TSTP Solution File: SET907+1 by Drodi---3.5.1
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%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : SET907+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n017.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 : Wed May 31 12:35:30 EDT 2023
% Result : Theorem 0.13s 0.36s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of formulae : 25 ( 13 unt; 0 def)
% Number of atoms : 51 ( 15 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 42 ( 16 ~; 11 |; 11 &)
% ( 1 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 39 (; 36 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [A,B] : unordered_pair(A,B) = unordered_pair(B,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [A,B] : set_union2(A,B) = set_union2(B,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [A,B] :
( subset(A,B)
=> set_union2(A,B) = B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [A,B,C] :
( subset(unordered_pair(A,B),C)
<=> ( in(A,C)
& in(B,C) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,conjecture,
! [A,B,C] :
( ( in(A,B)
& in(C,B) )
=> set_union2(unordered_pair(A,C),B) = B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
~ ! [A,B,C] :
( ( in(A,B)
& in(C,B) )
=> set_union2(unordered_pair(A,C),B) = B ),
inference(negated_conjecture,[status(cth)],[f12]) ).
fof(f16,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[status(esa)],[f2]) ).
fof(f17,plain,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
inference(cnf_transformation,[status(esa)],[f3]) ).
fof(f32,plain,
! [A,B] :
( ~ subset(A,B)
| set_union2(A,B) = B ),
inference(pre_NNF_transformation,[status(esa)],[f10]) ).
fof(f33,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| set_union2(X0,X1) = X1 ),
inference(cnf_transformation,[status(esa)],[f32]) ).
fof(f34,plain,
! [A,B,C] :
( ( ~ subset(unordered_pair(A,B),C)
| ( in(A,C)
& in(B,C) ) )
& ( subset(unordered_pair(A,B),C)
| ~ in(A,C)
| ~ in(B,C) ) ),
inference(NNF_transformation,[status(esa)],[f11]) ).
fof(f35,plain,
( ! [A,B,C] :
( ~ subset(unordered_pair(A,B),C)
| ( in(A,C)
& in(B,C) ) )
& ! [A,B,C] :
( subset(unordered_pair(A,B),C)
| ~ in(A,C)
| ~ in(B,C) ) ),
inference(miniscoping,[status(esa)],[f34]) ).
fof(f38,plain,
! [X0,X1,X2] :
( subset(unordered_pair(X0,X1),X2)
| ~ in(X0,X2)
| ~ in(X1,X2) ),
inference(cnf_transformation,[status(esa)],[f35]) ).
fof(f39,plain,
? [A,B,C] :
( in(A,B)
& in(C,B)
& set_union2(unordered_pair(A,C),B) != B ),
inference(pre_NNF_transformation,[status(esa)],[f13]) ).
fof(f40,plain,
( in(sk0_2,sk0_3)
& in(sk0_4,sk0_3)
& set_union2(unordered_pair(sk0_2,sk0_4),sk0_3) != sk0_3 ),
inference(skolemization,[status(esa)],[f39]) ).
fof(f41,plain,
in(sk0_2,sk0_3),
inference(cnf_transformation,[status(esa)],[f40]) ).
fof(f42,plain,
in(sk0_4,sk0_3),
inference(cnf_transformation,[status(esa)],[f40]) ).
fof(f43,plain,
set_union2(unordered_pair(sk0_2,sk0_4),sk0_3) != sk0_3,
inference(cnf_transformation,[status(esa)],[f40]) ).
fof(f46,plain,
set_union2(sk0_3,unordered_pair(sk0_2,sk0_4)) != sk0_3,
inference(paramodulation,[status(thm)],[f17,f43]) ).
fof(f69,plain,
! [X0] :
( subset(unordered_pair(sk0_4,X0),sk0_3)
| ~ in(X0,sk0_3) ),
inference(resolution,[status(thm)],[f38,f42]) ).
fof(f74,plain,
subset(unordered_pair(sk0_4,sk0_2),sk0_3),
inference(resolution,[status(thm)],[f69,f41]) ).
fof(f75,plain,
subset(unordered_pair(sk0_2,sk0_4),sk0_3),
inference(forward_demodulation,[status(thm)],[f16,f74]) ).
fof(f88,plain,
set_union2(unordered_pair(sk0_2,sk0_4),sk0_3) = sk0_3,
inference(resolution,[status(thm)],[f75,f33]) ).
fof(f89,plain,
set_union2(sk0_3,unordered_pair(sk0_2,sk0_4)) = sk0_3,
inference(forward_demodulation,[status(thm)],[f17,f88]) ).
fof(f90,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f89,f46]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET907+1 : TPTP v8.1.2. Released v3.2.0.
% 0.07/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.34 % Computer : n017.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue May 30 09:39:55 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.13/0.35 % Drodi V3.5.1
% 0.13/0.36 % Refutation found
% 0.13/0.36 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.36 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.37 % Elapsed time: 0.021710 seconds
% 0.13/0.37 % CPU time: 0.032959 seconds
% 0.13/0.37 % Memory used: 9.120 MB
%------------------------------------------------------------------------------