%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET976+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 : 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 02:11:05 PM UTC 2026
% Result : Theorem 0.08s 0.39s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 3
% Syntax : Number of formulae : 32 ( 6 unt; 0 def)
% Number of atoms : 107 ( 39 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 125 ( 50 ~; 48 |; 21 &)
% ( 5 <=>; 0 =>; 0 <=; 1 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 73 ( 63 !; 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(C,singleton(D)))
<=> ( B = D
& in(A,C) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
~ ! [A,B,C,D] :
( in(ordered_pair(A,B),cartesian_product2(C,singleton(D)))
<=> ( B = D
& in(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(C,singleton(D)))
<~> ( B = D
& in(A,C) ) ),
inference(pre_NNF_transformation,[status(thm)],[f10]) ).
fof(f33,plain,
? [A,B,C,D] :
( ( B != D
| ~ in(A,C)
| ~ in(ordered_pair(A,B),cartesian_product2(C,singleton(D))) )
& ( ( B = D
& in(A,C) )
| in(ordered_pair(A,B),cartesian_product2(C,singleton(D))) ) ),
inference(NNF_transformation,[status(thm)],[f32]) ).
fof(f34,plain,
( ( sK4_skl != sK6_skl
| ~ in(sK3_skl,sK5_skl)
| ~ in(ordered_pair(sK3_skl,sK4_skl),cartesian_product2(sK5_skl,singleton(sK6_skl))) )
& ( ( sK4_skl = sK6_skl
& in(sK3_skl,sK5_skl) )
| in(ordered_pair(sK3_skl,sK4_skl),cartesian_product2(sK5_skl,singleton(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,
( in(sK3_skl,sK5_skl)
| in(ordered_pair(sK3_skl,sK4_skl),cartesian_product2(sK5_skl,singleton(sK6_skl))) ),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f36,plain,
( sK4_skl = sK6_skl
| in(ordered_pair(sK3_skl,sK4_skl),cartesian_product2(sK5_skl,singleton(sK6_skl))) ),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f37,plain,
( sK4_skl != sK6_skl
| ~ in(sK3_skl,sK5_skl)
| ~ in(ordered_pair(sK3_skl,sK4_skl),cartesian_product2(sK5_skl,singleton(sK6_skl))) ),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f38,plain,
! [X0,X1] :
( X0 = X1
| ~ in(X0,singleton(X1)) ),
inference(destructive_equality_resolution,[status(thm)],[f17]) ).
fof(f39,plain,
! [X0] : in(X0,singleton(X0)),
inference(destructive_equality_resolution,[status(thm)],[f18]) ).
fof(f46,plain,
in(sK3_skl,sK5_skl),
inference(backward_subsumption_resolution,[status(thm)],[f35,f25]) ).
fof(f47,plain,
( sK4_skl != sK6_skl
| ~ in(ordered_pair(sK3_skl,sK4_skl),cartesian_product2(sK5_skl,singleton(sK6_skl))) ),
inference(backward_subsumption_resolution,[status(thm)],[f37,f25]) ).
fof(f50,plain,
( sK4_skl = sK6_skl
| in(sK4_skl,singleton(sK6_skl)) ),
inference(resolution,[status(thm)],[f26,f36]) ).
fof(f51,plain,
sK4_skl = sK6_skl,
inference(forward_subsumption_resolution,[status(thm)],[f50,f38]) ).
fof(f75,plain,
( sK4_skl != sK6_skl
| ~ in(ordered_pair(sK3_skl,sK4_skl),cartesian_product2(sK5_skl,singleton(sK4_skl))) ),
inference(forward_demodulation,[status(thm)],[f51,f47]) ).
fof(f76,plain,
( sK4_skl != sK4_skl
| ~ in(ordered_pair(sK3_skl,sK4_skl),cartesian_product2(sK5_skl,singleton(sK4_skl))) ),
inference(forward_demodulation,[status(thm)],[f51,f75]) ).
fof(f77,plain,
~ in(ordered_pair(sK3_skl,sK4_skl),cartesian_product2(sK5_skl,singleton(sK4_skl))),
inference(trivial_equality_resolution,[status(thm)],[f76]) ).
fof(f78,plain,
( ~ in(sK4_skl,singleton(sK4_skl))
| ~ in(sK3_skl,sK5_skl) ),
inference(resolution,[status(thm)],[f77,f27]) ).
fof(f79,plain,
~ in(sK4_skl,singleton(sK4_skl)),
inference(forward_subsumption_resolution,[status(thm)],[f78,f46]) ).
fof(f80,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f79,f39]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET976+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n007.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Mon Sep 21 05:42:51 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.37 % Drodi V4.1.1
% 0.08/0.39 % Refutation found
% 0.08/0.39 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.08/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.08/0.42 % Elapsed time: 0.054895 seconds
% 0.08/0.42 % CPU time: 0.152828 seconds
% 0.08/0.42 % Total memory used: 101.738 MB
% 0.08/0.42 % Net memory used: 101.347 MB
%------------------------------------------------------------------------------