TSTP Solution File: KLE142+2 by Drodi---3.5.1
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%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : KLE142+2 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n029.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 12:15:53 EDT 2023
% Result : Theorem 0.15s 0.33s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 13
% Syntax : Number of formulae : 73 ( 17 unt; 0 def)
% Number of atoms : 145 ( 39 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 137 ( 65 ~; 62 |; 4 &)
% ( 5 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 7 ( 5 usr; 5 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 74 (; 71 !; 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(f11,axiom,
! [A] : addition(one,multiplication(A,star(A))) = star(A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [A,B,C] :
( leq(C,addition(multiplication(A,C),B))
=> leq(C,multiplication(strong_iteration(A),B)) ),
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] :
( leq(strong_iteration(strong_iteration(X0)),strong_iteration(one))
& leq(strong_iteration(one),strong_iteration(strong_iteration(X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
~ ! [X0] :
( leq(strong_iteration(strong_iteration(X0)),strong_iteration(one))
& leq(strong_iteration(one),strong_iteration(strong_iteration(X0))) ),
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(f26,plain,
! [X0] : multiplication(X0,one) = X0,
inference(cnf_transformation,[status(esa)],[f6]) ).
fof(f27,plain,
! [X0] : multiplication(one,X0) = X0,
inference(cnf_transformation,[status(esa)],[f7]) ).
fof(f31,plain,
! [X0] : addition(one,multiplication(X0,star(X0))) = star(X0),
inference(cnf_transformation,[status(esa)],[f11]) ).
fof(f38,plain,
! [A,B,C] :
( ~ leq(C,addition(multiplication(A,C),B))
| leq(C,multiplication(strong_iteration(A),B)) ),
inference(pre_NNF_transformation,[status(esa)],[f16]) ).
fof(f39,plain,
! [X0,X1,X2] :
( ~ leq(X0,addition(multiplication(X1,X0),X2))
| leq(X0,multiplication(strong_iteration(X1),X2)) ),
inference(cnf_transformation,[status(esa)],[f38]) ).
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] :
( ~ leq(strong_iteration(strong_iteration(X0)),strong_iteration(one))
| ~ leq(strong_iteration(one),strong_iteration(strong_iteration(X0))) ),
inference(pre_NNF_transformation,[status(esa)],[f20]) ).
fof(f46,plain,
( ? [X0] : ~ leq(strong_iteration(strong_iteration(X0)),strong_iteration(one))
| ? [X0] : ~ leq(strong_iteration(one),strong_iteration(strong_iteration(X0))) ),
inference(miniscoping,[status(esa)],[f45]) ).
fof(f47,plain,
( ~ leq(strong_iteration(strong_iteration(sk0_0)),strong_iteration(one))
| ~ leq(strong_iteration(one),strong_iteration(strong_iteration(sk0_1))) ),
inference(skolemization,[status(esa)],[f46]) ).
fof(f48,plain,
( ~ leq(strong_iteration(strong_iteration(sk0_0)),strong_iteration(one))
| ~ leq(strong_iteration(one),strong_iteration(strong_iteration(sk0_1))) ),
inference(cnf_transformation,[status(esa)],[f47]) ).
fof(f49,plain,
( spl0_0
<=> leq(strong_iteration(strong_iteration(sk0_0)),strong_iteration(one)) ),
introduced(split_symbol_definition) ).
fof(f51,plain,
( ~ leq(strong_iteration(strong_iteration(sk0_0)),strong_iteration(one))
| spl0_0 ),
inference(component_clause,[status(thm)],[f49]) ).
fof(f52,plain,
( spl0_1
<=> leq(strong_iteration(one),strong_iteration(strong_iteration(sk0_1))) ),
introduced(split_symbol_definition) ).
fof(f54,plain,
( ~ leq(strong_iteration(one),strong_iteration(strong_iteration(sk0_1)))
| spl0_1 ),
inference(component_clause,[status(thm)],[f52]) ).
fof(f55,plain,
( ~ spl0_0
| ~ spl0_1 ),
inference(split_clause,[status(thm)],[f48,f49,f52]) ).
fof(f59,plain,
! [X0] :
( ~ leq(one,multiplication(X0,star(X0)))
| star(X0) = multiplication(X0,star(X0)) ),
inference(paramodulation,[status(thm)],[f31,f43]) ).
fof(f96,plain,
! [X0,X1] :
( ~ leq(X0,addition(X0,X1))
| leq(X0,multiplication(strong_iteration(one),X1)) ),
inference(paramodulation,[status(thm)],[f27,f39]) ).
fof(f115,plain,
! [X0] :
( ~ leq(X0,addition(X0,one))
| leq(X0,strong_iteration(one)) ),
inference(paramodulation,[status(thm)],[f26,f96]) ).
