TSTP Solution File: KLE039+1 by Drodi---3.5.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : KLE039+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n005.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 12:15:36 EDT 2023
% Result : Theorem 8.76s 1.50s
% Output : CNFRefutation 8.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 13
% Syntax : Number of formulae : 103 ( 88 unt; 0 def)
% Number of atoms : 122 ( 87 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 39 ( 20 ~; 15 |; 2 &)
% ( 1 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 170 (; 169 !; 1 ?)
% 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(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(f14,axiom,
! [A] : leq(addition(one,multiplication(star(A),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(f17,conjecture,
! [X0] : star(star(X0)) = star(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
~ ! [X0] : star(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(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(f35,plain,
! [X0] : leq(addition(one,multiplication(star(X0),X0)),star(X0)),
inference(cnf_transformation,[status(esa)],[f14]) ).
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] : star(star(X0)) != star(X0),
inference(pre_NNF_transformation,[status(esa)],[f18]) ).
fof(f41,plain,
star(star(sk0_0)) != star(sk0_0),
inference(skolemization,[status(esa)],[f40]) ).
fof(f42,plain,
star(star(sk0_0)) != star(sk0_0),
inference(cnf_transformation,[status(esa)],[f41]) ).
fof(f43,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X2,addition(X0,X1)),
inference(paramodulation,[status(thm)],[f19,f20]) ).
fof(f49,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(addition(X1,X0),X2),
inference(paramodulation,[status(thm)],[f19,f20]) ).
fof(f50,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X1,addition(X0,X2)),
inference(forward_demodulation,[status(thm)],[f20,f49]) ).
fof(f53,plain,
! [X0,X1] : addition(X0,addition(X0,X1)) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f22,f20]) ).
fof(f57,plain,
! [X0] : leq(X0,X0),
inference(resolution,[status(thm)],[f33,f22]) ).
fof(f77,plain,
! [X0,X1] : addition(X0,addition(X1,X0)) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f19,f53]) ).
fof(f113,plain,
! [X0,X1,X2] : addition(X0,addition(addition(X1,X0),X2)) = addition(addition(X0,X1),X2),
inference(paramodulation,[status(thm)],[f77,f20]) ).
fof(f114,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,X2))) = addition(addition(X0,X1),X2),
inference(forward_demodulation,[status(thm)],[f20,f113]) ).
fof(f115,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,X2))) = addition(X0,addition(X1,X2)),
inference(forward_demodulation,[status(thm)],[f20,f114]) ).
fof(f141,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(addition(X2,X1),addition(X0,X1)),
inference(paramodulation,[status(thm)],[f77,f43]) ).
fof(f142,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X2,addition(X1,addition(X0,X1))),
inference(forward_demodulation,[status(thm)],[f20,f141]) ).
fof(f143,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X2,addition(X1,X0)),
inference(forward_demodulation,[status(thm)],[f77,f142]) ).
fof(f185,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,X2))) = addition(X0,addition(X2,X1)),
inference(paramodulation,[status(thm)],[f43,f53]) ).
fof(f186,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X0,addition(X2,X1)),
inference(forward_demodulation,[status(thm)],[f115,f185]) ).
fof(f700,plain,
! [X0] : addition(addition(one,multiplication(X0,star(X0))),star(X0)) = star(X0),
inference(resolution,[status(thm)],[f34,f32]) ).
fof(f701,plain,
! [X0] : addition(one,addition(multiplication(X0,star(X0)),star(X0))) = star(X0),
inference(forward_demodulation,[status(thm)],[f20,f700]) ).
fof(f702,plain,
! [X0] : addition(one,addition(star(X0),multiplication(X0,star(X0)))) = star(X0),
inference(forward_demodulation,[status(thm)],[f186,f701]) ).
fof(f705,plain,
! [X0] : addition(addition(one,multiplication(star(X0),X0)),star(X0)) = star(X0),
inference(resolution,[status(thm)],[f35,f32]) ).
fof(f706,plain,
! [X0] : addition(one,addition(multiplication(star(X0),X0),star(X0))) = star(X0),
inference(forward_demodulation,[status(thm)],[f20,f705]) ).
fof(f707,plain,
! [X0] : addition(one,addition(star(X0),multiplication(star(X0),X0))) = star(X0),
inference(forward_demodulation,[status(thm)],[f186,f706]) ).
fof(f709,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X2),multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f19,f26]) ).
fof(f710,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = multiplication(X0,addition(X2,X1)),
inference(forward_demodulation,[status(thm)],[f26,f709]) ).
fof(f727,plain,
! [X0,X1] : multiplication(X0,addition(X1,one)) = addition(multiplication(X0,X1),X0),
inference(paramodulation,[status(thm)],[f24,f26]) ).
fof(f728,plain,
! [X0,X1] : multiplication(X0,addition(X1,one)) = addition(X0,multiplication(X0,X1)),
inference(forward_demodulation,[status(thm)],[f19,f727]) ).
fof(f979,plain,
! [X0,X1] : multiplication(addition(one,X0),X1) = addition(X1,multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f25,f27]) ).
