TSTP Solution File: KLE026+1 by Drodi---3.5.1
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%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : KLE026+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n015.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 12:15:34 EDT 2023
% Result : Theorem 1.88s 0.68s
% Output : CNFRefutation 1.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 10
% Syntax : Number of formulae : 47 ( 28 unt; 0 def)
% Number of atoms : 100 ( 53 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 81 ( 28 ~; 22 |; 24 &)
% ( 3 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 75 (; 66 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B] : addition(A,B) = addition(B,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [C,B,A] : addition(A,addition(B,C)) = addition(addition(A,B),C),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A] : addition(A,A) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [A,B,C] : multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [A] : multiplication(one,A) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [A,B,C] : multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [A,B] :
( leq(A,B)
<=> addition(A,B) = B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [X0] :
( test(X0)
<=> ? [X1] : complement(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [X0,X1] :
( complement(X1,X0)
<=> ( multiplication(X0,X1) = zero
& multiplication(X1,X0) = zero
& addition(X0,X1) = one ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,conjecture,
! [X0,X1,X2] :
( ( test(X1)
& test(X2) )
=> ( multiplication(X1,X0) = multiplication(multiplication(X1,X0),X2)
=> leq(multiplication(X1,X0),multiplication(X0,X2)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
~ ! [X0,X1,X2] :
( ( test(X1)
& test(X2) )
=> ( multiplication(X1,X0) = multiplication(multiplication(X1,X0),X2)
=> leq(multiplication(X1,X0),multiplication(X0,X2)) ) ),
inference(negated_conjecture,[status(cth)],[f17]) ).
fof(f19,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[status(esa)],[f1]) ).
fof(f20,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(addition(X0,X1),X2),
inference(cnf_transformation,[status(esa)],[f2]) ).
fof(f22,plain,
! [X0] : addition(X0,X0) = X0,
inference(cnf_transformation,[status(esa)],[f4]) ).
fof(f23,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
inference(cnf_transformation,[status(esa)],[f5]) ).
fof(f25,plain,
! [X0] : multiplication(one,X0) = X0,
inference(cnf_transformation,[status(esa)],[f7]) ).
fof(f27,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
inference(cnf_transformation,[status(esa)],[f9]) ).
fof(f30,plain,
! [A,B] :
( ( ~ leq(A,B)
| addition(A,B) = B )
& ( leq(A,B)
| addition(A,B) != B ) ),
inference(NNF_transformation,[status(esa)],[f12]) ).
fof(f31,plain,
( ! [A,B] :
( ~ leq(A,B)
| addition(A,B) = B )
& ! [A,B] :
( leq(A,B)
| addition(A,B) != B ) ),
inference(miniscoping,[status(esa)],[f30]) ).
fof(f33,plain,
! [X0,X1] :
( leq(X0,X1)
| addition(X0,X1) != X1 ),
inference(cnf_transformation,[status(esa)],[f31]) ).
fof(f34,plain,
! [X0] :
( ( ~ test(X0)
| ? [X1] : complement(X1,X0) )
& ( test(X0)
| ! [X1] : ~ complement(X1,X0) ) ),
inference(NNF_transformation,[status(esa)],[f13]) ).
fof(f35,plain,
( ! [X0] :
( ~ test(X0)
| ? [X1] : complement(X1,X0) )
& ! [X0] :
( test(X0)
| ! [X1] : ~ complement(X1,X0) ) ),
inference(miniscoping,[status(esa)],[f34]) ).
fof(f36,plain,
( ! [X0] :
( ~ test(X0)
| complement(sk0_0(X0),X0) )
& ! [X0] :
( test(X0)
| ! [X1] : ~ complement(X1,X0) ) ),
inference(skolemization,[status(esa)],[f35]) ).
fof(f37,plain,
! [X0] :
( ~ test(X0)
| complement(sk0_0(X0),X0) ),
inference(cnf_transformation,[status(esa)],[f36]) ).
fof(f39,plain,
! [X0,X1] :
( ( ~ complement(X1,X0)
| ( multiplication(X0,X1) = zero
& multiplication(X1,X0) = zero
& addition(X0,X1) = one ) )
& ( complement(X1,X0)
| multiplication(X0,X1) != zero
| multiplication(X1,X0) != zero
| addition(X0,X1) != one ) ),
inference(NNF_transformation,[status(esa)],[f14]) ).
fof(f40,plain,
( ! [X0,X1] :
( ~ complement(X1,X0)
| ( multiplication(X0,X1) = zero
& multiplication(X1,X0) = zero
& addition(X0,X1) = one ) )
& ! [X0,X1] :
( complement(X1,X0)
| multiplication(X0,X1) != zero
| multiplication(X1,X0) != zero
| addition(X0,X1) != one ) ),
inference(miniscoping,[status(esa)],[f39]) ).
fof(f43,plain,
! [X0,X1] :
( ~ complement(X0,X1)
| addition(X1,X0) = one ),
inference(cnf_transformation,[status(esa)],[f40]) ).
fof(f52,plain,
? [X0,X1,X2] :
( test(X1)
& test(X2)
& multiplication(X1,X0) = multiplication(multiplication(X1,X0),X2)
& ~ leq(multiplication(X1,X0),multiplication(X0,X2)) ),
inference(pre_NNF_transformation,[status(esa)],[f18]) ).
