TSTP Solution File: KLE081+1 by Drodi---3.5.1
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%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : KLE081+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n007.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 12:15:44 EDT 2023
% Result : Theorem 5.64s 1.17s
% Output : CNFRefutation 6.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 11
% Syntax : Number of formulae : 53 ( 48 unt; 0 def)
% Number of atoms : 63 ( 62 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 16 ( 6 ~; 0 |; 8 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 86 (; 84 !; 2 ?)
% 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(f7,axiom,
! [A] : multiplication(one,A) = A,
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(f11,axiom,
! [A] : multiplication(zero,A) = zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [X0] : addition(X0,multiplication(domain(X0),X0)) = multiplication(domain(X0),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [X0] : addition(domain(X0),one) = one,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,axiom,
! [X0,X1] : domain(addition(X0,X1)) = addition(domain(X0),domain(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,conjecture,
! [X0] :
( ! [X1] :
( addition(domain(X1),antidomain(X1)) = one
& multiplication(domain(X1),antidomain(X1)) = zero )
=> multiplication(antidomain(X0),X0) = zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,negated_conjecture,
~ ! [X0] :
( ! [X1] :
( addition(domain(X1),antidomain(X1)) = one
& multiplication(domain(X1),antidomain(X1)) = zero )
=> multiplication(antidomain(X0),X0) = zero ),
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(f24,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(one,X0) = X0,
inference(cnf_transformation,[status(esa)],[f7]) ).
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(f30,plain,
! [X0] : multiplication(zero,X0) = zero,
inference(cnf_transformation,[status(esa)],[f11]) ).
fof(f35,plain,
! [X0] : addition(X0,multiplication(domain(X0),X0)) = multiplication(domain(X0),X0),
inference(cnf_transformation,[status(esa)],[f13]) ).
fof(f37,plain,
! [X0] : addition(domain(X0),one) = one,
inference(cnf_transformation,[status(esa)],[f15]) ).
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(domain(X1),antidomain(X1)) = one
& multiplication(domain(X1),antidomain(X1)) = zero )
& multiplication(antidomain(X0),X0) != zero ),
inference(pre_NNF_transformation,[status(esa)],[f19]) ).
fof(f41,plain,
( ! [X1] : addition(domain(X1),antidomain(X1)) = one
& ! [X1] : multiplication(domain(X1),antidomain(X1)) = zero
& ? [X0] : multiplication(antidomain(X0),X0) != zero ),
inference(miniscoping,[status(esa)],[f40]) ).
fof(f42,plain,
( ! [X1] : addition(domain(X1),antidomain(X1)) = one
& ! [X1] : multiplication(domain(X1),antidomain(X1)) = zero
& multiplication(antidomain(sk0_0),sk0_0) != zero ),
inference(skolemization,[status(esa)],[f41]) ).
fof(f43,plain,
! [X0] : addition(domain(X0),antidomain(X0)) = one,
inference(cnf_transformation,[status(esa)],[f42]) ).
fof(f44,plain,
! [X0] : multiplication(domain(X0),antidomain(X0)) = zero,
inference(cnf_transformation,[status(esa)],[f42]) ).
fof(f45,plain,
multiplication(antidomain(sk0_0),sk0_0) != zero,
inference(cnf_transformation,[status(esa)],[f42]) ).
fof(f46,plain,
! [X0] : addition(one,domain(X0)) = one,
inference(forward_demodulation,[status(thm)],[f20,f37]) ).
fof(f78,plain,
! [X0,X1] : addition(X0,addition(X0,X1)) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f23,f21]) ).
fof(f96,plain,
! [X0,X1] : addition(X0,addition(X1,X0)) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f20,f78]) ).
fof(f114,plain,
! [X0,X1] : multiplication(domain(X0),multiplication(antidomain(X0),X1)) = multiplication(zero,X1),
inference(paramodulation,[status(thm)],[f44,f24]) ).
fof(f115,plain,
! [X0,X1] : multiplication(domain(X0),multiplication(antidomain(X0),X1)) = zero,
inference(forward_demodulation,[status(thm)],[f30,f114]) ).
fof(f176,plain,
! [X0] : addition(antidomain(X0),one) = addition(antidomain(X0),domain(X0)),
inference(paramodulation,[status(thm)],[f43,f96]) ).
