TSTP Solution File: KLE147+2 by Drodi---3.5.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : KLE147+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 12:15:54 EDT 2023
% Result : Theorem 70.10s 9.29s
% Output : CNFRefutation 71.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 13
% Syntax : Number of formulae : 85 ( 43 unt; 0 def)
% Number of atoms : 131 ( 47 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 88 ( 42 ~; 38 |; 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 : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 136 (; 130 !; 6 ?)
% 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(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(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] : addition(one,multiplication(A,star(A))) = star(A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [A,B,C] :
( leq(addition(multiplication(A,C),B),C)
=> leq(multiplication(star(A),B),C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [A] : strong_iteration(A) = addition(multiplication(A,strong_iteration(A)),one),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,axiom,
! [A,B] :
( leq(A,B)
<=> addition(A,B) = B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,conjecture,
! [X0,X1] :
( leq(strong_iteration(multiplication(star(X0),X1)),multiplication(star(X1),strong_iteration(multiplication(star(X0),X1))))
& leq(multiplication(star(X1),strong_iteration(multiplication(star(X0),X1))),strong_iteration(multiplication(star(X0),X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
~ ! [X0,X1] :
( leq(strong_iteration(multiplication(star(X0),X1)),multiplication(star(X1),strong_iteration(multiplication(star(X0),X1))))
& leq(multiplication(star(X1),strong_iteration(multiplication(star(X0),X1))),strong_iteration(multiplication(star(X0),X1))) ),
inference(negated_conjecture,[status(cth)],[f19]) ).
fof(f21,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[status(esa)],[f1]) ).
fof(f22,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(addition(X0,X1),X2),
inference(cnf_transformation,[status(esa)],[f2]) ).
fof(f24,plain,
! [X0] : addition(X0,X0) = X0,
inference(cnf_transformation,[status(esa)],[f4]) ).
fof(f25,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
inference(cnf_transformation,[status(esa)],[f5]) ).
fof(f27,plain,
! [X0] : multiplication(one,X0) = X0,
inference(cnf_transformation,[status(esa)],[f7]) ).
fof(f29,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
inference(cnf_transformation,[status(esa)],[f9]) ).
fof(f31,plain,
! [X0] : addition(one,multiplication(X0,star(X0))) = star(X0),
inference(cnf_transformation,[status(esa)],[f11]) ).
fof(f33,plain,
! [A,B,C] :
( ~ leq(addition(multiplication(A,C),B),C)
| leq(multiplication(star(A),B),C) ),
inference(pre_NNF_transformation,[status(esa)],[f13]) ).
fof(f34,plain,
! [X0,X1,X2] :
( ~ leq(addition(multiplication(X0,X1),X2),X1)
| leq(multiplication(star(X0),X2),X1) ),
inference(cnf_transformation,[status(esa)],[f33]) ).
fof(f37,plain,
! [X0] : strong_iteration(X0) = addition(multiplication(X0,strong_iteration(X0)),one),
inference(cnf_transformation,[status(esa)],[f15]) ).
fof(f41,plain,
! [A,B] :
( ( ~ leq(A,B)
| addition(A,B) = B )
& ( leq(A,B)
| addition(A,B) != B ) ),
inference(NNF_transformation,[status(esa)],[f18]) ).
fof(f42,plain,
( ! [A,B] :
( ~ leq(A,B)
| addition(A,B) = B )
& ! [A,B] :
( leq(A,B)
| addition(A,B) != B ) ),
inference(miniscoping,[status(esa)],[f41]) ).
fof(f43,plain,
! [X0,X1] :
( ~ leq(X0,X1)
| addition(X0,X1) = X1 ),
inference(cnf_transformation,[status(esa)],[f42]) ).
fof(f44,plain,
! [X0,X1] :
( leq(X0,X1)
| addition(X0,X1) != X1 ),
inference(cnf_transformation,[status(esa)],[f42]) ).
fof(f45,plain,
? [X0,X1] :
( ~ leq(strong_iteration(multiplication(star(X0),X1)),multiplication(star(X1),strong_iteration(multiplication(star(X0),X1))))
| ~ leq(multiplication(star(X1),strong_iteration(multiplication(star(X0),X1))),strong_iteration(multiplication(star(X0),X1))) ),
inference(pre_NNF_transformation,[status(esa)],[f20]) ).
fof(f46,plain,
( ? [X0,X1] : ~ leq(strong_iteration(multiplication(star(X0),X1)),multiplication(star(X1),strong_iteration(multiplication(star(X0),X1))))
| ? [X0,X1] : ~ leq(multiplication(star(X1),strong_iteration(multiplication(star(X0),X1))),strong_iteration(multiplication(star(X0),X1))) ),
inference(miniscoping,[status(esa)],[f45]) ).
