TSTP Solution File: KLE143+2 by Drodi---3.5.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : KLE143+2 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n026.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 31.53s 4.36s
% Output : CNFRefutation 32.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 14
% Syntax : Number of formulae : 79 ( 56 unt; 0 def)
% Number of atoms : 106 ( 55 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 50 ( 23 ~; 19 |; 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 : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 137 (; 134 !; 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(f8,axiom,
! [A,B,C] : multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
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(f15,axiom,
! [A] : strong_iteration(A) = addition(multiplication(A,strong_iteration(A)),one),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f18,axiom,
! [A,B] :
( leq(A,B)
<=> addition(A,B) = B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,conjecture,
! [X0] :
( leq(multiplication(strong_iteration(X0),strong_iteration(X0)),strong_iteration(X0))
& leq(strong_iteration(X0),multiplication(strong_iteration(X0),strong_iteration(X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
~ ! [X0] :
( leq(multiplication(strong_iteration(X0),strong_iteration(X0)),strong_iteration(X0))
& leq(strong_iteration(X0),multiplication(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(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(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(f44,plain,
! [X0,X1] :
( leq(X0,X1)
| addition(X0,X1) != X1 ),
inference(cnf_transformation,[status(esa)],[f42]) ).
fof(f45,plain,
? [X0] :
( ~ leq(multiplication(strong_iteration(X0),strong_iteration(X0)),strong_iteration(X0))
| ~ leq(strong_iteration(X0),multiplication(strong_iteration(X0),strong_iteration(X0))) ),
inference(pre_NNF_transformation,[status(esa)],[f20]) ).
fof(f46,plain,
( ? [X0] : ~ leq(multiplication(strong_iteration(X0),strong_iteration(X0)),strong_iteration(X0))
| ? [X0] : ~ leq(strong_iteration(X0),multiplication(strong_iteration(X0),strong_iteration(X0))) ),
inference(miniscoping,[status(esa)],[f45]) ).
fof(f47,plain,
( ~ leq(multiplication(strong_iteration(sk0_0),strong_iteration(sk0_0)),strong_iteration(sk0_0))
| ~ leq(strong_iteration(sk0_1),multiplication(strong_iteration(sk0_1),strong_iteration(sk0_1))) ),
inference(skolemization,[status(esa)],[f46]) ).
fof(f48,plain,
( ~ leq(multiplication(strong_iteration(sk0_0),strong_iteration(sk0_0)),strong_iteration(sk0_0))
| ~ leq(strong_iteration(sk0_1),multiplication(strong_iteration(sk0_1),strong_iteration(sk0_1))) ),
inference(cnf_transformation,[status(esa)],[f47]) ).
fof(f49,plain,
( spl0_0
<=> leq(multiplication(strong_iteration(sk0_0),strong_iteration(sk0_0)),strong_iteration(sk0_0)) ),
introduced(split_symbol_definition) ).
fof(f51,plain,
( ~ leq(multiplication(strong_iteration(sk0_0),strong_iteration(sk0_0)),strong_iteration(sk0_0))
| spl0_0 ),
inference(component_clause,[status(thm)],[f49]) ).
fof(f52,plain,
( spl0_1
<=> leq(strong_iteration(sk0_1),multiplication(strong_iteration(sk0_1),strong_iteration(sk0_1))) ),
introduced(split_symbol_definition) ).
fof(f54,plain,
( ~ leq(strong_iteration(sk0_1),multiplication(strong_iteration(sk0_1),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(f56,plain,
! [X0] : strong_iteration(X0) = addition(one,multiplication(X0,strong_iteration(X0))),
inference(forward_demodulation,[status(thm)],[f21,f37]) ).
fof(f256,plain,
! [X0] : leq(X0,X0),
inference(resolution,[status(thm)],[f24,f44]) ).
fof(f731,plain,
! [X0,X1,X2] :
( ~ leq(X0,addition(X1,multiplication(X2,X0)))
| leq(X0,multiplication(strong_iteration(X2),X1)) ),
inference(paramodulation,[status(thm)],[f21,f39]) ).
fof(f822,plain,
! [X0,X1] : addition(one,addition(multiplication(X0,strong_iteration(X0)),X1)) = addition(strong_iteration(X0),X1),
inference(paramodulation,[status(thm)],[f56,f22]) ).
fof(f829,plain,
! [X0,X1] : addition(X0,addition(X0,X1)) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f24,f22]) ).
fof(f836,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X2),multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f21,f28]) ).
fof(f837,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = multiplication(X0,addition(X2,X1)),
inference(forward_demodulation,[status(thm)],[f28,f836]) ).
fof(f850,plain,
! [X0,X1] : multiplication(X0,addition(one,X1)) = addition(X0,multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f26,f28]) ).
