%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET979+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 : n009.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 : 10
% Number of leaves : 3
% Syntax : Number of formulae : 17 ( 5 unt; 0 def)
% Number of atoms : 29 ( 28 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 29 ( 17 ~; 8 |; 4 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 34 ( 25 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,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/sandbox/benchmark/theBenchmark.p') ).
fof(f9,conjecture,
! [A,B,C] :
( cartesian_product2(C,unordered_pair(A,B)) = set_union2(cartesian_product2(C,singleton(A)),cartesian_product2(C,singleton(B)))
& cartesian_product2(unordered_pair(A,B),C) = set_union2(cartesian_product2(singleton(A),C),cartesian_product2(singleton(B),C)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
~ ! [A,B,C] :
( cartesian_product2(C,unordered_pair(A,B)) = set_union2(cartesian_product2(C,singleton(A)),cartesian_product2(C,singleton(B)))
& cartesian_product2(unordered_pair(A,B),C) = set_union2(cartesian_product2(singleton(A),C),cartesian_product2(singleton(B),C)) ),
inference(negated_conjecture,[status(cth)],[f9]) ).
fof(f11,axiom,
! [A,B] : unordered_pair(A,B) = set_union2(singleton(A),singleton(B)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f26,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)],[f8]) ).
fof(f27,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)],[f26]) ).
fof(f28,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)],[f26]) ).
fof(f29,plain,
? [A,B,C] :
( cartesian_product2(C,unordered_pair(A,B)) != set_union2(cartesian_product2(C,singleton(A)),cartesian_product2(C,singleton(B)))
| cartesian_product2(unordered_pair(A,B),C) != set_union2(cartesian_product2(singleton(A),C),cartesian_product2(singleton(B),C)) ),
inference(pre_NNF_transformation,[status(thm)],[f10]) ).
fof(f30,plain,
( ? [A,B,C] : cartesian_product2(C,unordered_pair(A,B)) != set_union2(cartesian_product2(C,singleton(A)),cartesian_product2(C,singleton(B)))
| ? [A,B,C] : cartesian_product2(unordered_pair(A,B),C) != set_union2(cartesian_product2(singleton(A),C),cartesian_product2(singleton(B),C)) ),
inference(miniscoping,[status(thm)],[f29]) ).
fof(f31,plain,
( cartesian_product2(sK7_skl,unordered_pair(sK5_skl,sK6_skl)) != set_union2(cartesian_product2(sK7_skl,singleton(sK5_skl)),cartesian_product2(sK7_skl,singleton(sK6_skl)))
| cartesian_product2(unordered_pair(sK2_skl,sK3_skl),sK4_skl) != set_union2(cartesian_product2(singleton(sK2_skl),sK4_skl),cartesian_product2(singleton(sK3_skl),sK4_skl)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl,sK3_skl,sK4_skl,sK5_skl,sK6_skl,sK7_skl]),skolemize(A,sK2_skl),skolemize(B,sK3_skl),skolemize(C,sK4_skl),skolemize(A,sK5_skl),skolemize(B,sK6_skl),skolemize(C,sK7_skl)],[f30]) ).
fof(f32,plain,
( cartesian_product2(sK7_skl,unordered_pair(sK5_skl,sK6_skl)) != set_union2(cartesian_product2(sK7_skl,singleton(sK5_skl)),cartesian_product2(sK7_skl,singleton(sK6_skl)))
| cartesian_product2(unordered_pair(sK2_skl,sK3_skl),sK4_skl) != set_union2(cartesian_product2(singleton(sK2_skl),sK4_skl),cartesian_product2(singleton(sK3_skl),sK4_skl)) ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f33,plain,
! [X0,X1] : unordered_pair(X0,X1) = set_union2(singleton(X0),singleton(X1)),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f34,plain,
( cartesian_product2(sK7_skl,unordered_pair(sK5_skl,sK6_skl)) != set_union2(cartesian_product2(sK7_skl,singleton(sK5_skl)),cartesian_product2(sK7_skl,singleton(sK6_skl)))
| cartesian_product2(unordered_pair(sK2_skl,sK3_skl),sK4_skl) != cartesian_product2(set_union2(singleton(sK2_skl),singleton(sK3_skl)),sK4_skl) ),
inference(forward_demodulation,[status(thm)],[f27,f32]) ).
fof(f35,plain,
( cartesian_product2(sK7_skl,unordered_pair(sK5_skl,sK6_skl)) != cartesian_product2(sK7_skl,set_union2(singleton(sK5_skl),singleton(sK6_skl)))
| cartesian_product2(unordered_pair(sK2_skl,sK3_skl),sK4_skl) != cartesian_product2(set_union2(singleton(sK2_skl),singleton(sK3_skl)),sK4_skl) ),
inference(forward_demodulation,[status(thm)],[f28,f34]) ).
fof(f36,plain,
( cartesian_product2(sK7_skl,unordered_pair(sK5_skl,sK6_skl)) != cartesian_product2(sK7_skl,unordered_pair(sK5_skl,sK6_skl))
| cartesian_product2(unordered_pair(sK2_skl,sK3_skl),sK4_skl) != cartesian_product2(set_union2(singleton(sK2_skl),singleton(sK3_skl)),sK4_skl) ),
inference(backward_demodulation,[status(thm)],[f33,f35]) ).
fof(f37,plain,
( cartesian_product2(sK7_skl,unordered_pair(sK5_skl,sK6_skl)) != cartesian_product2(sK7_skl,unordered_pair(sK5_skl,sK6_skl))
| cartesian_product2(unordered_pair(sK2_skl,sK3_skl),sK4_skl) != cartesian_product2(unordered_pair(sK2_skl,sK3_skl),sK4_skl) ),
inference(forward_demodulation,[status(thm)],[f33,f36]) ).
fof(f38,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f37]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET979+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 : n009.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 05:45:58 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.37 % 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: 0.041896 seconds
% 0.13/0.41 % CPU time: 0.125421 seconds
% 0.13/0.41 % Total memory used: 52.027 MB
% 0.13/0.41 % Net memory used: 51.654 MB
%------------------------------------------------------------------------------