fof(f47,plain,
( ~ leq(strong_iteration(multiplication(star(sk0_0),sk0_1)),multiplication(star(sk0_1),strong_iteration(multiplication(star(sk0_0),sk0_1))))
| ~ leq(multiplication(star(sk0_3),strong_iteration(multiplication(star(sk0_2),sk0_3))),strong_iteration(multiplication(star(sk0_2),sk0_3))) ),
inference(skolemization,[status(esa)],[f46]) ).
fof(f48,plain,
( ~ leq(strong_iteration(multiplication(star(sk0_0),sk0_1)),multiplication(star(sk0_1),strong_iteration(multiplication(star(sk0_0),sk0_1))))
| ~ leq(multiplication(star(sk0_3),strong_iteration(multiplication(star(sk0_2),sk0_3))),strong_iteration(multiplication(star(sk0_2),sk0_3))) ),
inference(cnf_transformation,[status(esa)],[f47]) ).
fof(f49,plain,
( spl0_0
<=> leq(strong_iteration(multiplication(star(sk0_0),sk0_1)),multiplication(star(sk0_1),strong_iteration(multiplication(star(sk0_0),sk0_1)))) ),
introduced(split_symbol_definition) ).
fof(f51,plain,
( ~ leq(strong_iteration(multiplication(star(sk0_0),sk0_1)),multiplication(star(sk0_1),strong_iteration(multiplication(star(sk0_0),sk0_1))))
| spl0_0 ),
inference(component_clause,[status(thm)],[f49]) ).
fof(f52,plain,
( spl0_1
<=> leq(multiplication(star(sk0_3),strong_iteration(multiplication(star(sk0_2),sk0_3))),strong_iteration(multiplication(star(sk0_2),sk0_3))) ),
introduced(split_symbol_definition) ).
fof(f54,plain,
( ~ leq(multiplication(star(sk0_3),strong_iteration(multiplication(star(sk0_2),sk0_3))),strong_iteration(multiplication(star(sk0_2),sk0_3)))
| spl0_1 ),
inference(component_clause,[status(thm)],[f52]) ).
fof(f55,plain,
( ~ spl0_0
| ~ spl0_1 ),
inference(split_clause,[status(thm)],[f48,f49,f52]) ).
fof(f56,plain,
! [X0] : strong_iteration(X0) = addition(one,multiplication(X0,strong_iteration(X0))),
inference(forward_demodulation,[status(thm)],[f21,f37]) ).
fof(f64,plain,
! [X0,X1,X2] :
( ~ leq(addition(multiplication(X0,X1),X2),X1)
| addition(multiplication(star(X0),X2),X1) = X1 ),
inference(resolution,[status(thm)],[f34,f43]) ).
fof(f164,plain,
! [X0] : leq(X0,X0),
inference(resolution,[status(thm)],[f24,f44]) ).
fof(f422,plain,
! [X0,X1] :
( leq(X0,X1)
| addition(X1,X0) != X1 ),
inference(paramodulation,[status(thm)],[f21,f44]) ).
fof(f423,plain,
! [X0,X1] :
( ~ leq(X0,X1)
| addition(X1,X0) = X1 ),
inference(paramodulation,[status(thm)],[f21,f43]) ).
fof(f631,plain,
! [X0,X1] : addition(X0,addition(X0,X1)) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f24,f22]) ).
fof(f737,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = addition(multiplication(X1,X2),multiplication(X0,X2)),
inference(paramodulation,[status(thm)],[f21,f29]) ).
fof(f738,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = multiplication(addition(X1,X0),X2),
inference(forward_demodulation,[status(thm)],[f29,f737]) ).
fof(f744,plain,
! [X0,X1] : multiplication(addition(one,X0),X1) = addition(X1,multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f27,f29]) ).
fof(f750,plain,
! [X0,X1] : multiplication(addition(X0,one),X1) = addition(multiplication(X0,X1),X1),
inference(paramodulation,[status(thm)],[f27,f29]) ).
fof(f751,plain,
! [X0,X1] : multiplication(addition(X0,one),X1) = addition(X1,multiplication(X0,X1)),
inference(forward_demodulation,[status(thm)],[f21,f750]) ).
fof(f1533,plain,
! [X0,X1] : leq(X0,addition(X0,X1)),
inference(resolution,[status(thm)],[f631,f44]) ).
fof(f1599,plain,
! [X0,X1] :
( ~ leq(addition(X0,X1),X0)
| addition(X0,X1) = X0 ),
inference(paramodulation,[status(thm)],[f631,f423]) ).
