TSTP Solution File: KLE025+1 by Drodi---3.5.1
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%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : KLE025+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n003.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 12:15:33 EDT 2023
% Result : Theorem 6.44s 1.21s
% Output : CNFRefutation 6.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 8
% Syntax : Number of formulae : 39 ( 22 unt; 0 def)
% Number of atoms : 89 ( 55 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 77 ( 27 ~; 21 |; 21 &)
% ( 3 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 5 ( 1 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 : 59 (; 53 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B] : addition(A,B) = addition(B,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [A] : addition(A,zero) = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [A,B,C] : multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [A] : multiplication(A,one) = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [A,B,C] : multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [X0,X1] :
( test(X0)
=> ( c(X0) = X1
<=> complement(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,conjecture,
! [X0,X1,X2] :
( ( test(X1)
& test(X2) )
=> ( multiplication(multiplication(X1,X0),c(X2)) = zero
=> multiplication(X1,X0) = multiplication(multiplication(X1,X0),X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
~ ! [X0,X1,X2] :
( ( test(X1)
& test(X2) )
=> ( multiplication(multiplication(X1,X0),c(X2)) = zero
=> multiplication(X1,X0) = multiplication(multiplication(X1,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(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(f24,plain,
! [X0] : multiplication(X0,one) = X0,
inference(cnf_transformation,[status(esa)],[f6]) ).
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(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(f45,plain,
! [X0,X1] :
( ~ test(X0)
| ( c(X0) = X1
<=> complement(X0,X1) ) ),
inference(pre_NNF_transformation,[status(esa)],[f15]) ).
fof(f46,plain,
! [X0,X1] :
( ~ test(X0)
| ( ( c(X0) != X1
| complement(X0,X1) )
& ( c(X0) = X1
| ~ complement(X0,X1) ) ) ),
inference(NNF_transformation,[status(esa)],[f45]) ).
fof(f47,plain,
! [X0] :
( ~ test(X0)
| ( ! [X1] :
( c(X0) != X1
| complement(X0,X1) )
& ! [X1] :
( c(X0) = X1
| ~ complement(X0,X1) ) ) ),
inference(miniscoping,[status(esa)],[f46]) ).
fof(f48,plain,
! [X0,X1] :
( ~ test(X0)
| c(X0) != X1
| complement(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f47]) ).
fof(f52,plain,
? [X0,X1,X2] :
( test(X1)
& test(X2)
& multiplication(multiplication(X1,X0),c(X2)) = zero
& multiplication(X1,X0) != multiplication(multiplication(X1,X0),X2) ),
inference(pre_NNF_transformation,[status(esa)],[f18]) ).
fof(f53,plain,
? [X1,X2] :
( test(X1)
& test(X2)
& ? [X0] :
( multiplication(multiplication(X1,X0),c(X2)) = zero
& multiplication(X1,X0) != multiplication(multiplication(X1,X0),X2) ) ),
inference(miniscoping,[status(esa)],[f52]) ).
fof(f54,plain,
( test(sk0_1)
& test(sk0_2)
& multiplication(multiplication(sk0_1,sk0_3),c(sk0_2)) = zero
& multiplication(sk0_1,sk0_3) != multiplication(multiplication(sk0_1,sk0_3),sk0_2) ),
inference(skolemization,[status(esa)],[f53]) ).
fof(f56,plain,
test(sk0_2),
inference(cnf_transformation,[status(esa)],[f54]) ).
fof(f57,plain,
multiplication(multiplication(sk0_1,sk0_3),c(sk0_2)) = zero,
inference(cnf_transformation,[status(esa)],[f54]) ).
fof(f58,plain,
multiplication(sk0_1,sk0_3) != multiplication(multiplication(sk0_1,sk0_3),sk0_2),
inference(cnf_transformation,[status(esa)],[f54]) ).
fof(f59,plain,
! [X0] :
( ~ test(X0)
| complement(X0,c(X0)) ),
inference(destructive_equality_resolution,[status(esa)],[f48]) ).
fof(f60,plain,
multiplication(sk0_1,sk0_3) != multiplication(sk0_1,multiplication(sk0_3,sk0_2)),
inference(backward_demodulation,[status(thm)],[f23,f58]) ).
fof(f61,plain,
multiplication(sk0_1,multiplication(sk0_3,c(sk0_2))) = zero,
inference(backward_demodulation,[status(thm)],[f23,f57]) ).
fof(f103,plain,
! [X0] :
( addition(c(X0),X0) = one
| ~ test(X0) ),
inference(resolution,[status(thm)],[f43,f59]) ).
fof(f104,plain,
! [X0] :
( addition(X0,c(X0)) = one
| ~ test(X0) ),
inference(forward_demodulation,[status(thm)],[f19,f103]) ).
fof(f158,plain,
! [X0] : multiplication(sk0_1,addition(X0,multiplication(sk0_3,c(sk0_2)))) = addition(multiplication(sk0_1,X0),zero),
inference(paramodulation,[status(thm)],[f61,f26]) ).
fof(f159,plain,
! [X0] : multiplication(sk0_1,addition(X0,multiplication(sk0_3,c(sk0_2)))) = multiplication(sk0_1,X0),
inference(forward_demodulation,[status(thm)],[f21,f158]) ).
fof(f398,plain,
! [X0] : multiplication(sk0_1,multiplication(sk0_3,addition(X0,c(sk0_2)))) = multiplication(sk0_1,multiplication(sk0_3,X0)),
inference(paramodulation,[status(thm)],[f26,f159]) ).
fof(f885,plain,
addition(sk0_2,c(sk0_2)) = one,
inference(resolution,[status(thm)],[f104,f56]) ).
fof(f18328,plain,
multiplication(sk0_1,multiplication(sk0_3,one)) = multiplication(sk0_1,multiplication(sk0_3,sk0_2)),
inference(paramodulation,[status(thm)],[f885,f398]) ).
fof(f18329,plain,
multiplication(sk0_1,sk0_3) = multiplication(sk0_1,multiplication(sk0_3,sk0_2)),
inference(forward_demodulation,[status(thm)],[f24,f18328]) ).
fof(f18330,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f18329,f60]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : KLE025+1 : TPTP v8.1.2. Released v4.0.0.
% 0.03/0.12 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.12/0.34 % Computer : n003.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Tue May 30 11:49:53 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.12/0.35 % Drodi V3.5.1
% 6.44/1.21 % Refutation found
% 6.44/1.21 % SZS status Theorem for theBenchmark: Theorem is valid
% 6.44/1.21 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 7.02/1.26 % Elapsed time: 0.903349 seconds
% 7.02/1.26 % CPU time: 6.992951 seconds
% 7.02/1.26 % Memory used: 174.915 MB
%------------------------------------------------------------------------------