TSTP Solution File: KLE145+1 by Drodi---3.5.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : KLE145+1 : 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 12:15:54 EDT 2023
% Result : Theorem 73.91s 9.66s
% Output : CNFRefutation 75.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 36
% Number of leaves : 20
% Syntax : Number of formulae : 176 ( 103 unt; 0 def)
% Number of atoms : 256 ( 132 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 171 ( 91 ~; 72 |; 2 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 3 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 276 (; 275 !; 1 ?)
% 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(f3,axiom,
! [A] : addition(A,zero) = A,
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(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(f10,axiom,
! [A] : multiplication(zero,A) = zero,
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(f12,axiom,
! [A] : addition(one,multiplication(star(A),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(f14,axiom,
! [A,B,C] :
( leq(addition(multiplication(C,A),B),C)
=> leq(multiplication(B,star(A)),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(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] : star(strong_iteration(X0)) = strong_iteration(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
~ ! [X0] : star(strong_iteration(X0)) = 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(f23,plain,
! [X0] : addition(X0,zero) = X0,
inference(cnf_transformation,[status(esa)],[f3]) ).
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(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(f28,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
inference(cnf_transformation,[status(esa)],[f8]) ).
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(f30,plain,
! [X0] : multiplication(zero,X0) = zero,
inference(cnf_transformation,[status(esa)],[f10]) ).
fof(f31,plain,
! [X0] : addition(one,multiplication(X0,star(X0))) = star(X0),
inference(cnf_transformation,[status(esa)],[f11]) ).
fof(f32,plain,
! [X0] : addition(one,multiplication(star(X0),X0)) = star(X0),
inference(cnf_transformation,[status(esa)],[f12]) ).
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(f35,plain,
! [A,B,C] :
( ~ leq(addition(multiplication(C,A),B),C)
| leq(multiplication(B,star(A)),C) ),
inference(pre_NNF_transformation,[status(esa)],[f14]) ).
fof(f36,plain,
! [X0,X1,X2] :
( ~ leq(addition(multiplication(X0,X1),X2),X0)
| leq(multiplication(X2,star(X1)),X0) ),
inference(cnf_transformation,[status(esa)],[f35]) ).
fof(f37,plain,
! [X0] : strong_iteration(X0) = addition(multiplication(X0,strong_iteration(X0)),one),
inference(cnf_transformation,[status(esa)],[f15]) ).
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] : star(strong_iteration(X0)) != strong_iteration(X0),
inference(pre_NNF_transformation,[status(esa)],[f20]) ).
fof(f46,plain,
star(strong_iteration(sk0_0)) != strong_iteration(sk0_0),
inference(skolemization,[status(esa)],[f45]) ).
fof(f47,plain,
star(strong_iteration(sk0_0)) != strong_iteration(sk0_0),
inference(cnf_transformation,[status(esa)],[f46]) ).
fof(f48,plain,
! [X0] : strong_iteration(X0) = addition(one,multiplication(X0,strong_iteration(X0))),
inference(forward_demodulation,[status(thm)],[f21,f37]) ).
fof(f84,plain,
! [X0,X1] :
( ~ leq(multiplication(X0,X1),X0)
| leq(multiplication(multiplication(X0,X1),star(X1)),X0) ),
inference(paramodulation,[status(thm)],[f24,f36]) ).
fof(f85,plain,
! [X0,X1] :
( ~ leq(multiplication(X0,X1),X0)
| leq(multiplication(X0,multiplication(X1,star(X1))),X0) ),
inference(forward_demodulation,[status(thm)],[f25,f84]) ).
fof(f289,plain,
! [X0,X1] :
( ~ leq(X0,addition(multiplication(X1,X0),one))
| leq(X0,strong_iteration(X1)) ),
inference(paramodulation,[status(thm)],[f26,f39]) ).
fof(f290,plain,
! [X0,X1] :
( ~ leq(X0,addition(one,multiplication(X1,X0)))
| leq(X0,strong_iteration(X1)) ),
inference(forward_demodulation,[status(thm)],[f21,f289]) ).
