TSTP Solution File: KLE041+1 by Drodi---3.6.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : KLE041+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n031.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 : Tue Apr 30 20:24:16 EDT 2024
% Result : Theorem 9.44s 1.50s
% Output : CNFRefutation 9.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 13
% Syntax : Number of formulae : 98 ( 67 unt; 0 def)
% Number of atoms : 133 ( 66 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 64 ( 29 ~; 25 |; 4 &)
% ( 3 <=>; 3 =>; 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 : 125 ( 123 !; 2 ?)
% 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(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(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,X1] :
( leq(X0,X1)
=> leq(star(X0),star(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
~ ! [X0,X1] :
( leq(X0,X1)
=> leq(star(X0),star(X1)) ),
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(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(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,X1] :
( leq(X0,X1)
& ~ leq(star(X0),star(X1)) ),
inference(pre_NNF_transformation,[status(esa)],[f18]) ).
fof(f41,plain,
( leq(sk0_0,sk0_1)
& ~ leq(star(sk0_0),star(sk0_1)) ),
inference(skolemization,[status(esa)],[f40]) ).
fof(f42,plain,
leq(sk0_0,sk0_1),
inference(cnf_transformation,[status(esa)],[f41]) ).
fof(f43,plain,
~ leq(star(sk0_0),star(sk0_1)),
inference(cnf_transformation,[status(esa)],[f41]) ).
fof(f44,plain,
addition(sk0_0,sk0_1) = sk0_1,
inference(resolution,[status(thm)],[f32,f42]) ).
fof(f56,plain,
! [X0] : leq(X0,X0),
inference(resolution,[status(thm)],[f22,f33]) ).
fof(f186,plain,
! [X0] : addition(sk0_0,addition(sk0_1,X0)) = addition(sk0_1,X0),
inference(paramodulation,[status(thm)],[f44,f20]) ).
fof(f192,plain,
! [X0,X1] : addition(X0,addition(X0,X1)) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f22,f20]) ).
fof(f201,plain,
! [X0,X1] : leq(X0,addition(X0,X1)),
inference(resolution,[status(thm)],[f192,f33]) ).
fof(f231,plain,
! [X0,X1] : leq(X0,addition(X1,X0)),
inference(paramodulation,[status(thm)],[f19,f201]) ).
fof(f234,plain,
! [X0,X1] : addition(X0,addition(X1,X0)) = addition(X1,X0),
inference(resolution,[status(thm)],[f231,f32]) ).
fof(f264,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X2),multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f19,f26]) ).
fof(f265,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = multiplication(X0,addition(X2,X1)),
inference(forward_demodulation,[status(thm)],[f26,f264]) ).
fof(f280,plain,
! [X0,X1] : multiplication(X0,addition(one,X1)) = addition(X0,multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f24,f26]) ).
fof(f292,plain,
! [X0,X1] : multiplication(X0,addition(X1,one)) = addition(multiplication(X0,X1),X0),
inference(paramodulation,[status(thm)],[f24,f26]) ).
fof(f293,plain,
! [X0,X1] : multiplication(X0,addition(X1,one)) = addition(X0,multiplication(X0,X1)),
inference(forward_demodulation,[status(thm)],[f19,f292]) ).
fof(f315,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = addition(multiplication(X1,X2),multiplication(X0,X2)),
inference(paramodulation,[status(thm)],[f19,f27]) ).
fof(f316,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = multiplication(addition(X1,X0),X2),
inference(forward_demodulation,[status(thm)],[f27,f315]) ).
fof(f332,plain,
! [X0,X1] : multiplication(addition(X0,one),X1) = addition(multiplication(X0,X1),X1),
inference(paramodulation,[status(thm)],[f25,f27]) ).
fof(f333,plain,
! [X0,X1] : multiplication(addition(X0,one),X1) = addition(X1,multiplication(X0,X1)),
inference(forward_demodulation,[status(thm)],[f19,f332]) ).