fof(f1600,plain,
! [X0,X1] :
( leq(addition(X0,X1),X0)
| addition(X0,X1) != X0 ),
inference(paramodulation,[status(thm)],[f631,f422]) ).
fof(f1631,plain,
! [X0,X1,X2] : leq(multiplication(X0,X1),multiplication(addition(X0,X2),X1)),
inference(paramodulation,[status(thm)],[f29,f1533]) ).
fof(f1635,plain,
! [X0,X1] : leq(X0,addition(X1,X0)),
inference(paramodulation,[status(thm)],[f21,f1533]) ).
fof(f1647,plain,
! [X0,X1,X2] : leq(X0,addition(X1,addition(X2,X0))),
inference(paramodulation,[status(thm)],[f22,f1635]) ).
fof(f1683,plain,
! [X0,X1,X2] : leq(X0,addition(addition(X1,X0),X2)),
inference(paramodulation,[status(thm)],[f21,f1647]) ).
fof(f1684,plain,
! [X0,X1,X2] : leq(X0,addition(X1,addition(X0,X2))),
inference(forward_demodulation,[status(thm)],[f22,f1683]) ).
fof(f1782,plain,
! [X0] : addition(one,star(X0)) = addition(one,multiplication(X0,star(X0))),
inference(paramodulation,[status(thm)],[f31,f631]) ).
fof(f1783,plain,
! [X0] : addition(one,star(X0)) = star(X0),
inference(forward_demodulation,[status(thm)],[f31,f1782]) ).
fof(f2001,plain,
! [X0,X1] : strong_iteration(multiplication(X0,X1)) = addition(one,multiplication(X0,multiplication(X1,strong_iteration(multiplication(X0,X1))))),
inference(paramodulation,[status(thm)],[f25,f56]) ).
fof(f2856,plain,
! [X0,X1] :
( ~ leq(addition(X0,X1),X0)
| leq(X1,X0) ),
inference(resolution,[status(thm)],[f1599,f422]) ).
fof(f2959,plain,
( ~ leq(addition(multiplication(star(sk0_1),strong_iteration(multiplication(star(sk0_0),sk0_1))),strong_iteration(multiplication(star(sk0_0),sk0_1))),multiplication(star(sk0_1),strong_iteration(multiplication(star(sk0_0),sk0_1))))
| spl0_0 ),
inference(resolution,[status(thm)],[f2856,f51]) ).
fof(f2960,plain,
( ~ leq(addition(strong_iteration(multiplication(star(sk0_0),sk0_1)),multiplication(star(sk0_1),strong_iteration(multiplication(star(sk0_0),sk0_1)))),multiplication(star(sk0_1),strong_iteration(multiplication(star(sk0_0),sk0_1))))
| spl0_0 ),
inference(forward_demodulation,[status(thm)],[f21,f2959]) ).
fof(f2961,plain,
( ~ leq(multiplication(addition(star(sk0_1),one),strong_iteration(multiplication(star(sk0_0),sk0_1))),multiplication(star(sk0_1),strong_iteration(multiplication(star(sk0_0),sk0_1))))
| spl0_0 ),
inference(forward_demodulation,[status(thm)],[f751,f2960]) ).
fof(f2962,plain,
( ~ leq(multiplication(addition(one,star(sk0_1)),strong_iteration(multiplication(star(sk0_0),sk0_1))),multiplication(star(sk0_1),strong_iteration(multiplication(star(sk0_0),sk0_1))))
| spl0_0 ),
inference(forward_demodulation,[status(thm)],[f738,f2961]) ).
fof(f2963,plain,
( ~ leq(multiplication(star(sk0_1),strong_iteration(multiplication(star(sk0_0),sk0_1))),multiplication(star(sk0_1),strong_iteration(multiplication(star(sk0_0),sk0_1))))
| spl0_0 ),
inference(forward_demodulation,[status(thm)],[f1783,f2962]) ).
fof(f2964,plain,
( $false
| spl0_0 ),
inference(forward_subsumption_resolution,[status(thm)],[f2963,f164]) ).
fof(f2965,plain,
spl0_0,
inference(contradiction_clause,[status(thm)],[f2964]) ).
fof(f3089,plain,
( addition(strong_iteration(multiplication(star(sk0_2),sk0_3)),multiplication(star(sk0_3),strong_iteration(multiplication(star(sk0_2),sk0_3)))) != strong_iteration(multiplication(star(sk0_2),sk0_3))
| spl0_1 ),
inference(resolution,[status(thm)],[f54,f422]) ).
fof(f3090,plain,
( multiplication(addition(star(sk0_3),one),strong_iteration(multiplication(star(sk0_2),sk0_3))) != strong_iteration(multiplication(star(sk0_2),sk0_3))
| spl0_1 ),
inference(forward_demodulation,[status(thm)],[f751,f3089]) ).
