%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET977+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 : n019.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 0.14s 0.39s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 6
% Syntax : Number of formulae : 40 ( 5 unt; 2 def)
% Number of atoms : 108 ( 45 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 123 ( 55 ~; 43 |; 18 &)
% ( 5 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 3 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 75 ( 68 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [A] :
( A = empty_set
<=> ! [B] : ~ in(B,A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [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,axiom,
! [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(f11,conjecture,
! [A,B] :
( A != empty_set
=> ( cartesian_product2(A,singleton(B)) != empty_set
& cartesian_product2(singleton(B),A) != empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
~ ! [A,B] :
( A != empty_set
=> ( cartesian_product2(A,singleton(B)) != empty_set
& cartesian_product2(singleton(B),A) != empty_set ) ),
inference(negated_conjecture,[status(cth)],[f11]) ).
fof(f16,plain,
! [A] :
( ( ? [B] : in(B,A)
| A = empty_set )
& ( ! [B] : ~ in(B,A)
| A != empty_set ) ),
inference(NNF_transformation,[status(thm)],[f3]) ).
fof(f17,plain,
( ! [A] :
( ? [B] : in(B,A)
| A = empty_set )
& ! [A] :
( ! [B] : ~ in(B,A)
| A != empty_set ) ),
inference(miniscoping,[status(thm)],[f16]) ).
fof(f18,plain,
( ! [A] :
( in(sK0_skl(A),A)
| A = empty_set )
& ! [A] :
( ! [B] : ~ in(B,A)
| A != empty_set ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(B,sK0_skl(A))],[f17]) ).
fof(f19,plain,
! [X0,X1] :
( ~ in(X1,X0)
| X0 != empty_set ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f20,plain,
! [X0] :
( in(sK0_skl(X0),X0)
| X0 = empty_set ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f28,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)],[f9]) ).
fof(f29,plain,
( ! [A,B,C,D] :
( ~ in(B,D)
| A != C
| in(ordered_pair(A,B),cartesian_product2(singleton(C),D)) )
& ! [A,B,C,D] :
( ( in(B,D)
& A = C )
| ~ in(ordered_pair(A,B),cartesian_product2(singleton(C),D)) ) ),
inference(miniscoping,[status(thm)],[f28]) ).
fof(f32,plain,
! [X0,X1,X2,X3] :
( ~ in(X1,X3)
| X0 != X2
| in(ordered_pair(X0,X1),cartesian_product2(singleton(X2),X3)) ),
inference(cnf_transformation,[status(thm)],[f29]) ).
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)],[f10]) ).
fof(f34,plain,
( ! [A,B,C,D] :
( B != D
| ~ in(A,C)
| in(ordered_pair(A,B),cartesian_product2(C,singleton(D))) )
& ! [A,B,C,D] :
( ( B = D
& in(A,C) )
| ~ in(ordered_pair(A,B),cartesian_product2(C,singleton(D))) ) ),
inference(miniscoping,[status(thm)],[f33]) ).
fof(f37,plain,
! [X0,X1,X2,X3] :
( X1 != X3
| ~ in(X0,X2)
| in(ordered_pair(X0,X1),cartesian_product2(X2,singleton(X3))) ),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f38,plain,
? [A,B] :
( ( cartesian_product2(A,singleton(B)) = empty_set
| cartesian_product2(singleton(B),A) = empty_set )
& A != empty_set ),
inference(pre_NNF_transformation,[status(thm)],[f12]) ).
fof(f39,plain,
? [A] :
( ( ? [B] : cartesian_product2(A,singleton(B)) = empty_set
| ? [B] : cartesian_product2(singleton(B),A) = empty_set )
& A != empty_set ),
inference(miniscoping,[status(thm)],[f38]) ).
fof(f40,plain,
( ( cartesian_product2(sK3_skl,singleton(sK5_skl)) = empty_set
| cartesian_product2(singleton(sK4_skl),sK3_skl) = empty_set )
& sK3_skl != empty_set ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl,sK4_skl,sK5_skl]),skolemize(A,sK3_skl),skolemize(B,sK4_skl),skolemize(B,sK5_skl)],[f39]) ).
fof(f41,plain,
sK3_skl != empty_set,
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f42,plain,
( cartesian_product2(sK3_skl,singleton(sK5_skl)) = empty_set
| cartesian_product2(singleton(sK4_skl),sK3_skl) = empty_set ),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f43,definition,
( sQ0_spl
<=> cartesian_product2(singleton(sK4_skl),sK3_skl) = empty_set ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f44,plain,
( ~ sQ0_spl
| cartesian_product2(singleton(sK4_skl),sK3_skl) = empty_set ),
inference(component_clause,[status(thm)],[f43]) ).
fof(f46,definition,
( sQ1_spl
<=> cartesian_product2(sK3_skl,singleton(sK5_skl)) = empty_set ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f47,plain,
( ~ sQ1_spl
| cartesian_product2(sK3_skl,singleton(sK5_skl)) = empty_set ),
inference(component_clause,[status(thm)],[f46]) ).
fof(f49,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f42,f43,f46]) ).
fof(f50,plain,
! [X0] : ~ in(X0,empty_set),
inference(destructive_equality_resolution,[status(thm)],[f19]) ).
fof(f51,plain,
! [X0,X1,X2] :
( ~ in(X1,X2)
| in(ordered_pair(X0,X1),cartesian_product2(singleton(X0),X2)) ),
inference(destructive_equality_resolution,[status(thm)],[f32]) ).
fof(f52,plain,
! [X0,X1,X2] :
( ~ in(X0,X2)
| in(ordered_pair(X0,X1),cartesian_product2(X2,singleton(X1))) ),
inference(destructive_equality_resolution,[status(thm)],[f37]) ).
fof(f58,plain,
! [X0] :
( ~ sQ0_spl
| ~ in(X0,sK3_skl)
| in(ordered_pair(sK4_skl,X0),empty_set) ),
inference(paramodulation,[status(thm)],[f44,f51]) ).
fof(f66,plain,
! [X0] :
( ~ sQ0_spl
| ~ in(X0,sK3_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f58,f50]) ).
fof(f78,plain,
( ~ sQ0_spl
| sK3_skl = empty_set ),
inference(resolution,[status(thm)],[f20,f66]) ).
fof(f80,plain,
( ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f78,f41]) ).
fof(f81,plain,
~ sQ0_spl,
inference(contradiction_clause,[status(thm)],[f80]) ).
fof(f101,plain,
! [X0] :
( ~ sQ1_spl
| ~ in(X0,sK3_skl)
| in(ordered_pair(X0,sK5_skl),empty_set) ),
inference(paramodulation,[status(thm)],[f47,f52]) ).
fof(f102,plain,
! [X0] :
( ~ sQ1_spl
| ~ in(X0,sK3_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f101,f50]) ).
fof(f114,plain,
( ~ sQ1_spl
| sK3_skl = empty_set ),
inference(resolution,[status(thm)],[f102,f20]) ).
fof(f115,plain,
( ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f114,f41]) ).
fof(f116,plain,
~ sQ1_spl,
inference(contradiction_clause,[status(thm)],[f115]) ).
fof(f117,plain,
$false,
inference(sat_refutation,[status(thm)],[f49,f81,f116]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET977+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n019.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 05:46:05 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 0.14/0.39 % Refutation found
% 0.14/0.39 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.42 % Elapsed time: 0.050012 seconds
% 0.14/0.42 % CPU time: 0.144787 seconds
% 0.14/0.42 % Total memory used: 79.710 MB
% 0.14/0.42 % Net memory used: 79.414 MB
%------------------------------------------------------------------------------