fof(f398,plain,
! [X0,X1] :
( ~ leq(addition(multiplication(X0,X1),one),X0)
| leq(star(X1),X0) ),
inference(paramodulation,[status(thm)],[f27,f36]) ).
fof(f399,plain,
! [X0,X1] :
( ~ leq(addition(one,multiplication(X0,X1)),X0)
| leq(star(X1),X0) ),
inference(forward_demodulation,[status(thm)],[f21,f398]) ).
fof(f434,plain,
! [X0,X1] :
( ~ leq(addition(X0,X1),X0)
| leq(multiplication(star(one),X1),X0) ),
inference(paramodulation,[status(thm)],[f27,f34]) ).
fof(f625,plain,
! [X0,X1,X2] :
( addition(multiplication(star(X0),X1),X2) = X2
| ~ leq(addition(multiplication(X0,X2),X1),X2) ),
inference(resolution,[status(thm)],[f43,f34]) ).
fof(f630,plain,
! [X0,X1] :
( addition(multiplication(X0,multiplication(X1,star(X1))),X0) = X0
| ~ leq(multiplication(X0,X1),X0) ),
inference(resolution,[status(thm)],[f43,f85]) ).
fof(f631,plain,
! [X0,X1] :
( addition(X0,multiplication(X0,multiplication(X1,star(X1)))) = X0
| ~ leq(multiplication(X0,X1),X0) ),
inference(forward_demodulation,[status(thm)],[f21,f630]) ).
fof(f637,plain,
! [X0,X1,X2] :
( addition(X0,multiplication(strong_iteration(X1),X2)) = multiplication(strong_iteration(X1),X2)
| ~ leq(X0,addition(multiplication(X1,X0),X2)) ),
inference(resolution,[status(thm)],[f43,f39]) ).
fof(f639,plain,
! [X0,X1] :
( ~ leq(X0,X1)
| addition(X1,X0) = X1 ),
inference(paramodulation,[status(thm)],[f21,f43]) ).
fof(f681,plain,
! [X0] : leq(X0,X0),
inference(resolution,[status(thm)],[f44,f24]) ).
fof(f687,plain,
! [X0,X1] :
( leq(X0,X1)
| addition(X1,X0) != X1 ),
inference(paramodulation,[status(thm)],[f21,f44]) ).
fof(f725,plain,
! [X0,X1] :
( addition(X0,X1) = X0
| addition(X1,X0) != X0 ),
inference(resolution,[status(thm)],[f639,f44]) ).
fof(f776,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X2,addition(X0,X1)),
inference(paramodulation,[status(thm)],[f21,f22]) ).
fof(f784,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(addition(X1,X0),X2),
inference(paramodulation,[status(thm)],[f21,f22]) ).
fof(f785,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X1,addition(X0,X2)),
inference(forward_demodulation,[status(thm)],[f22,f784]) ).
fof(f788,plain,
! [X0,X1] : addition(X0,addition(X0,X1)) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f24,f22]) ).
fof(f802,plain,
! [X0,X1,X2] :
( ~ leq(addition(X0,X1),X2)
| addition(X0,addition(X1,X2)) = X2 ),
inference(paramodulation,[status(thm)],[f22,f43]) ).
fof(f915,plain,
! [X0,X1] : multiplication(X0,addition(one,X1)) = addition(X0,multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f26,f28]) ).
fof(f925,plain,
! [X0,X1] : multiplication(X0,addition(X1,one)) = addition(multiplication(X0,X1),X0),
inference(paramodulation,[status(thm)],[f26,f28]) ).
fof(f926,plain,
! [X0,X1] : multiplication(X0,addition(X1,one)) = addition(X0,multiplication(X0,X1)),
inference(forward_demodulation,[status(thm)],[f21,f925]) ).
fof(f1211,plain,
( spl0_23
<=> one = star(one) ),
introduced(split_symbol_definition) ).
fof(f1212,plain,
( one = star(one)
| ~ spl0_23 ),
inference(component_clause,[status(thm)],[f1211]) ).