fof(f3091,plain,
( multiplication(addition(one,star(sk0_3)),strong_iteration(multiplication(star(sk0_2),sk0_3))) != strong_iteration(multiplication(star(sk0_2),sk0_3))
| spl0_1 ),
inference(forward_demodulation,[status(thm)],[f738,f3090]) ).
fof(f3092,plain,
( multiplication(star(sk0_3),strong_iteration(multiplication(star(sk0_2),sk0_3))) != strong_iteration(multiplication(star(sk0_2),sk0_3))
| spl0_1 ),
inference(forward_demodulation,[status(thm)],[f1783,f3091]) ).
fof(f3377,plain,
! [X0,X1] :
( leq(addition(X0,X1),X0)
| ~ leq(X1,X0) ),
inference(resolution,[status(thm)],[f1600,f423]) ).
fof(f3571,plain,
! [X0,X1] :
( leq(addition(X0,X1),X1)
| ~ leq(X0,X1) ),
inference(paramodulation,[status(thm)],[f21,f3377]) ).
fof(f3580,plain,
! [X0,X1] :
( ~ leq(multiplication(X0,X1),X1)
| addition(multiplication(star(X0),X1),X1) = X1 ),
inference(resolution,[status(thm)],[f3571,f64]) ).
fof(f3581,plain,
! [X0,X1] :
( ~ leq(multiplication(X0,X1),X1)
| addition(X1,multiplication(star(X0),X1)) = X1 ),
inference(forward_demodulation,[status(thm)],[f21,f3580]) ).
fof(f9345,plain,
! [X0,X1] : leq(multiplication(one,X0),multiplication(star(X1),X0)),
inference(paramodulation,[status(thm)],[f1783,f1631]) ).
fof(f9346,plain,
! [X0,X1] : leq(X0,multiplication(star(X1),X0)),
inference(forward_demodulation,[status(thm)],[f27,f9345]) ).
fof(f9382,plain,
! [X0,X1] : addition(multiplication(star(X0),X1),X1) = multiplication(star(X0),X1),
inference(resolution,[status(thm)],[f9346,f423]) ).
fof(f9383,plain,
! [X0,X1] : addition(X0,multiplication(star(X1),X0)) = multiplication(star(X1),X0),
inference(forward_demodulation,[status(thm)],[f21,f9382]) ).
fof(f9399,plain,
! [X0,X1] :
( ~ leq(multiplication(X0,X1),X1)
| multiplication(star(X0),X1) = X1 ),
inference(backward_demodulation,[status(thm)],[f9383,f3581]) ).
fof(f15234,plain,
! [X0,X1,X2] : leq(X0,addition(X1,multiplication(addition(one,X2),X0))),
inference(paramodulation,[status(thm)],[f744,f1684]) ).
fof(f40243,plain,
( ~ leq(multiplication(sk0_3,strong_iteration(multiplication(star(sk0_2),sk0_3))),strong_iteration(multiplication(star(sk0_2),sk0_3)))
| spl0_1 ),
inference(resolution,[status(thm)],[f9399,f3092]) ).
fof(f59141,plain,
! [X0,X1,X2] : leq(X0,addition(X1,multiplication(star(X2),X0))),
inference(paramodulation,[status(thm)],[f1783,f15234]) ).
fof(f59223,plain,
! [X0,X1] : leq(multiplication(X0,strong_iteration(multiplication(star(X1),X0))),strong_iteration(multiplication(star(X1),X0))),
inference(paramodulation,[status(thm)],[f2001,f59141]) ).
fof(f59266,plain,
( $false
| spl0_1 ),
inference(backward_subsumption_resolution,[status(thm)],[f40243,f59223]) ).
fof(f59267,plain,
spl0_1,
inference(contradiction_clause,[status(thm)],[f59266]) ).
fof(f59268,plain,
$false,
inference(sat_refutation,[status(thm)],[f55,f2965,f59267]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.11 % Problem : KLE147+2 : TPTP v8.1.2. Released v4.0.0.
% 0.02/0.12 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.11/0.32 % Computer : n007.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 11:34:17 EDT 2023
% 0.11/0.32 % CPUTime :
% 0.11/0.33 % Drodi V3.5.1
% 70.10/9.29 % Refutation found
% 70.10/9.29 % SZS status Theorem for theBenchmark: Theorem is valid
% 70.10/9.29 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 72.04/9.53 % Elapsed time: 9.182118 seconds
% 72.04/9.53 % CPU time: 71.306405 seconds
% 72.04/9.53 % Memory used: 702.673 MB
%------------------------------------------------------------------------------