%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET628+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 : n009.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 02:10:17 PM UTC 2026
% Result : Theorem 0.07s 5.39s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 7
% Syntax : Number of formulae : 49 ( 4 unt; 2 def)
% Number of atoms : 150 ( 22 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 160 ( 59 ~; 72 |; 20 &)
% ( 8 <=>; 0 =>; 0 <=; 1 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 3 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 69 ( 62 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [B,C] :
( intersect(B,C)
<=> ? [D] :
( member(D,C)
& member(D,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [B] : ~ member(B,empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [B,C] :
( B = C
<=> ! [D] :
( member(D,B)
<=> member(D,C) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [B,C] :
( not_equal(B,C)
<=> B != C ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,conjecture,
! [B] :
( intersect(B,B)
<=> not_equal(B,empty_set) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
~ ! [B] :
( intersect(B,B)
<=> not_equal(B,empty_set) ),
inference(negated_conjecture,[status(cth)],[f7]) ).
fof(f9,plain,
! [B,C] :
( ( ! [D] :
( ~ member(D,C)
| ~ member(D,B) )
| intersect(B,C) )
& ( ? [D] :
( member(D,C)
& member(D,B) )
| ~ intersect(B,C) ) ),
inference(NNF_transformation,[status(thm)],[f1]) ).
fof(f10,plain,
( ! [B,C] :
( ! [D] :
( ~ member(D,C)
| ~ member(D,B) )
| intersect(B,C) )
& ! [B,C] :
( ? [D] :
( member(D,C)
& member(D,B) )
| ~ intersect(B,C) ) ),
inference(miniscoping,[status(thm)],[f9]) ).
fof(f11,plain,
( ! [B,C] :
( ! [D] :
( ~ member(D,C)
| ~ member(D,B) )
| intersect(B,C) )
& ! [B,C] :
( ( member(sK0_skl(C,B),C)
& member(sK0_skl(C,B),B) )
| ~ intersect(B,C) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(D,sK0_skl(C,B))],[f10]) ).
fof(f13,plain,
! [X0,X1] :
( member(sK0_skl(X1,X0),X1)
| ~ intersect(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f14,plain,
! [X0,X1,X2] :
( ~ member(X2,X1)
| ~ member(X2,X0)
| intersect(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f15,plain,
! [X0] : ~ member(X0,empty_set),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f16,plain,
! [B,C] :
( ( ? [D] :
( ( member(D,C)
| member(D,B) )
& ( ~ member(D,C)
| ~ member(D,B) ) )
| B = C )
& ( ! [D] :
( ( ~ member(D,C)
| member(D,B) )
& ( member(D,C)
| ~ member(D,B) ) )
| B != C ) ),
inference(NNF_transformation,[status(thm)],[f3]) ).
fof(f17,plain,
( ! [B,C] :
( ? [D] :
( ( member(D,C)
| member(D,B) )
& ( ~ member(D,C)
| ~ member(D,B) ) )
| B = C )
& ! [B,C] :
( ( ! [D] :
( ~ member(D,C)
| member(D,B) )
& ! [D] :
( member(D,C)
| ~ member(D,B) ) )
| B != C ) ),
inference(miniscoping,[status(thm)],[f16]) ).
fof(f18,plain,
( ! [B,C] :
( ( ( member(sK1_skl(C,B),C)
| member(sK1_skl(C,B),B) )
& ( ~ member(sK1_skl(C,B),C)
| ~ member(sK1_skl(C,B),B) ) )
| B = C )
& ! [B,C] :
( ( ! [D] :
( ~ member(D,C)
| member(D,B) )
& ! [D] :
( member(D,C)
| ~ member(D,B) ) )
| B != C ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl]),skolemize(D,sK1_skl(C,B))],[f17]) ).
fof(f22,plain,
! [X0,X1] :
( member(sK1_skl(X1,X0),X1)
| member(sK1_skl(X1,X0),X0)
| X0 = X1 ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f23,plain,
! [B,C] :
( ( B = C
| not_equal(B,C) )
& ( B != C
| ~ not_equal(B,C) ) ),
inference(NNF_transformation,[status(thm)],[f4]) ).
fof(f24,plain,
( ! [B,C] :
( B = C
| not_equal(B,C) )
& ! [B,C] :
( B != C
| ~ not_equal(B,C) ) ),
inference(miniscoping,[status(thm)],[f23]) ).
fof(f25,plain,
! [X0,X1] :
( X0 != X1
| ~ not_equal(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f26,plain,
! [X0,X1] :
( X0 = X1
| not_equal(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f34,plain,
? [B] :
( intersect(B,B)
<~> not_equal(B,empty_set) ),
inference(pre_NNF_transformation,[status(thm)],[f8]) ).
fof(f35,plain,
? [B] :
( ( ~ not_equal(B,empty_set)
| ~ intersect(B,B) )
& ( not_equal(B,empty_set)
| intersect(B,B) ) ),
inference(NNF_transformation,[status(thm)],[f34]) ).
