%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET886+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 : n018.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 02:10:54 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 : 22 ( 13 unt; 0 def)
% Number of atoms : 31 ( 19 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 20 ( 11 ~; 4 |; 2 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 30 ( 27 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B] : unordered_pair(A,B) = unordered_pair(B,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [A,B,C] :
( subset(unordered_pair(A,B),singleton(C))
=> A = C ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,conjecture,
! [A,B,C] :
( subset(unordered_pair(A,B),singleton(C))
=> unordered_pair(A,B) = singleton(C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,negated_conjecture,
~ ! [A,B,C] :
( subset(unordered_pair(A,B),singleton(C))
=> unordered_pair(A,B) = singleton(C) ),
inference(negated_conjecture,[status(cth)],[f6]) ).
fof(f8,axiom,
! [A] : unordered_pair(A,A) = singleton(A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f16,plain,
! [A,B,C] :
( A = C
| ~ subset(unordered_pair(A,B),singleton(C)) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f17,plain,
! [A,C] :
( A = C
| ! [B] : ~ subset(unordered_pair(A,B),singleton(C)) ),
inference(miniscoping,[status(thm)],[f16]) ).
fof(f18,plain,
! [X0,X1,X2] :
( X0 = X2
| ~ subset(unordered_pair(X0,X1),singleton(X2)) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f19,plain,
? [A,B,C] :
( unordered_pair(A,B) != singleton(C)
& subset(unordered_pair(A,B),singleton(C)) ),
inference(pre_NNF_transformation,[status(thm)],[f7]) ).
fof(f20,plain,
( unordered_pair(sK2_skl,sK3_skl) != singleton(sK4_skl)
& subset(unordered_pair(sK2_skl,sK3_skl),singleton(sK4_skl)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl,sK3_skl,sK4_skl]),skolemize(A,sK2_skl),skolemize(B,sK3_skl),skolemize(C,sK4_skl)],[f19]) ).
fof(f21,plain,
subset(unordered_pair(sK2_skl,sK3_skl),singleton(sK4_skl)),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f22,plain,
unordered_pair(sK2_skl,sK3_skl) != singleton(sK4_skl),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f23,plain,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f28,plain,
sK2_skl = sK4_skl,
inference(resolution,[status(thm)],[f18,f21]) ).
fof(f30,plain,
! [X0,X1,X2] :
( X1 = X2
| ~ subset(unordered_pair(X0,X1),singleton(X2)) ),
inference(paramodulation,[status(thm)],[f9,f18]) ).
fof(f32,plain,
subset(unordered_pair(sK2_skl,sK3_skl),singleton(sK2_skl)),
inference(backward_demodulation,[status(thm)],[f28,f21]) ).
fof(f33,plain,
unordered_pair(sK2_skl,sK3_skl) != singleton(sK2_skl),
inference(backward_demodulation,[status(thm)],[f28,f22]) ).
fof(f36,plain,
sK3_skl = sK2_skl,
inference(resolution,[status(thm)],[f30,f32]) ).
fof(f40,plain,
unordered_pair(sK2_skl,sK2_skl) != singleton(sK2_skl),
inference(backward_demodulation,[status(thm)],[f36,f33]) ).
fof(f42,plain,
singleton(sK2_skl) != singleton(sK2_skl),
inference(forward_demodulation,[status(thm)],[f23,f40]) ).
fof(f43,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f42]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET886+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n018.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Mon Sep 21 05:45:14 UTC 2026
% 0.08/0.36 % 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
% 0.13/0.44 % Elapsed time: 0.064431 seconds
% 0.13/0.44 % CPU time: 0.174452 seconds
% 0.13/0.44 % Total memory used: 55.928 MB
% 0.13/0.44 % Net memory used: 55.496 MB
%------------------------------------------------------------------------------