sK2_skl,sK3_skl) != union(symmetric_difference(sK2_skl,sK3_skl),intersection(sK2_skl,sK3_skl)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl,sK3_skl]),skolemize(B,sK2_skl),skolemize(C,sK3_skl)],[f53]) ).
fof(f55,plain,
union(sK2_skl,sK3_skl) != union(symmetric_difference(sK2_skl,sK3_skl),intersection(sK2_skl,sK3_skl)),
inference(cnf_transformation,[status(thm)],[f54]) ).
fof(f63,plain,
! [X0,X1,X2] : union(X0,X1) = union(X0,union(intersection(X0,X2),X1)),
inference(paramodulation,[status(thm)],[f18,f17]) ).
fof(f71,plain,
union(sK2_skl,sK3_skl) != union(intersection(sK2_skl,sK3_skl),symmetric_difference(sK2_skl,sK3_skl)),
inference(paramodulation,[status(thm)],[f35,f55]) ).
fof(f107,plain,
! [X0,X1] : union(intersection(X0,X1),difference(X1,X0)) = X1,
inference(paramodulation,[status(thm)],[f36,f19]) ).
fof(f111,plain,
! [X0,X1,X2] : union(X0,X1) = union(intersection(X0,X2),union(difference(X0,X2),X1)),
inference(paramodulation,[status(thm)],[f19,f17]) ).
fof(f195,plain,
! [X0,X1] : union(X0,difference(X1,X0)) = union(X0,X1),
inference(paramodulation,[status(thm)],[f107,f63]) ).
fof(f641,plain,
! [X0,X1] : union(X0,difference(X1,X0)) = union(intersection(X0,X1),symmetric_difference(X0,X1)),
inference(paramodulation,[status(thm)],[f16,f111]) ).
fof(f676,plain,
union(sK2_skl,sK3_skl) != union(sK2_skl,sK3_skl),
inference(backward_demodulation,[status(thm)],[f677,f71]) ).
fof(f677,plain,
! [X0,X1] : union(X0,X1) = union(intersection(X0,X1),symmetric_difference(X0,X1)),
inference(forward_demodulation,[status(thm)],[f195,f641]) ).
fof(f705,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f676]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SET619+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.02 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.03/0.50 % Computer : n012.cluster.edu
% 0.03/0.50 % Model : x86_64 x86_64
% 0.03/0.50 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.50 % Memory : 8046.5625MB
% 0.03/0.50 % OS : Linux 6.8.0-71-generic
% 0.03/0.50 % CPULimit : 300
% 0.03/0.50 % WCLimit : 300
% 0.03/0.50 % DateTime : Mon Sep 21 05:29:22 UTC 2026
% 0.03/0.51 % CPUTime :
% 0.03/0.51 % Drodi V4.1.1
% 0.08/0.55 % Refutation found
% 0.08/0.55 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.08/0.55 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.08/0.56 % Elapsed time: 0.052976 seconds
% 0.08/0.56 % CPU time: 0.222610 seconds
% 0.08/0.56 % Total memory used: 105.962 MB
% 0.08/0.56 % Net memory used: 105.406 MB
%------------------------------------------------------------------------------