fof(f116,plain,
! [X0] :
( leq(X0,strong_iteration(one))
| addition(X0,addition(X0,one)) != addition(X0,one) ),
inference(resolution,[status(thm)],[f115,f44]) ).
fof(f141,plain,
( spl0_10
<=> star(strong_iteration(one)) = multiplication(strong_iteration(one),star(strong_iteration(one))) ),
introduced(split_symbol_definition) ).
fof(f142,plain,
( star(strong_iteration(one)) = multiplication(strong_iteration(one),star(strong_iteration(one)))
| ~ spl0_10 ),
inference(component_clause,[status(thm)],[f141]) ).
fof(f144,plain,
( spl0_11
<=> leq(one,addition(one,star(strong_iteration(one)))) ),
introduced(split_symbol_definition) ).
fof(f146,plain,
( ~ leq(one,addition(one,star(strong_iteration(one))))
| spl0_11 ),
inference(component_clause,[status(thm)],[f144]) ).
fof(f147,plain,
( star(strong_iteration(one)) = multiplication(strong_iteration(one),star(strong_iteration(one)))
| ~ leq(one,addition(one,star(strong_iteration(one)))) ),
inference(resolution,[status(thm)],[f59,f96]) ).
fof(f148,plain,
( spl0_10
| ~ spl0_11 ),
inference(split_clause,[status(thm)],[f147,f141,f144]) ).
fof(f391,plain,
! [X0,X1] : addition(X0,addition(X0,X1)) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f24,f22]) ).
fof(f398,plain,
! [X0] :
( leq(X0,strong_iteration(one))
| addition(X0,one) != addition(X0,one) ),
inference(backward_demodulation,[status(thm)],[f391,f116]) ).
fof(f399,plain,
! [X0] : leq(X0,strong_iteration(one)),
inference(trivial_equality_resolution,[status(esa)],[f398]) ).
fof(f402,plain,
( $false
| spl0_0 ),
inference(backward_subsumption_resolution,[status(thm)],[f51,f399]) ).
fof(f403,plain,
spl0_0,
inference(contradiction_clause,[status(thm)],[f402]) ).
fof(f449,plain,
( addition(strong_iteration(one),strong_iteration(strong_iteration(sk0_1))) != strong_iteration(strong_iteration(sk0_1))
| spl0_1 ),
inference(resolution,[status(thm)],[f54,f44]) ).
fof(f452,plain,
! [X0] :
( ~ leq(X0,addition(multiplication(one,X0),star(strong_iteration(one))))
| leq(X0,star(strong_iteration(one)))
| ~ spl0_10 ),
inference(paramodulation,[status(thm)],[f142,f39]) ).
fof(f453,plain,
! [X0] :
( ~ leq(X0,addition(X0,star(strong_iteration(one))))
| leq(X0,star(strong_iteration(one)))
| ~ spl0_10 ),
inference(forward_demodulation,[status(thm)],[f27,f452]) ).
fof(f460,plain,
! [X0] :
( leq(X0,star(strong_iteration(one)))
| addition(X0,addition(X0,star(strong_iteration(one)))) != addition(X0,star(strong_iteration(one)))
| ~ spl0_10 ),
inference(resolution,[status(thm)],[f453,f44]) ).
fof(f461,plain,
! [X0] :
( leq(X0,star(strong_iteration(one)))
| addition(X0,star(strong_iteration(one))) != addition(X0,star(strong_iteration(one)))
| ~ spl0_10 ),
inference(forward_demodulation,[status(thm)],[f391,f460]) ).
fof(f462,plain,
! [X0] :
( leq(X0,star(strong_iteration(one)))
| ~ spl0_10 ),
inference(trivial_equality_resolution,[status(esa)],[f461]) ).
fof(f486,plain,
! [X0] :
( addition(X0,star(strong_iteration(one))) = star(strong_iteration(one))
| ~ spl0_10 ),
inference(resolution,[status(thm)],[f462,f43]) ).
fof(f490,plain,
( addition(one,addition(one,star(strong_iteration(one)))) != addition(one,star(strong_iteration(one)))
| spl0_11 ),
inference(resolution,[status(thm)],[f146,f44]) ).
fof(f491,plain,
( addition(one,star(strong_iteration(one))) != addition(one,star(strong_iteration(one)))
| spl0_11 ),
inference(forward_demodulation,[status(thm)],[f391,f490]) ).
fof(f492,plain,
( $false
| spl0_11 ),
inference(trivial_equality_resolution,[status(esa)],[f491]) ).
fof(f493,plain,
spl0_11,
inference(contradiction_clause,[status(thm)],[f492]) ).
