TSTP Solution File: KLE027+1 by Drodi---3.6.0
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%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : KLE027+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n013.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 : Tue Apr 30 20:24:13 EDT 2024
% Result : Theorem 0.16s 0.40s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 11
% Syntax : Number of formulae : 56 ( 35 unt; 0 def)
% Number of atoms : 111 ( 60 equ)
% Maximal formula atoms : 8 ( 1 avg)
% Number of connectives : 91 ( 36 ~; 27 |; 21 &)
% ( 4 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 7 con; 0-2 aty)
% Number of variables : 94 ( 81 !; 13 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B] : addition(A,B) = addition(B,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [A] : addition(A,zero) = 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(f11,axiom,
! [A] : multiplication(zero,A) = zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [X0] :
( test(X0)
<=> ? [X1] : complement(X1,X0) ),
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,X2,X3,X4] :
( ( test(X3)
& test(X4) )
=> addition(multiplication(X3,addition(multiplication(X3,X0),multiplication(c(X3),X1))),multiplication(c(X3),X2)) = addition(multiplication(X3,X0),multiplication(c(X3),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
~ ! [X0,X1,X2,X3,X4] :
( ( test(X3)
& test(X4) )
=> addition(multiplication(X3,addition(multiplication(X3,X0),multiplication(c(X3),X1))),multiplication(c(X3),X2)) = addition(multiplication(X3,X0),multiplication(c(X3),X2)) ),
inference(negated_conjecture,[status(cth)],[f17]) ).
fof(f19,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[status(esa)],[f1]) ).
fof(f21,plain,
! [X0] : addition(X0,zero) = X0,
inference(cnf_transformation,[status(esa)],[f3]) ).
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(f29,plain,
! [X0] : multiplication(zero,X0) = zero,
inference(cnf_transformation,[status(esa)],[f11]) ).
fof(f34,plain,
! [X0] :
( ( ~ test(X0)
| ? [X1] : complement(X1,X0) )
& ( test(X0)
| ! [X1] : ~ complement(X1,X0) ) ),
inference(NNF_transformation,[status(esa)],[f13]) ).
fof(f35,plain,
( ! [X0] :
( ~ test(X0)
| ? [X1] : complement(X1,X0) )
& ! [X0] :
( test(X0)
| ! [X1] : ~ complement(X1,X0) ) ),
inference(miniscoping,[status(esa)],[f34]) ).
fof(f36,plain,
( ! [X0] :
( ~ test(X0)
| complement(sk0_0(X0),X0) )
& ! [X0] :
( test(X0)
| ! [X1] : ~ complement(X1,X0) ) ),
inference(skolemization,[status(esa)],[f35]) ).
fof(f37,plain,
! [X0] :
( ~ test(X0)
| complement(sk0_0(X0),X0) ),
inference(cnf_transformation,[status(esa)],[f36]) ).
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,X2,X3,X4] :
( test(X3)
& test(X4)
& addition(multiplication(X3,addition(multiplication(X3,X0),multiplication(c(X3),X1))),multiplication(c(X3),X2)) != addition(multiplication(X3,X0),multiplication(c(X3),X2)) ),
inference(pre_NNF_transformation,[status(esa)],[f18]) ).
fof(f53,plain,
? [X3] :
( test(X3)
& ? [X4] : test(X4)
& ? [X0,X1,X2] : addition(multiplication(X3,addition(multiplication(X3,X0),multiplication(c(X3),X1))),multiplication(c(X3),X2)) != addition(multiplication(X3,X0),multiplication(c(X3),X2)) ),
inference(miniscoping,[status(esa)],[f52]) ).
fof(f54,plain,
( test(sk0_1)
& test(sk0_2)
& addition(multiplication(sk0_1,addition(multiplication(sk0_1,sk0_3),multiplication(c(sk0_1),sk0_4))),multiplication(c(sk0_1),sk0_5)) != addition(multiplication(sk0_1,sk0_3),multiplication(c(sk0_1),sk0_5)) ),
inference(skolemization,[status(esa)],[f53]) ).
fof(f55,plain,
test(sk0_1),
inference(cnf_transformation,[status(esa)],[f54]) ).
fof(f57,plain,
addition(multiplication(sk0_1,addition(multiplication(sk0_1,sk0_3),multiplication(c(sk0_1),sk0_4))),multiplication(c(sk0_1),sk0_5)) != addition(multiplication(sk0_1,sk0_3),multiplication(c(sk0_1),sk0_5)),
inference(cnf_transformation,[status(esa)],[f54]) ).
fof(f58,plain,
! [X0] :
( ~ test(X0)
| complement(X0,c(X0)) ),
inference(destructive_equality_resolution,[status(esa)],[f48]) ).
