TSTP Solution File: KLE040+2 by Drodi---3.5.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : KLE040+2 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n010.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 12:15:37 EDT 2023
% Result : Theorem 0.20s 0.50s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 14
% Syntax : Number of formulae : 94 ( 45 unt; 0 def)
% Number of atoms : 147 ( 55 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 101 ( 48 ~; 44 |; 4 &)
% ( 3 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 5 ( 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 : 130 (; 127 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B] : addition(A,B) = addition(B,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [C,B,A] : addition(A,addition(B,C)) = addition(addition(A,B),C),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A] : addition(A,A) = 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(f7,axiom,
! [A] : multiplication(one,A) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [A,B,C] : multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [A,B] :
( leq(A,B)
<=> addition(A,B) = B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [A] : leq(addition(one,multiplication(A,star(A))),star(A)),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [A,B,C] :
( leq(addition(multiplication(A,B),C),A)
=> leq(multiplication(C,star(B)),A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,conjecture,
! [X0] :
( leq(multiplication(star(X0),star(X0)),star(X0))
& leq(star(X0),multiplication(star(X0),star(X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
~ ! [X0] :
( leq(multiplication(star(X0),star(X0)),star(X0))
& leq(star(X0),multiplication(star(X0),star(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(f23,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
inference(cnf_transformation,[status(esa)],[f5]) ).
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(f38,plain,
! [A,B,C] :
( ~ leq(addition(multiplication(A,B),C),A)
| leq(multiplication(C,star(B)),A) ),
inference(pre_NNF_transformation,[status(esa)],[f16]) ).
fof(f39,plain,
! [X0,X1,X2] :
( ~ leq(addition(multiplication(X0,X1),X2),X0)
| leq(multiplication(X2,star(X1)),X0) ),
inference(cnf_transformation,[status(esa)],[f38]) ).
fof(f40,plain,
? [X0] :
( ~ leq(multiplication(star(X0),star(X0)),star(X0))
| ~ leq(star(X0),multiplication(star(X0),star(X0))) ),
inference(pre_NNF_transformation,[status(esa)],[f18]) ).
fof(f41,plain,
( ? [X0] : ~ leq(multiplication(star(X0),star(X0)),star(X0))
| ? [X0] : ~ leq(star(X0),multiplication(star(X0),star(X0))) ),
inference(miniscoping,[status(esa)],[f40]) ).
fof(f42,plain,
( ~ leq(multiplication(star(sk0_0),star(sk0_0)),star(sk0_0))
| ~ leq(star(sk0_1),multiplication(star(sk0_1),star(sk0_1))) ),
inference(skolemization,[status(esa)],[f41]) ).
fof(f43,plain,
( ~ leq(multiplication(star(sk0_0),star(sk0_0)),star(sk0_0))
| ~ leq(star(sk0_1),multiplication(star(sk0_1),star(sk0_1))) ),
inference(cnf_transformation,[status(esa)],[f42]) ).
fof(f44,plain,
( spl0_0
<=> leq(multiplication(star(sk0_0),star(sk0_0)),star(sk0_0)) ),
introduced(split_symbol_definition) ).
fof(f46,plain,
( ~ leq(multiplication(star(sk0_0),star(sk0_0)),star(sk0_0))
| spl0_0 ),
inference(component_clause,[status(thm)],[f44]) ).
fof(f47,plain,
( spl0_1
<=> leq(star(sk0_1),multiplication(star(sk0_1),star(sk0_1))) ),
introduced(split_symbol_definition) ).
fof(f49,plain,
( ~ leq(star(sk0_1),multiplication(star(sk0_1),star(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(f54,plain,
! [X0,X1,X2] :
( ~ leq(addition(multiplication(X0,X1),X2),X1)
| addition(multiplication(star(X0),X2),X1) = X1 ),
inference(resolution,[status(thm)],[f37,f32]) ).
fof(f159,plain,
! [X0] : leq(X0,X0),
inference(resolution,[status(thm)],[f22,f33]) ).
fof(f184,plain,
! [X0,X1] :
( ~ leq(multiplication(X0,X1),X0)
| leq(multiplication(multiplication(X0,X1),star(X1)),X0) ),
inference(paramodulation,[status(thm)],[f22,f39]) ).
fof(f185,plain,
! [X0,X1] :
( ~ leq(multiplication(X0,X1),X0)
| leq(multiplication(X0,multiplication(X1,star(X1))),X0) ),
inference(forward_demodulation,[status(thm)],[f23,f184]) ).
fof(f369,plain,
! [X0,X1] :
( ~ leq(addition(X0,X1),X0)
| addition(multiplication(star(one),X1),X0) = X0 ),
inference(paramodulation,[status(thm)],[f25,f54]) ).
fof(f667,plain,
! [X0,X1] :
( leq(X0,X1)
| addition(X1,X0) != X1 ),
inference(paramodulation,[status(thm)],[f19,f33]) ).