fof(f343,plain,
! [X0,X1,X2] :
( ~ leq(multiplication(addition(X0,X1),X2),X2)
| leq(multiplication(star(X0),multiplication(X1,X2)),X2) ),
inference(paramodulation,[status(thm)],[f27,f37]) ).
fof(f1077,plain,
! [X0] : addition(addition(one,multiplication(X0,star(X0))),star(X0)) = star(X0),
inference(resolution,[status(thm)],[f34,f32]) ).
fof(f1078,plain,
! [X0] : addition(one,addition(multiplication(X0,star(X0)),star(X0))) = star(X0),
inference(forward_demodulation,[status(thm)],[f20,f1077]) ).
fof(f1079,plain,
! [X0] : addition(one,addition(star(X0),multiplication(X0,star(X0)))) = star(X0),
inference(forward_demodulation,[status(thm)],[f19,f1078]) ).
fof(f2597,plain,
! [X0,X1] : leq(X0,multiplication(X0,addition(one,X1))),
inference(paramodulation,[status(thm)],[f280,f201]) ).
fof(f3354,plain,
! [X0] : multiplication(addition(X0,one),X0) = multiplication(X0,addition(X0,one)),
inference(paramodulation,[status(thm)],[f293,f333]) ).
fof(f5424,plain,
! [X0] : addition(one,multiplication(addition(X0,one),star(X0))) = star(X0),
inference(forward_demodulation,[status(thm)],[f333,f1079]) ).
fof(f5441,plain,
! [X0,X1] : leq(X0,multiplication(X0,star(X1))),
inference(paramodulation,[status(thm)],[f5424,f2597]) ).
fof(f5496,plain,
! [X0] : addition(multiplication(addition(X0,one),star(X0)),star(X0)) = addition(one,multiplication(addition(X0,one),star(X0))),
inference(paramodulation,[status(thm)],[f5424,f234]) ).
fof(f5497,plain,
! [X0] : addition(star(X0),multiplication(addition(X0,one),star(X0))) = addition(one,multiplication(addition(X0,one),star(X0))),
inference(forward_demodulation,[status(thm)],[f19,f5496]) ).
fof(f5498,plain,
! [X0] : multiplication(addition(addition(X0,one),one),star(X0)) = addition(one,multiplication(addition(X0,one),star(X0))),
inference(forward_demodulation,[status(thm)],[f333,f5497]) ).
fof(f5499,plain,
! [X0] : multiplication(addition(one,addition(X0,one)),star(X0)) = addition(one,multiplication(addition(X0,one),star(X0))),
inference(forward_demodulation,[status(thm)],[f316,f5498]) ).
fof(f5500,plain,
! [X0] : multiplication(addition(X0,one),star(X0)) = addition(one,multiplication(addition(X0,one),star(X0))),
inference(forward_demodulation,[status(thm)],[f234,f5499]) ).
fof(f5501,plain,
! [X0] : multiplication(addition(X0,one),star(X0)) = star(X0),
inference(forward_demodulation,[status(thm)],[f5424,f5500]) ).
fof(f5506,plain,
! [X0] : addition(one,star(X0)) = addition(one,multiplication(addition(X0,one),star(X0))),
inference(paramodulation,[status(thm)],[f5424,f192]) ).
fof(f5507,plain,
! [X0] : addition(one,star(X0)) = star(X0),
inference(forward_demodulation,[status(thm)],[f5424,f5506]) ).
fof(f5642,plain,
! [X0] : multiplication(addition(X0,one),addition(star(X0),one)) = addition(addition(X0,one),star(X0)),
inference(paramodulation,[status(thm)],[f5501,f293]) ).
fof(f5643,plain,
! [X0] : multiplication(addition(X0,one),addition(one,star(X0))) = addition(addition(X0,one),star(X0)),
inference(forward_demodulation,[status(thm)],[f265,f5642]) ).
