%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET921+1 : TPTP v9.3.1. Released v3.2.0.
% 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 02:10:58 PM UTC 2026
% Result : Theorem 0.13s 0.57s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 7
% Syntax : Number of formulae : 50 ( 2 unt; 4 def)
% Number of atoms : 187 ( 47 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 227 ( 90 ~; 94 |; 32 &)
% ( 10 <=>; 0 =>; 0 <=; 1 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 5 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 88 ( 78 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [A,B] :
( B = singleton(A)
<=> ! [C] :
( in(C,B)
<=> C = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,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(f6,conjecture,
! [A,B,C] :
( in(A,set_difference(B,singleton(C)))
<=> ( A != C
& in(A,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,negated_conjecture,
~ ! [A,B,C] :
( in(A,set_difference(B,singleton(C)))
<=> ( A != C
& in(A,B) ) ),
inference(negated_conjecture,[status(cth)],[f6]) ).
fof(f10,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)],[f2]) ).
fof(f11,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)],[f10]) ).
fof(f12,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))],[f11]) ).
fof(f13,plain,
! [X0,X1,X2] :
( X2 = X1
| ~ in(X2,X0)
| X0 != singleton(X1) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f14,plain,
! [X0,X1,X2] :
( X2 != X1
| in(X2,X0)
| X0 != singleton(X1) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f17,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)],[f3]) ).
fof(f18,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)],[f17]) ).
fof(f19,plain,
( ! [A,B,C] :
( ( ( ( ~ in(sK1_skl(C,B,A),B)
& in(sK1_skl(C,B,A),A) )
| in(sK1_skl(C,B,A),C) )
& ( in(sK1_skl(C,B,A),B)
| ~ in(sK1_skl(C,B,A),A)
| ~ in(sK1_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,[sK1_skl]),skolemize(D,sK1_skl(C,B,A))],[f18]) ).
fof(f20,plain,
! [X0,X1,X2,X3] :
( in(X3,X1)
| ~ in(X3,X0)
| X0 != set_difference(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f21,plain,
! [X0,X1,X2,X3] :
( ~ in(X3,X2)
| ~ in(X3,X0)
| X0 != set_difference(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f22,plain,
! [X0,X1,X2,X3] :
( in(X3,X2)
| ~ in(X3,X1)
| in(X3,X0)
| X0 != set_difference(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f30,plain,
? [A,B,C] :
( in(A,set_difference(B,singleton(C)))
<~> ( A != C
& in(A,B) ) ),
inference(pre_NNF_transformation,[status(thm)],[f7]) ).
fof(f31,plain,
? [A,B,C] :
( ( A = C
| ~ in(A,B)
| ~ in(A,set_difference(B,singleton(C))) )
& ( ( A != C
& in(A,B) )
| in(A,set_difference(B,singleton(C))) ) ),
inference(NNF_transformation,[status(thm)],[f30]) ).
fof(f32,plain,
( ( sK4_skl = sK6_skl
| ~ in(sK4_skl,sK5_skl)
| ~ in(sK4_skl,set_difference(sK5_skl,singleton(sK6_skl))) )
& ( ( sK4_skl != sK6_skl
& in(sK4_skl,sK5_skl) )
| in(sK4_skl,set_difference(sK5_skl,singleton(sK6_skl))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4_skl,sK5_skl,sK6_skl]),skolemize(A,sK4_skl),skolemize(B,sK5_skl),skolemize(C,sK6_skl)],[f31]) ).
fof(f33,plain,
( in(sK4_skl,sK5_skl)
| in(sK4_skl,set_difference(sK5_skl,singleton(sK6_skl))) ),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f34,plain,
( sK4_skl != sK6_skl
| in(sK4_skl,set_difference(sK5_skl,singleton(sK6_skl))) ),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f35,plain,
( sK4_skl = sK6_skl
| ~ in(sK4_skl,sK5_skl)
| ~ in(sK4_skl,set_difference(sK5_skl,singleton(sK6_skl))) ),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f36,definition,
( sQ0_spl
<=> in(sK4_skl,set_difference(sK5_skl,singleton(sK6_skl))) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f37,plain,
( ~ sQ0_spl
| in(sK4_skl,set_difference(sK5_skl,singleton(sK6_skl))) ),
inference(component_clause,[status(thm)],[f36]) ).
fof(f38,plain,
( sQ0_spl
| ~ in(sK4_skl,set_difference(sK5_skl,singleton(sK6_skl))) ),
inference(component_clause,[status(thm)],[f36]) ).
