%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU162+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n007.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 02:19:28 PM UTC 2026
% Result : Theorem 0.12s 0.38s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 18
% Syntax : Number of formulae : 84 ( 19 unt; 7 def)
% Number of atoms : 238 ( 76 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 253 ( 99 ~; 102 |; 34 &)
% ( 15 <=>; 2 =>; 0 <=; 1 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 8 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 134 ( 125 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f6,axiom,
! [A,B] :
( A = B
<=> ( subset(B,A)
& subset(A,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [A,B] :
( B = singleton(A)
<=> ! [C] :
( in(C,B)
<=> C = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [A,B,C] :
( C = set_difference(A,B)
<=> ! [D] :
( in(D,C)
<=> ( ~ in(D,B)
& in(D,A) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f42,lemma,
! [A,B] :
( set_difference(A,B) = empty_set
<=> subset(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f43,lemma,
! [A,B,C] :
( subset(A,B)
=> ( subset(A,set_difference(B,singleton(C)))
| in(C,A) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f47,axiom,
? [A] : empty(A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f65,lemma,
! [A,B] : subset(set_difference(A,B),A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f71,axiom,
! [A] : set_difference(A,empty_set) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f78,axiom,
! [A] : set_difference(empty_set,A) = empty_set,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f82,conjecture,
! [A,B] :
( set_difference(A,singleton(B)) = A
<=> ~ in(B,A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f83,negated_conjecture,
~ ! [A,B] :
( set_difference(A,singleton(B)) = A
<=> ~ in(B,A) ),
inference(negated_conjecture,[status(cth)],[f82]) ).
fof(f85,axiom,
! [A] :
( empty(A)
=> A = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f101,plain,
! [A,B] :
( ( ~ subset(B,A)
| ~ subset(A,B)
| A = B )
& ( ( subset(B,A)
& subset(A,B) )
| A != B ) ),
inference(NNF_transformation,[status(thm)],[f6]) ).
fof(f102,plain,
( ! [A,B] :
( ~ subset(B,A)
| ~ subset(A,B)
| A = B )
& ! [A,B] :
( ( subset(B,A)
& subset(A,B) )
| A != B ) ),
inference(miniscoping,[status(thm)],[f101]) ).
fof(f105,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[status(thm)],[f102]) ).
fof(f106,plain,
! [A,B] :
( ( ? [C] :
( ( C = A
| in(C,B) )
& ( C != A
| ~ in(C,B) ) )
| B = singleton(A) )
& ( ! [C] :
( ( C != A
| in(C,B) )
& ( C = A
| ~ in(C,B) ) )
| B != singleton(A) ) ),
inference(NNF_transformation,[status(thm)],[f7]) ).
fof(f107,plain,
( ! [A,B] :
( ? [C] :
( ( C = A
| in(C,B) )
& ( C != A
| ~ in(C,B) ) )
| B = singleton(A) )
& ! [A,B] :
( ( ! [C] :
( C != A
| in(C,B) )
& ! [C] :
( C = A
| ~ in(C,B) ) )
| B != singleton(A) ) ),
inference(miniscoping,[status(thm)],[f106]) ).
fof(f108,plain,
( ! [A,B] :
( ( ( sK0_skl(B,A) = A
| in(sK0_skl(B,A),B) )
& ( sK0_skl(B,A) != A
| ~ in(sK0_skl(B,A),B) ) )
| B = singleton(A) )
& ! [A,B] :
( ( ! [C] :
( C != A
| in(C,B) )
& ! [C] :
( C = A
| ~ in(C,B) ) )
| B != singleton(A) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(C,sK0_skl(B,A))],[f107]) ).
fof(f110,plain,
! [X0,X1,X2] :
( X2 != X1
| in(X2,X0)
| X0 != singleton(X1) ),
inference(cnf_transformation,[status(thm)],[f108]) ).
