%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET630+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 : n010.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 02:10:18 PM UTC 2026
% Result : Theorem 0.10s 0.40s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 6
% Syntax : Number of formulae : 27 ( 17 unt; 0 def)
% Number of atoms : 51 ( 4 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 47 ( 23 ~; 16 |; 6 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 56 ( 54 !; 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,D] :
( intersect(B,union(C,D))
<=> ( intersect(B,D)
| intersect(B,C) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [B,C] : disjoint(intersection(B,C),difference(B,C)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [B,C] :
( disjoint(B,C)
<=> ~ intersect(B,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [B,C] : intersection(B,C) = intersection(C,B),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,conjecture,
! [B,C] : disjoint(intersection(B,C),symmetric_difference(B,C)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
~ ! [B,C] : disjoint(intersection(B,C),symmetric_difference(B,C)),
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,
! [B,C,D] :
( ( ( ~ intersect(B,D)
& ~ intersect(B,C) )
| intersect(B,union(C,D)) )
& ( intersect(B,D)
| intersect(B,C)
| ~ intersect(B,union(C,D)) ) ),
inference(NNF_transformation,[status(thm)],[f2]) ).
fof(f16,plain,
( ! [B,C,D] :
( ( ~ intersect(B,D)
& ~ intersect(B,C) )
| intersect(B,union(C,D)) )
& ! [B,C,D] :
( intersect(B,D)
| intersect(B,C)
| ~ intersect(B,union(C,D)) ) ),
inference(miniscoping,[status(thm)],[f15]) ).
fof(f17,plain,
! [X0,X1,X2] :
( intersect(X0,X2)
| intersect(X0,X1)
| ~ intersect(X0,union(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f20,plain,
! [X0,X1] : disjoint(intersection(X0,X1),difference(X0,X1)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f32,plain,
! [B,C] :
( ( intersect(B,C)
| disjoint(B,C) )
& ( ~ intersect(B,C)
| ~ disjoint(B,C) ) ),
inference(NNF_transformation,[status(thm)],[f6]) ).
fof(f33,plain,
( ! [B,C] :
( intersect(B,C)
| disjoint(B,C) )
& ! [B,C] :
( ~ intersect(B,C)
| ~ disjoint(B,C) ) ),
inference(miniscoping,[status(thm)],[f32]) ).
fof(f34,plain,
! [X0,X1] :
( ~ intersect(X0,X1)
| ~ disjoint(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f35,plain,
! [X0,X1] :
( intersect(X0,X1)
| disjoint(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f37,plain,
! [X0,X1] : intersection(X0,X1) = intersection(X1,X0),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f48,plain,
? [B,C] : ~ disjoint(intersection(B,C),symmetric_difference(B,C)),
inference(pre_NNF_transformation,[status(thm)],[f13]) ).
fof(f49,plain,
~ disjoint(intersection(sK2_skl,sK3_skl),symmetric_difference(sK2_skl,sK3_skl)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl,sK3_skl]),skolemize(B,sK2_skl),skolemize(C,sK3_skl)],[f48]) ).
fof(f50,plain,
~ disjoint(intersection(sK2_skl,sK3_skl),symmetric_difference(sK2_skl,sK3_skl)),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f79,plain,
intersect(intersection(sK2_skl,sK3_skl),symmetric_difference(sK2_skl,sK3_skl)),
inference(resolution,[status(thm)],[f35,f50]) ).
fof(f81,plain,
! [X0,X1] : ~ intersect(intersection(X0,X1),difference(X0,X1)),
inference(resolution,[status(thm)],[f20,f34]) ).
fof(f84,plain,
! [X0,X1,X2] :
( intersect(intersection(X0,X1),X2)
| ~ intersect(intersection(X0,X1),union(difference(X0,X1),X2)) ),
inference(resolution,[status(thm)],[f81,f17]) ).
fof(f86,plain,
! [X0,X1] : ~ intersect(intersection(X0,X1),difference(X1,X0)),
inference(paramodulation,[status(thm)],[f37,f81]) ).
fof(f98,plain,
! [X0,X1] : ~ intersect(intersection(X0,X1),union(difference(X0,X1),difference(X1,X0))),
inference(resolution,[status(thm)],[f86,f84]) ).
fof(f104,plain,
! [X0,X1] : ~ intersect(intersection(X0,X1),symmetric_difference(X0,X1)),
inference(forward_demodulation,[status(thm)],[f14,f98]) ).
fof(f105,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f79,f104]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET630+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n010.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 21 05:30:40 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.38 % Drodi V4.1.1
% 0.10/0.40 % Refutation found
% 0.10/0.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.10/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.10/0.42 % Elapsed time: 0.047609 seconds
% 0.10/0.42 % CPU time: 0.143217 seconds
% 0.10/0.42 % Total memory used: 101.911 MB
% 0.10/0.42 % Net memory used: 101.533 MB
%------------------------------------------------------------------------------