fof(f516,plain,
! [X0] :
( addition(star(strong_iteration(one)),X0) = star(strong_iteration(one))
| ~ spl0_10 ),
inference(paramodulation,[status(thm)],[f21,f486]) ).
fof(f520,plain,
! [X0,X1] :
( ~ leq(X0,star(strong_iteration(one)))
| leq(X0,multiplication(strong_iteration(X1),star(strong_iteration(one))))
| ~ spl0_10 ),
inference(paramodulation,[status(thm)],[f486,f39]) ).
fof(f521,plain,
! [X0,X1] :
( leq(X0,multiplication(strong_iteration(X1),star(strong_iteration(one))))
| ~ spl0_10 ),
inference(forward_subsumption_resolution,[status(thm)],[f520,f462]) ).
fof(f556,plain,
! [X0] :
( ~ leq(star(strong_iteration(one)),X0)
| star(strong_iteration(one)) = X0
| ~ spl0_10 ),
inference(paramodulation,[status(thm)],[f516,f43]) ).
fof(f566,plain,
! [X0] :
( star(strong_iteration(one)) = multiplication(strong_iteration(X0),star(strong_iteration(one)))
| ~ spl0_10 ),
inference(resolution,[status(thm)],[f556,f521]) ).
fof(f654,plain,
! [X0,X1] :
( ~ leq(star(strong_iteration(one)),addition(star(strong_iteration(one)),X0))
| leq(star(strong_iteration(one)),multiplication(strong_iteration(strong_iteration(X1)),X0))
| ~ spl0_10 ),
inference(paramodulation,[status(thm)],[f566,f39]) ).
fof(f655,plain,
! [X0,X1] :
( ~ leq(star(strong_iteration(one)),star(strong_iteration(one)))
| leq(star(strong_iteration(one)),multiplication(strong_iteration(strong_iteration(X0)),X1))
| ~ spl0_10 ),
inference(forward_demodulation,[status(thm)],[f516,f654]) ).
fof(f656,plain,
! [X0,X1] :
( leq(star(strong_iteration(one)),multiplication(strong_iteration(strong_iteration(X0)),X1))
| ~ spl0_10 ),
inference(forward_subsumption_resolution,[status(thm)],[f655,f462]) ).
fof(f661,plain,
! [X0] :
( leq(star(strong_iteration(one)),strong_iteration(strong_iteration(X0)))
| ~ spl0_10 ),
inference(paramodulation,[status(thm)],[f26,f656]) ).
fof(f672,plain,
! [X0] :
( star(strong_iteration(one)) = strong_iteration(strong_iteration(X0))
| ~ spl0_10 ),
inference(resolution,[status(thm)],[f661,f556]) ).
fof(f681,plain,
( addition(strong_iteration(one),strong_iteration(strong_iteration(sk0_1))) != star(strong_iteration(one))
| ~ spl0_10
| spl0_1 ),
inference(backward_demodulation,[status(thm)],[f672,f449]) ).
fof(f682,plain,
( addition(strong_iteration(one),star(strong_iteration(one))) != star(strong_iteration(one))
| ~ spl0_10
| spl0_1 ),
inference(forward_demodulation,[status(thm)],[f672,f681]) ).
fof(f683,plain,
( star(strong_iteration(one)) != star(strong_iteration(one))
| ~ spl0_10
| spl0_1 ),
inference(forward_demodulation,[status(thm)],[f486,f682]) ).
fof(f684,plain,
( $false
| ~ spl0_10
| spl0_1 ),
inference(trivial_equality_resolution,[status(esa)],[f683]) ).
fof(f685,plain,
( ~ spl0_10
| spl0_1 ),
inference(contradiction_clause,[status(thm)],[f684]) ).
fof(f686,plain,
$false,
inference(sat_refutation,[status(thm)],[f55,f148,f403,f493,f685]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.10 % Problem : KLE142+2 : TPTP v8.1.2. Released v4.0.0.
% 0.05/0.10 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.10/0.30 % Computer : n029.cluster.edu
% 0.10/0.30 % Model : x86_64 x86_64
% 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30 % Memory : 8042.1875MB
% 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30 % CPULimit : 300
% 0.10/0.30 % WCLimit : 300
% 0.10/0.30 % DateTime : Tue May 30 12:02:06 EDT 2023
% 0.10/0.31 % CPUTime :
% 0.10/0.31 % Drodi V3.5.1
% 0.15/0.33 % Refutation found
% 0.15/0.33 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.15/0.33 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.17/0.58 % Elapsed time: 0.041184 seconds
% 0.17/0.58 % CPU time: 0.062440 seconds
% 0.17/0.58 % Memory used: 7.920 MB
%------------------------------------------------------------------------------