%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET580+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 : n003.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 02:10:07 PM UTC 2026
% Result : Theorem 0.11s 0.38s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 10
% Syntax : Number of formulae : 63 ( 5 unt; 5 def)
% Number of atoms : 178 ( 4 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 193 ( 78 ~; 87 |; 15 &)
% ( 11 <=>; 0 =>; 0 <=; 2 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 6 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 77 ( 71 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [B,C,D] :
( member(D,union(B,C))
<=> ( member(D,C)
| member(D,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [B,C,D] :
( member(D,difference(B,C))
<=> ( ~ member(D,C)
& member(D,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [B,C] : symmetric_difference(B,C) = union(difference(B,C),difference(C,B)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [B,C] : symmetric_difference(B,C) = symmetric_difference(C,B),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,conjecture,
! [B,C,D] :
( member(B,symmetric_difference(C,D))
<=> ~ ( member(B,C)
<=> member(B,D) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
~ ! [B,C,D] :
( member(B,symmetric_difference(C,D))
<=> ~ ( member(B,C)
<=> member(B,D) ) ),
inference(negated_conjecture,[status(cth)],[f7]) ).
fof(f9,plain,
! [B,C,D] :
( ( ( ~ member(D,C)
& ~ member(D,B) )
| member(D,union(B,C)) )
& ( member(D,C)
| member(D,B)
| ~ member(D,union(B,C)) ) ),
inference(NNF_transformation,[status(thm)],[f1]) ).
fof(f10,plain,
( ! [B,C,D] :
( ( ~ member(D,C)
& ~ member(D,B) )
| member(D,union(B,C)) )
& ! [B,C,D] :
( member(D,C)
| member(D,B)
| ~ member(D,union(B,C)) ) ),
inference(miniscoping,[status(thm)],[f9]) ).
fof(f11,plain,
! [X0,X1,X2] :
( member(X0,X2)
| member(X0,X1)
| ~ member(X0,union(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f12,plain,
! [X0,X1,X2] :
( ~ member(X0,X1)
| member(X0,union(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f13,plain,
! [X0,X1,X2] :
( ~ member(X0,X2)
| member(X0,union(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f14,plain,
! [B,C,D] :
( ( member(D,C)
| ~ member(D,B)
| member(D,difference(B,C)) )
& ( ( ~ member(D,C)
& member(D,B) )
| ~ member(D,difference(B,C)) ) ),
inference(NNF_transformation,[status(thm)],[f2]) ).
fof(f15,plain,
( ! [B,C,D] :
( member(D,C)
| ~ member(D,B)
| member(D,difference(B,C)) )
& ! [B,C,D] :
( ( ~ member(D,C)
& member(D,B) )
| ~ member(D,difference(B,C)) ) ),
inference(miniscoping,[status(thm)],[f14]) ).
fof(f16,plain,
! [X0,X1,X2] :
( member(X0,X1)
| ~ member(X0,difference(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f17,plain,
! [X0,X1,X2] :
( ~ member(X0,X2)
| ~ member(X0,difference(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f18,plain,
! [X0,X1,X2] :
( member(X0,X2)
| ~ member(X0,X1)
| member(X0,difference(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f19,plain,
! [X0,X1] : symmetric_difference(X0,X1) = union(difference(X0,X1),difference(X1,X0)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f21,plain,
! [X0,X1] : symmetric_difference(X0,X1) = symmetric_difference(X1,X0),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f29,plain,
? [B,C,D] :
( member(B,symmetric_difference(C,D))
<~> ( member(B,C)
<~> member(B,D) ) ),
inference(pre_NNF_transformation,[status(thm)],[f8]) ).
fof(f30,plain,
? [B,C,D] :
( ( ( ( ~ member(B,D)
| member(B,C) )
& ( member(B,D)
| ~ member(B,C) ) )
| ~ member(B,symmetric_difference(C,D)) )
& ( ( ( ~ member(B,D)
| ~ member(B,C) )
& ( member(B,D)
| member(B,C) ) )
| member(B,symmetric_difference(C,D)) ) ),
inference(NNF_transformation,[status(thm)],[f29]) ).