fof(f718,plain,
! [X0,X1] : addition(X0,addition(X0,X1)) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f22,f20]) ).
fof(f724,plain,
! [X0,X1] : leq(X0,addition(X0,X1)),
inference(resolution,[status(thm)],[f718,f33]) ).
fof(f733,plain,
! [X0,X1] : addition(X0,addition(X1,X0)) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f19,f718]) ).
fof(f762,plain,
! [X0,X1] : leq(X0,addition(X1,X0)),
inference(paramodulation,[status(thm)],[f19,f724]) ).
fof(f836,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = addition(multiplication(X1,X2),multiplication(X0,X2)),
inference(paramodulation,[status(thm)],[f19,f27]) ).
fof(f837,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = multiplication(addition(X1,X0),X2),
inference(forward_demodulation,[status(thm)],[f27,f836]) ).
fof(f852,plain,
! [X0,X1] : multiplication(addition(X0,one),X1) = addition(multiplication(X0,X1),X1),
inference(paramodulation,[status(thm)],[f25,f27]) ).
fof(f853,plain,
! [X0,X1] : multiplication(addition(X0,one),X1) = addition(X1,multiplication(X0,X1)),
inference(forward_demodulation,[status(thm)],[f19,f852]) ).
fof(f881,plain,
! [X0,X1,X2] : leq(multiplication(X0,X1),multiplication(addition(X2,X0),X1)),
inference(paramodulation,[status(thm)],[f27,f762]) ).
fof(f893,plain,
! [X0] : addition(addition(one,multiplication(X0,star(X0))),star(X0)) = star(X0),
inference(resolution,[status(thm)],[f34,f32]) ).
fof(f894,plain,
! [X0] : addition(one,addition(multiplication(X0,star(X0)),star(X0))) = star(X0),
inference(forward_demodulation,[status(thm)],[f20,f893]) ).
fof(f895,plain,
! [X0] : addition(one,addition(star(X0),multiplication(X0,star(X0)))) = star(X0),
inference(forward_demodulation,[status(thm)],[f19,f894]) ).
fof(f896,plain,
! [X0] : addition(one,multiplication(addition(X0,one),star(X0))) = star(X0),
inference(forward_demodulation,[status(thm)],[f853,f895]) ).
fof(f901,plain,
( ~ leq(addition(multiplication(sk0_0,star(sk0_0)),star(sk0_0)),star(sk0_0))
| spl0_0 ),
inference(resolution,[status(thm)],[f46,f37]) ).
fof(f902,plain,
( ~ leq(addition(star(sk0_0),multiplication(sk0_0,star(sk0_0))),star(sk0_0))
| spl0_0 ),
inference(forward_demodulation,[status(thm)],[f19,f901]) ).
fof(f903,plain,
( ~ leq(multiplication(addition(sk0_0,one),star(sk0_0)),star(sk0_0))
| spl0_0 ),
inference(forward_demodulation,[status(thm)],[f853,f902]) ).
fof(f904,plain,
( ~ leq(multiplication(addition(one,sk0_0),star(sk0_0)),star(sk0_0))
| spl0_0 ),
inference(forward_demodulation,[status(thm)],[f837,f903]) ).
fof(f908,plain,
( addition(star(sk0_0),multiplication(addition(one,sk0_0),star(sk0_0))) != star(sk0_0)
| spl0_0 ),
inference(resolution,[status(thm)],[f904,f667]) ).
fof(f909,plain,
( multiplication(addition(addition(one,sk0_0),one),star(sk0_0)) != star(sk0_0)
| spl0_0 ),
inference(forward_demodulation,[status(thm)],[f853,f908]) ).
fof(f910,plain,
( multiplication(addition(one,addition(one,sk0_0)),star(sk0_0)) != star(sk0_0)
| spl0_0 ),
inference(forward_demodulation,[status(thm)],[f837,f909]) ).
fof(f911,plain,
( multiplication(addition(one,sk0_0),star(sk0_0)) != star(sk0_0)
| spl0_0 ),
inference(forward_demodulation,[status(thm)],[f718,f910]) ).
fof(f917,plain,
! [X0,X1] : leq(X0,multiplication(addition(X1,one),X0)),
inference(paramodulation,[status(thm)],[f25,f881]) ).
fof(f955,plain,
! [X0] :
( ~ leq(multiplication(X0,one),X0)
| leq(multiplication(X0,star(one)),X0) ),
inference(paramodulation,[status(thm)],[f25,f185]) ).
fof(f956,plain,
! [X0] :
( ~ leq(X0,X0)
| leq(multiplication(X0,star(one)),X0) ),
inference(forward_demodulation,[status(thm)],[f24,f955]) ).
fof(f957,plain,
! [X0] : leq(multiplication(X0,star(one)),X0),
inference(forward_subsumption_resolution,[status(thm)],[f956,f159]) ).