fof(f177,plain,
! [A,B,C] :
( ( ? [D] :
( ( ( ~ in(D,B)
& in(D,A) )
| in(D,C) )
& ( in(D,B)
| ~ in(D,A)
| ~ in(D,C) ) )
| C = set_difference(A,B) )
& ( ! [D] :
( ( in(D,B)
| ~ in(D,A)
| in(D,C) )
& ( ( ~ in(D,B)
& in(D,A) )
| ~ in(D,C) ) )
| C != set_difference(A,B) ) ),
inference(NNF_transformation,[status(thm)],[f16]) ).
fof(f178,plain,
( ! [A,B,C] :
( ? [D] :
( ( ( ~ in(D,B)
& in(D,A) )
| in(D,C) )
& ( in(D,B)
| ~ in(D,A)
| ~ in(D,C) ) )
| C = set_difference(A,B) )
& ! [A,B,C] :
( ( ! [D] :
( in(D,B)
| ~ in(D,A)
| in(D,C) )
& ! [D] :
( ( ~ in(D,B)
& in(D,A) )
| ~ in(D,C) ) )
| C != set_difference(A,B) ) ),
inference(miniscoping,[status(thm)],[f177]) ).
fof(f179,plain,
( ! [A,B,C] :
( ( ( ( ~ in(sK15_skl(C,B,A),B)
& in(sK15_skl(C,B,A),A) )
| in(sK15_skl(C,B,A),C) )
& ( in(sK15_skl(C,B,A),B)
| ~ in(sK15_skl(C,B,A),A)
| ~ in(sK15_skl(C,B,A),C) ) )
| C = set_difference(A,B) )
& ! [A,B,C] :
( ( ! [D] :
( in(D,B)
| ~ in(D,A)
| in(D,C) )
& ! [D] :
( ( ~ in(D,B)
& in(D,A) )
| ~ in(D,C) ) )
| C != set_difference(A,B) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15_skl]),skolemize(D,sK15_skl(C,B,A))],[f178]) ).
fof(f181,plain,
! [X0,X1,X2,X3] :
( ~ in(X3,X2)
| ~ in(X3,X0)
| X0 != set_difference(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f179]) ).
fof(f221,plain,
! [A,B] :
( ( ~ subset(A,B)
| set_difference(A,B) = empty_set )
& ( subset(A,B)
| set_difference(A,B) != empty_set ) ),
inference(NNF_transformation,[status(thm)],[f42]) ).
fof(f222,plain,
( ! [A,B] :
( ~ subset(A,B)
| set_difference(A,B) = empty_set )
& ! [A,B] :
( subset(A,B)
| set_difference(A,B) != empty_set ) ),
inference(miniscoping,[status(thm)],[f221]) ).
fof(f223,plain,
! [X0,X1] :
( subset(X0,X1)
| set_difference(X0,X1) != empty_set ),
inference(cnf_transformation,[status(thm)],[f222]) ).
fof(f224,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| set_difference(X0,X1) = empty_set ),
inference(cnf_transformation,[status(thm)],[f222]) ).
fof(f225,plain,
! [A,B,C] :
( subset(A,set_difference(B,singleton(C)))
| in(C,A)
| ~ subset(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f43]) ).
fof(f226,plain,
! [A,B] :
( ! [C] :
( subset(A,set_difference(B,singleton(C)))
| in(C,A) )
| ~ subset(A,B) ),
inference(miniscoping,[status(thm)],[f225]) ).
fof(f227,plain,
! [X0,X1,X2] :
( subset(X0,set_difference(X1,singleton(X2)))
| in(X2,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f226]) ).
fof(f240,plain,
empty(sK16_skl),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16_skl]),skolemize(A,sK16_skl)],[f47]) ).
fof(f241,plain,
empty(sK16_skl),
inference(cnf_transformation,[status(thm)],[f240]) ).
fof(f279,plain,
! [X0,X1] : subset(set_difference(X0,X1),X0),
inference(cnf_transformation,[status(thm)],[f65]) ).
fof(f299,plain,
! [X0] : set_difference(X0,empty_set) = X0,
inference(cnf_transformation,[status(thm)],[f71]) ).
