TSTP Solution File: KLE015+1 by Drodi---3.5.1
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%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : KLE015+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n019.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 12:15:30 EDT 2023
% Result : Theorem 46.80s 6.28s
% Output : CNFRefutation 47.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 12
% Syntax : Number of formulae : 61 ( 39 unt; 0 def)
% Number of atoms : 114 ( 69 equ)
% Maximal formula atoms : 8 ( 1 avg)
% Number of connectives : 86 ( 33 ~; 28 |; 18 &)
% ( 4 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 94 (; 92 !; 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(f3,axiom,
! [A] : addition(A,zero) = A,
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(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(f14,axiom,
! [X0,X1] :
( complement(X1,X0)
<=> ( multiplication(X0,X1) = zero
& multiplication(X1,X0) = zero
& addition(X0,X1) = one ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [X0,X1] :
( test(X0)
=> ( c(X0) = X1
<=> complement(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,conjecture,
! [X0,X1] :
( ( test(X1)
& test(X0) )
=> multiplication(multiplication(addition(X0,X1),c(X0)),c(X1)) = zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
~ ! [X0,X1] :
( ( test(X1)
& test(X0) )
=> multiplication(multiplication(addition(X0,X1),c(X0)),c(X1)) = zero ),
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(f21,plain,
! [X0] : addition(X0,zero) = X0,
inference(cnf_transformation,[status(esa)],[f3]) ).
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(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(f39,plain,
! [X0,X1] :
( ( ~ complement(X1,X0)
| ( multiplication(X0,X1) = zero
& multiplication(X1,X0) = zero
& addition(X0,X1) = one ) )
& ( complement(X1,X0)
| multiplication(X0,X1) != zero
| multiplication(X1,X0) != zero
| addition(X0,X1) != one ) ),
inference(NNF_transformation,[status(esa)],[f14]) ).
fof(f40,plain,
( ! [X0,X1] :
( ~ complement(X1,X0)
| ( multiplication(X0,X1) = zero
& multiplication(X1,X0) = zero
& addition(X0,X1) = one ) )
& ! [X0,X1] :
( complement(X1,X0)
| multiplication(X0,X1) != zero
| multiplication(X1,X0) != zero
| addition(X0,X1) != one ) ),
inference(miniscoping,[status(esa)],[f39]) ).
fof(f42,plain,
! [X0,X1] :
( ~ complement(X0,X1)
| multiplication(X0,X1) = zero ),
inference(cnf_transformation,[status(esa)],[f40]) ).
fof(f43,plain,
! [X0,X1] :
( ~ complement(X0,X1)
| addition(X1,X0) = one ),
inference(cnf_transformation,[status(esa)],[f40]) ).
fof(f45,plain,
! [X0,X1] :
( ~ test(X0)
| ( c(X0) = X1
<=> complement(X0,X1) ) ),
inference(pre_NNF_transformation,[status(esa)],[f15]) ).
fof(f46,plain,
! [X0,X1] :
( ~ test(X0)
| ( ( c(X0) != X1
| complement(X0,X1) )
& ( c(X0) = X1
| ~ complement(X0,X1) ) ) ),
inference(NNF_transformation,[status(esa)],[f45]) ).
fof(f47,plain,
! [X0] :
( ~ test(X0)
| ( ! [X1] :
( c(X0) != X1
| complement(X0,X1) )
& ! [X1] :
( c(X0) = X1
| ~ complement(X0,X1) ) ) ),
inference(miniscoping,[status(esa)],[f46]) ).
fof(f48,plain,
! [X0,X1] :
( ~ test(X0)
| c(X0) != X1
| complement(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f47]) ).
fof(f52,plain,
? [X0,X1] :
( test(X1)
& test(X0)
& multiplication(multiplication(addition(X0,X1),c(X0)),c(X1)) != zero ),
inference(pre_NNF_transformation,[status(esa)],[f18]) ).
fof(f53,plain,
( test(sk0_2)
& test(sk0_1)
& multiplication(multiplication(addition(sk0_1,sk0_2),c(sk0_1)),c(sk0_2)) != zero ),
inference(skolemization,[status(esa)],[f52]) ).
fof(f54,plain,
test(sk0_2),
inference(cnf_transformation,[status(esa)],[f53]) ).
fof(f55,plain,
test(sk0_1),
inference(cnf_transformation,[status(esa)],[f53]) ).
fof(f56,plain,
multiplication(multiplication(addition(sk0_1,sk0_2),c(sk0_1)),c(sk0_2)) != zero,
inference(cnf_transformation,[status(esa)],[f53]) ).
fof(f57,plain,
! [X0] :
( ~ test(X0)
| complement(X0,c(X0)) ),
inference(destructive_equality_resolution,[status(esa)],[f48]) ).
fof(f58,plain,
! [X0] : X0 = addition(zero,X0),
inference(paramodulation,[status(thm)],[f21,f19]) ).
