TSTP Solution File: KLE064+1 by Drodi---3.5.1
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%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : KLE064+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n006.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 12:15:42 EDT 2023
% Result : Theorem 0.19s 0.49s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 8
% Syntax : Number of formulae : 37 ( 28 unt; 0 def)
% Number of atoms : 50 ( 35 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 23 ( 10 ~; 6 |; 4 &)
% ( 1 <=>; 0 =>; 2 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 4 ( 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 : 64 (; 62 !; 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(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,
! [X0] : addition(X0,multiplication(domain(X0),X0)) = multiplication(domain(X0),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,axiom,
! [X0,X1] : domain(addition(X0,X1)) = addition(domain(X0),domain(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,conjecture,
! [X0,X1] :
( addition(X0,multiplication(domain(X1),X0)) = multiplication(domain(X1),X0)
<= addition(domain(X0),domain(X1)) = domain(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,negated_conjecture,
~ ! [X0,X1] :
( addition(X0,multiplication(domain(X1),X0)) = multiplication(domain(X1),X0)
<= addition(domain(X0),domain(X1)) = domain(X1) ),
inference(negated_conjecture,[status(cth)],[f18]) ).
fof(f20,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[status(esa)],[f1]) ).
fof(f21,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,X0) = X0,
inference(cnf_transformation,[status(esa)],[f4]) ).
fof(f28,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
inference(cnf_transformation,[status(esa)],[f9]) ).
fof(f31,plain,
! [A,B] :
( ( ~ leq(A,B)
| addition(A,B) = B )
& ( leq(A,B)
| addition(A,B) != B ) ),
inference(NNF_transformation,[status(esa)],[f12]) ).
fof(f32,plain,
( ! [A,B] :
( ~ leq(A,B)
| addition(A,B) = B )
& ! [A,B] :
( leq(A,B)
| addition(A,B) != B ) ),
inference(miniscoping,[status(esa)],[f31]) ).
fof(f33,plain,
! [X0,X1] :
( ~ leq(X0,X1)
| addition(X0,X1) = X1 ),
inference(cnf_transformation,[status(esa)],[f32]) ).
fof(f34,plain,
! [X0,X1] :
( leq(X0,X1)
| addition(X0,X1) != X1 ),
inference(cnf_transformation,[status(esa)],[f32]) ).
fof(f35,plain,
! [X0] : addition(X0,multiplication(domain(X0),X0)) = multiplication(domain(X0),X0),
inference(cnf_transformation,[status(esa)],[f13]) ).
fof(f39,plain,
! [X0,X1] : domain(addition(X0,X1)) = addition(domain(X0),domain(X1)),
inference(cnf_transformation,[status(esa)],[f17]) ).
fof(f40,plain,
? [X0,X1] :
( addition(X0,multiplication(domain(X1),X0)) != multiplication(domain(X1),X0)
& addition(domain(X0),domain(X1)) = domain(X1) ),
inference(pre_NNF_transformation,[status(esa)],[f19]) ).
fof(f41,plain,
( addition(sk0_0,multiplication(domain(sk0_1),sk0_0)) != multiplication(domain(sk0_1),sk0_0)
& addition(domain(sk0_0),domain(sk0_1)) = domain(sk0_1) ),
inference(skolemization,[status(esa)],[f40]) ).
fof(f42,plain,
addition(sk0_0,multiplication(domain(sk0_1),sk0_0)) != multiplication(domain(sk0_1),sk0_0),
inference(cnf_transformation,[status(esa)],[f41]) ).
fof(f43,plain,
addition(domain(sk0_0),domain(sk0_1)) = domain(sk0_1),
inference(cnf_transformation,[status(esa)],[f41]) ).
fof(f44,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X2,addition(X0,X1)),
inference(paramodulation,[status(thm)],[f20,f21]) ).
fof(f55,plain,
! [X0,X1] : addition(X0,addition(X0,X1)) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f23,f21]) ).
fof(f125,plain,
domain(addition(sk0_0,sk0_1)) = domain(sk0_1),
inference(backward_demodulation,[status(thm)],[f39,f43]) ).
fof(f126,plain,
! [X0,X1] : domain(addition(X0,X1)) = addition(domain(X1),domain(X0)),
inference(paramodulation,[status(thm)],[f20,f39]) ).
fof(f127,plain,
! [X0,X1] : domain(addition(X0,X1)) = domain(addition(X1,X0)),
inference(forward_demodulation,[status(thm)],[f39,f126]) ).
fof(f330,plain,
! [X0,X1] : leq(X0,addition(X0,X1)),
inference(resolution,[status(thm)],[f34,f55]) ).
fof(f614,plain,
! [X0,X1,X2] : leq(X0,addition(X1,addition(X0,X2))),
inference(paramodulation,[status(thm)],[f44,f330]) ).
fof(f1037,plain,
! [X0,X1] : leq(X0,addition(X1,multiplication(domain(X0),X0))),
inference(paramodulation,[status(thm)],[f35,f614]) ).
fof(f2111,plain,
! [X0,X1] : leq(X0,multiplication(addition(X1,domain(X0)),X0)),
inference(paramodulation,[status(thm)],[f28,f1037]) ).
fof(f2638,plain,
! [X0,X1] : leq(X0,multiplication(domain(addition(X1,X0)),X0)),
inference(paramodulation,[status(thm)],[f39,f2111]) ).
fof(f2782,plain,
! [X0,X1] : leq(X0,multiplication(domain(addition(X0,X1)),X0)),
inference(paramodulation,[status(thm)],[f127,f2638]) ).
fof(f2928,plain,
leq(sk0_0,multiplication(domain(sk0_1),sk0_0)),
inference(paramodulation,[status(thm)],[f125,f2782]) ).
fof(f2964,plain,
addition(sk0_0,multiplication(domain(sk0_1),sk0_0)) = multiplication(domain(sk0_1),sk0_0),
inference(resolution,[status(thm)],[f2928,f33]) ).
fof(f2965,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f2964,f42]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : KLE064+1 : TPTP v8.1.2. Released v4.0.0.
% 0.11/0.12 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.12/0.33 % Computer : n006.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
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Tue May 30 11:43:32 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.12/0.34 % Drodi V3.5.1
% 0.19/0.49 % Refutation found
% 0.19/0.49 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.19/0.49 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.19/0.51 % Elapsed time: 0.170691 seconds
% 0.19/0.51 % CPU time: 1.229211 seconds
% 0.19/0.51 % Memory used: 52.164 MB
%------------------------------------------------------------------------------