TSTP Solution File: KLE044+2 by Drodi---3.5.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : KLE044+2 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n007.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 12:15:38 EDT 2023
% Result : Theorem 2.51s 0.93s
% Output : CNFRefutation 2.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 12
% Syntax : Number of formulae : 81 ( 46 unt; 0 def)
% Number of atoms : 120 ( 55 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 74 ( 35 ~; 31 |; 4 &)
% ( 3 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 3 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 112 (; 109 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B] : addition(A,B) = addition(B,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [C,B,A] : addition(A,addition(B,C)) = addition(addition(A,B),C),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A] : addition(A,A) = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [A] : multiplication(A,one) = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [A] : multiplication(one,A) = A,
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(f12,axiom,
! [A,B] :
( leq(A,B)
<=> addition(A,B) = B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [A] : leq(addition(one,multiplication(A,star(A))),star(A)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [A,B,C] :
( leq(addition(multiplication(A,B),C),B)
=> leq(multiplication(star(A),C),B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,conjecture,
! [X0] :
( leq(star(addition(one,X0)),star(X0))
& leq(star(X0),star(addition(one,X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
~ ! [X0] :
( leq(star(addition(one,X0)),star(X0))
& leq(star(X0),star(addition(one,X0))) ),
inference(negated_conjecture,[status(cth)],[f17]) ).
fof(f19,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[status(esa)],[f1]) ).
fof(f20,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(addition(X0,X1),X2),
inference(cnf_transformation,[status(esa)],[f2]) ).
fof(f22,plain,
! [X0] : addition(X0,X0) = X0,
inference(cnf_transformation,[status(esa)],[f4]) ).
fof(f24,plain,
! [X0] : multiplication(X0,one) = X0,
inference(cnf_transformation,[status(esa)],[f6]) ).
fof(f25,plain,
! [X0] : multiplication(one,X0) = X0,
inference(cnf_transformation,[status(esa)],[f7]) ).
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(f34,plain,
! [X0] : leq(addition(one,multiplication(X0,star(X0))),star(X0)),
inference(cnf_transformation,[status(esa)],[f13]) ).
fof(f36,plain,
! [A,B,C] :
( ~ leq(addition(multiplication(A,B),C),B)
| leq(multiplication(star(A),C),B) ),
inference(pre_NNF_transformation,[status(esa)],[f15]) ).
fof(f37,plain,
! [X0,X1,X2] :
( ~ leq(addition(multiplication(X0,X1),X2),X1)
| leq(multiplication(star(X0),X2),X1) ),
inference(cnf_transformation,[status(esa)],[f36]) ).
fof(f40,plain,
? [X0] :
( ~ leq(star(addition(one,X0)),star(X0))
| ~ leq(star(X0),star(addition(one,X0))) ),
inference(pre_NNF_transformation,[status(esa)],[f18]) ).
fof(f41,plain,
( ? [X0] : ~ leq(star(addition(one,X0)),star(X0))
| ? [X0] : ~ leq(star(X0),star(addition(one,X0))) ),
inference(miniscoping,[status(esa)],[f40]) ).
fof(f42,plain,
( ~ leq(star(addition(one,sk0_0)),star(sk0_0))
| ~ leq(star(sk0_1),star(addition(one,sk0_1))) ),
inference(skolemization,[status(esa)],[f41]) ).
fof(f43,plain,
( ~ leq(star(addition(one,sk0_0)),star(sk0_0))
| ~ leq(star(sk0_1),star(addition(one,sk0_1))) ),
inference(cnf_transformation,[status(esa)],[f42]) ).
fof(f44,plain,
( spl0_0
<=> leq(star(addition(one,sk0_0)),star(sk0_0)) ),
introduced(split_symbol_definition) ).
fof(f46,plain,
( ~ leq(star(addition(one,sk0_0)),star(sk0_0))
| spl0_0 ),
inference(component_clause,[status(thm)],[f44]) ).
fof(f47,plain,
( spl0_1
<=> leq(star(sk0_1),star(addition(one,sk0_1))) ),
introduced(split_symbol_definition) ).
fof(f49,plain,
( ~ leq(star(sk0_1),star(addition(one,sk0_1)))
| spl0_1 ),
inference(component_clause,[status(thm)],[f47]) ).
fof(f50,plain,
( ~ spl0_0
| ~ spl0_1 ),
inference(split_clause,[status(thm)],[f43,f44,f47]) ).
fof(f51,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X2,addition(X0,X1)),
inference(paramodulation,[status(thm)],[f19,f20]) ).
fof(f57,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(addition(X1,X0),X2),
inference(paramodulation,[status(thm)],[f19,f20]) ).
fof(f58,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X1,addition(X0,X2)),
inference(forward_demodulation,[status(thm)],[f20,f57]) ).