fof(f31,plain,
( ( ( ( ~ member(sK1_skl,sK3_skl)
| member(sK1_skl,sK2_skl) )
& ( member(sK1_skl,sK3_skl)
| ~ member(sK1_skl,sK2_skl) ) )
| ~ member(sK1_skl,symmetric_difference(sK2_skl,sK3_skl)) )
& ( ( ( ~ member(sK1_skl,sK3_skl)
| ~ member(sK1_skl,sK2_skl) )
& ( member(sK1_skl,sK3_skl)
| member(sK1_skl,sK2_skl) ) )
| member(sK1_skl,symmetric_difference(sK2_skl,sK3_skl)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl,sK2_skl,sK3_skl]),skolemize(B,sK1_skl),skolemize(C,sK2_skl),skolemize(D,sK3_skl)],[f30]) ).
fof(f32,plain,
( member(sK1_skl,sK3_skl)
| member(sK1_skl,sK2_skl)
| member(sK1_skl,symmetric_difference(sK2_skl,sK3_skl)) ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f33,plain,
( ~ member(sK1_skl,sK3_skl)
| ~ member(sK1_skl,sK2_skl)
| member(sK1_skl,symmetric_difference(sK2_skl,sK3_skl)) ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f34,plain,
( member(sK1_skl,sK3_skl)
| ~ member(sK1_skl,sK2_skl)
| ~ member(sK1_skl,symmetric_difference(sK2_skl,sK3_skl)) ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f35,plain,
( ~ member(sK1_skl,sK3_skl)
| member(sK1_skl,sK2_skl)
| ~ member(sK1_skl,symmetric_difference(sK2_skl,sK3_skl)) ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f36,definition,
( sQ0_spl
<=> member(sK1_skl,symmetric_difference(sK2_skl,sK3_skl)) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f37,plain,
( ~ sQ0_spl
| member(sK1_skl,symmetric_difference(sK2_skl,sK3_skl)) ),
inference(component_clause,[status(thm)],[f36]) ).
fof(f38,plain,
( sQ0_spl
| ~ member(sK1_skl,symmetric_difference(sK2_skl,sK3_skl)) ),
inference(component_clause,[status(thm)],[f36]) ).
fof(f39,definition,
( sQ1_spl
<=> member(sK1_skl,sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f42,definition,
( sQ2_spl
<=> member(sK1_skl,sK3_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f43,plain,
( ~ sQ2_spl
| member(sK1_skl,sK3_skl) ),
inference(component_clause,[status(thm)],[f42]) ).
fof(f45,plain,
( sQ2_spl
| sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f32,f36,f39,f42]) ).
fof(f46,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f33,f36,f39,f42]) ).
fof(f47,plain,
( sQ2_spl
| ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f34,f36,f39,f42]) ).
fof(f48,plain,
( ~ sQ2_spl
| sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f35,f36,f39,f42]) ).
fof(f53,plain,
( ~ sQ0_spl
| member(sK1_skl,symmetric_difference(sK3_skl,sK2_skl)) ),
inference(paramodulation,[status(thm)],[f21,f37]) ).
fof(f65,plain,
! [X0,X1,X2] :
( ~ member(X0,difference(X2,X1))
| member(X0,symmetric_difference(X1,X2)) ),
inference(paramodulation,[status(thm)],[f19,f13]) ).
fof(f66,plain,
! [X0,X1,X2] :
( ~ member(X0,difference(X1,X2))
| member(X0,symmetric_difference(X1,X2)) ),
inference(paramodulation,[status(thm)],[f19,f12]) ).
fof(f75,plain,
! [X0,X1,X2] :
( member(X0,difference(X2,X1))
| member(X0,difference(X1,X2))
| ~ member(X0,symmetric_difference(X1,X2)) ),
inference(paramodulation,[status(thm)],[f19,f11]) ).
fof(f78,plain,
! [X0,X1,X2] :
( member(X0,symmetric_difference(X1,X2))
| member(X0,X2)
| ~ member(X0,X1) ),
inference(resolution,[status(thm)],[f18,f66]) ).
