TSTP Solution File: KLE024+2 by Drodi---3.5.1
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%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : KLE024+2 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n012.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 2.27s 0.68s
% Output : CNFRefutation 2.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 8
% Syntax : Number of formulae : 44 ( 29 unt; 0 def)
% Number of atoms : 92 ( 59 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 73 ( 25 ~; 19 |; 21 &)
% ( 3 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 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 : 67 (; 61 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [C,B,A] : addition(A,addition(B,C)) = addition(addition(A,B),C),
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(f11,axiom,
! [A] : multiplication(zero,A) = zero,
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(f15,axiom,
! [X0,X1] :
( test(X0)
=> ( c(X0) = X1
<=> complement(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,conjecture,
! [X0,X1,X2] :
( ( test(X1)
& test(X2) )
=> ( addition(multiplication(X0,c(X2)),multiplication(c(X1),X0)) = multiplication(c(X1),X0)
=> multiplication(multiplication(X1,X0),c(X2)) = zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
~ ! [X0,X1,X2] :
( ( test(X1)
& test(X2) )
=> ( addition(multiplication(X0,c(X2)),multiplication(c(X1),X0)) = multiplication(c(X1),X0)
=> multiplication(multiplication(X1,X0),c(X2)) = zero ) ),
inference(negated_conjecture,[status(cth)],[f19]) ).
fof(f22,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(addition(X0,X1),X2),
inference(cnf_transformation,[status(esa)],[f2]) ).
fof(f23,plain,
! [X0] : addition(X0,zero) = X0,
inference(cnf_transformation,[status(esa)],[f3]) ).
fof(f25,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
inference(cnf_transformation,[status(esa)],[f5]) ).
fof(f28,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
inference(cnf_transformation,[status(esa)],[f8]) ).
fof(f31,plain,
! [X0] : multiplication(zero,X0) = zero,
inference(cnf_transformation,[status(esa)],[f11]) ).
fof(f41,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(f42,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)],[f41]) ).
fof(f44,plain,
! [X0,X1] :
( ~ complement(X0,X1)
| multiplication(X0,X1) = zero ),
inference(cnf_transformation,[status(esa)],[f42]) ).
fof(f47,plain,
! [X0,X1] :
( ~ test(X0)
| ( c(X0) = X1
<=> complement(X0,X1) ) ),
inference(pre_NNF_transformation,[status(esa)],[f15]) ).
fof(f48,plain,
! [X0,X1] :
( ~ test(X0)
| ( ( c(X0) != X1
| complement(X0,X1) )
& ( c(X0) = X1
| ~ complement(X0,X1) ) ) ),
inference(NNF_transformation,[status(esa)],[f47]) ).
fof(f49,plain,
! [X0] :
( ~ test(X0)
| ( ! [X1] :
( c(X0) != X1
| complement(X0,X1) )
& ! [X1] :
( c(X0) = X1
| ~ complement(X0,X1) ) ) ),
inference(miniscoping,[status(esa)],[f48]) ).
fof(f50,plain,
! [X0,X1] :
( ~ test(X0)
| c(X0) != X1
| complement(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f49]) ).
fof(f58,plain,
? [X0,X1,X2] :
( test(X1)
& test(X2)
& addition(multiplication(X0,c(X2)),multiplication(c(X1),X0)) = multiplication(c(X1),X0)
& multiplication(multiplication(X1,X0),c(X2)) != zero ),
inference(pre_NNF_transformation,[status(esa)],[f20]) ).
fof(f59,plain,
? [X1,X2] :
( test(X1)
& test(X2)
& ? [X0] :
( addition(multiplication(X0,c(X2)),multiplication(c(X1),X0)) = multiplication(c(X1),X0)
& multiplication(multiplication(X1,X0),c(X2)) != zero ) ),
inference(miniscoping,[status(esa)],[f58]) ).
fof(f60,plain,
( test(sk0_1)
& test(sk0_2)
& addition(multiplication(sk0_3,c(sk0_2)),multiplication(c(sk0_1),sk0_3)) = multiplication(c(sk0_1),sk0_3)
& multiplication(multiplication(sk0_1,sk0_3),c(sk0_2)) != zero ),
inference(skolemization,[status(esa)],[f59]) ).
fof(f61,plain,
test(sk0_1),
inference(cnf_transformation,[status(esa)],[f60]) ).
fof(f63,plain,
addition(multiplication(sk0_3,c(sk0_2)),multiplication(c(sk0_1),sk0_3)) = multiplication(c(sk0_1),sk0_3),
inference(cnf_transformation,[status(esa)],[f60]) ).