fof(f1274,plain,
! [X0,X1] :
( ~ leq(addition(X0,X1),X0)
| leq(multiplication(one,X1),X0)
| ~ spl0_23 ),
inference(backward_demodulation,[status(thm)],[f1212,f434]) ).
fof(f1275,plain,
! [X0,X1] :
( ~ leq(addition(X0,X1),X0)
| leq(X1,X0)
| ~ spl0_23 ),
inference(forward_demodulation,[status(thm)],[f27,f1274]) ).
fof(f1470,plain,
! [X0,X1] :
( ~ leq(addition(X0,X1),X1)
| leq(X0,X1)
| ~ spl0_23 ),
inference(paramodulation,[status(thm)],[f21,f1275]) ).
fof(f2318,plain,
! [X0,X1] : addition(addition(X0,X1),X0) = addition(X0,X1),
inference(resolution,[status(thm)],[f788,f725]) ).
fof(f2319,plain,
! [X0,X1] : addition(X0,addition(X1,X0)) = addition(X0,X1),
inference(forward_demodulation,[status(thm)],[f22,f2318]) ).
fof(f2320,plain,
! [X0,X1] : leq(X0,addition(X0,X1)),
inference(resolution,[status(thm)],[f788,f44]) ).
fof(f2378,plain,
! [X0,X1] : leq(X0,addition(X1,X0)),
inference(paramodulation,[status(thm)],[f21,f2320]) ).
fof(f2388,plain,
! [X0,X1,X2] : leq(X0,addition(X1,addition(X2,X0))),
inference(paramodulation,[status(thm)],[f22,f2378]) ).
fof(f2421,plain,
strong_iteration(zero) = addition(one,zero),
inference(paramodulation,[status(thm)],[f30,f48]) ).
fof(f2422,plain,
strong_iteration(zero) = one,
inference(forward_demodulation,[status(thm)],[f23,f2421]) ).
fof(f2426,plain,
! [X0] : addition(one,strong_iteration(X0)) = addition(one,multiplication(X0,strong_iteration(X0))),
inference(paramodulation,[status(thm)],[f48,f788]) ).
fof(f2427,plain,
! [X0] : addition(one,strong_iteration(X0)) = strong_iteration(X0),
inference(forward_demodulation,[status(thm)],[f48,f2426]) ).
fof(f2490,plain,
! [X0,X1] : multiplication(addition(X0,one),X1) = addition(multiplication(X0,X1),X1),
inference(paramodulation,[status(thm)],[f27,f29]) ).
fof(f2491,plain,
! [X0,X1] : multiplication(addition(X0,one),X1) = addition(X1,multiplication(X0,X1)),
inference(forward_demodulation,[status(thm)],[f21,f2490]) ).
fof(f2505,plain,
! [X0,X1,X2] : leq(multiplication(X0,X1),multiplication(addition(X2,X0),X1)),
inference(paramodulation,[status(thm)],[f29,f2378]) ).
fof(f3162,plain,
! [X0,X1,X2] : leq(X0,addition(addition(X1,X0),X2)),
inference(paramodulation,[status(thm)],[f21,f2388]) ).
fof(f3163,plain,
! [X0,X1,X2] : leq(X0,addition(X1,addition(X0,X2))),
inference(forward_demodulation,[status(thm)],[f22,f3162]) ).
fof(f3373,plain,
! [X0,X1] :
( leq(addition(X0,X1),X1)
| addition(X1,X0) != X1 ),
inference(paramodulation,[status(thm)],[f2319,f687]) ).
fof(f3379,plain,
! [X0,X1] :
( ~ leq(addition(X0,X1),X1)
| addition(X1,X0) = X1 ),
inference(paramodulation,[status(thm)],[f2319,f639]) ).
fof(f3601,plain,
! [X0] : addition(multiplication(star(X0),X0),star(X0)) = addition(multiplication(star(X0),X0),one),
inference(paramodulation,[status(thm)],[f32,f2319]) ).