fof(f61,plain,
! [X0,X1] : addition(X0,addition(X0,X1)) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f22,f20]) ).
fof(f71,plain,
! [X0,X1] : addition(X0,addition(X1,X0)) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f19,f61]) ).
fof(f82,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X2,X0))) = addition(X0,addition(X1,X2)),
inference(paramodulation,[status(thm)],[f20,f71]) ).
fof(f99,plain,
! [X0,X1,X2] : addition(X0,addition(addition(X1,X0),X2)) = addition(addition(X0,X1),X2),
inference(paramodulation,[status(thm)],[f71,f20]) ).
fof(f100,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,X2))) = addition(addition(X0,X1),X2),
inference(forward_demodulation,[status(thm)],[f20,f99]) ).
fof(f101,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,X2))) = addition(X0,addition(X1,X2)),
inference(forward_demodulation,[status(thm)],[f20,f100]) ).
fof(f123,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(addition(X2,X1),addition(X0,X1)),
inference(paramodulation,[status(thm)],[f71,f51]) ).
fof(f124,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X2,addition(X1,addition(X0,X1))),
inference(forward_demodulation,[status(thm)],[f20,f123]) ).
fof(f125,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X2,addition(X1,X0)),
inference(forward_demodulation,[status(thm)],[f71,f124]) ).
fof(f167,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,X2))) = addition(X0,addition(X2,X1)),
inference(paramodulation,[status(thm)],[f51,f61]) ).
fof(f168,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X0,addition(X2,X1)),
inference(forward_demodulation,[status(thm)],[f101,f167]) ).
fof(f580,plain,
! [X0] : addition(addition(one,multiplication(X0,star(X0))),star(X0)) = star(X0),
inference(resolution,[status(thm)],[f34,f32]) ).
fof(f581,plain,
! [X0] : addition(one,addition(multiplication(X0,star(X0)),star(X0))) = star(X0),
inference(forward_demodulation,[status(thm)],[f20,f580]) ).
fof(f582,plain,
! [X0] : addition(one,addition(star(X0),multiplication(X0,star(X0)))) = star(X0),
inference(forward_demodulation,[status(thm)],[f168,f581]) ).
fof(f633,plain,
! [X0,X1] : multiplication(addition(one,X0),X1) = addition(X1,multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f25,f27]) ).
fof(f1621,plain,
! [X0,X1] :
( ~ leq(addition(multiplication(X0,X1),one),X1)
| leq(star(X0),X1) ),
inference(paramodulation,[status(thm)],[f24,f37]) ).
fof(f1622,plain,
! [X0,X1] :
( ~ leq(addition(one,multiplication(X0,X1)),X1)
| leq(star(X0),X1) ),
inference(forward_demodulation,[status(thm)],[f19,f1621]) ).
fof(f1652,plain,
! [X0] : addition(multiplication(X0,star(X0)),star(X0)) = addition(multiplication(X0,star(X0)),addition(one,star(X0))),
inference(paramodulation,[status(thm)],[f582,f82]) ).
fof(f1653,plain,
! [X0] : addition(star(X0),multiplication(X0,star(X0))) = addition(multiplication(X0,star(X0)),addition(one,star(X0))),
inference(forward_demodulation,[status(thm)],[f19,f1652]) ).
fof(f1654,plain,
! [X0] : multiplication(addition(one,X0),star(X0)) = addition(multiplication(X0,star(X0)),addition(one,star(X0))),
inference(forward_demodulation,[status(thm)],[f633,f1653]) ).
fof(f1655,plain,
! [X0] : multiplication(addition(one,X0),star(X0)) = addition(star(X0),addition(one,multiplication(X0,star(X0)))),
inference(forward_demodulation,[status(thm)],[f125,f1654]) ).
fof(f1656,plain,
! [X0] : multiplication(addition(one,X0),star(X0)) = addition(one,addition(star(X0),multiplication(X0,star(X0)))),
inference(forward_demodulation,[status(thm)],[f58,f1655]) ).
fof(f1657,plain,
! [X0] : multiplication(addition(one,X0),star(X0)) = star(X0),
inference(forward_demodulation,[status(thm)],[f582,f1656]) ).
fof(f1701,plain,
! [X0] : addition(one,star(X0)) = addition(one,addition(star(X0),multiplication(X0,star(X0)))),
inference(paramodulation,[status(thm)],[f582,f61]) ).
fof(f1702,plain,
! [X0] : addition(one,star(X0)) = star(X0),
inference(forward_demodulation,[status(thm)],[f582,f1701]) ).
fof(f1718,plain,
! [X0,X1] : addition(star(X0),addition(one,X1)) = addition(X1,star(X0)),
inference(paramodulation,[status(thm)],[f1702,f125]) ).
