%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET971+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 02:11:04 PM UTC 2026
% Result : Theorem 0.08s 0.40s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 4
% Syntax : Number of formulae : 21 ( 14 unt; 0 def)
% Number of atoms : 32 ( 18 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 20 ( 9 ~; 2 |; 6 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 32 ( 28 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [A,B,C,D] : cartesian_product2(set_intersection2(A,B),set_intersection2(C,D)) = set_intersection2(cartesian_product2(A,C),cartesian_product2(B,D)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,conjecture,
! [A,B,C,D] :
( ( subset(C,D)
& subset(A,B) )
=> set_intersection2(cartesian_product2(A,D),cartesian_product2(B,C)) = cartesian_product2(A,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
~ ! [A,B,C,D] :
( ( subset(C,D)
& subset(A,B) )
=> set_intersection2(cartesian_product2(A,D),cartesian_product2(B,C)) = cartesian_product2(A,C) ),
inference(negated_conjecture,[status(cth)],[f7]) ).
fof(f9,axiom,
! [A,B] :
( subset(A,B)
=> set_intersection2(A,B) = A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,plain,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f19,plain,
! [X0,X1,X2,X3] : cartesian_product2(set_intersection2(X0,X1),set_intersection2(X2,X3)) = set_intersection2(cartesian_product2(X0,X2),cartesian_product2(X1,X3)),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f20,plain,
? [A,B,C,D] :
( set_intersection2(cartesian_product2(A,D),cartesian_product2(B,C)) != cartesian_product2(A,C)
& subset(C,D)
& subset(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f8]) ).
fof(f21,plain,
( set_intersection2(cartesian_product2(sK2_skl,sK5_skl),cartesian_product2(sK3_skl,sK4_skl)) != cartesian_product2(sK2_skl,sK4_skl)
& subset(sK4_skl,sK5_skl)
& subset(sK2_skl,sK3_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl,sK3_skl,sK4_skl,sK5_skl]),skolemize(A,sK2_skl),skolemize(B,sK3_skl),skolemize(C,sK4_skl),skolemize(D,sK5_skl)],[f20]) ).
fof(f22,plain,
subset(sK2_skl,sK3_skl),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f23,plain,
subset(sK4_skl,sK5_skl),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f24,plain,
set_intersection2(cartesian_product2(sK2_skl,sK5_skl),cartesian_product2(sK3_skl,sK4_skl)) != cartesian_product2(sK2_skl,sK4_skl),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f25,plain,
! [A,B] :
( set_intersection2(A,B) = A
| ~ subset(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f9]) ).
fof(f26,plain,
! [X0,X1] :
( set_intersection2(X0,X1) = X0
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f31,plain,
set_intersection2(sK4_skl,sK5_skl) = sK4_skl,
inference(resolution,[status(thm)],[f26,f23]) ).
fof(f32,plain,
set_intersection2(sK2_skl,sK3_skl) = sK2_skl,
inference(resolution,[status(thm)],[f26,f22]) ).
fof(f43,plain,
! [X0,X1] : cartesian_product2(sK2_skl,set_intersection2(X0,X1)) = set_intersection2(cartesian_product2(sK2_skl,X0),cartesian_product2(sK3_skl,X1)),
inference(paramodulation,[status(thm)],[f32,f19]) ).
fof(f44,plain,
cartesian_product2(sK2_skl,set_intersection2(sK5_skl,sK4_skl)) != cartesian_product2(sK2_skl,sK4_skl),
inference(backward_demodulation,[status(thm)],[f43,f24]) ).
fof(f45,plain,
cartesian_product2(sK2_skl,set_intersection2(sK4_skl,sK5_skl)) != cartesian_product2(sK2_skl,sK4_skl),
inference(paramodulation,[status(thm)],[f10,f44]) ).
fof(f47,plain,
cartesian_product2(sK2_skl,sK4_skl) != cartesian_product2(sK2_skl,sK4_skl),
inference(forward_demodulation,[status(thm)],[f31,f45]) ).
fof(f48,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f47]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET971+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n014.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 05:45:20 UTC 2026
% 0.08/0.37 % CPUTime :
% 0.08/0.38 % Drodi V4.1.1
% 0.08/0.40 % Refutation found
% 0.08/0.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.08/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.08/0.42 % Elapsed time: 0.045532 seconds
% 0.08/0.42 % CPU time: 0.135038 seconds
% 0.08/0.42 % Total memory used: 54.022 MB
% 0.08/0.42 % Net memory used: 53.646 MB
%------------------------------------------------------------------------------