fof(f962,plain,
! [X0] : addition(multiplication(X0,star(one)),X0) = X0,
inference(resolution,[status(thm)],[f957,f32]) ).
fof(f963,plain,
! [X0] : addition(X0,multiplication(X0,star(one))) = X0,
inference(forward_demodulation,[status(thm)],[f19,f962]) ).
fof(f973,plain,
! [X0,X1] : leq(X0,multiplication(addition(one,X1),X0)),
inference(paramodulation,[status(thm)],[f19,f917]) ).
fof(f981,plain,
addition(one,star(one)) = one,
inference(paramodulation,[status(thm)],[f25,f963]) ).
fof(f984,plain,
leq(one,star(one)),
inference(paramodulation,[status(thm)],[f963,f34]) ).
fof(f1037,plain,
addition(one,star(one)) = star(one),
inference(resolution,[status(thm)],[f984,f32]) ).
fof(f1038,plain,
one = star(one),
inference(forward_demodulation,[status(thm)],[f981,f1037]) ).
fof(f1074,plain,
! [X0,X1] :
( ~ leq(addition(X0,X1),X0)
| addition(multiplication(one,X1),X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f1038,f369]) ).
fof(f1075,plain,
! [X0,X1] :
( ~ leq(addition(X0,X1),X0)
| addition(X1,X0) = X0 ),
inference(forward_demodulation,[status(thm)],[f25,f1074]) ).
fof(f1150,plain,
! [X0,X1] :
( ~ leq(addition(X0,X1),X0)
| addition(addition(X0,X1),X0) = X0 ),
inference(paramodulation,[status(thm)],[f718,f1075]) ).
fof(f1151,plain,
! [X0,X1] :
( ~ leq(addition(X0,X1),X0)
| addition(X0,addition(X1,X0)) = X0 ),
inference(forward_demodulation,[status(thm)],[f20,f1150]) ).
fof(f1152,plain,
! [X0,X1] :
( ~ leq(addition(X0,X1),X0)
| addition(X0,X1) = X0 ),
inference(forward_demodulation,[status(thm)],[f733,f1151]) ).
fof(f1169,plain,
! [X0,X1] :
( ~ leq(addition(X0,X1),X1)
| addition(X1,X0) = X1 ),
inference(paramodulation,[status(thm)],[f19,f1152]) ).
fof(f1283,plain,
! [X0,X1] : leq(X0,multiplication(star(X1),X0)),
inference(paramodulation,[status(thm)],[f896,f973]) ).
fof(f1286,plain,
! [X0] :
( ~ leq(star(X0),multiplication(addition(X0,one),star(X0)))
| addition(multiplication(addition(X0,one),star(X0)),one) = multiplication(addition(X0,one),star(X0)) ),
inference(paramodulation,[status(thm)],[f896,f1169]) ).
fof(f1287,plain,
! [X0] :
( ~ leq(star(X0),multiplication(addition(X0,one),star(X0)))
| addition(one,multiplication(addition(X0,one),star(X0))) = multiplication(addition(X0,one),star(X0)) ),
inference(forward_demodulation,[status(thm)],[f19,f1286]) ).
fof(f1288,plain,
! [X0] :
( ~ leq(star(X0),multiplication(addition(X0,one),star(X0)))
| star(X0) = multiplication(addition(X0,one),star(X0)) ),
inference(forward_demodulation,[status(thm)],[f896,f1287]) ).
fof(f1289,plain,
! [X0] : star(X0) = multiplication(addition(X0,one),star(X0)),
inference(forward_subsumption_resolution,[status(thm)],[f1288,f917]) ).
fof(f1348,plain,
! [X0] : star(X0) = multiplication(addition(one,X0),star(X0)),
inference(paramodulation,[status(thm)],[f19,f1289]) ).
fof(f1425,plain,
( star(sk0_0) != star(sk0_0)
| spl0_0 ),
inference(backward_demodulation,[status(thm)],[f1348,f911]) ).
fof(f1426,plain,
( $false
| spl0_0 ),
inference(trivial_equality_resolution,[status(esa)],[f1425]) ).
fof(f1427,plain,
spl0_0,
inference(contradiction_clause,[status(thm)],[f1426]) ).
fof(f1440,plain,
( $false
| spl0_1 ),
inference(forward_subsumption_resolution,[status(thm)],[f49,f1283]) ).
fof(f1441,plain,
spl0_1,
inference(contradiction_clause,[status(thm)],[f1440]) ).
fof(f1442,plain,
$false,
inference(sat_refutation,[status(thm)],[f50,f1427,f1441]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : KLE040+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 : n010.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 11:36:52 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.13/0.35 % Drodi V3.5.1
% 0.20/0.50 % Refutation found
% 0.20/0.50 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.20/0.50 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 1.19/0.51 % Elapsed time: 0.168266 seconds
% 1.19/0.51 % CPU time: 1.214715 seconds
% 1.19/0.51 % Memory used: 53.764 MB
%------------------------------------------------------------------------------