fof(f860,plain,
! [X0,X1] : multiplication(X0,addition(X1,one)) = addition(multiplication(X0,X1),X0),
inference(paramodulation,[status(thm)],[f26,f28]) ).
fof(f861,plain,
! [X0,X1] : multiplication(X0,addition(X1,one)) = addition(X0,multiplication(X0,X1)),
inference(forward_demodulation,[status(thm)],[f21,f860]) ).
fof(f886,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = addition(multiplication(X1,X2),multiplication(X0,X2)),
inference(paramodulation,[status(thm)],[f21,f29]) ).
fof(f887,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = multiplication(addition(X1,X0),X2),
inference(forward_demodulation,[status(thm)],[f29,f886]) ).
fof(f893,plain,
! [X0,X1] : multiplication(addition(one,X0),X1) = addition(X1,multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f27,f29]) ).
fof(f894,plain,
! [X0,X1,X2,X3] : multiplication(addition(multiplication(X0,X1),X2),X3) = addition(multiplication(X0,multiplication(X1,X3)),multiplication(X2,X3)),
inference(paramodulation,[status(thm)],[f25,f29]) ).
fof(f959,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,X1),one),X2) = addition(multiplication(X0,multiplication(X1,X2)),X2),
inference(paramodulation,[status(thm)],[f27,f894]) ).
fof(f960,plain,
! [X0,X1,X2] : multiplication(addition(one,multiplication(X0,X1)),X2) = addition(multiplication(X0,multiplication(X1,X2)),X2),
inference(forward_demodulation,[status(thm)],[f887,f959]) ).
fof(f961,plain,
! [X0,X1,X2] : multiplication(addition(one,multiplication(X0,X1)),X2) = addition(X2,multiplication(X0,multiplication(X1,X2))),
inference(forward_demodulation,[status(thm)],[f21,f960]) ).
fof(f991,plain,
! [X0,X1] : multiplication(strong_iteration(X0),X1) = addition(X1,multiplication(X0,multiplication(strong_iteration(X0),X1))),
inference(paramodulation,[status(thm)],[f56,f961]) ).
fof(f1739,plain,
! [X0,X1] : leq(X0,addition(X0,X1)),
inference(resolution,[status(thm)],[f829,f44]) ).
fof(f1766,plain,
! [X0,X1] : addition(X0,multiplication(strong_iteration(X1),X0)) = addition(X0,multiplication(X1,multiplication(strong_iteration(X1),X0))),
inference(paramodulation,[status(thm)],[f991,f829]) ).
fof(f1767,plain,
! [X0,X1] : addition(X0,multiplication(strong_iteration(X1),X0)) = multiplication(strong_iteration(X1),X0),
inference(forward_demodulation,[status(thm)],[f991,f1766]) ).
fof(f1827,plain,
! [X0,X1] : leq(X0,multiplication(strong_iteration(X1),X0)),
inference(paramodulation,[status(thm)],[f991,f1739]) ).
fof(f4572,plain,
! [X0,X1,X2,X3] : multiplication(X0,multiplication(X1,addition(X2,X3))) = multiplication(multiplication(X0,X1),addition(X3,X2)),
inference(paramodulation,[status(thm)],[f25,f837]) ).
fof(f4573,plain,
! [X0,X1,X2,X3] : multiplication(X0,multiplication(X1,addition(X2,X3))) = multiplication(X0,multiplication(X1,addition(X3,X2))),
inference(forward_demodulation,[status(thm)],[f25,f4572]) ).
fof(f4824,plain,
! [X0,X1] : addition(one,multiplication(strong_iteration(X0),multiplication(X1,strong_iteration(X1)))) = addition(strong_iteration(X1),multiplication(strong_iteration(X0),multiplication(X1,strong_iteration(X1)))),
inference(paramodulation,[status(thm)],[f1767,f822]) ).
fof(f4825,plain,
! [X0,X1] : addition(one,multiplication(strong_iteration(X0),multiplication(X1,strong_iteration(X1)))) = multiplication(addition(one,multiplication(strong_iteration(X0),X1)),strong_iteration(X1)),
inference(forward_demodulation,[status(thm)],[f961,f4824]) ).
fof(f4918,plain,
! [X0,X1] : multiplication(X0,strong_iteration(X1)) = addition(X0,multiplication(X0,multiplication(X1,strong_iteration(X1)))),
inference(paramodulation,[status(thm)],[f56,f850]) ).
fof(f7936,plain,
! [X0] : multiplication(addition(one,X0),X0) = multiplication(X0,addition(X0,one)),
inference(paramodulation,[status(thm)],[f861,f893]) ).