fof(f1719,plain,
! [X0,X1] : addition(one,addition(star(X0),X1)) = addition(X1,star(X0)),
inference(forward_demodulation,[status(thm)],[f58,f1718]) ).
fof(f1859,plain,
! [X0] : multiplication(addition(one,X0),star(addition(one,X0))) = star(addition(one,X0)),
inference(paramodulation,[status(thm)],[f61,f1657]) ).
fof(f2369,plain,
( ~ leq(addition(one,multiplication(addition(one,sk0_0),star(sk0_0))),star(sk0_0))
| spl0_0 ),
inference(resolution,[status(thm)],[f1622,f46]) ).
fof(f2370,plain,
( ~ leq(addition(one,star(sk0_0)),star(sk0_0))
| spl0_0 ),
inference(forward_demodulation,[status(thm)],[f1657,f2369]) ).
fof(f2371,plain,
( ~ leq(star(sk0_0),star(sk0_0))
| spl0_0 ),
inference(forward_demodulation,[status(thm)],[f1702,f2370]) ).
fof(f2373,plain,
( ~ leq(addition(one,multiplication(sk0_0,star(sk0_0))),star(sk0_0))
| spl0_0 ),
inference(resolution,[status(thm)],[f2371,f1622]) ).
fof(f2374,plain,
( $false
| spl0_0 ),
inference(forward_subsumption_resolution,[status(thm)],[f2373,f34]) ).
fof(f2375,plain,
spl0_0,
inference(contradiction_clause,[status(thm)],[f2374]) ).
fof(f2376,plain,
( ~ leq(addition(one,multiplication(sk0_1,star(addition(one,sk0_1)))),star(addition(one,sk0_1)))
| spl0_1 ),
inference(resolution,[status(thm)],[f49,f1622]) ).
fof(f2380,plain,
( addition(addition(one,multiplication(sk0_1,star(addition(one,sk0_1)))),star(addition(one,sk0_1))) != star(addition(one,sk0_1))
| spl0_1 ),
inference(resolution,[status(thm)],[f2376,f33]) ).
fof(f2381,plain,
( addition(one,addition(multiplication(sk0_1,star(addition(one,sk0_1))),star(addition(one,sk0_1)))) != star(addition(one,sk0_1))
| spl0_1 ),
inference(forward_demodulation,[status(thm)],[f20,f2380]) ).
fof(f2382,plain,
( addition(one,addition(star(addition(one,sk0_1)),multiplication(sk0_1,star(addition(one,sk0_1))))) != star(addition(one,sk0_1))
| spl0_1 ),
inference(forward_demodulation,[status(thm)],[f168,f2381]) ).
fof(f2383,plain,
( addition(multiplication(sk0_1,star(addition(one,sk0_1))),star(addition(one,sk0_1))) != star(addition(one,sk0_1))
| spl0_1 ),
inference(forward_demodulation,[status(thm)],[f1719,f2382]) ).
fof(f2384,plain,
( addition(star(addition(one,sk0_1)),multiplication(sk0_1,star(addition(one,sk0_1)))) != star(addition(one,sk0_1))
| spl0_1 ),
inference(forward_demodulation,[status(thm)],[f19,f2383]) ).
fof(f2385,plain,
( multiplication(addition(one,sk0_1),star(addition(one,sk0_1))) != star(addition(one,sk0_1))
| spl0_1 ),
inference(forward_demodulation,[status(thm)],[f633,f2384]) ).
fof(f2386,plain,
( star(addition(one,sk0_1)) != star(addition(one,sk0_1))
| spl0_1 ),
inference(forward_demodulation,[status(thm)],[f1859,f2385]) ).
fof(f2387,plain,
( $false
| spl0_1 ),
inference(trivial_equality_resolution,[status(esa)],[f2386]) ).
fof(f2388,plain,
spl0_1,
inference(contradiction_clause,[status(thm)],[f2387]) ).
fof(f2389,plain,
$false,
inference(sat_refutation,[status(thm)],[f50,f2375,f2388]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.10 % Problem : KLE044+2 : TPTP v8.1.2. Released v4.0.0.
% 0.09/0.11 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.10/0.31 % Computer : n007.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Tue May 30 11:34:32 EDT 2023
% 0.10/0.31 % CPUTime :
% 0.17/0.32 % Drodi V3.5.1
% 2.51/0.93 % Refutation found
% 2.51/0.93 % SZS status Theorem for theBenchmark: Theorem is valid
% 2.51/0.93 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 3.31/0.96 % Elapsed time: 0.639680 seconds
% 3.31/0.96 % CPU time: 3.073475 seconds
% 3.31/0.96 % Memory used: 67.651 MB
%------------------------------------------------------------------------------