fof(f59,plain,
addition(multiplication(c(sk0_1),sk0_5),multiplication(sk0_1,addition(multiplication(sk0_1,sk0_3),multiplication(c(sk0_1),sk0_4)))) != addition(multiplication(sk0_1,sk0_3),multiplication(c(sk0_1),sk0_5)),
inference(forward_demodulation,[status(thm)],[f19,f57]) ).
fof(f61,plain,
complement(sk0_1,c(sk0_1)),
inference(resolution,[status(thm)],[f58,f55]) ).
fof(f155,plain,
complement(sk0_0(sk0_1),sk0_1),
inference(resolution,[status(thm)],[f37,f55]) ).
fof(f252,plain,
multiplication(sk0_0(sk0_1),sk0_1) = zero,
inference(resolution,[status(thm)],[f42,f155]) ).
fof(f254,plain,
multiplication(sk0_1,c(sk0_1)) = zero,
inference(resolution,[status(thm)],[f42,f61]) ).
fof(f298,plain,
! [X0] : multiplication(addition(X0,sk0_0(sk0_1)),sk0_1) = addition(multiplication(X0,sk0_1),zero),
inference(paramodulation,[status(thm)],[f252,f27]) ).
fof(f299,plain,
! [X0] : multiplication(addition(X0,sk0_0(sk0_1)),sk0_1) = multiplication(X0,sk0_1),
inference(forward_demodulation,[status(thm)],[f21,f298]) ).
fof(f339,plain,
! [X0] : multiplication(sk0_1,multiplication(c(sk0_1),X0)) = multiplication(zero,X0),
inference(paramodulation,[status(thm)],[f254,f23]) ).
fof(f340,plain,
! [X0] : multiplication(sk0_1,multiplication(c(sk0_1),X0)) = zero,
inference(forward_demodulation,[status(thm)],[f29,f339]) ).
fof(f455,plain,
! [X0,X1] : multiplication(sk0_1,addition(X0,multiplication(c(sk0_1),X1))) = addition(multiplication(sk0_1,X0),zero),
inference(paramodulation,[status(thm)],[f340,f26]) ).
fof(f456,plain,
! [X0,X1] : multiplication(sk0_1,addition(X0,multiplication(c(sk0_1),X1))) = multiplication(sk0_1,X0),
inference(forward_demodulation,[status(thm)],[f21,f455]) ).
fof(f462,plain,
addition(multiplication(c(sk0_1),sk0_5),multiplication(sk0_1,multiplication(sk0_1,sk0_3))) != addition(multiplication(sk0_1,sk0_3),multiplication(c(sk0_1),sk0_5)),
inference(backward_demodulation,[status(thm)],[f456,f59]) ).
fof(f1309,plain,
addition(sk0_1,sk0_0(sk0_1)) = one,
inference(resolution,[status(thm)],[f43,f155]) ).
fof(f1325,plain,
multiplication(one,sk0_1) = multiplication(sk0_1,sk0_1),
inference(paramodulation,[status(thm)],[f1309,f299]) ).
fof(f1326,plain,
sk0_1 = multiplication(sk0_1,sk0_1),
inference(forward_demodulation,[status(thm)],[f25,f1325]) ).
fof(f1377,plain,
! [X0] : multiplication(sk0_1,multiplication(sk0_1,X0)) = multiplication(sk0_1,X0),
inference(paramodulation,[status(thm)],[f1326,f23]) ).
fof(f1378,plain,
addition(multiplication(c(sk0_1),sk0_5),multiplication(sk0_1,sk0_3)) != addition(multiplication(sk0_1,sk0_3),multiplication(c(sk0_1),sk0_5)),
inference(backward_demodulation,[status(thm)],[f1377,f462]) ).
fof(f1379,plain,
addition(multiplication(sk0_1,sk0_3),multiplication(c(sk0_1),sk0_5)) != addition(multiplication(sk0_1,sk0_3),multiplication(c(sk0_1),sk0_5)),
inference(forward_demodulation,[status(thm)],[f19,f1378]) ).
fof(f1380,plain,
$false,
inference(trivial_equality_resolution,[status(esa)],[f1379]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : KLE027+1 : TPTP v8.1.2. Released v4.0.0.
% 0.06/0.11 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.11/0.32 % Computer : n013.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Tue Apr 30 00:54:34 EDT 2024
% 0.11/0.32 % CPUTime :
% 0.11/0.33 % Drodi V3.6.0
% 0.16/0.40 % Refutation found
% 0.16/0.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.16/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.16/0.42 % Elapsed time: 0.092395 seconds
% 0.16/0.42 % CPU time: 0.587175 seconds
% 0.16/0.42 % Total memory used: 68.438 MB
% 0.16/0.42 % Net memory used: 68.222 MB
%------------------------------------------------------------------------------