%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET975+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 : n014.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 02:11:05 PM UTC 2026
% Result : Theorem 0.13s 0.39s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 6
% Syntax : Number of formulae : 46 ( 2 unt; 3 def)
% Number of atoms : 149 ( 38 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 170 ( 67 ~; 73 |; 21 &)
% ( 8 <=>; 0 =>; 0 <=; 1 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 4 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 76 ( 66 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [A,B] :
( B = singleton(A)
<=> ! [C] :
( in(C,B)
<=> C = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [A,B,C,D] :
( in(ordered_pair(A,B),cartesian_product2(C,D))
<=> ( in(B,D)
& in(A,C) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,conjecture,
! [A,B,C,D] :
( in(ordered_pair(A,B),cartesian_product2(singleton(C),D))
<=> ( in(B,D)
& A = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
~ ! [A,B,C,D] :
( in(ordered_pair(A,B),cartesian_product2(singleton(C),D))
<=> ( in(B,D)
& A = C ) ),
inference(negated_conjecture,[status(cth)],[f9]) ).
fof(f14,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)],[f3]) ).
fof(f15,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)],[f14]) ).
fof(f16,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))],[f15]) ).
fof(f17,plain,
! [X0,X1,X2] :
( X2 = X1
| ~ in(X2,X0)
| X0 != singleton(X1) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f18,plain,
! [X0,X1,X2] :
( X2 != X1
| in(X2,X0)
| X0 != singleton(X1) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f23,plain,
! [A,B,C,D] :
( ( ~ in(B,D)
| ~ in(A,C)
| in(ordered_pair(A,B),cartesian_product2(C,D)) )
& ( ( in(B,D)
& in(A,C) )
| ~ in(ordered_pair(A,B),cartesian_product2(C,D)) ) ),
inference(NNF_transformation,[status(thm)],[f6]) ).
fof(f24,plain,
( ! [A,B,C,D] :
( ~ in(B,D)
| ~ in(A,C)
| in(ordered_pair(A,B),cartesian_product2(C,D)) )
& ! [A,B,C,D] :
( ( in(B,D)
& in(A,C) )
| ~ in(ordered_pair(A,B),cartesian_product2(C,D)) ) ),
inference(miniscoping,[status(thm)],[f23]) ).
fof(f25,plain,
! [X0,X1,X2,X3] :
( in(X0,X2)
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f26,plain,
! [X0,X1,X2,X3] :
( in(X1,X3)
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f27,plain,
! [X0,X1,X2,X3] :
( ~ in(X1,X3)
| ~ in(X0,X2)
| in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f32,plain,
? [A,B,C,D] :
( in(ordered_pair(A,B),cartesian_product2(singleton(C),D))
<~> ( in(B,D)
& A = C ) ),
inference(pre_NNF_transformation,[status(thm)],[f10]) ).
fof(f33,plain,
? [A,B,C,D] :
( ( ~ in(B,D)
| A != C
| ~ in(ordered_pair(A,B),cartesian_product2(singleton(C),D)) )
& ( ( in(B,D)
& A = C )
| in(ordered_pair(A,B),cartesian_product2(singleton(C),D)) ) ),
inference(NNF_transformation,[status(thm)],[f32]) ).
fof(f34,plain,
( ( ~ in(sK4_skl,sK6_skl)
| sK3_skl != sK5_skl
| ~ in(ordered_pair(sK3_skl,sK4_skl),cartesian_product2(singleton(sK5_skl),sK6_skl)) )
& ( ( in(sK4_skl,sK6_skl)
& sK3_skl = sK5_skl )
| in(ordered_pair(sK3_skl,sK4_skl),cartesian_product2(singleton(sK5_skl),sK6_skl)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl,sK4_skl,sK5_skl,sK6_skl]),skolemize(A,sK3_skl),skolemize(B,sK4_skl),skolemize(C,sK5_skl),skolemize(D,sK6_skl)],[f33]) ).
fof(f35,plain,
( sK3_skl = sK5_skl
| in(ordered_pair(sK3_skl,sK4_skl),cartesian_product2(singleton(sK5_skl),sK6_skl)) ),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f36,plain,
( in(sK4_skl,sK6_skl)
| in(ordered_pair(sK3_skl,sK4_skl),cartesian_product2(singleton(sK5_skl),sK6_skl)) ),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f37,plain,
( ~ in(sK4_skl,sK6_skl)
| sK3_skl != sK5_skl
| ~ in(ordered_pair(sK3_skl,sK4_skl),cartesian_product2(singleton(sK5_skl),sK6_skl)) ),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f38,definition,
( sQ0_spl
<=> in(ordered_pair(sK3_skl,sK4_skl),cartesian_product2(singleton(sK5_skl),sK6_skl)) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f39,plain,
( ~ sQ0_spl
| in(ordered_pair(sK3_skl,sK4_skl),cartesian_product2(singleton(sK5_skl),sK6_skl)) ),
inference(component_clause,[status(thm)],[f38]) ).