fof(f3602,plain,
! [X0] : addition(star(X0),multiplication(star(X0),X0)) = addition(multiplication(star(X0),X0),one),
inference(forward_demodulation,[status(thm)],[f21,f3601]) ).
fof(f3603,plain,
! [X0] : multiplication(star(X0),addition(X0,one)) = addition(multiplication(star(X0),X0),one),
inference(forward_demodulation,[status(thm)],[f926,f3602]) ).
fof(f3604,plain,
! [X0] : multiplication(star(X0),addition(X0,one)) = addition(one,multiplication(star(X0),X0)),
inference(forward_demodulation,[status(thm)],[f21,f3603]) ).
fof(f3605,plain,
! [X0] : multiplication(star(X0),addition(X0,one)) = star(X0),
inference(forward_demodulation,[status(thm)],[f32,f3604]) ).
fof(f3606,plain,
! [X0,X1] : leq(one,addition(X0,star(X1))),
inference(paramodulation,[status(thm)],[f32,f3163]) ).
fof(f3608,plain,
! [X0] : leq(multiplication(star(X0),X0),star(X0)),
inference(paramodulation,[status(thm)],[f32,f2378]) ).
fof(f3610,plain,
! [X0] : addition(one,star(X0)) = addition(one,multiplication(star(X0),X0)),
inference(paramodulation,[status(thm)],[f32,f788]) ).
fof(f3611,plain,
! [X0] : addition(one,star(X0)) = star(X0),
inference(forward_demodulation,[status(thm)],[f32,f3610]) ).
fof(f3793,plain,
! [X0,X1] : addition(one,multiplication(X0,multiplication(X1,star(multiplication(X0,X1))))) = star(multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f25,f31]) ).
fof(f3800,plain,
! [X0] :
( star(strong_iteration(X0)) = multiplication(strong_iteration(X0),star(strong_iteration(X0)))
| ~ leq(one,addition(multiplication(X0,one),star(strong_iteration(X0)))) ),
inference(paramodulation,[status(thm)],[f31,f637]) ).
fof(f3801,plain,
! [X0] :
( star(strong_iteration(X0)) = multiplication(strong_iteration(X0),star(strong_iteration(X0)))
| ~ leq(one,addition(X0,star(strong_iteration(X0)))) ),
inference(forward_demodulation,[status(thm)],[f26,f3800]) ).
fof(f3802,plain,
! [X0] : star(strong_iteration(X0)) = multiplication(strong_iteration(X0),star(strong_iteration(X0))),
inference(forward_subsumption_resolution,[status(thm)],[f3801,f3606]) ).
fof(f3831,plain,
! [X0] :
( ~ leq(one,multiplication(X0,star(X0)))
| star(X0) = multiplication(X0,star(X0)) ),
inference(paramodulation,[status(thm)],[f31,f43]) ).
fof(f3846,plain,
! [X0,X1] : multiplication(X0,star(X1)) = addition(X0,multiplication(X0,multiplication(X1,star(X1)))),
inference(paramodulation,[status(thm)],[f31,f915]) ).
fof(f3859,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),addition(one,X2)) = addition(X0,addition(X1,multiplication(addition(X0,X1),X2))),
inference(paramodulation,[status(thm)],[f22,f915]) ).
fof(f3963,plain,
! [X0,X1,X2] : leq(X0,addition(X1,multiplication(X0,addition(one,X2)))),
inference(paramodulation,[status(thm)],[f915,f3163]) ).
fof(f3983,plain,
! [X0,X1] :
( multiplication(X0,star(X1)) = X0
| ~ leq(multiplication(X0,X1),X0) ),
inference(backward_demodulation,[status(thm)],[f3846,f631]) ).
fof(f5083,plain,
! [X0] : addition(multiplication(star(X0),X0),star(X0)) = star(X0),
inference(resolution,[status(thm)],[f3608,f43]) ).
fof(f5084,plain,
! [X0] : addition(star(X0),multiplication(star(X0),X0)) = star(X0),
inference(forward_demodulation,[status(thm)],[f21,f5083]) ).
