%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET620+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 : n016.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 0.12s 5.40s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 7
% Syntax : Number of formulae : 25 ( 25 unt; 0 def)
% Number of atoms : 25 ( 24 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 7 ( 7 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 4 ( 1 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 : 41 ( 39 !; 2 ?)
% 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] : difference(B,intersection(B,C)) = difference(B,C),
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(f8,axiom,
! [B,C] : union(B,C) = union(C,B),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [B,C] : intersection(B,C) = intersection(C,B),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [B,C] : symmetric_difference(B,C) = symmetric_difference(C,B),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,conjecture,
! [B,C] : symmetric_difference(B,C) = difference(union(B,C),intersection(B,C)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
~ ! [B,C] : symmetric_difference(B,C) = difference(union(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] : difference(X0,intersection(X0,X1)) = difference(X0,X1),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f18,plain,
! [X0,X1,X2] : difference(union(X0,X1),X2) = union(difference(X0,X2),difference(X1,X2)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f39,plain,
! [X0,X1] : union(X0,X1) = union(X1,X0),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f40,plain,
! [X0,X1] : intersection(X0,X1) = intersection(X1,X0),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f41,plain,
! [X0,X1] : symmetric_difference(X0,X1) = symmetric_difference(X1,X0),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f57,plain,
? [B,C] : symmetric_difference(B,C) != difference(union(B,C),intersection(B,C)),
inference(pre_NNF_transformation,[status(thm)],[f15]) ).
fof(f58,plain,
symmetric_difference(sK2_skl,sK3_skl) != difference(union(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)],[f57]) ).
fof(f59,plain,
symmetric_difference(sK2_skl,sK3_skl) != difference(union(sK2_skl,sK3_skl),intersection(sK2_skl,sK3_skl)),
inference(cnf_transformation,[status(thm)],[f58]) ).
fof(f66,plain,
symmetric_difference(sK2_skl,sK3_skl) != difference(union(sK3_skl,sK2_skl),intersection(sK2_skl,sK3_skl)),
inference(paramodulation,[status(thm)],[f39,f59]) ).
fof(f72,plain,
symmetric_difference(sK2_skl,sK3_skl) != difference(union(sK3_skl,sK2_skl),intersection(sK3_skl,sK2_skl)),
inference(paramodulation,[status(thm)],[f40,f66]) ).
fof(f82,plain,
! [X0,X1] : difference(X0,intersection(X1,X0)) = difference(X0,X1),
inference(paramodulation,[status(thm)],[f40,f17]) ).
fof(f118,plain,
! [X0,X1,X2] : difference(union(X0,X1),intersection(X0,X2)) = union(difference(X0,X2),difference(X1,intersection(X0,X2))),
inference(paramodulation,[status(thm)],[f17,f18]) ).
fof(f340,plain,
! [X0,X1] : difference(union(X0,X1),intersection(X0,X1)) = union(difference(X0,X1),difference(X1,X0)),
inference(paramodulation,[status(thm)],[f82,f118]) ).
fof(f351,plain,
! [X0,X1] : difference(union(X0,X1),intersection(X0,X1)) = symmetric_difference(X0,X1),
inference(forward_demodulation,[status(thm)],[f16,f340]) ).
fof(f353,plain,
symmetric_difference(sK2_skl,sK3_skl) != symmetric_difference(sK3_skl,sK2_skl),
inference(backward_demodulation,[status(thm)],[f351,f72]) ).
fof(f383,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f353,f41]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET620+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/5.35 % Computer : n016.cluster.edu
% 0.08/5.35 % Model : x86_64 x86_64
% 0.08/5.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/5.35 % Memory : 8046.5625MB
% 0.08/5.35 % OS : Linux 6.8.0-71-generic
% 0.08/5.36 % CPULimit : 300
% 0.08/5.36 % WCLimit : 300
% 0.08/5.36 % DateTime : Mon Sep 21 05:34:27 UTC 2026
% 0.08/5.36 % CPUTime :
% 0.08/5.37 % Drodi V4.1.1
% 0.12/5.40 % Refutation found
% 0.12/5.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/5.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/5.43 % Elapsed time: 0.066645 seconds
% 0.12/5.43 % CPU time: 0.217931 seconds
% 0.12/5.43 % Total memory used: 103.455 MB
% 0.12/5.43 % Net memory used: 103.063 MB
%------------------------------------------------------------------------------