fof(f36,plain,
( ( ~ not_equal(sK3_skl,empty_set)
| ~ intersect(sK3_skl,sK3_skl) )
& ( not_equal(sK3_skl,empty_set)
| intersect(sK3_skl,sK3_skl) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl]),skolemize(B,sK3_skl)],[f35]) ).
fof(f37,plain,
( not_equal(sK3_skl,empty_set)
| intersect(sK3_skl,sK3_skl) ),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f38,plain,
( ~ not_equal(sK3_skl,empty_set)
| ~ intersect(sK3_skl,sK3_skl) ),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f39,definition,
( sQ0_spl
<=> intersect(sK3_skl,sK3_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f40,plain,
( ~ sQ0_spl
| intersect(sK3_skl,sK3_skl) ),
inference(component_clause,[status(thm)],[f39]) ).
fof(f41,plain,
( sQ0_spl
| ~ intersect(sK3_skl,sK3_skl) ),
inference(component_clause,[status(thm)],[f39]) ).
fof(f42,definition,
( sQ1_spl
<=> not_equal(sK3_skl,empty_set) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f43,plain,
( ~ sQ1_spl
| not_equal(sK3_skl,empty_set) ),
inference(component_clause,[status(thm)],[f42]) ).
fof(f44,plain,
( sQ1_spl
| ~ not_equal(sK3_skl,empty_set) ),
inference(component_clause,[status(thm)],[f42]) ).
fof(f45,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f37,f39,f42]) ).
fof(f46,plain,
( ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f38,f39,f42]) ).
fof(f47,plain,
! [X0] : ~ not_equal(X0,X0),
inference(destructive_equality_resolution,[status(thm)],[f25]) ).
fof(f51,plain,
! [X0] :
( member(sK1_skl(empty_set,X0),X0)
| X0 = empty_set ),
inference(resolution,[status(thm)],[f22,f15]) ).
fof(f57,plain,
! [X0,X1] :
( ~ member(sK1_skl(empty_set,X0),X1)
| intersect(X1,X0)
| X0 = empty_set ),
inference(resolution,[status(thm)],[f51,f14]) ).
fof(f68,plain,
( sQ1_spl
| sK3_skl = empty_set ),
inference(resolution,[status(thm)],[f44,f26]) ).
fof(f74,plain,
( ~ sQ0_spl
| sQ1_spl
| intersect(sK3_skl,empty_set) ),
inference(backward_demodulation,[status(thm)],[f68,f40]) ).
fof(f75,plain,
( ~ sQ0_spl
| sQ1_spl
| intersect(empty_set,empty_set) ),
inference(forward_demodulation,[status(thm)],[f68,f74]) ).
fof(f76,plain,
( ~ sQ0_spl
| sQ1_spl
| member(sK0_skl(empty_set,empty_set),empty_set) ),
inference(resolution,[status(thm)],[f75,f13]) ).
fof(f79,plain,
( ~ sQ0_spl
| sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f76,f15]) ).
fof(f80,plain,
( ~ sQ0_spl
| sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f79]) ).
fof(f84,plain,
! [X0] :
( X0 = empty_set
| intersect(X0,X0)
| X0 = empty_set ),
inference(resolution,[status(thm)],[f57,f51]) ).
fof(f86,plain,
! [X0] :
( intersect(X0,X0)
| X0 = empty_set ),
inference(duplicate_literals_removal,[status(thm)],[f84]) ).
fof(f94,plain,
( sQ0_spl
| sK3_skl = empty_set ),
inference(resolution,[status(thm)],[f86,f41]) ).
fof(f99,plain,
( ~ sQ1_spl
| sQ0_spl
| not_equal(empty_set,empty_set) ),
inference(backward_demodulation,[status(thm)],[f94,f43]) ).
fof(f101,plain,
( ~ sQ1_spl
| sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f99,f47]) ).
fof(f102,plain,
( ~ sQ1_spl
| sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f101]) ).
fof(f103,plain,
$false,
inference(sat_refutation,[status(thm)],[f45,f46,f80,f102]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET628+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/5.35 % Computer : n009.cluster.edu
% 0.07/5.35 % Model : x86_64 x86_64
% 0.07/5.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/5.35 % Memory : 8046.5625MB
% 0.07/5.35 % OS : Linux 6.8.0-71-generic
% 0.07/5.36 % CPULimit : 300
% 0.07/5.36 % WCLimit : 300
% 0.07/5.36 % DateTime : Mon Sep 21 05:30:17 UTC 2026
% 0.07/5.36 % CPUTime :
% 0.07/5.37 % Drodi V4.1.1
% 0.07/5.39 % Refutation found
% 0.07/5.39 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.07/5.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/5.42 % Elapsed time: 0.049827 seconds
% 0.13/5.42 % CPU time: 0.148343 seconds
% 0.13/5.42 % Total memory used: 80.131 MB
% 0.13/5.42 % Net memory used: 79.706 MB
%------------------------------------------------------------------------------