TSTP Solution File: KLE027+3 by Drodi---3.5.1
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%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : KLE027+3 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n009.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 6.72s 1.22s
% Output : CNFRefutation 6.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 10
% Syntax : Number of formulae : 58 ( 33 unt; 0 def)
% Number of atoms : 117 ( 64 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 99 ( 40 ~; 31 |; 21 &)
% ( 4 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 7 con; 0-2 aty)
% Number of variables : 97 (; 84 !; 13 ?)
% 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(f6,axiom,
! [A] : multiplication(A,one) = A,
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(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(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,X3,X4] :
( ( test(X3)
& test(X4) )
=> addition(multiplication(X3,addition(multiplication(X3,X0),multiplication(c(X3),X1))),multiplication(c(X3),X2)) = addition(multiplication(X3,X0),multiplication(c(X3),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
~ ! [X0,X1,X2,X3,X4] :
( ( test(X3)
& test(X4) )
=> addition(multiplication(X3,addition(multiplication(X3,X0),multiplication(c(X3),X1))),multiplication(c(X3),X2)) = addition(multiplication(X3,X0),multiplication(c(X3),X2)) ),
inference(negated_conjecture,[status(cth)],[f19]) ).
fof(f21,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[status(esa)],[f1]) ).
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(f26,plain,
! [X0] : multiplication(X0,one) = X0,
inference(cnf_transformation,[status(esa)],[f6]) ).
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(f36,plain,
! [X0] :
( ( ~ test(X0)
| ? [X1] : complement(X1,X0) )
& ( test(X0)
| ! [X1] : ~ complement(X1,X0) ) ),
inference(NNF_transformation,[status(esa)],[f13]) ).
fof(f37,plain,
( ! [X0] :
( ~ test(X0)
| ? [X1] : complement(X1,X0) )
& ! [X0] :
( test(X0)
| ! [X1] : ~ complement(X1,X0) ) ),
inference(miniscoping,[status(esa)],[f36]) ).
fof(f38,plain,
( ! [X0] :
( ~ test(X0)
| complement(sk0_0(X0),X0) )
& ! [X0] :
( test(X0)
| ! [X1] : ~ complement(X1,X0) ) ),
inference(skolemization,[status(esa)],[f37]) ).
fof(f39,plain,
! [X0] :
( ~ test(X0)
| complement(sk0_0(X0),X0) ),
inference(cnf_transformation,[status(esa)],[f38]) ).
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(f43,plain,
! [X0,X1] :
( ~ complement(X0,X1)
| multiplication(X1,X0) = zero ),
inference(cnf_transformation,[status(esa)],[f42]) ).
fof(f44,plain,
! [X0,X1] :
( ~ complement(X0,X1)
| multiplication(X0,X1) = zero ),
inference(cnf_transformation,[status(esa)],[f42]) ).
fof(f45,plain,
! [X0,X1] :
( ~ complement(X0,X1)
| addition(X1,X0) = one ),
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,X3,X4] :
( test(X3)
& test(X4)
& addition(multiplication(X3,addition(multiplication(X3,X0),multiplication(c(X3),X1))),multiplication(c(X3),X2)) != addition(multiplication(X3,X0),multiplication(c(X3),X2)) ),
inference(pre_NNF_transformation,[status(esa)],[f20]) ).
fof(f59,plain,
? [X3] :
( test(X3)
& ? [X4] : test(X4)
& ? [X0,X1,X2] : addition(multiplication(X3,addition(multiplication(X3,X0),multiplication(c(X3),X1))),multiplication(c(X3),X2)) != addition(multiplication(X3,X0),multiplication(c(X3),X2)) ),
inference(miniscoping,[status(esa)],[f58]) ).
fof(f60,plain,
( test(sk0_1)
& test(sk0_2)
& addition(multiplication(sk0_1,addition(multiplication(sk0_1,sk0_3),multiplication(c(sk0_1),sk0_4))),multiplication(c(sk0_1),sk0_5)) != addition(multiplication(sk0_1,sk0_3),multiplication(c(sk0_1),sk0_5)) ),
inference(skolemization,[status(esa)],[f59]) ).
fof(f61,plain,
test(sk0_1),
inference(cnf_transformation,[status(esa)],[f60]) ).
fof(f63,plain,
addition(multiplication(sk0_1,addition(multiplication(sk0_1,sk0_3),multiplication(c(sk0_1),sk0_4))),multiplication(c(sk0_1),sk0_5)) != addition(multiplication(sk0_1,sk0_3),multiplication(c(sk0_1),sk0_5)),
inference(cnf_transformation,[status(esa)],[f60]) ).
fof(f64,plain,
! [X0] :
( ~ test(X0)
| complement(X0,c(X0)) ),
inference(destructive_equality_resolution,[status(esa)],[f50]) ).
fof(f65,plain,
addition(multiplication(c(sk0_1),sk0_5),multiplication(sk0_1,addition(multiplication(sk0_1,sk0_3),multiplication(c(sk0_1),sk0_4)))) != addition(multiplication(sk0_1,sk0_3),multiplication(c(sk0_1),sk0_5)),
inference(forward_demodulation,[status(thm)],[f21,f63]) ).