fof(f8819,plain,
! [X0] : multiplication(strong_iteration(X0),multiplication(X0,strong_iteration(X0))) = multiplication(multiplication(X0,strong_iteration(X0)),addition(multiplication(X0,strong_iteration(X0)),one)),
inference(paramodulation,[status(thm)],[f56,f7936]) ).
fof(f8820,plain,
! [X0] : multiplication(strong_iteration(X0),multiplication(X0,strong_iteration(X0))) = multiplication(X0,multiplication(strong_iteration(X0),addition(multiplication(X0,strong_iteration(X0)),one))),
inference(forward_demodulation,[status(thm)],[f25,f8819]) ).
fof(f8821,plain,
! [X0] : multiplication(strong_iteration(X0),multiplication(X0,strong_iteration(X0))) = multiplication(X0,multiplication(strong_iteration(X0),addition(one,multiplication(X0,strong_iteration(X0))))),
inference(forward_demodulation,[status(thm)],[f4573,f8820]) ).
fof(f8822,plain,
! [X0] : multiplication(strong_iteration(X0),multiplication(X0,strong_iteration(X0))) = multiplication(X0,multiplication(strong_iteration(X0),strong_iteration(X0))),
inference(forward_demodulation,[status(thm)],[f56,f8821]) ).
fof(f10820,plain,
! [X0] : multiplication(strong_iteration(X0),strong_iteration(X0)) = multiplication(addition(one,multiplication(strong_iteration(X0),X0)),strong_iteration(X0)),
inference(paramodulation,[status(thm)],[f961,f4918]) ).
fof(f10821,plain,
! [X0] : multiplication(strong_iteration(X0),strong_iteration(X0)) = addition(one,multiplication(strong_iteration(X0),multiplication(X0,strong_iteration(X0)))),
inference(forward_demodulation,[status(thm)],[f4825,f10820]) ).
fof(f10822,plain,
! [X0] : multiplication(strong_iteration(X0),strong_iteration(X0)) = addition(one,multiplication(X0,multiplication(strong_iteration(X0),strong_iteration(X0)))),
inference(forward_demodulation,[status(thm)],[f8822,f10821]) ).
fof(f22427,plain,
! [X0] :
( ~ leq(multiplication(strong_iteration(X0),strong_iteration(X0)),multiplication(strong_iteration(X0),strong_iteration(X0)))
| leq(multiplication(strong_iteration(X0),strong_iteration(X0)),multiplication(strong_iteration(X0),one)) ),
inference(paramodulation,[status(thm)],[f10822,f731]) ).
fof(f22428,plain,
! [X0] :
( ~ leq(multiplication(strong_iteration(X0),strong_iteration(X0)),multiplication(strong_iteration(X0),strong_iteration(X0)))
| leq(multiplication(strong_iteration(X0),strong_iteration(X0)),strong_iteration(X0)) ),
inference(forward_demodulation,[status(thm)],[f26,f22427]) ).
fof(f22429,plain,
! [X0] : leq(multiplication(strong_iteration(X0),strong_iteration(X0)),strong_iteration(X0)),
inference(forward_subsumption_resolution,[status(thm)],[f22428,f256]) ).
fof(f22484,plain,
( $false
| spl0_0 ),
inference(backward_subsumption_resolution,[status(thm)],[f51,f22429]) ).
fof(f22485,plain,
spl0_0,
inference(contradiction_clause,[status(thm)],[f22484]) ).
fof(f22486,plain,
( $false
| spl0_1 ),
inference(forward_subsumption_resolution,[status(thm)],[f54,f1827]) ).
fof(f22487,plain,
spl0_1,
inference(contradiction_clause,[status(thm)],[f22486]) ).
fof(f22488,plain,
$false,
inference(sat_refutation,[status(thm)],[f55,f22485,f22487]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : KLE143+2 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.11 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.09/0.31 % Computer : n026.cluster.edu
% 0.09/0.31 % Model : x86_64 x86_64
% 0.09/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.31 % Memory : 8042.1875MB
% 0.09/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.31 % CPULimit : 300
% 0.09/0.31 % WCLimit : 300
% 0.09/0.31 % DateTime : Tue May 30 12:02:28 EDT 2023
% 0.09/0.31 % CPUTime :
% 0.09/0.32 % Drodi V3.5.1
% 31.53/4.36 % Refutation found
% 31.53/4.36 % SZS status Theorem for theBenchmark: Theorem is valid
% 31.53/4.36 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 32.67/4.53 % Elapsed time: 4.184692 seconds
% 32.67/4.53 % CPU time: 32.403513 seconds
% 32.67/4.53 % Memory used: 440.731 MB
%------------------------------------------------------------------------------