fof(f314,plain,
! [X0] : set_difference(empty_set,X0) = empty_set,
inference(cnf_transformation,[status(thm)],[f78]) ).
fof(f325,plain,
? [A,B] :
( set_difference(A,singleton(B)) = A
<~> ~ in(B,A) ),
inference(pre_NNF_transformation,[status(thm)],[f83]) ).
fof(f326,plain,
? [A,B] :
( ( in(B,A)
| set_difference(A,singleton(B)) != A )
& ( ~ in(B,A)
| set_difference(A,singleton(B)) = A ) ),
inference(NNF_transformation,[status(thm)],[f325]) ).
fof(f327,plain,
( ( in(sK22_skl,sK21_skl)
| set_difference(sK21_skl,singleton(sK22_skl)) != sK21_skl )
& ( ~ in(sK22_skl,sK21_skl)
| set_difference(sK21_skl,singleton(sK22_skl)) = sK21_skl ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK21_skl,sK22_skl]),skolemize(A,sK21_skl),skolemize(B,sK22_skl)],[f326]) ).
fof(f328,plain,
( ~ in(sK22_skl,sK21_skl)
| set_difference(sK21_skl,singleton(sK22_skl)) = sK21_skl ),
inference(cnf_transformation,[status(thm)],[f327]) ).
fof(f329,plain,
( in(sK22_skl,sK21_skl)
| set_difference(sK21_skl,singleton(sK22_skl)) != sK21_skl ),
inference(cnf_transformation,[status(thm)],[f327]) ).
fof(f331,plain,
! [A] :
( A = empty_set
| ~ empty(A) ),
inference(pre_NNF_transformation,[status(thm)],[f85]) ).
fof(f332,plain,
! [X0] :
( X0 = empty_set
| ~ empty(X0) ),
inference(cnf_transformation,[status(thm)],[f331]) ).
fof(f360,definition,
( sQ0_spl
<=> set_difference(sK21_skl,singleton(sK22_skl)) = sK21_skl ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f361,plain,
( ~ sQ0_spl
| set_difference(sK21_skl,singleton(sK22_skl)) = sK21_skl ),
inference(component_clause,[status(thm)],[f360]) ).
fof(f362,plain,
( sQ0_spl
| set_difference(sK21_skl,singleton(sK22_skl)) != sK21_skl ),
inference(component_clause,[status(thm)],[f360]) ).
fof(f363,definition,
( sQ1_spl
<=> in(sK22_skl,sK21_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f366,plain,
( ~ sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f328,f360,f363]) ).
fof(f367,plain,
( sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f329,f360,f363]) ).
fof(f371,plain,
! [X0] : in(X0,singleton(X0)),
inference(destructive_equality_resolution,[status(thm)],[f110]) ).
fof(f390,plain,
! [X0,X1,X2] :
( ~ in(X0,X2)
| ~ in(X0,set_difference(X1,X2)) ),
inference(destructive_equality_resolution,[status(thm)],[f181]) ).
fof(f398,plain,
! [X0] : subset(X0,X0),
inference(paramodulation,[status(thm)],[f299,f279]) ).
fof(f406,plain,
! [X0] : subset(empty_set,X0),
inference(resolution,[status(thm)],[f223,f314]) ).
fof(f408,plain,
! [X0] :
( subset(empty_set,X0)
| empty_set != empty_set ),
inference(paramodulation,[status(thm)],[f314,f223]) ).
fof(f410,definition,
( sQ2_spl
<=> empty_set = empty_set ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f412,plain,
( sQ2_spl
| empty_set != empty_set ),
inference(component_clause,[status(thm)],[f410]) ).
fof(f413,definition,
! [X0] :
( sQ3_spl
<=> subset(empty_set,X0) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f416,plain,
( sQ3_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f408,f410,f413]) ).
fof(f418,plain,
( sQ2_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f412]) ).
fof(f419,plain,
sQ2_spl,
inference(contradiction_clause,[status(thm)],[f418]) ).
fof(f433,plain,
! [X0] :
( ~ sQ0_spl
| ~ in(X0,singleton(sK22_skl))
| ~ in(X0,sK21_skl) ),
inference(paramodulation,[status(thm)],[f361,f390]) ).
