TSTP Solution File: SET886+1 by Drodi---3.6.0
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%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : SET886+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n023.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Apr 30 20:40:38 EDT 2024
% Result : Theorem 0.16s 0.32s
% Output : CNFRefutation 0.16s
% 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/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [A,B,C] :
( subset(unordered_pair(A,B),singleton(C))
=> A = C ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f9,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[status(esa)],[f1]) ).
fof(f16,plain,
! [A,B,C] :
( ~ subset(unordered_pair(A,B),singleton(C))
| A = C ),
inference(pre_NNF_transformation,[status(esa)],[f5]) ).
fof(f17,plain,
! [A,C] :
( ! [B] : ~ subset(unordered_pair(A,B),singleton(C))
| A = C ),
inference(miniscoping,[status(esa)],[f16]) ).
fof(f18,plain,
! [X0,X1,X2] :
( ~ subset(unordered_pair(X0,X1),singleton(X2))
| X0 = X2 ),
inference(cnf_transformation,[status(esa)],[f17]) ).
fof(f19,plain,
? [A,B,C] :
( subset(unordered_pair(A,B),singleton(C))
& unordered_pair(A,B) != singleton(C) ),
inference(pre_NNF_transformation,[status(esa)],[f7]) ).
fof(f20,plain,
( subset(unordered_pair(sk0_2,sk0_3),singleton(sk0_4))
& unordered_pair(sk0_2,sk0_3) != singleton(sk0_4) ),
inference(skolemization,[status(esa)],[f19]) ).
fof(f21,plain,
subset(unordered_pair(sk0_2,sk0_3),singleton(sk0_4)),
inference(cnf_transformation,[status(esa)],[f20]) ).
fof(f22,plain,
unordered_pair(sk0_2,sk0_3) != singleton(sk0_4),
inference(cnf_transformation,[status(esa)],[f20]) ).
fof(f23,plain,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
inference(cnf_transformation,[status(esa)],[f8]) ).
fof(f24,plain,
sk0_2 = sk0_4,
inference(resolution,[status(thm)],[f18,f21]) ).
fof(f25,plain,
! [X0,X1,X2] :
( ~ subset(unordered_pair(X0,X1),singleton(X2))
| X1 = X2 ),
inference(paramodulation,[status(thm)],[f9,f18]) ).
fof(f28,plain,
subset(unordered_pair(sk0_2,sk0_3),singleton(sk0_2)),
inference(backward_demodulation,[status(thm)],[f24,f21]) ).
fof(f29,plain,
unordered_pair(sk0_2,sk0_3) != singleton(sk0_2),
inference(backward_demodulation,[status(thm)],[f24,f22]) ).
fof(f33,plain,
sk0_3 = sk0_2,
inference(resolution,[status(thm)],[f28,f25]) ).
fof(f36,plain,
unordered_pair(sk0_2,sk0_2) != singleton(sk0_2),
inference(backward_demodulation,[status(thm)],[f33,f29]) ).
fof(f37,plain,
singleton(sk0_2) != singleton(sk0_2),
inference(forward_demodulation,[status(thm)],[f23,f36]) ).
fof(f38,plain,
$false,
inference(trivial_equality_resolution,[status(esa)],[f37]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SET886+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.10 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.09/0.30 % Computer : n023.cluster.edu
% 0.09/0.30 % Model : x86_64 x86_64
% 0.09/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.30 % Memory : 8042.1875MB
% 0.09/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.30 % CPULimit : 300
% 0.09/0.30 % WCLimit : 300
% 0.09/0.30 % DateTime : Mon Apr 29 22:05:40 EDT 2024
% 0.09/0.31 % CPUTime :
% 0.16/0.31 % Drodi V3.6.0
% 0.16/0.32 % Refutation found
% 0.16/0.32 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.16/0.32 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.16/0.34 % Elapsed time: 0.016589 seconds
% 0.16/0.34 % CPU time: 0.013749 seconds
% 0.16/0.34 % Total memory used: 4.654 MB
% 0.16/0.34 % Net memory used: 4.571 MB
%------------------------------------------------------------------------------