fof(f5644,plain,
! [X0] : multiplication(addition(X0,one),star(X0)) = addition(addition(X0,one),star(X0)),
inference(forward_demodulation,[status(thm)],[f5507,f5643]) ).
fof(f5645,plain,
! [X0] : star(X0) = addition(addition(X0,one),star(X0)),
inference(forward_demodulation,[status(thm)],[f5501,f5644]) ).
fof(f5646,plain,
! [X0] : star(X0) = addition(X0,addition(one,star(X0))),
inference(forward_demodulation,[status(thm)],[f20,f5645]) ).
fof(f5647,plain,
! [X0] : star(X0) = addition(X0,star(X0)),
inference(forward_demodulation,[status(thm)],[f5507,f5646]) ).
fof(f5703,plain,
addition(sk0_0,star(sk0_1)) = addition(sk0_1,star(sk0_1)),
inference(paramodulation,[status(thm)],[f5647,f186]) ).
fof(f5704,plain,
addition(sk0_0,star(sk0_1)) = star(sk0_1),
inference(forward_demodulation,[status(thm)],[f5647,f5703]) ).
fof(f5846,plain,
! [X0] :
( ~ leq(star(X0),star(X0))
| leq(multiplication(star(X0),multiplication(one,star(X0))),star(X0)) ),
inference(paramodulation,[status(thm)],[f5501,f343]) ).
fof(f5847,plain,
! [X0] :
( ~ leq(star(X0),star(X0))
| leq(multiplication(star(X0),star(X0)),star(X0)) ),
inference(forward_demodulation,[status(thm)],[f25,f5846]) ).
fof(f5848,plain,
! [X0] : leq(multiplication(star(X0),star(X0)),star(X0)),
inference(forward_subsumption_resolution,[status(thm)],[f5847,f56]) ).
fof(f5991,plain,
! [X0] :
( ~ leq(multiplication(star(sk0_1),X0),X0)
| leq(multiplication(star(sk0_0),multiplication(star(sk0_1),X0)),X0) ),
inference(paramodulation,[status(thm)],[f5704,f343]) ).
fof(f6988,plain,
! [X0] : addition(multiplication(star(X0),star(X0)),star(X0)) = star(X0),
inference(resolution,[status(thm)],[f5848,f32]) ).
fof(f6989,plain,
! [X0] : addition(star(X0),multiplication(star(X0),star(X0))) = star(X0),
inference(forward_demodulation,[status(thm)],[f19,f6988]) ).
fof(f6990,plain,
! [X0] : multiplication(addition(star(X0),one),star(X0)) = star(X0),
inference(forward_demodulation,[status(thm)],[f333,f6989]) ).
fof(f6991,plain,
! [X0] : multiplication(star(X0),addition(star(X0),one)) = star(X0),
inference(forward_demodulation,[status(thm)],[f3354,f6990]) ).
fof(f6992,plain,
! [X0] : multiplication(star(X0),addition(one,star(X0))) = star(X0),
inference(forward_demodulation,[status(thm)],[f265,f6991]) ).
fof(f6993,plain,
! [X0] : multiplication(star(X0),star(X0)) = star(X0),
inference(forward_demodulation,[status(thm)],[f5507,f6992]) ).
fof(f7010,plain,
( spl0_53
<=> leq(star(sk0_1),star(sk0_1)) ),
introduced(split_symbol_definition) ).
fof(f7012,plain,
( ~ leq(star(sk0_1),star(sk0_1))
| spl0_53 ),
inference(component_clause,[status(thm)],[f7010]) ).
fof(f7013,plain,
( spl0_54
<=> leq(multiplication(star(sk0_0),multiplication(star(sk0_1),star(sk0_1))),star(sk0_1)) ),
introduced(split_symbol_definition) ).