fof(f989,plain,
! [X0,X1] : multiplication(addition(X0,one),X1) = addition(multiplication(X0,X1),X1),
inference(paramodulation,[status(thm)],[f25,f27]) ).
fof(f990,plain,
! [X0,X1] : multiplication(addition(X0,one),X1) = addition(X1,multiplication(X0,X1)),
inference(forward_demodulation,[status(thm)],[f19,f989]) ).
fof(f1442,plain,
! [X0] : addition(addition(star(X0),multiplication(X0,star(X0))),star(X0)) = addition(addition(star(X0),multiplication(X0,star(X0))),one),
inference(paramodulation,[status(thm)],[f702,f77]) ).
fof(f1443,plain,
! [X0] : addition(star(X0),addition(multiplication(X0,star(X0)),star(X0))) = addition(addition(star(X0),multiplication(X0,star(X0))),one),
inference(forward_demodulation,[status(thm)],[f20,f1442]) ).
fof(f1444,plain,
! [X0] : addition(star(X0),addition(star(X0),multiplication(X0,star(X0)))) = addition(addition(star(X0),multiplication(X0,star(X0))),one),
inference(forward_demodulation,[status(thm)],[f186,f1443]) ).
fof(f1445,plain,
! [X0] : addition(star(X0),multiplication(X0,star(X0))) = addition(addition(star(X0),multiplication(X0,star(X0))),one),
inference(forward_demodulation,[status(thm)],[f53,f1444]) ).
fof(f1446,plain,
! [X0] : multiplication(addition(X0,one),star(X0)) = addition(addition(star(X0),multiplication(X0,star(X0))),one),
inference(forward_demodulation,[status(thm)],[f990,f1445]) ).
fof(f1447,plain,
! [X0] : multiplication(addition(X0,one),star(X0)) = addition(star(X0),addition(multiplication(X0,star(X0)),one)),
inference(forward_demodulation,[status(thm)],[f20,f1446]) ).
fof(f1448,plain,
! [X0] : multiplication(addition(X0,one),star(X0)) = addition(star(X0),addition(one,multiplication(X0,star(X0)))),
inference(forward_demodulation,[status(thm)],[f186,f1447]) ).
fof(f1449,plain,
! [X0] : multiplication(addition(X0,one),star(X0)) = addition(one,addition(star(X0),multiplication(X0,star(X0)))),
inference(forward_demodulation,[status(thm)],[f50,f1448]) ).
fof(f1450,plain,
! [X0] : multiplication(addition(X0,one),star(X0)) = star(X0),
inference(forward_demodulation,[status(thm)],[f702,f1449]) ).
fof(f1451,plain,
! [X0] : addition(one,star(X0)) = addition(one,addition(star(X0),multiplication(X0,star(X0)))),
inference(paramodulation,[status(thm)],[f702,f53]) ).
fof(f1452,plain,
! [X0] : addition(one,star(X0)) = star(X0),
inference(forward_demodulation,[status(thm)],[f702,f1451]) ).
fof(f1475,plain,
! [X0,X1] : multiplication(star(X0),X1) = addition(X1,multiplication(star(X0),X1)),
inference(paramodulation,[status(thm)],[f1452,f979]) ).
fof(f1477,plain,
! [X0,X1] : addition(star(X0),addition(one,X1)) = addition(X1,star(X0)),
inference(paramodulation,[status(thm)],[f1452,f143]) ).
fof(f1478,plain,
! [X0,X1] : addition(one,addition(star(X0),X1)) = addition(X1,star(X0)),
inference(forward_demodulation,[status(thm)],[f50,f1477]) ).
fof(f1497,plain,
! [X0] : addition(multiplication(star(X0),X0),star(X0)) = star(X0),
inference(backward_demodulation,[status(thm)],[f1478,f707]) ).
fof(f1498,plain,
! [X0] : addition(star(X0),multiplication(star(X0),X0)) = star(X0),
inference(forward_demodulation,[status(thm)],[f19,f1497]) ).
fof(f1499,plain,
! [X0] : multiplication(star(X0),addition(X0,one)) = star(X0),
inference(forward_demodulation,[status(thm)],[f728,f1498]) ).
fof(f1522,plain,
! [X0] : multiplication(addition(X0,one),addition(star(X0),one)) = addition(addition(X0,one),star(X0)),
inference(paramodulation,[status(thm)],[f1450,f728]) ).
fof(f1523,plain,
! [X0] : multiplication(addition(X0,one),addition(one,star(X0))) = addition(addition(X0,one),star(X0)),
inference(forward_demodulation,[status(thm)],[f710,f1522]) ).
fof(f1524,plain,
! [X0] : multiplication(addition(X0,one),star(X0)) = addition(addition(X0,one),star(X0)),
inference(forward_demodulation,[status(thm)],[f1452,f1523]) ).
fof(f1525,plain,
! [X0] : star(X0) = addition(addition(X0,one),star(X0)),
inference(forward_demodulation,[status(thm)],[f1450,f1524]) ).