fof(f39,definition,
( sQ1_spl
<=> in(sK4_skl,sK5_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f41,plain,
( sQ1_spl
| ~ in(sK4_skl,sK5_skl) ),
inference(component_clause,[status(thm)],[f39]) ).
fof(f42,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f33,f36,f39]) ).
fof(f43,definition,
( sQ2_spl
<=> sK4_skl = sK6_skl ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f44,plain,
( ~ sQ2_spl
| sK4_skl = sK6_skl ),
inference(component_clause,[status(thm)],[f43]) ).
fof(f46,plain,
( ~ sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f34,f36,f43]) ).
fof(f47,plain,
( sQ2_spl
| ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f35,f36,f39,f43]) ).
fof(f48,plain,
! [X0,X1] :
( X0 = X1
| ~ in(X0,singleton(X1)) ),
inference(destructive_equality_resolution,[status(thm)],[f13]) ).
fof(f49,plain,
! [X0] : in(X0,singleton(X0)),
inference(destructive_equality_resolution,[status(thm)],[f14]) ).
fof(f50,plain,
! [X0,X1,X2] :
( in(X0,X1)
| ~ in(X0,set_difference(X1,X2)) ),
inference(destructive_equality_resolution,[status(thm)],[f20]) ).
fof(f51,plain,
! [X0,X1,X2] :
( ~ in(X0,X2)
| ~ in(X0,set_difference(X1,X2)) ),
inference(destructive_equality_resolution,[status(thm)],[f21]) ).
fof(f52,plain,
! [X0,X1,X2] :
( in(X0,X2)
| ~ in(X0,X1)
| in(X0,set_difference(X1,X2)) ),
inference(destructive_equality_resolution,[status(thm)],[f22]) ).
fof(f56,plain,
( ~ sQ0_spl
| in(sK4_skl,sK5_skl) ),
inference(resolution,[status(thm)],[f50,f37]) ).
fof(f57,plain,
( ~ sQ0_spl
| sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f56,f41]) ).
fof(f58,plain,
( ~ sQ0_spl
| sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f57]) ).
fof(f60,plain,
( sQ0_spl
| in(sK4_skl,singleton(sK6_skl))
| ~ in(sK4_skl,sK5_skl) ),
inference(resolution,[status(thm)],[f52,f38]) ).
fof(f65,definition,
( sQ3_spl
<=> in(sK4_skl,singleton(sK6_skl)) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f66,plain,
( ~ sQ3_spl
| in(sK4_skl,singleton(sK6_skl)) ),
inference(component_clause,[status(thm)],[f65]) ).
fof(f68,plain,
( sQ0_spl
| sQ3_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f60,f39,f65,f36]) ).
fof(f69,plain,
( ~ sQ0_spl
| ~ sQ2_spl
| in(sK4_skl,set_difference(sK5_skl,singleton(sK4_skl))) ),
inference(forward_demodulation,[status(thm)],[f44,f37]) ).
fof(f70,plain,
( ~ sQ0_spl
| ~ sQ2_spl
| ~ in(sK4_skl,singleton(sK4_skl)) ),
inference(resolution,[status(thm)],[f69,f51]) ).
fof(f73,plain,
( ~ sQ0_spl
| ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f70,f49]) ).
fof(f74,plain,
( ~ sQ0_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f73]) ).
fof(f75,plain,
( ~ sQ3_spl
| sK4_skl = sK6_skl ),
inference(resolution,[status(thm)],[f66,f48]) ).
fof(f77,plain,
( ~ sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f75,f43,f65]) ).
fof(f78,plain,
$false,
inference(sat_refutation,[status(thm)],[f42,f46,f47,f58,f68,f74,f77]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET921+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.54 % Computer : n010.cluster.edu
% 0.09/0.54 % Model : x86_64 x86_64
% 0.09/0.54 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.54 % Memory : 8046.5625MB
% 0.09/0.54 % OS : Linux 6.8.0-71-generic
% 0.09/0.54 % CPULimit : 300
% 0.09/0.54 % WCLimit : 300
% 0.09/0.54 % DateTime : Mon Sep 21 05:44:10 UTC 2026
% 0.09/0.54 % CPUTime :
% 0.09/0.55 % Drodi V4.1.1
% 0.13/0.57 % Refutation found
% 0.13/0.57 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.57 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.61 % Elapsed time: 0.051000 seconds
% 0.13/0.61 % CPU time: 0.144558 seconds
% 0.13/0.61 % Total memory used: 80.237 MB
% 0.13/0.61 % Net memory used: 79.816 MB
%------------------------------------------------------------------------------