fof(f5085,plain,
! [X0] : multiplication(star(X0),addition(one,X0)) = star(X0),
inference(forward_demodulation,[status(thm)],[f915,f5084]) ).
fof(f5839,plain,
! [X0] :
( star(X0) = one
| ~ leq(multiplication(one,X0),one) ),
inference(paramodulation,[status(thm)],[f27,f3983]) ).
fof(f5840,plain,
! [X0] :
( star(X0) = one
| ~ leq(X0,one) ),
inference(forward_demodulation,[status(thm)],[f27,f5839]) ).
fof(f5885,plain,
! [X0] :
( star(X0) = one
| addition(one,X0) != one ),
inference(resolution,[status(thm)],[f5840,f687]) ).
fof(f6368,plain,
! [X0] :
( star(strong_iteration(X0)) = one
| strong_iteration(X0) != one ),
inference(paramodulation,[status(thm)],[f2427,f5885]) ).
fof(f6428,plain,
( spl0_74
<=> strong_iteration(zero) = one ),
introduced(split_symbol_definition) ).
fof(f6430,plain,
( strong_iteration(zero) != one
| spl0_74 ),
inference(component_clause,[status(thm)],[f6428]) ).
fof(f6431,plain,
( star(one) = one
| strong_iteration(zero) != one ),
inference(paramodulation,[status(thm)],[f2422,f6368]) ).
fof(f6432,plain,
( spl0_23
| ~ spl0_74 ),
inference(split_clause,[status(thm)],[f6431,f1211,f6428]) ).
fof(f7831,plain,
! [X0,X1] :
( addition(X0,multiplication(X1,X0)) != X0
| addition(multiplication(star(X1),X0),X0) = X0 ),
inference(resolution,[status(thm)],[f3373,f625]) ).
fof(f7832,plain,
! [X0,X1] :
( addition(X0,multiplication(X1,X0)) != X0
| addition(X0,multiplication(star(X1),X0)) = X0 ),
inference(forward_demodulation,[status(thm)],[f21,f7831]) ).
fof(f8013,plain,
( one != one
| spl0_74 ),
inference(forward_demodulation,[status(thm)],[f2422,f6430]) ).
fof(f8014,plain,
( $false
| spl0_74 ),
inference(trivial_equality_resolution,[status(esa)],[f8013]) ).
fof(f8015,plain,
spl0_74,
inference(contradiction_clause,[status(thm)],[f8014]) ).
fof(f9029,plain,
! [X0,X1,X2] : addition(addition(X0,X1),X2) = addition(X0,addition(X2,X1)),
inference(paramodulation,[status(thm)],[f21,f785]) ).
fof(f9030,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X0,addition(X2,X1)),
inference(forward_demodulation,[status(thm)],[f22,f9029]) ).
fof(f9410,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,addition(X2,X3))) = addition(addition(X3,X1),addition(X0,X2)),
inference(paramodulation,[status(thm)],[f776,f776]) ).
fof(f9411,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,addition(X2,X3))) = addition(X3,addition(X1,addition(X0,X2))),
inference(forward_demodulation,[status(thm)],[f22,f9410]) ).
fof(f9412,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,addition(X2,X3))) = addition(addition(X1,X3),addition(X0,X2)),
inference(paramodulation,[status(thm)],[f785,f776]) ).
fof(f9413,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,addition(X2,X3))) = addition(X1,addition(X3,addition(X0,X2))),
inference(forward_demodulation,[status(thm)],[f22,f9412]) ).
fof(f9482,plain,
! [X0,X1,X2,X3] : addition(X0,addition(addition(X1,X2),X3)) = addition(X3,addition(X2,addition(X0,X1))),
inference(paramodulation,[status(thm)],[f776,f776]) ).
fof(f9483,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,addition(X2,X3))) = addition(X3,addition(X2,addition(X0,X1))),
inference(forward_demodulation,[status(thm)],[f22,f9482]) ).
