TSTP Solution File: KLE035+1 by Drodi---3.5.1
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%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : KLE035+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n008.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 12:15:36 EDT 2023
% Result : Theorem 0.09s 0.36s
% Output : CNFRefutation 0.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 7
% Syntax : Number of formulae : 36 ( 26 unt; 0 def)
% Number of atoms : 62 ( 24 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 40 ( 14 ~; 7 |; 16 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 54 (; 50 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B] : addition(A,B) = addition(B,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [A] : addition(A,zero) = 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(f8,axiom,
! [A,B,C] : multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
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(f17,conjecture,
! [X0,X1,X2,X3] :
( ( test(X3)
& test(X2)
& leq(multiplication(multiplication(X2,X0),c(X3)),zero)
& leq(multiplication(multiplication(X2,X1),c(X3)),zero) )
=> leq(multiplication(multiplication(X2,addition(X0,X1)),c(X3)),zero) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( ( test(X3)
& test(X2)
& leq(multiplication(multiplication(X2,X0),c(X3)),zero)
& leq(multiplication(multiplication(X2,X1),c(X3)),zero) )
=> leq(multiplication(multiplication(X2,addition(X0,X1)),c(X3)),zero) ),
inference(negated_conjecture,[status(cth)],[f17]) ).
fof(f19,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[status(esa)],[f1]) ).
fof(f21,plain,
! [X0] : addition(X0,zero) = X0,
inference(cnf_transformation,[status(esa)],[f3]) ).
fof(f23,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
inference(cnf_transformation,[status(esa)],[f5]) ).
fof(f26,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
inference(cnf_transformation,[status(esa)],[f8]) ).
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(f32,plain,
! [X0,X1] :
( ~ leq(X0,X1)
| addition(X0,X1) = X1 ),
inference(cnf_transformation,[status(esa)],[f31]) ).
fof(f33,plain,
! [X0,X1] :
( leq(X0,X1)
| addition(X0,X1) != X1 ),
inference(cnf_transformation,[status(esa)],[f31]) ).
fof(f52,plain,
? [X0,X1,X2,X3] :
( test(X3)
& test(X2)
& leq(multiplication(multiplication(X2,X0),c(X3)),zero)
& leq(multiplication(multiplication(X2,X1),c(X3)),zero)
& ~ leq(multiplication(multiplication(X2,addition(X0,X1)),c(X3)),zero) ),
inference(pre_NNF_transformation,[status(esa)],[f18]) ).
fof(f53,plain,
( test(sk0_4)
& test(sk0_3)
& leq(multiplication(multiplication(sk0_3,sk0_1),c(sk0_4)),zero)
& leq(multiplication(multiplication(sk0_3,sk0_2),c(sk0_4)),zero)
& ~ leq(multiplication(multiplication(sk0_3,addition(sk0_1,sk0_2)),c(sk0_4)),zero) ),
inference(skolemization,[status(esa)],[f52]) ).
fof(f56,plain,
leq(multiplication(multiplication(sk0_3,sk0_1),c(sk0_4)),zero),
inference(cnf_transformation,[status(esa)],[f53]) ).
fof(f57,plain,
leq(multiplication(multiplication(sk0_3,sk0_2),c(sk0_4)),zero),
inference(cnf_transformation,[status(esa)],[f53]) ).
fof(f58,plain,
~ leq(multiplication(multiplication(sk0_3,addition(sk0_1,sk0_2)),c(sk0_4)),zero),
inference(cnf_transformation,[status(esa)],[f53]) ).
fof(f60,plain,
! [X0] : addition(zero,X0) = X0,
inference(paramodulation,[status(thm)],[f19,f21]) ).
fof(f104,plain,
~ leq(multiplication(sk0_3,multiplication(addition(sk0_1,sk0_2),c(sk0_4))),zero),
inference(backward_demodulation,[status(thm)],[f23,f58]) ).
fof(f105,plain,
leq(multiplication(sk0_3,multiplication(sk0_2,c(sk0_4))),zero),
inference(backward_demodulation,[status(thm)],[f23,f57]) ).
fof(f106,plain,
leq(multiplication(sk0_3,multiplication(sk0_1,c(sk0_4))),zero),
inference(backward_demodulation,[status(thm)],[f23,f56]) ).
fof(f124,plain,
! [X0] :
( ~ leq(X0,zero)
| X0 = zero ),
inference(paramodulation,[status(thm)],[f21,f32]) ).
fof(f127,plain,
! [X0] : leq(zero,X0),
inference(resolution,[status(thm)],[f33,f60]) ).
fof(f252,plain,
multiplication(sk0_3,multiplication(sk0_2,c(sk0_4))) = zero,
inference(resolution,[status(thm)],[f105,f124]) ).
fof(f273,plain,
! [X0] : multiplication(sk0_3,addition(X0,multiplication(sk0_2,c(sk0_4)))) = addition(multiplication(sk0_3,X0),zero),
inference(paramodulation,[status(thm)],[f252,f26]) ).
fof(f274,plain,
! [X0] : multiplication(sk0_3,addition(X0,multiplication(sk0_2,c(sk0_4)))) = multiplication(sk0_3,X0),
inference(forward_demodulation,[status(thm)],[f21,f273]) ).
fof(f285,plain,
multiplication(sk0_3,multiplication(sk0_1,c(sk0_4))) = zero,
inference(resolution,[status(thm)],[f106,f124]) ).
fof(f373,plain,
! [X0] : multiplication(sk0_3,multiplication(addition(X0,sk0_2),c(sk0_4))) = multiplication(sk0_3,multiplication(X0,c(sk0_4))),
inference(paramodulation,[status(thm)],[f27,f274]) ).
fof(f1956,plain,
~ leq(multiplication(sk0_3,multiplication(sk0_1,c(sk0_4))),zero),
inference(backward_demodulation,[status(thm)],[f373,f104]) ).
fof(f1957,plain,
~ leq(zero,zero),
inference(forward_demodulation,[status(thm)],[f285,f1956]) ).
fof(f1958,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f1957,f127]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.10 % Problem : KLE035+1 : TPTP v8.1.2. Released v4.0.0.
% 0.04/0.11 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.09/0.31 % Computer : n008.cluster.edu
% 0.09/0.31 % Model : x86_64 x86_64
% 0.09/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.31 % Memory : 8042.1875MB
% 0.09/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.31 % CPULimit : 300
% 0.09/0.31 % WCLimit : 300
% 0.09/0.31 % DateTime : Tue May 30 11:50:23 EDT 2023
% 0.09/0.31 % CPUTime :
% 0.09/0.32 % Drodi V3.5.1
% 0.09/0.36 % Refutation found
% 0.09/0.36 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.09/0.36 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.30/0.59 % Elapsed time: 0.059760 seconds
% 0.30/0.59 % CPU time: 0.122822 seconds
% 0.30/0.59 % Memory used: 16.590 MB
%------------------------------------------------------------------------------