fof(f64,plain,
multiplication(multiplication(sk0_1,sk0_3),c(sk0_2)) != zero,
inference(cnf_transformation,[status(esa)],[f60]) ).
fof(f65,plain,
! [X0] :
( ~ test(X0)
| complement(X0,c(X0)) ),
inference(destructive_equality_resolution,[status(esa)],[f50]) ).
fof(f66,plain,
multiplication(sk0_1,multiplication(sk0_3,c(sk0_2))) != zero,
inference(forward_demodulation,[status(thm)],[f25,f64]) ).
fof(f83,plain,
! [X0] : addition(multiplication(sk0_3,c(sk0_2)),addition(multiplication(c(sk0_1),sk0_3),X0)) = addition(multiplication(c(sk0_1),sk0_3),X0),
inference(paramodulation,[status(thm)],[f63,f22]) ).
fof(f485,plain,
complement(sk0_1,c(sk0_1)),
inference(resolution,[status(thm)],[f65,f61]) ).
fof(f1408,plain,
multiplication(sk0_1,c(sk0_1)) = zero,
inference(resolution,[status(thm)],[f485,f44]) ).
fof(f1426,plain,
! [X0] : multiplication(sk0_1,addition(X0,c(sk0_1))) = addition(multiplication(sk0_1,X0),zero),
inference(paramodulation,[status(thm)],[f1408,f28]) ).
fof(f1427,plain,
! [X0] : multiplication(sk0_1,addition(X0,c(sk0_1))) = multiplication(sk0_1,X0),
inference(forward_demodulation,[status(thm)],[f23,f1426]) ).
fof(f1430,plain,
! [X0] : multiplication(sk0_1,multiplication(c(sk0_1),X0)) = multiplication(zero,X0),
inference(paramodulation,[status(thm)],[f1408,f25]) ).
fof(f1431,plain,
! [X0] : multiplication(sk0_1,multiplication(c(sk0_1),X0)) = zero,
inference(forward_demodulation,[status(thm)],[f31,f1430]) ).
fof(f1465,plain,
! [X0,X1] : multiplication(sk0_1,addition(X0,multiplication(c(sk0_1),X1))) = addition(multiplication(sk0_1,X0),zero),
inference(paramodulation,[status(thm)],[f1431,f28]) ).
fof(f1466,plain,
! [X0,X1] : multiplication(sk0_1,addition(X0,multiplication(c(sk0_1),X1))) = multiplication(sk0_1,X0),
inference(forward_demodulation,[status(thm)],[f23,f1465]) ).
fof(f1548,plain,
! [X0,X1] : multiplication(sk0_1,addition(X0,addition(X1,c(sk0_1)))) = multiplication(sk0_1,addition(X0,X1)),
inference(paramodulation,[status(thm)],[f22,f1427]) ).
fof(f2993,plain,
multiplication(sk0_1,addition(multiplication(c(sk0_1),sk0_3),c(sk0_1))) = multiplication(sk0_1,addition(multiplication(sk0_3,c(sk0_2)),multiplication(c(sk0_1),sk0_3))),
inference(paramodulation,[status(thm)],[f83,f1548]) ).
fof(f2994,plain,
multiplication(sk0_1,multiplication(c(sk0_1),sk0_3)) = multiplication(sk0_1,addition(multiplication(sk0_3,c(sk0_2)),multiplication(c(sk0_1),sk0_3))),
inference(forward_demodulation,[status(thm)],[f1427,f2993]) ).
fof(f2995,plain,
zero = multiplication(sk0_1,addition(multiplication(sk0_3,c(sk0_2)),multiplication(c(sk0_1),sk0_3))),
inference(forward_demodulation,[status(thm)],[f1431,f2994]) ).
fof(f2996,plain,
zero = multiplication(sk0_1,multiplication(sk0_3,c(sk0_2))),
inference(forward_demodulation,[status(thm)],[f1466,f2995]) ).
fof(f2997,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f2996,f66]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : KLE024+2 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.34 % Computer : n012.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 11:42:55 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.13/0.35 % Drodi V3.5.1
% 2.27/0.68 % Refutation found
% 2.27/0.68 % SZS status Theorem for theBenchmark: Theorem is valid
% 2.27/0.68 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 2.57/0.70 % Elapsed time: 0.349626 seconds
% 2.57/0.70 % CPU time: 2.639780 seconds
% 2.57/0.70 % Memory used: 94.059 MB
%------------------------------------------------------------------------------