fof(f11870,plain,
! [X0,X1] : leq(X0,multiplication(addition(X1,one),X0)),
inference(paramodulation,[status(thm)],[f27,f2505]) ).
fof(f11948,plain,
! [X0,X1] : leq(X0,multiplication(addition(one,X1),X0)),
inference(paramodulation,[status(thm)],[f21,f11870]) ).
fof(f11968,plain,
! [X0,X1] : leq(X0,multiplication(star(X1),X0)),
inference(paramodulation,[status(thm)],[f3611,f11948]) ).
fof(f11997,plain,
! [X0,X1] : addition(X0,multiplication(star(X1),X0)) = multiplication(star(X1),X0),
inference(resolution,[status(thm)],[f11968,f43]) ).
fof(f12019,plain,
! [X0,X1] :
( addition(X0,multiplication(X1,X0)) != X0
| multiplication(star(X1),X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f11997,f7832]) ).
fof(f18006,plain,
! [X0] : leq(addition(X0,one),star(X0)),
inference(paramodulation,[status(thm)],[f3605,f11968]) ).
fof(f18105,plain,
! [X0] :
( multiplication(star(X0),star(addition(X0,one))) = star(X0)
| ~ leq(star(X0),star(X0)) ),
inference(paramodulation,[status(thm)],[f3605,f3983]) ).
fof(f18106,plain,
! [X0] : multiplication(star(X0),star(addition(X0,one))) = star(X0),
inference(forward_subsumption_resolution,[status(thm)],[f18105,f681]) ).
fof(f18170,plain,
! [X0] : addition(X0,addition(one,star(X0))) = star(X0),
inference(resolution,[status(thm)],[f18006,f802]) ).
fof(f18171,plain,
! [X0] : addition(X0,star(X0)) = star(X0),
inference(forward_demodulation,[status(thm)],[f3611,f18170]) ).
fof(f18358,plain,
! [X0] :
( ~ leq(addition(star(X0),X0),X0)
| star(X0) = X0 ),
inference(paramodulation,[status(thm)],[f18171,f3379]) ).
fof(f18359,plain,
! [X0] :
( ~ leq(addition(X0,star(X0)),X0)
| star(X0) = X0 ),
inference(forward_demodulation,[status(thm)],[f21,f18358]) ).
fof(f18360,plain,
! [X0] :
( ~ leq(star(X0),X0)
| star(X0) = X0 ),
inference(forward_demodulation,[status(thm)],[f18171,f18359]) ).
fof(f20524,plain,
~ leq(star(strong_iteration(sk0_0)),strong_iteration(sk0_0)),
inference(resolution,[status(thm)],[f18360,f47]) ).
fof(f21399,plain,
~ leq(star(strong_iteration(sk0_0)),addition(one,multiplication(sk0_0,star(strong_iteration(sk0_0))))),
inference(resolution,[status(thm)],[f290,f20524]) ).
fof(f22085,plain,
~ leq(addition(one,multiplication(addition(one,multiplication(sk0_0,star(strong_iteration(sk0_0)))),strong_iteration(sk0_0))),addition(one,multiplication(sk0_0,star(strong_iteration(sk0_0))))),
inference(resolution,[status(thm)],[f21399,f399]) ).
fof(f24409,plain,
( ~ leq(addition(addition(one,multiplication(addition(one,multiplication(sk0_0,star(strong_iteration(sk0_0)))),strong_iteration(sk0_0))),addition(one,multiplication(sk0_0,star(strong_iteration(sk0_0))))),addition(one,multiplication(sk0_0,star(strong_iteration(sk0_0)))))
| ~ spl0_23 ),
inference(resolution,[status(thm)],[f22085,f1470]) ).
fof(f24410,plain,
( ~ leq(addition(one,addition(multiplication(addition(one,multiplication(sk0_0,star(strong_iteration(sk0_0)))),strong_iteration(sk0_0)),addition(one,multiplication(sk0_0,star(strong_iteration(sk0_0)))))),addition(one,multiplication(sk0_0,star(strong_iteration(sk0_0)))))
| ~ spl0_23 ),
inference(forward_demodulation,[status(thm)],[f22,f24409]) ).