fof(f53,plain,
? [X1,X2] :
( test(X1)
& test(X2)
& ? [X0] :
( multiplication(X1,X0) = multiplication(multiplication(X1,X0),X2)
& ~ leq(multiplication(X1,X0),multiplication(X0,X2)) ) ),
inference(miniscoping,[status(esa)],[f52]) ).
fof(f54,plain,
( test(sk0_1)
& test(sk0_2)
& multiplication(sk0_1,sk0_3) = multiplication(multiplication(sk0_1,sk0_3),sk0_2)
& ~ leq(multiplication(sk0_1,sk0_3),multiplication(sk0_3,sk0_2)) ),
inference(skolemization,[status(esa)],[f53]) ).
fof(f55,plain,
test(sk0_1),
inference(cnf_transformation,[status(esa)],[f54]) ).
fof(f57,plain,
multiplication(sk0_1,sk0_3) = multiplication(multiplication(sk0_1,sk0_3),sk0_2),
inference(cnf_transformation,[status(esa)],[f54]) ).
fof(f58,plain,
~ leq(multiplication(sk0_1,sk0_3),multiplication(sk0_3,sk0_2)),
inference(cnf_transformation,[status(esa)],[f54]) ).
fof(f60,plain,
multiplication(sk0_1,sk0_3) = multiplication(sk0_1,multiplication(sk0_3,sk0_2)),
inference(backward_demodulation,[status(thm)],[f23,f57]) ).
fof(f72,plain,
addition(multiplication(sk0_1,sk0_3),multiplication(sk0_3,sk0_2)) != multiplication(sk0_3,sk0_2),
inference(resolution,[status(thm)],[f33,f58]) ).
fof(f104,plain,
! [X0,X1] : addition(X0,addition(X0,X1)) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f22,f20]) ).
fof(f1103,plain,
! [X0] :
( addition(X0,sk0_0(X0)) = one
| ~ test(X0) ),
inference(resolution,[status(thm)],[f43,f37]) ).
fof(f1191,plain,
addition(sk0_1,sk0_0(sk0_1)) = one,
inference(resolution,[status(thm)],[f1103,f55]) ).
fof(f1201,plain,
addition(sk0_1,one) = addition(sk0_1,sk0_0(sk0_1)),
inference(paramodulation,[status(thm)],[f1191,f104]) ).
fof(f1202,plain,
addition(one,sk0_1) = addition(sk0_1,sk0_0(sk0_1)),
inference(forward_demodulation,[status(thm)],[f19,f1201]) ).
fof(f1203,plain,
addition(one,sk0_1) = one,
inference(forward_demodulation,[status(thm)],[f1191,f1202]) ).
fof(f2465,plain,
! [X0] : multiplication(addition(sk0_1,X0),multiplication(sk0_3,sk0_2)) = addition(multiplication(sk0_1,sk0_3),multiplication(X0,multiplication(sk0_3,sk0_2))),
inference(paramodulation,[status(thm)],[f60,f27]) ).
fof(f3210,plain,
multiplication(addition(sk0_1,one),multiplication(sk0_3,sk0_2)) = addition(multiplication(sk0_1,sk0_3),multiplication(sk0_3,sk0_2)),
inference(paramodulation,[status(thm)],[f25,f2465]) ).
fof(f3211,plain,
multiplication(addition(one,sk0_1),multiplication(sk0_3,sk0_2)) = addition(multiplication(sk0_1,sk0_3),multiplication(sk0_3,sk0_2)),
inference(forward_demodulation,[status(thm)],[f19,f3210]) ).
fof(f3212,plain,
multiplication(one,multiplication(sk0_3,sk0_2)) = addition(multiplication(sk0_1,sk0_3),multiplication(sk0_3,sk0_2)),
inference(forward_demodulation,[status(thm)],[f1203,f3211]) ).
fof(f3213,plain,
multiplication(sk0_3,sk0_2) = addition(multiplication(sk0_1,sk0_3),multiplication(sk0_3,sk0_2)),
inference(forward_demodulation,[status(thm)],[f25,f3212]) ).
fof(f3214,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f3213,f72]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : KLE026+1 : TPTP v8.1.2. Released v4.0.0.
% 0.06/0.12 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.10/0.32 % Computer : n015.cluster.edu
% 0.10/0.32 % Model : x86_64 x86_64
% 0.10/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.32 % Memory : 8042.1875MB
% 0.10/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.32 % CPULimit : 300
% 0.10/0.32 % WCLimit : 300
% 0.10/0.32 % DateTime : Tue May 30 12:02:49 EDT 2023
% 0.10/0.32 % CPUTime :
% 0.10/0.33 % Drodi V3.5.1
% 1.88/0.68 % Refutation found
% 1.88/0.68 % SZS status Theorem for theBenchmark: Theorem is valid
% 1.88/0.68 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 1.88/0.70 % Elapsed time: 0.372868 seconds
% 1.88/0.70 % CPU time: 2.464714 seconds
% 1.88/0.70 % Memory used: 90.706 MB
%------------------------------------------------------------------------------