%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET968+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n012.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 0.04s 0.33s
% Output : CNFRefutation 0.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 3
% Syntax : Number of formulae : 16 ( 14 unt; 0 def)
% Number of atoms : 18 ( 17 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 10 ( 8 ~; 0 |; 2 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 33 ( 29 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
! [A,B,C] :
( cartesian_product2(C,set_union2(A,B)) = set_union2(cartesian_product2(C,A),cartesian_product2(C,B))
& cartesian_product2(set_union2(A,B),C) = set_union2(cartesian_product2(A,C),cartesian_product2(B,C)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,conjecture,
! [A,B,C,D] : cartesian_product2(set_union2(A,B),set_union2(C,D)) = set_union2(set_union2(set_union2(cartesian_product2(A,C),cartesian_product2(A,D)),cartesian_product2(B,C)),cartesian_product2(B,D)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
~ ! [A,B,C,D] : cartesian_product2(set_union2(A,B),set_union2(C,D)) = set_union2(set_union2(set_union2(cartesian_product2(A,C),cartesian_product2(A,D)),cartesian_product2(B,C)),cartesian_product2(B,D)),
inference(negated_conjecture,[status(cth)],[f8]) ).
fof(f10,axiom,
! [A,B,C] : set_union2(set_union2(A,B),C) = set_union2(A,set_union2(B,C)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,plain,
( ! [A,B,C] : cartesian_product2(C,set_union2(A,B)) = set_union2(cartesian_product2(C,A),cartesian_product2(C,B))
& ! [A,B,C] : cartesian_product2(set_union2(A,B),C) = set_union2(cartesian_product2(A,C),cartesian_product2(B,C)) ),
inference(miniscoping,[status(thm)],[f7]) ).
fof(f25,plain,
! [X0,X1,X2] : cartesian_product2(set_union2(X0,X1),X2) = set_union2(cartesian_product2(X0,X2),cartesian_product2(X1,X2)),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f26,plain,
! [X0,X1,X2] : cartesian_product2(X0,set_union2(X1,X2)) = set_union2(cartesian_product2(X0,X1),cartesian_product2(X0,X2)),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f27,plain,
? [A,B,C,D] : cartesian_product2(set_union2(A,B),set_union2(C,D)) != set_union2(set_union2(set_union2(cartesian_product2(A,C),cartesian_product2(A,D)),cartesian_product2(B,C)),cartesian_product2(B,D)),
inference(pre_NNF_transformation,[status(thm)],[f9]) ).
fof(f28,plain,
cartesian_product2(set_union2(sK2_skl,sK3_skl),set_union2(sK4_skl,sK5_skl)) != set_union2(set_union2(set_union2(cartesian_product2(sK2_skl,sK4_skl),cartesian_product2(sK2_skl,sK5_skl)),cartesian_product2(sK3_skl,sK4_skl)),cartesian_product2(sK3_skl,sK5_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)],[f27]) ).
fof(f29,plain,
cartesian_product2(set_union2(sK2_skl,sK3_skl),set_union2(sK4_skl,sK5_skl)) != set_union2(set_union2(set_union2(cartesian_product2(sK2_skl,sK4_skl),cartesian_product2(sK2_skl,sK5_skl)),cartesian_product2(sK3_skl,sK4_skl)),cartesian_product2(sK3_skl,sK5_skl)),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f30,plain,
! [X0,X1,X2] : set_union2(set_union2(X0,X1),X2) = set_union2(X0,set_union2(X1,X2)),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f31,plain,
cartesian_product2(set_union2(sK2_skl,sK3_skl),set_union2(sK4_skl,sK5_skl)) != set_union2(set_union2(cartesian_product2(sK2_skl,set_union2(sK4_skl,sK5_skl)),cartesian_product2(sK3_skl,sK4_skl)),cartesian_product2(sK3_skl,sK5_skl)),
inference(forward_demodulation,[status(thm)],[f26,f29]) ).
fof(f32,plain,
cartesian_product2(set_union2(sK2_skl,sK3_skl),set_union2(sK4_skl,sK5_skl)) != set_union2(cartesian_product2(sK2_skl,set_union2(sK4_skl,sK5_skl)),set_union2(cartesian_product2(sK3_skl,sK4_skl),cartesian_product2(sK3_skl,sK5_skl))),
inference(backward_demodulation,[status(thm)],[f30,f31]) ).
fof(f33,plain,
cartesian_product2(set_union2(sK2_skl,sK3_skl),set_union2(sK4_skl,sK5_skl)) != set_union2(cartesian_product2(sK2_skl,set_union2(sK4_skl,sK5_skl)),cartesian_product2(sK3_skl,set_union2(sK4_skl,sK5_skl))),
inference(forward_demodulation,[status(thm)],[f26,f32]) ).
fof(f34,plain,
cartesian_product2(set_union2(sK2_skl,sK3_skl),set_union2(sK4_skl,sK5_skl)) != cartesian_product2(set_union2(sK2_skl,sK3_skl),set_union2(sK4_skl,sK5_skl)),
inference(forward_demodulation,[status(thm)],[f25,f33]) ).
fof(f35,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f34]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SET968+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.02 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.04/0.30 % Computer : n012.cluster.edu
% 0.04/0.30 % Model : x86_64 x86_64
% 0.04/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.30 % Memory : 8046.5625MB
% 0.04/0.30 % OS : Linux 6.8.0-71-generic
% 0.04/0.30 % CPULimit : 300
% 0.04/0.30 % WCLimit : 300
% 0.04/0.30 % DateTime : Mon Sep 21 05:45:08 UTC 2026
% 0.04/0.30 % CPUTime :
% 0.04/0.31 % Drodi V4.1.1
% 0.04/0.33 % Refutation found
% 0.04/0.33 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.04/0.33 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.09/0.35 % Elapsed time: 0.042936 seconds
% 0.09/0.35 % CPU time: 0.111397 seconds
% 0.09/0.35 % Total memory used: 60.269 MB
% 0.09/0.35 % Net memory used: 59.816 MB
%------------------------------------------------------------------------------