fof(f79,plain,
! [X0,X1,X2] :
( member(X0,symmetric_difference(X2,X1))
| member(X0,X2)
| ~ member(X0,X1) ),
inference(resolution,[status(thm)],[f18,f65]) ).
fof(f98,plain,
( ~ sQ0_spl
| member(sK1_skl,difference(sK2_skl,sK3_skl))
| member(sK1_skl,difference(sK3_skl,sK2_skl)) ),
inference(resolution,[status(thm)],[f75,f53]) ).
fof(f104,definition,
( sQ3_spl
<=> member(sK1_skl,difference(sK3_skl,sK2_skl)) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f105,plain,
( ~ sQ3_spl
| member(sK1_skl,difference(sK3_skl,sK2_skl)) ),
inference(component_clause,[status(thm)],[f104]) ).
fof(f107,definition,
( sQ4_spl
<=> member(sK1_skl,difference(sK2_skl,sK3_skl)) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f108,plain,
( ~ sQ4_spl
| member(sK1_skl,difference(sK2_skl,sK3_skl)) ),
inference(component_clause,[status(thm)],[f107]) ).
fof(f110,plain,
( ~ sQ0_spl
| sQ4_spl
| sQ3_spl ),
inference(split_clause,[status(thm)],[f98,f104,f107,f36]) ).
fof(f112,plain,
( ~ sQ4_spl
| member(sK1_skl,symmetric_difference(sK2_skl,sK3_skl)) ),
inference(resolution,[status(thm)],[f108,f66]) ).
fof(f114,plain,
( ~ sQ4_spl
| ~ member(sK1_skl,sK3_skl) ),
inference(resolution,[status(thm)],[f108,f17]) ).
fof(f115,plain,
( ~ sQ4_spl
| member(sK1_skl,sK2_skl) ),
inference(resolution,[status(thm)],[f108,f16]) ).
fof(f116,plain,
( ~ sQ4_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f112,f36,f107]) ).
fof(f119,plain,
( ~ sQ3_spl
| ~ member(sK1_skl,sK2_skl) ),
inference(resolution,[status(thm)],[f105,f17]) ).
fof(f120,plain,
( ~ sQ3_spl
| member(sK1_skl,sK3_skl) ),
inference(resolution,[status(thm)],[f105,f16]) ).
fof(f121,plain,
( ~ sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f120,f42,f104]) ).
fof(f122,plain,
( ~ sQ3_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f119,f39,f104]) ).
fof(f123,plain,
( sQ0_spl
| member(sK1_skl,sK2_skl)
| ~ member(sK1_skl,sK3_skl) ),
inference(resolution,[status(thm)],[f38,f79]) ).
fof(f124,plain,
( sQ0_spl
| member(sK1_skl,sK3_skl)
| ~ member(sK1_skl,sK2_skl) ),
inference(resolution,[status(thm)],[f38,f78]) ).
fof(f127,plain,
( sQ0_spl
| sQ1_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f123,f42,f39,f36]) ).
fof(f128,plain,
( sQ0_spl
| sQ2_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f124,f39,f42,f36]) ).
fof(f129,plain,
( ~ sQ4_spl
| sQ1_spl ),
inference(split_clause,[status(thm)],[f115,f39,f107]) ).
fof(f134,plain,
( ~ sQ2_spl
| ~ sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f43,f114]) ).
fof(f135,plain,
( ~ sQ2_spl
| ~ sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f134]) ).
fof(f136,plain,
$false,
inference(sat_refutation,[status(thm)],[f45,f46,f47,f48,f110,f116,f121,f122,f127,f128,f129,f135]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET580+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n003.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Mon Sep 21 05:28:47 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.11/0.36 % Drodi V4.1.1
% 0.11/0.38 % Refutation found
% 0.11/0.38 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.11/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.11/0.40 % Elapsed time: 0.045647 seconds
% 0.11/0.40 % CPU time: 0.139100 seconds
% 0.11/0.40 % Total memory used: 85.891 MB
% 0.11/0.40 % Net memory used: 85.556 MB
%------------------------------------------------------------------------------