fof(f177,plain,
! [X0] : addition(one,antidomain(X0)) = addition(antidomain(X0),domain(X0)),
inference(forward_demodulation,[status(thm)],[f20,f176]) ).
fof(f178,plain,
! [X0] : addition(one,antidomain(X0)) = addition(domain(X0),antidomain(X0)),
inference(forward_demodulation,[status(thm)],[f20,f177]) ).
fof(f179,plain,
! [X0] : addition(one,antidomain(X0)) = one,
inference(forward_demodulation,[status(thm)],[f43,f178]) ).
fof(f860,plain,
! [X0,X1] : multiplication(addition(one,X0),X1) = addition(X1,multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f26,f28]) ).
fof(f1913,plain,
! [X0,X1] : multiplication(one,X0) = addition(X0,multiplication(antidomain(X1),X0)),
inference(paramodulation,[status(thm)],[f179,f860]) ).
fof(f1914,plain,
! [X0,X1] : X0 = addition(X0,multiplication(antidomain(X1),X0)),
inference(forward_demodulation,[status(thm)],[f26,f1913]) ).
fof(f1915,plain,
! [X0,X1] : multiplication(one,X0) = addition(X0,multiplication(domain(X1),X0)),
inference(paramodulation,[status(thm)],[f46,f860]) ).
fof(f1916,plain,
! [X0,X1] : X0 = addition(X0,multiplication(domain(X1),X0)),
inference(forward_demodulation,[status(thm)],[f26,f1915]) ).
fof(f1946,plain,
! [X0] : multiplication(addition(one,domain(X0)),X0) = multiplication(domain(X0),X0),
inference(paramodulation,[status(thm)],[f35,f860]) ).
fof(f1947,plain,
! [X0] : multiplication(one,X0) = multiplication(domain(X0),X0),
inference(forward_demodulation,[status(thm)],[f46,f1946]) ).
fof(f1948,plain,
! [X0] : X0 = multiplication(domain(X0),X0),
inference(forward_demodulation,[status(thm)],[f26,f1947]) ).
fof(f2088,plain,
! [X0,X1] : multiplication(addition(X0,domain(X1)),X1) = addition(multiplication(X0,X1),X1),
inference(paramodulation,[status(thm)],[f1948,f28]) ).
fof(f2089,plain,
! [X0,X1] : multiplication(addition(X0,domain(X1)),X1) = addition(X1,multiplication(X0,X1)),
inference(forward_demodulation,[status(thm)],[f20,f2088]) ).
fof(f3211,plain,
! [X0,X1] : multiplication(domain(addition(X0,X1)),X1) = addition(X1,multiplication(domain(X0),X1)),
inference(paramodulation,[status(thm)],[f39,f2089]) ).
fof(f3212,plain,
! [X0,X1] : multiplication(domain(addition(X0,X1)),X1) = X1,
inference(forward_demodulation,[status(thm)],[f1916,f3211]) ).
fof(f3318,plain,
! [X0,X1] : multiplication(domain(X0),multiplication(antidomain(X1),X0)) = multiplication(antidomain(X1),X0),
inference(paramodulation,[status(thm)],[f1914,f3212]) ).
fof(f8423,plain,
! [X0] : zero = multiplication(antidomain(X0),X0),
inference(paramodulation,[status(thm)],[f115,f3318]) ).
fof(f8505,plain,
zero != zero,
inference(backward_demodulation,[status(thm)],[f8423,f45]) ).
fof(f8506,plain,
$false,
inference(trivial_equality_resolution,[status(esa)],[f8505]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : KLE081+1 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.33 % Computer : n007.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Tue May 30 11:34:47 EDT 2023
% 0.13/0.33 % CPUTime :
% 0.13/0.34 % Drodi V3.5.1
% 5.64/1.17 % Refutation found
% 5.64/1.17 % SZS status Theorem for theBenchmark: Theorem is valid
% 5.64/1.17 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 6.29/1.21 % Elapsed time: 0.872233 seconds
% 6.29/1.21 % CPU time: 6.668504 seconds
% 6.29/1.21 % Memory used: 124.594 MB
%------------------------------------------------------------------------------