fof(f24411,plain,
( ~ leq(addition(one,addition(multiplication(sk0_0,star(strong_iteration(sk0_0))),addition(multiplication(addition(one,multiplication(sk0_0,star(strong_iteration(sk0_0)))),strong_iteration(sk0_0)),one))),addition(one,multiplication(sk0_0,star(strong_iteration(sk0_0)))))
| ~ spl0_23 ),
inference(forward_demodulation,[status(thm)],[f9483,f24410]) ).
fof(f24412,plain,
( ~ leq(addition(one,addition(multiplication(sk0_0,star(strong_iteration(sk0_0))),addition(one,multiplication(addition(one,multiplication(sk0_0,star(strong_iteration(sk0_0)))),strong_iteration(sk0_0))))),addition(one,multiplication(sk0_0,star(strong_iteration(sk0_0)))))
| ~ spl0_23 ),
inference(forward_demodulation,[status(thm)],[f9411,f24411]) ).
fof(f24413,plain,
( ~ leq(addition(one,addition(one,addition(multiplication(addition(one,multiplication(sk0_0,star(strong_iteration(sk0_0)))),strong_iteration(sk0_0)),multiplication(sk0_0,star(strong_iteration(sk0_0)))))),addition(one,multiplication(sk0_0,star(strong_iteration(sk0_0)))))
| ~ spl0_23 ),
inference(forward_demodulation,[status(thm)],[f9413,f24412]) ).
fof(f24414,plain,
( ~ leq(addition(one,addition(multiplication(addition(one,multiplication(sk0_0,star(strong_iteration(sk0_0)))),strong_iteration(sk0_0)),multiplication(sk0_0,star(strong_iteration(sk0_0))))),addition(one,multiplication(sk0_0,star(strong_iteration(sk0_0)))))
| ~ spl0_23 ),
inference(forward_demodulation,[status(thm)],[f788,f24413]) ).
fof(f24415,plain,
( ~ leq(addition(one,addition(multiplication(sk0_0,star(strong_iteration(sk0_0))),multiplication(addition(one,multiplication(sk0_0,star(strong_iteration(sk0_0)))),strong_iteration(sk0_0)))),addition(one,multiplication(sk0_0,star(strong_iteration(sk0_0)))))
| ~ spl0_23 ),
inference(forward_demodulation,[status(thm)],[f9030,f24414]) ).
fof(f24416,plain,
( ~ leq(multiplication(addition(one,multiplication(sk0_0,star(strong_iteration(sk0_0)))),addition(one,strong_iteration(sk0_0))),addition(one,multiplication(sk0_0,star(strong_iteration(sk0_0)))))
| ~ spl0_23 ),
inference(forward_demodulation,[status(thm)],[f3859,f24415]) ).
fof(f24417,plain,
( ~ leq(multiplication(addition(one,multiplication(sk0_0,star(strong_iteration(sk0_0)))),strong_iteration(sk0_0)),addition(one,multiplication(sk0_0,star(strong_iteration(sk0_0)))))
| ~ spl0_23 ),
inference(forward_demodulation,[status(thm)],[f2427,f24416]) ).
fof(f27645,plain,
! [X0] : multiplication(star(strong_iteration(X0)),strong_iteration(X0)) = star(strong_iteration(X0)),
inference(paramodulation,[status(thm)],[f2427,f5085]) ).
fof(f59820,plain,
! [X0,X1,X2] : leq(X0,addition(X1,multiplication(X0,star(X2)))),
inference(paramodulation,[status(thm)],[f3611,f3963]) ).
fof(f59894,plain,
! [X0,X1,X2] : leq(X0,multiplication(addition(X1,X0),star(X2))),
inference(paramodulation,[status(thm)],[f29,f59820]) ).
fof(f60009,plain,
! [X0] : star(addition(X0,one)) = multiplication(addition(X0,one),star(addition(X0,one))),
inference(resolution,[status(thm)],[f59894,f3831]) ).