fof(f7014,plain,
( leq(multiplication(star(sk0_0),multiplication(star(sk0_1),star(sk0_1))),star(sk0_1))
| ~ spl0_54 ),
inference(component_clause,[status(thm)],[f7013]) ).
fof(f7016,plain,
( ~ leq(star(sk0_1),star(sk0_1))
| leq(multiplication(star(sk0_0),multiplication(star(sk0_1),star(sk0_1))),star(sk0_1)) ),
inference(paramodulation,[status(thm)],[f6993,f5991]) ).
fof(f7017,plain,
( ~ spl0_53
| spl0_54 ),
inference(split_clause,[status(thm)],[f7016,f7010,f7013]) ).
fof(f7087,plain,
( $false
| spl0_53 ),
inference(forward_subsumption_resolution,[status(thm)],[f7012,f56]) ).
fof(f7088,plain,
spl0_53,
inference(contradiction_clause,[status(thm)],[f7087]) ).
fof(f7089,plain,
( leq(multiplication(star(sk0_0),star(sk0_1)),star(sk0_1))
| ~ spl0_54 ),
inference(forward_demodulation,[status(thm)],[f6993,f7014]) ).
fof(f7300,plain,
( addition(multiplication(star(sk0_0),star(sk0_1)),star(sk0_1)) = star(sk0_1)
| ~ spl0_54 ),
inference(resolution,[status(thm)],[f7089,f32]) ).
fof(f7301,plain,
( addition(star(sk0_1),multiplication(star(sk0_0),star(sk0_1))) = star(sk0_1)
| ~ spl0_54 ),
inference(forward_demodulation,[status(thm)],[f19,f7300]) ).
fof(f7302,plain,
( multiplication(addition(star(sk0_0),one),star(sk0_1)) = star(sk0_1)
| ~ spl0_54 ),
inference(forward_demodulation,[status(thm)],[f333,f7301]) ).
fof(f7303,plain,
( multiplication(addition(one,star(sk0_0)),star(sk0_1)) = star(sk0_1)
| ~ spl0_54 ),
inference(forward_demodulation,[status(thm)],[f316,f7302]) ).
fof(f7304,plain,
( multiplication(star(sk0_0),star(sk0_1)) = star(sk0_1)
| ~ spl0_54 ),
inference(forward_demodulation,[status(thm)],[f5507,f7303]) ).
fof(f7315,plain,
( leq(star(sk0_0),star(sk0_1))
| ~ spl0_54 ),
inference(paramodulation,[status(thm)],[f7304,f5441]) ).
fof(f7316,plain,
( $false
| ~ spl0_54 ),
inference(forward_subsumption_resolution,[status(thm)],[f7315,f43]) ).
fof(f7317,plain,
~ spl0_54,
inference(contradiction_clause,[status(thm)],[f7316]) ).
fof(f7318,plain,
$false,
inference(sat_refutation,[status(thm)],[f7017,f7088,f7317]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.09 % Problem : KLE041+1 : TPTP v8.1.2. Released v4.0.0.
% 0.04/0.10 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.09/0.29 % Computer : n031.cluster.edu
% 0.09/0.29 % Model : x86_64 x86_64
% 0.09/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29 % Memory : 8042.1875MB
% 0.09/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29 % CPULimit : 300
% 0.09/0.29 % WCLimit : 300
% 0.09/0.29 % DateTime : Tue Apr 30 01:35:43 EDT 2024
% 0.09/0.30 % CPUTime :
% 0.09/0.30 % Drodi V3.6.0
% 9.44/1.50 % Refutation found
% 9.44/1.50 % SZS status Theorem for theBenchmark: Theorem is valid
% 9.44/1.50 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 9.44/1.55 % Elapsed time: 1.239041 seconds
% 9.44/1.55 % CPU time: 9.706912 seconds
% 9.44/1.55 % Total memory used: 140.414 MB
% 9.44/1.55 % Net memory used: 137.820 MB
%------------------------------------------------------------------------------