fof(f1526,plain,
! [X0] : star(X0) = addition(X0,addition(one,star(X0))),
inference(forward_demodulation,[status(thm)],[f20,f1525]) ).
fof(f1527,plain,
! [X0] : star(X0) = addition(X0,star(X0)),
inference(forward_demodulation,[status(thm)],[f1452,f1526]) ).
fof(f1611,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(f1635,plain,
! [X0,X1] :
( ~ leq(multiplication(X0,X1),X1)
| leq(multiplication(star(X0),multiplication(X0,X1)),X1) ),
inference(paramodulation,[status(thm)],[f22,f37]) ).
fof(f1683,plain,
! [X0] : multiplication(star(X0),addition(one,X0)) = star(X0),
inference(paramodulation,[status(thm)],[f710,f1499]) ).
fof(f1832,plain,
! [X0] : multiplication(star(star(X0)),star(X0)) = star(star(X0)),
inference(paramodulation,[status(thm)],[f1452,f1683]) ).
fof(f3854,plain,
! [X0,X1] : multiplication(star(star(X0)),multiplication(star(X0),X1)) = multiplication(star(star(X0)),X1),
inference(paramodulation,[status(thm)],[f1832,f23]) ).
fof(f4969,plain,
! [X0] :
( ~ leq(star(X0),star(X0))
| leq(multiplication(star(X0),multiplication(one,star(X0))),star(X0)) ),
inference(paramodulation,[status(thm)],[f1450,f1611]) ).
fof(f4970,plain,
! [X0] :
( ~ leq(star(X0),star(X0))
| leq(multiplication(star(X0),star(X0)),star(X0)) ),
inference(forward_demodulation,[status(thm)],[f25,f4969]) ).
fof(f4971,plain,
! [X0] : leq(multiplication(star(X0),star(X0)),star(X0)),
inference(forward_subsumption_resolution,[status(thm)],[f4970,f57]) ).
fof(f5157,plain,
! [X0] : addition(multiplication(star(X0),star(X0)),star(X0)) = star(X0),
inference(resolution,[status(thm)],[f4971,f32]) ).
fof(f5158,plain,
! [X0] : addition(star(X0),multiplication(star(X0),star(X0))) = star(X0),
inference(forward_demodulation,[status(thm)],[f19,f5157]) ).
fof(f5159,plain,
! [X0] : multiplication(star(X0),star(X0)) = star(X0),
inference(forward_demodulation,[status(thm)],[f1475,f5158]) ).
fof(f5287,plain,
! [X0] :
( ~ leq(star(X0),star(X0))
| leq(multiplication(star(star(X0)),multiplication(star(X0),star(X0))),star(X0)) ),
inference(paramodulation,[status(thm)],[f5159,f1635]) ).
fof(f5288,plain,
! [X0] :
( ~ leq(star(X0),star(X0))
| leq(multiplication(star(star(X0)),star(X0)),star(X0)) ),
inference(forward_demodulation,[status(thm)],[f3854,f5287]) ).
fof(f5289,plain,
! [X0] :
( ~ leq(star(X0),star(X0))
| leq(star(star(X0)),star(X0)) ),
inference(forward_demodulation,[status(thm)],[f1832,f5288]) ).
fof(f5290,plain,
! [X0] : leq(star(star(X0)),star(X0)),
inference(forward_subsumption_resolution,[status(thm)],[f5289,f57]) ).
fof(f5329,plain,
! [X0] : addition(star(star(X0)),star(X0)) = star(X0),
inference(resolution,[status(thm)],[f5290,f32]) ).
fof(f5330,plain,
! [X0] : addition(star(X0),star(star(X0))) = star(X0),
inference(forward_demodulation,[status(thm)],[f19,f5329]) ).
fof(f5331,plain,
! [X0] : star(star(X0)) = star(X0),
inference(forward_demodulation,[status(thm)],[f1527,f5330]) ).
fof(f5334,plain,
star(sk0_0) != star(sk0_0),
inference(backward_demodulation,[status(thm)],[f5331,f42]) ).
fof(f5335,plain,
$false,
inference(trivial_equality_resolution,[status(esa)],[f5334]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : KLE039+1 : TPTP v8.1.2. Released v4.0.0.
% 0.03/0.11 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.10/0.32 % Computer : n005.cluster.edu
% 0.10/0.32 % Model : x86_64 x86_64
% 0.10/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.32 % Memory : 8042.1875MB
% 0.10/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.32 % CPULimit : 300
% 0.10/0.32 % WCLimit : 300
% 0.10/0.32 % DateTime : Tue May 30 11:45:36 EDT 2023
% 0.10/0.32 % CPUTime :
% 0.10/0.32 % Drodi V3.5.1
% 8.76/1.50 % Refutation found
% 8.76/1.50 % SZS status Theorem for theBenchmark: Theorem is valid
% 8.76/1.50 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 8.76/1.56 % Elapsed time: 1.222447 seconds
% 8.76/1.56 % CPU time: 9.269671 seconds
% 8.76/1.56 % Memory used: 114.911 MB
%------------------------------------------------------------------------------