%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET891+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 : n026.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 02:10:55 PM UTC 2026
% Result : Theorem 0.14s 0.39s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 3
% Syntax : Number of formulae : 12 ( 12 unt; 0 def)
% Number of atoms : 12 ( 11 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 6 ( 6 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 14 ( 12 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f6,axiom,
! [A,B] : union(unordered_pair(A,B)) = set_union2(A,B),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,conjecture,
! [A,B] : union(unordered_pair(singleton(A),singleton(B))) = unordered_pair(A,B),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
~ ! [A,B] : union(unordered_pair(singleton(A),singleton(B))) = unordered_pair(A,B),
inference(negated_conjecture,[status(cth)],[f9]) ).
fof(f11,axiom,
! [A,B] : unordered_pair(A,B) = set_union2(singleton(A),singleton(B)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,plain,
! [X0,X1] : union(unordered_pair(X0,X1)) = set_union2(X0,X1),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f27,plain,
? [A,B] : union(unordered_pair(singleton(A),singleton(B))) != unordered_pair(A,B),
inference(pre_NNF_transformation,[status(thm)],[f10]) ).
fof(f28,plain,
union(unordered_pair(singleton(sK2_skl),singleton(sK3_skl))) != unordered_pair(sK2_skl,sK3_skl),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl,sK3_skl]),skolemize(A,sK2_skl),skolemize(B,sK3_skl)],[f27]) ).
fof(f29,plain,
union(unordered_pair(singleton(sK2_skl),singleton(sK3_skl))) != unordered_pair(sK2_skl,sK3_skl),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f30,plain,
! [X0,X1] : unordered_pair(X0,X1) = set_union2(singleton(X0),singleton(X1)),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f31,plain,
set_union2(singleton(sK2_skl),singleton(sK3_skl)) != unordered_pair(sK2_skl,sK3_skl),
inference(forward_demodulation,[status(thm)],[f22,f29]) ).
fof(f32,plain,
unordered_pair(sK2_skl,sK3_skl) != unordered_pair(sK2_skl,sK3_skl),
inference(backward_demodulation,[status(thm)],[f30,f31]) ).
fof(f33,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f32]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET891+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.35 % Computer : n026.cluster.edu
% 0.11/0.35 % Model : x86_64 x86_64
% 0.11/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.35 % Memory : 8046.5625MB
% 0.11/0.35 % OS : Linux 6.8.0-71-generic
% 0.11/0.35 % CPULimit : 300
% 0.11/0.35 % WCLimit : 300
% 0.11/0.35 % DateTime : Mon Sep 21 05:45:36 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.37 % 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
% 0.14/0.41 % Elapsed time: 0.047438 seconds
% 0.14/0.41 % CPU time: 0.140773 seconds
% 0.14/0.41 % Total memory used: 66.314 MB
% 0.14/0.41 % Net memory used: 65.816 MB
%------------------------------------------------------------------------------