TSTP Solution File: KLE027+1 by Drodi---3.5.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : KLE027+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 59.66s 7.99s
% Output : CNFRefutation 60.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 11
% Syntax : Number of formulae : 56 ( 35 unt; 0 def)
% Number of atoms : 111 ( 60 equ)
% Maximal formula atoms : 8 ( 1 avg)
% Number of connectives : 91 ( 36 ~; 27 |; 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 : 94 (; 81 !; 13 ?)
% 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(f7,axiom,
! [A] : multiplication(one,A) = 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(f9,axiom,
! [A,B,C] : multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [A] : multiplication(zero,A) = zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [X0] :
( test(X0)
<=> ? [X1] : complement(X1,X0) ),
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,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/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,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)],[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(f25,plain,
! [X0] : multiplication(one,X0) = X0,
inference(cnf_transformation,[status(esa)],[f7]) ).
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(f29,plain,
! [X0] : multiplication(zero,X0) = zero,
inference(cnf_transformation,[status(esa)],[f11]) ).
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(f42,plain,
! [X0,X1] :
( ~ complement(X0,X1)
| multiplication(X0,X1) = zero ),
inference(cnf_transformation,[status(esa)],[f40]) ).
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,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)],[f18]) ).
fof(f53,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)],[f52]) ).
fof(f54,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)],[f53]) ).
fof(f55,plain,
test(sk0_1),
inference(cnf_transformation,[status(esa)],[f54]) ).
fof(f57,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)],[f54]) ).
fof(f58,plain,
! [X0] :
( ~ test(X0)
| complement(X0,c(X0)) ),
inference(destructive_equality_resolution,[status(esa)],[f48]) ).
fof(f59,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)],[f19,f57]) ).
fof(f75,plain,
complement(sk0_1,c(sk0_1)),
inference(resolution,[status(thm)],[f58,f55]) ).
fof(f1649,plain,
complement(sk0_0(sk0_1),sk0_1),
inference(resolution,[status(thm)],[f37,f55]) ).
fof(f1654,plain,
multiplication(sk0_1,c(sk0_1)) = zero,
inference(resolution,[status(thm)],[f42,f75]) ).
fof(f1658,plain,
multiplication(sk0_0(sk0_1),sk0_1) = zero,
inference(resolution,[status(thm)],[f1649,f42]) ).
fof(f2258,plain,
! [X0] : multiplication(sk0_1,multiplication(c(sk0_1),X0)) = multiplication(zero,X0),
inference(paramodulation,[status(thm)],[f1654,f23]) ).
fof(f2259,plain,
! [X0] : multiplication(sk0_1,multiplication(c(sk0_1),X0)) = zero,
inference(forward_demodulation,[status(thm)],[f29,f2258]) ).
fof(f2966,plain,
! [X0] : multiplication(addition(X0,sk0_0(sk0_1)),sk0_1) = addition(multiplication(X0,sk0_1),zero),
inference(paramodulation,[status(thm)],[f1658,f27]) ).
fof(f2967,plain,
! [X0] : multiplication(addition(X0,sk0_0(sk0_1)),sk0_1) = multiplication(X0,sk0_1),
inference(forward_demodulation,[status(thm)],[f21,f2966]) ).
fof(f9972,plain,
addition(sk0_1,sk0_0(sk0_1)) = one,
inference(resolution,[status(thm)],[f43,f1649]) ).
fof(f12921,plain,
multiplication(one,sk0_1) = multiplication(sk0_1,sk0_1),
inference(paramodulation,[status(thm)],[f9972,f2967]) ).
fof(f12922,plain,
sk0_1 = multiplication(sk0_1,sk0_1),
inference(forward_demodulation,[status(thm)],[f25,f12921]) ).
fof(f13096,plain,
! [X0] : multiplication(sk0_1,multiplication(sk0_1,X0)) = multiplication(sk0_1,X0),
inference(paramodulation,[status(thm)],[f12922,f23]) ).
fof(f39266,plain,
! [X0,X1] : multiplication(sk0_1,addition(X0,multiplication(c(sk0_1),X1))) = addition(multiplication(sk0_1,X0),zero),
inference(paramodulation,[status(thm)],[f2259,f26]) ).
fof(f39267,plain,
! [X0,X1] : multiplication(sk0_1,addition(X0,multiplication(c(sk0_1),X1))) = multiplication(sk0_1,X0),
inference(forward_demodulation,[status(thm)],[f21,f39266]) ).
fof(f39273,plain,
addition(multiplication(c(sk0_1),sk0_5),multiplication(sk0_1,multiplication(sk0_1,sk0_3))) != addition(multiplication(sk0_1,sk0_3),multiplication(c(sk0_1),sk0_5)),
inference(backward_demodulation,[status(thm)],[f39267,f59]) ).
fof(f39274,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(forward_demodulation,[status(thm)],[f13096,f39273]) ).
fof(f39275,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)],[f19,f39274]) ).
fof(f39276,plain,
$false,
inference(trivial_equality_resolution,[status(esa)],[f39275]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : KLE027+1 : TPTP v8.1.2. Released v4.0.0.
% 0.03/0.11 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.11/0.32 % Computer : n015.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Tue May 30 12:01:34 EDT 2023
% 0.11/0.32 % CPUTime :
% 0.11/0.33 % Drodi V3.5.1
% 59.66/7.99 % Refutation found
% 59.66/7.99 % SZS status Theorem for theBenchmark: Theorem is valid
% 59.66/7.99 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 61.09/8.15 % Elapsed time: 7.811625 seconds
% 61.09/8.15 % CPU time: 61.016430 seconds
% 61.09/8.15 % Memory used: 475.298 MB
%------------------------------------------------------------------------------