fof(f75,plain,
! [X0,X1] : addition(X0,addition(X0,X1)) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f22,f20]) ).
fof(f136,plain,
! [X0,X1] : leq(X0,addition(X0,X1)),
inference(resolution,[status(thm)],[f33,f75]) ).
fof(f274,plain,
! [X0,X1,X2] : leq(multiplication(X0,X1),multiplication(addition(X0,X2),X1)),
inference(paramodulation,[status(thm)],[f27,f136]) ).
fof(f1347,plain,
! [X0] :
( multiplication(X0,c(X0)) = zero
| ~ test(X0) ),
inference(resolution,[status(thm)],[f42,f57]) ).
fof(f1349,plain,
! [X0] :
( addition(c(X0),X0) = one
| ~ test(X0) ),
inference(resolution,[status(thm)],[f43,f57]) ).
fof(f2759,plain,
multiplication(sk0_1,c(sk0_1)) = zero,
inference(resolution,[status(thm)],[f1347,f55]) ).
fof(f2760,plain,
multiplication(sk0_2,c(sk0_2)) = zero,
inference(resolution,[status(thm)],[f1347,f54]) ).
fof(f2769,plain,
! [X0] : multiplication(addition(sk0_1,X0),c(sk0_1)) = addition(zero,multiplication(X0,c(sk0_1))),
inference(paramodulation,[status(thm)],[f2759,f27]) ).
fof(f2770,plain,
! [X0] : multiplication(addition(sk0_1,X0),c(sk0_1)) = multiplication(X0,c(sk0_1)),
inference(forward_demodulation,[status(thm)],[f58,f2769]) ).
fof(f2787,plain,
! [X0] : multiplication(sk0_2,addition(c(sk0_2),X0)) = addition(zero,multiplication(sk0_2,X0)),
inference(paramodulation,[status(thm)],[f2760,f26]) ).
fof(f2788,plain,
! [X0] : multiplication(sk0_2,addition(c(sk0_2),X0)) = multiplication(sk0_2,X0),
inference(forward_demodulation,[status(thm)],[f58,f2787]) ).
fof(f3840,plain,
multiplication(multiplication(sk0_2,c(sk0_1)),c(sk0_2)) != zero,
inference(backward_demodulation,[status(thm)],[f2770,f56]) ).
fof(f25685,plain,
addition(c(sk0_1),sk0_1) = one,
inference(resolution,[status(thm)],[f1349,f55]) ).
fof(f34695,plain,
! [X0] : leq(multiplication(c(sk0_1),X0),multiplication(one,X0)),
inference(paramodulation,[status(thm)],[f25685,f274]) ).
fof(f34696,plain,
! [X0] : leq(multiplication(c(sk0_1),X0),X0),
inference(forward_demodulation,[status(thm)],[f25,f34695]) ).
fof(f34762,plain,
! [X0] : addition(multiplication(c(sk0_1),X0),X0) = X0,
inference(resolution,[status(thm)],[f34696,f32]) ).
fof(f34891,plain,
! [X0] : addition(X0,multiplication(c(sk0_1),X0)) = X0,
inference(paramodulation,[status(thm)],[f19,f34762]) ).
fof(f40488,plain,
multiplication(sk0_2,c(sk0_2)) = multiplication(sk0_2,multiplication(c(sk0_1),c(sk0_2))),
inference(paramodulation,[status(thm)],[f34891,f2788]) ).
fof(f40489,plain,
zero = multiplication(sk0_2,multiplication(c(sk0_1),c(sk0_2))),
inference(forward_demodulation,[status(thm)],[f2760,f40488]) ).
fof(f40490,plain,
zero = multiplication(multiplication(sk0_2,c(sk0_1)),c(sk0_2)),
inference(forward_demodulation,[status(thm)],[f23,f40489]) ).
fof(f40491,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f40490,f3840]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : KLE015+1 : TPTP v8.1.2. Released v4.0.0.
% 0.09/0.10 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.09/0.30 % Computer : n019.cluster.edu
% 0.09/0.30 % Model : x86_64 x86_64
% 0.09/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.30 % Memory : 8042.1875MB
% 0.09/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.30 % CPULimit : 300
% 0.09/0.30 % WCLimit : 300
% 0.09/0.30 % DateTime : Tue May 30 11:48:55 EDT 2023
% 0.09/0.31 % CPUTime :
% 0.15/0.31 % Drodi V3.5.1
% 46.80/6.28 % Refutation found
% 46.80/6.28 % SZS status Theorem for theBenchmark: Theorem is valid
% 46.80/6.28 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 47.36/6.40 % Elapsed time: 6.078326 seconds
% 47.36/6.40 % CPU time: 47.625915 seconds
% 47.36/6.40 % Memory used: 419.100 MB
%------------------------------------------------------------------------------