fof(f40,plain,
( sQ0_spl
| ~ in(ordered_pair(sK3_skl,sK4_skl),cartesian_product2(singleton(sK5_skl),sK6_skl)) ),
inference(component_clause,[status(thm)],[f38]) ).
fof(f41,definition,
( sQ1_spl
<=> sK3_skl = sK5_skl ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f42,plain,
( ~ sQ1_spl
| sK3_skl = sK5_skl ),
inference(component_clause,[status(thm)],[f41]) ).
fof(f43,plain,
( sQ1_spl
| sK3_skl != sK5_skl ),
inference(component_clause,[status(thm)],[f41]) ).
fof(f44,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f35,f38,f41]) ).
fof(f45,definition,
( sQ2_spl
<=> in(sK4_skl,sK6_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f46,plain,
( ~ sQ2_spl
| in(sK4_skl,sK6_skl) ),
inference(component_clause,[status(thm)],[f45]) ).
fof(f48,plain,
( sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f36,f38,f45]) ).
fof(f49,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f37,f38,f41,f45]) ).
fof(f50,plain,
! [X0,X1] :
( X0 = X1
| ~ in(X0,singleton(X1)) ),
inference(destructive_equality_resolution,[status(thm)],[f17]) ).
fof(f51,plain,
! [X0] : in(X0,singleton(X0)),
inference(destructive_equality_resolution,[status(thm)],[f18]) ).
fof(f55,plain,
( ~ sQ0_spl
| in(sK3_skl,singleton(sK5_skl)) ),
inference(resolution,[status(thm)],[f25,f39]) ).
fof(f56,plain,
( ~ sQ0_spl
| sK3_skl = sK5_skl ),
inference(resolution,[status(thm)],[f55,f50]) ).
fof(f58,plain,
( ~ sQ0_spl
| sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f56,f43]) ).
fof(f59,plain,
( ~ sQ0_spl
| sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f58]) ).
fof(f61,plain,
! [X0,X1] :
( ~ sQ2_spl
| ~ in(X0,X1)
| in(ordered_pair(X0,sK4_skl),cartesian_product2(X1,sK6_skl)) ),
inference(resolution,[status(thm)],[f27,f46]) ).
fof(f63,plain,
( sQ0_spl
| ~ sQ1_spl
| ~ in(ordered_pair(sK5_skl,sK4_skl),cartesian_product2(singleton(sK5_skl),sK6_skl)) ),
inference(forward_demodulation,[status(thm)],[f42,f40]) ).
fof(f110,plain,
! [X0] :
( ~ sQ2_spl
| in(ordered_pair(X0,sK4_skl),cartesian_product2(singleton(X0),sK6_skl)) ),
inference(resolution,[status(thm)],[f61,f51]) ).
fof(f116,plain,
( sQ0_spl
| ~ sQ1_spl
| ~ sQ2_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f63,f110]) ).
fof(f122,plain,
( sQ0_spl
| ~ sQ1_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f116]) ).
fof(f123,plain,
( ~ sQ0_spl
| ~ sQ1_spl
| in(ordered_pair(sK5_skl,sK4_skl),cartesian_product2(singleton(sK5_skl),sK6_skl)) ),
inference(forward_demodulation,[status(thm)],[f42,f39]) ).
fof(f127,plain,
( ~ sQ0_spl
| ~ sQ1_spl
| in(sK4_skl,sK6_skl) ),
inference(resolution,[status(thm)],[f123,f26]) ).
fof(f131,plain,
( ~ sQ0_spl
| ~ sQ1_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f127,f45,f41,f38]) ).
fof(f132,plain,
$false,
inference(sat_refutation,[status(thm)],[f44,f48,f49,f59,f122,f131]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET975+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n014.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 05:45:04 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.13/0.37 % Drodi V4.1.1
% 0.13/0.39 % Refutation found
% 0.13/0.39 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.41 % Elapsed time: 0.045839 seconds
% 0.13/0.41 % CPU time: 0.137729 seconds
% 0.13/0.41 % Total memory used: 79.519 MB
% 0.13/0.41 % Net memory used: 79.211 MB
%------------------------------------------------------------------------------