fof(f80319,plain,
! [X0] :
( addition(star(addition(X0,one)),multiplication(X0,star(addition(X0,one)))) != star(addition(X0,one))
| star(X0) = star(addition(X0,one)) ),
inference(paramodulation,[status(thm)],[f18106,f12019]) ).
fof(f80320,plain,
! [X0] :
( multiplication(addition(X0,one),star(addition(X0,one))) != star(addition(X0,one))
| star(X0) = star(addition(X0,one)) ),
inference(forward_demodulation,[status(thm)],[f2491,f80319]) ).
fof(f80321,plain,
! [X0] :
( star(addition(X0,one)) != star(addition(X0,one))
| star(X0) = star(addition(X0,one)) ),
inference(forward_demodulation,[status(thm)],[f60009,f80320]) ).
fof(f80322,plain,
! [X0] : star(X0) = star(addition(X0,one)),
inference(trivial_equality_resolution,[status(esa)],[f80321]) ).
fof(f81272,plain,
! [X0] : star(X0) = star(addition(one,X0)),
inference(paramodulation,[status(thm)],[f21,f80322]) ).
fof(f82131,plain,
! [X0] : star(multiplication(X0,strong_iteration(X0))) = star(strong_iteration(X0)),
inference(paramodulation,[status(thm)],[f48,f81272]) ).
fof(f84736,plain,
! [X0] : addition(one,multiplication(X0,multiplication(strong_iteration(X0),star(strong_iteration(X0))))) = star(multiplication(X0,strong_iteration(X0))),
inference(paramodulation,[status(thm)],[f82131,f3793]) ).
fof(f84737,plain,
! [X0] : addition(one,multiplication(X0,star(strong_iteration(X0)))) = star(multiplication(X0,strong_iteration(X0))),
inference(forward_demodulation,[status(thm)],[f3802,f84736]) ).
fof(f84738,plain,
! [X0] : addition(one,multiplication(X0,star(strong_iteration(X0)))) = star(strong_iteration(X0)),
inference(forward_demodulation,[status(thm)],[f82131,f84737]) ).
fof(f85383,plain,
( ~ leq(multiplication(addition(one,multiplication(sk0_0,star(strong_iteration(sk0_0)))),strong_iteration(sk0_0)),star(strong_iteration(sk0_0)))
| ~ spl0_23 ),
inference(backward_demodulation,[status(thm)],[f84738,f24417]) ).
fof(f85384,plain,
( ~ leq(multiplication(star(strong_iteration(sk0_0)),strong_iteration(sk0_0)),star(strong_iteration(sk0_0)))
| ~ spl0_23 ),
inference(forward_demodulation,[status(thm)],[f84738,f85383]) ).
fof(f85385,plain,
( ~ leq(star(strong_iteration(sk0_0)),star(strong_iteration(sk0_0)))
| ~ spl0_23 ),
inference(forward_demodulation,[status(thm)],[f27645,f85384]) ).
fof(f85386,plain,
( $false
| ~ spl0_23 ),
inference(forward_subsumption_resolution,[status(thm)],[f85385,f681]) ).
fof(f85387,plain,
~ spl0_23,
inference(contradiction_clause,[status(thm)],[f85386]) ).
fof(f85388,plain,
$false,
inference(sat_refutation,[status(thm)],[f6432,f8015,f85387]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : KLE145+1 : TPTP v8.1.2. Released v4.0.0.
% 0.03/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.12/0.33 % Computer : n029.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Tue May 30 12:01:37 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.12/0.34 % Drodi V3.5.1
% 73.91/9.66 % Refutation found
% 73.91/9.66 % SZS status Theorem for theBenchmark: Theorem is valid
% 73.91/9.66 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 75.51/9.89 % Elapsed time: 9.516100 seconds
% 75.51/9.89 % CPU time: 75.077734 seconds
% 75.51/9.89 % Memory used: 955.229 MB
%------------------------------------------------------------------------------