fof(f444,plain,
( ~ sQ0_spl
| ~ in(sK22_skl,sK21_skl) ),
inference(resolution,[status(thm)],[f433,f371]) ).
fof(f445,plain,
( ~ sQ0_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f444,f363,f360]) ).
fof(f473,plain,
sK16_skl = empty_set,
inference(resolution,[status(thm)],[f332,f241]) ).
fof(f478,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| set_difference(X0,X1) = sK16_skl ),
inference(backward_demodulation,[status(thm)],[f473,f224]) ).
fof(f482,plain,
! [X0] : subset(sK16_skl,X0),
inference(backward_demodulation,[status(thm)],[f473,f406]) ).
fof(f483,plain,
! [X0,X1] :
( subset(X0,X1)
| set_difference(X0,X1) != sK16_skl ),
inference(backward_demodulation,[status(thm)],[f473,f223]) ).
fof(f484,plain,
! [X0] : set_difference(empty_set,X0) = sK16_skl,
inference(backward_demodulation,[status(thm)],[f473,f314]) ).
fof(f487,plain,
! [X0] : set_difference(sK16_skl,X0) = sK16_skl,
inference(forward_demodulation,[status(thm)],[f473,f484]) ).
fof(f517,plain,
! [X0,X1] :
( ~ subset(X0,set_difference(X0,X1))
| X0 = set_difference(X0,X1) ),
inference(resolution,[status(thm)],[f105,f279]) ).
fof(f531,plain,
! [X0] :
( ~ subset(sK16_skl,X0)
| sK16_skl = sK16_skl ),
inference(paramodulation,[status(thm)],[f487,f478]) ).
fof(f533,definition,
( sQ7_spl
<=> sK16_skl = sK16_skl ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f536,definition,
! [X0] :
( sQ8_spl
<=> ~ subset(sK16_skl,X0) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f537,plain,
! [X0] :
( ~ sQ8_spl
| ~ subset(sK16_skl,X0) ),
inference(component_clause,[status(thm)],[f536]) ).
fof(f539,plain,
( sQ8_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f531,f533,f536]) ).
fof(f543,plain,
! [X0] :
( subset(sK16_skl,X0)
| sK16_skl != sK16_skl ),
inference(paramodulation,[status(thm)],[f487,f483]) ).
fof(f545,definition,
! [X0] :
( sQ9_spl
<=> subset(sK16_skl,X0) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f548,plain,
( sQ9_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f543,f533,f545]) ).
fof(f550,plain,
( ~ sQ8_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f537,f482]) ).
fof(f551,plain,
~ sQ8_spl,
inference(contradiction_clause,[status(thm)],[f550]) ).
fof(f560,plain,
! [X0,X1] :
( in(X1,X0)
| ~ subset(X0,X0)
| X0 = set_difference(X0,singleton(X1)) ),
inference(resolution,[status(thm)],[f517,f227]) ).
fof(f563,plain,
! [X0,X1] :
( in(X1,X0)
| X0 = set_difference(X0,singleton(X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[f560,f398]) ).
fof(f571,plain,
( sQ0_spl
| in(sK22_skl,sK21_skl) ),
inference(resolution,[status(thm)],[f563,f362]) ).
fof(f586,plain,
( sQ0_spl
| sQ1_spl ),
inference(split_clause,[status(thm)],[f571,f363,f360]) ).
fof(f597,plain,
$false,
inference(sat_refutation,[status(thm)],[f366,f367,f416,f419,f445,f539,f548,f551,f586]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU162+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n007.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 05:52:05 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.37 % Drodi V4.1.1
% 0.12/0.38 % Refutation found
% 0.12/0.38 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.41 % Elapsed time: 0.057267 seconds
% 0.12/0.41 % CPU time: 0.132890 seconds
% 0.12/0.41 % Total memory used: 53.718 MB
% 0.12/0.41 % Net memory used: 53.652 MB
%------------------------------------------------------------------------------