TSTP Solution File: KLE005+1 by Drodi---3.5.1
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%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : KLE005+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n032.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 12:15:25 EDT 2023
% Result : Theorem 0.08s 0.29s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 11
% Syntax : Number of formulae : 44 ( 16 unt; 0 def)
% Number of atoms : 104 ( 58 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 103 ( 43 ~; 42 |; 10 &)
% ( 6 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 4 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 40 (; 40 !; 0 ?)
% 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(f10,axiom,
! [A] : multiplication(A,zero) = zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [A] : multiplication(zero,A) = zero,
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(f16,axiom,
! [X0] :
( ~ test(X0)
=> c(X0) = zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,conjecture,
c(one) = zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
c(one) != 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(f21,plain,
! [X0] : addition(X0,zero) = X0,
inference(cnf_transformation,[status(esa)],[f3]) ).
fof(f28,plain,
! [X0] : multiplication(X0,zero) = zero,
inference(cnf_transformation,[status(esa)],[f10]) ).
fof(f29,plain,
! [X0] : multiplication(zero,X0) = zero,
inference(cnf_transformation,[status(esa)],[f11]) ).
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(f44,plain,
! [X0,X1] :
( complement(X0,X1)
| multiplication(X1,X0) != zero
| multiplication(X0,X1) != zero
| 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(f49,plain,
! [X0,X1] :
( ~ test(X0)
| c(X0) = X1
| ~ complement(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f47]) ).
fof(f50,plain,
! [X0] :
( test(X0)
| c(X0) = zero ),
inference(pre_NNF_transformation,[status(esa)],[f16]) ).
fof(f51,plain,
! [X0] :
( test(X0)
| c(X0) = zero ),
inference(cnf_transformation,[status(esa)],[f50]) ).
fof(f52,plain,
c(one) != zero,
inference(cnf_transformation,[status(esa)],[f18]) ).
fof(f55,plain,
( spl0_0
<=> zero = zero ),
introduced(split_symbol_definition) ).
fof(f57,plain,
( zero != zero
| spl0_0 ),
inference(component_clause,[status(thm)],[f55]) ).
fof(f58,plain,
( spl0_1
<=> test(one) ),
introduced(split_symbol_definition) ).
fof(f61,plain,
( zero != zero
| test(one) ),
inference(paramodulation,[status(thm)],[f51,f52]) ).
fof(f62,plain,
( ~ spl0_0
| spl0_1 ),
inference(split_clause,[status(thm)],[f61,f55,f58]) ).
fof(f63,plain,
( $false
| spl0_0 ),
inference(trivial_equality_resolution,[status(esa)],[f57]) ).
fof(f64,plain,
spl0_0,
inference(contradiction_clause,[status(thm)],[f63]) ).
fof(f113,plain,
! [X0] : X0 = addition(zero,X0),
inference(paramodulation,[status(thm)],[f21,f19]) ).
fof(f130,plain,
! [X0] :
( complement(X0,zero)
| multiplication(zero,X0) != zero
| multiplication(X0,zero) != zero
| X0 != one ),
inference(paramodulation,[status(thm)],[f113,f44]) ).
fof(f131,plain,
! [X0] :
( complement(X0,zero)
| zero != zero
| multiplication(X0,zero) != zero
| X0 != one ),
inference(forward_demodulation,[status(thm)],[f29,f130]) ).
fof(f132,plain,
! [X0] :
( complement(X0,zero)
| zero != zero
| zero != zero
| X0 != one ),
inference(forward_demodulation,[status(thm)],[f28,f131]) ).
fof(f133,plain,
! [X0] :
( complement(X0,zero)
| zero != zero
| X0 != one ),
inference(duplicate_literals_removal,[status(esa)],[f132]) ).
fof(f134,plain,
! [X0] :
( complement(X0,zero)
| X0 != one ),
inference(trivial_equality_resolution,[status(esa)],[f133]) ).
fof(f135,plain,
complement(one,zero),
inference(destructive_equality_resolution,[status(esa)],[f134]) ).
fof(f137,plain,
( spl0_10
<=> c(one) = zero ),
introduced(split_symbol_definition) ).
fof(f138,plain,
( c(one) = zero
| ~ spl0_10 ),
inference(component_clause,[status(thm)],[f137]) ).
fof(f140,plain,
( ~ test(one)
| c(one) = zero ),
inference(resolution,[status(thm)],[f135,f49]) ).
fof(f141,plain,
( ~ spl0_1
| spl0_10 ),
inference(split_clause,[status(thm)],[f140,f58,f137]) ).
fof(f142,plain,
( $false
| ~ spl0_10 ),
inference(forward_subsumption_resolution,[status(thm)],[f138,f52]) ).
fof(f143,plain,
~ spl0_10,
inference(contradiction_clause,[status(thm)],[f142]) ).
fof(f144,plain,
$false,
inference(sat_refutation,[status(thm)],[f62,f64,f141,f143]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.08 % Problem : KLE005+1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.09 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.08/0.28 % Computer : n032.cluster.edu
% 0.08/0.28 % Model : x86_64 x86_64
% 0.08/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.28 % Memory : 8042.1875MB
% 0.08/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.08/0.28 % CPULimit : 300
% 0.08/0.28 % WCLimit : 300
% 0.08/0.28 % DateTime : Tue May 30 11:47:46 EDT 2023
% 0.08/0.28 % CPUTime :
% 0.08/0.28 % Drodi V3.5.1
% 0.08/0.29 % Refutation found
% 0.08/0.29 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.08/0.29 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.30 % Elapsed time: 0.015802 seconds
% 0.12/0.30 % CPU time: 0.024543 seconds
% 0.12/0.30 % Memory used: 14.377 MB
%------------------------------------------------------------------------------