fof(f489,plain,
! [X0] :
( multiplication(X0,sk0_0(X0)) = zero
| ~ test(X0) ),
inference(resolution,[status(thm)],[f43,f39]) ).
fof(f491,plain,
! [X0] :
( addition(X0,sk0_0(X0)) = one
| ~ test(X0) ),
inference(resolution,[status(thm)],[f45,f39]) ).
fof(f1847,plain,
! [X0] :
( ~ test(X0)
| multiplication(X0,c(X0)) = zero ),
inference(resolution,[status(thm)],[f64,f44]) ).
fof(f2167,plain,
multiplication(sk0_1,sk0_0(sk0_1)) = zero,
inference(resolution,[status(thm)],[f489,f61]) ).
fof(f2195,plain,
! [X0] : multiplication(sk0_1,addition(X0,sk0_0(sk0_1))) = addition(multiplication(sk0_1,X0),zero),
inference(paramodulation,[status(thm)],[f2167,f28]) ).
fof(f2196,plain,
! [X0] : multiplication(sk0_1,addition(X0,sk0_0(sk0_1))) = multiplication(sk0_1,X0),
inference(forward_demodulation,[status(thm)],[f23,f2195]) ).
fof(f2203,plain,
addition(sk0_1,sk0_0(sk0_1)) = one,
inference(resolution,[status(thm)],[f491,f61]) ).
fof(f5399,plain,
multiplication(sk0_1,one) = multiplication(sk0_1,sk0_1),
inference(paramodulation,[status(thm)],[f2203,f2196]) ).
fof(f5400,plain,
sk0_1 = multiplication(sk0_1,sk0_1),
inference(forward_demodulation,[status(thm)],[f26,f5399]) ).
fof(f5451,plain,
! [X0] : multiplication(sk0_1,multiplication(sk0_1,X0)) = multiplication(sk0_1,X0),
inference(paramodulation,[status(thm)],[f5400,f25]) ).
fof(f5555,plain,
! [X0,X1] : multiplication(sk0_1,addition(multiplication(sk0_1,X0),X1)) = addition(multiplication(sk0_1,X0),multiplication(sk0_1,X1)),
inference(paramodulation,[status(thm)],[f5451,f28]) ).
fof(f5556,plain,
! [X0,X1] : multiplication(sk0_1,addition(multiplication(sk0_1,X0),X1)) = multiplication(sk0_1,addition(X0,X1)),
inference(forward_demodulation,[status(thm)],[f28,f5555]) ).
fof(f5560,plain,
addition(multiplication(c(sk0_1),sk0_5),multiplication(sk0_1,addition(sk0_3,multiplication(c(sk0_1),sk0_4)))) != addition(multiplication(sk0_1,sk0_3),multiplication(c(sk0_1),sk0_5)),
inference(backward_demodulation,[status(thm)],[f5556,f65]) ).
fof(f6271,plain,
multiplication(sk0_1,c(sk0_1)) = zero,
inference(resolution,[status(thm)],[f1847,f61]) ).
fof(f6656,plain,
! [X0] : multiplication(sk0_1,multiplication(c(sk0_1),X0)) = multiplication(zero,X0),
inference(paramodulation,[status(thm)],[f6271,f25]) ).
fof(f6657,plain,
! [X0] : multiplication(sk0_1,multiplication(c(sk0_1),X0)) = zero,
inference(forward_demodulation,[status(thm)],[f31,f6656]) ).
fof(f6785,plain,
! [X0,X1] : multiplication(sk0_1,addition(X0,multiplication(c(sk0_1),X1))) = addition(multiplication(sk0_1,X0),zero),
inference(paramodulation,[status(thm)],[f6657,f28]) ).
fof(f6786,plain,
! [X0,X1] : multiplication(sk0_1,addition(X0,multiplication(c(sk0_1),X1))) = multiplication(sk0_1,X0),
inference(forward_demodulation,[status(thm)],[f23,f6785]) ).
fof(f6793,plain,
addition(multiplication(c(sk0_1),sk0_5),multiplication(sk0_1,sk0_3)) != addition(multiplication(sk0_1,sk0_3),multiplication(c(sk0_1),sk0_5)),
inference(backward_demodulation,[status(thm)],[f6786,f5560]) ).
fof(f6794,plain,
addition(multiplication(sk0_1,sk0_3),multiplication(c(sk0_1),sk0_5)) != addition(multiplication(sk0_1,sk0_3),multiplication(c(sk0_1),sk0_5)),
inference(forward_demodulation,[status(thm)],[f21,f6793]) ).
fof(f6795,plain,
$false,
inference(trivial_equality_resolution,[status(esa)],[f6794]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : KLE027+3 : TPTP v8.1.2. Released v4.0.0.
% 0.03/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.14/0.34 % Computer : n009.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Tue May 30 11:42:46 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.14/0.35 % Drodi V3.5.1
% 6.72/1.22 % Refutation found
% 6.72/1.22 % SZS status Theorem for theBenchmark: Theorem is valid
% 6.72/1.22 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 6.96/1.27 % Elapsed time: 0.911306 seconds
% 6.96/1.27 % CPU time: 7.039222 seconds
% 6.96/1.27 % Memory used: 124.039 MB
%------------------------------------------------------------------------------