TSTP Solution File: KLE010+3 by Drodi---3.5.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : KLE010+3 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n024.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 12:15:28 EDT 2023
% Result : Theorem 3.16s 0.81s
% Output : CNFRefutation 3.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 16
% Syntax : Number of formulae : 102 ( 46 unt; 0 def)
% Number of atoms : 195 ( 94 equ)
% Maximal formula atoms : 8 ( 1 avg)
% Number of connectives : 176 ( 83 ~; 64 |; 19 &)
% ( 7 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 7 ( 5 usr; 4 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 96 (; 91 !; 5 ?)
% 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(f6,axiom,
! [A] : multiplication(A,one) = A,
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(f19,conjecture,
! [X0,X1] :
( ( test(X1)
& test(X0) )
=> one = addition(addition(addition(addition(multiplication(X1,X0),multiplication(c(X1),X0)),multiplication(X0,X1)),multiplication(c(X0),X1)),multiplication(c(X0),c(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
~ ! [X0,X1] :
( ( test(X1)
& test(X0) )
=> one = addition(addition(addition(addition(multiplication(X1,X0),multiplication(c(X1),X0)),multiplication(X0,X1)),multiplication(c(X0),X1)),multiplication(c(X0),c(X1))) ),
inference(negated_conjecture,[status(cth)],[f19]) ).
fof(f21,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[status(esa)],[f1]) ).
fof(f22,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,zero) = X0,
inference(cnf_transformation,[status(esa)],[f3]) ).
fof(f24,plain,
! [X0] : addition(X0,X0) = X0,
inference(cnf_transformation,[status(esa)],[f4]) ).
fof(f26,plain,
! [X0] : multiplication(X0,one) = X0,
inference(cnf_transformation,[status(esa)],[f6]) ).
fof(f27,plain,
! [X0] : multiplication(one,X0) = X0,
inference(cnf_transformation,[status(esa)],[f7]) ).
fof(f28,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
inference(cnf_transformation,[status(esa)],[f8]) ).
fof(f29,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,
! [X0] : multiplication(zero,X0) = zero,
inference(cnf_transformation,[status(esa)],[f11]) ).
fof(f36,plain,
! [X0] :
( ( ~ test(X0)
| ? [X1] : complement(X1,X0) )
& ( test(X0)
| ! [X1] : ~ complement(X1,X0) ) ),
inference(NNF_transformation,[status(esa)],[f13]) ).
fof(f37,plain,
( ! [X0] :
( ~ test(X0)
| ? [X1] : complement(X1,X0) )
& ! [X0] :
( test(X0)
| ! [X1] : ~ complement(X1,X0) ) ),
inference(miniscoping,[status(esa)],[f36]) ).
fof(f38,plain,
( ! [X0] :
( ~ test(X0)
| complement(sk0_0(X0),X0) )
& ! [X0] :
( test(X0)
| ! [X1] : ~ complement(X1,X0) ) ),
inference(skolemization,[status(esa)],[f37]) ).
fof(f39,plain,
! [X0] :
( ~ test(X0)
| complement(sk0_0(X0),X0) ),
inference(cnf_transformation,[status(esa)],[f38]) ).
fof(f40,plain,
! [X0,X1] :
( test(X0)
| ~ complement(X1,X0) ),
inference(cnf_transformation,[status(esa)],[f38]) ).
fof(f41,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(f42,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)],[f41]) ).
fof(f44,plain,
! [X0,X1] :
( ~ complement(X0,X1)
| multiplication(X0,X1) = zero ),
inference(cnf_transformation,[status(esa)],[f42]) ).
fof(f45,plain,
! [X0,X1] :
( ~ complement(X0,X1)
| addition(X1,X0) = one ),
inference(cnf_transformation,[status(esa)],[f42]) ).
fof(f46,plain,
! [X0,X1] :
( complement(X0,X1)
| multiplication(X1,X0) != zero
| multiplication(X0,X1) != zero
| addition(X1,X0) != one ),
inference(cnf_transformation,[status(esa)],[f42]) ).
fof(f47,plain,
! [X0,X1] :
( ~ test(X0)
| ( c(X0) = X1
<=> complement(X0,X1) ) ),
inference(pre_NNF_transformation,[status(esa)],[f15]) ).
fof(f48,plain,
! [X0,X1] :
( ~ test(X0)
| ( ( c(X0) != X1
| complement(X0,X1) )
& ( c(X0) = X1
| ~ complement(X0,X1) ) ) ),
inference(NNF_transformation,[status(esa)],[f47]) ).
fof(f49,plain,
! [X0] :
( ~ test(X0)
| ( ! [X1] :
( c(X0) != X1
| complement(X0,X1) )
& ! [X1] :
( c(X0) = X1
| ~ complement(X0,X1) ) ) ),
inference(miniscoping,[status(esa)],[f48]) ).
fof(f50,plain,
! [X0,X1] :
( ~ test(X0)
| c(X0) != X1
| complement(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f49]) ).
fof(f58,plain,
? [X0,X1] :
( test(X1)
& test(X0)
& one != addition(addition(addition(addition(multiplication(X1,X0),multiplication(c(X1),X0)),multiplication(X0,X1)),multiplication(c(X0),X1)),multiplication(c(X0),c(X1))) ),
inference(pre_NNF_transformation,[status(esa)],[f20]) ).
fof(f59,plain,
( test(sk0_2)
& test(sk0_1)
& one != addition(addition(addition(addition(multiplication(sk0_2,sk0_1),multiplication(c(sk0_2),sk0_1)),multiplication(sk0_1,sk0_2)),multiplication(c(sk0_1),sk0_2)),multiplication(c(sk0_1),c(sk0_2))) ),
inference(skolemization,[status(esa)],[f58]) ).
fof(f60,plain,
test(sk0_2),
inference(cnf_transformation,[status(esa)],[f59]) ).
fof(f61,plain,
test(sk0_1),
inference(cnf_transformation,[status(esa)],[f59]) ).
fof(f62,plain,
one != addition(addition(addition(addition(multiplication(sk0_2,sk0_1),multiplication(c(sk0_2),sk0_1)),multiplication(sk0_1,sk0_2)),multiplication(c(sk0_1),sk0_2)),multiplication(c(sk0_1),c(sk0_2))),
inference(cnf_transformation,[status(esa)],[f59]) ).
fof(f85,plain,
! [X0,X1] : addition(X0,addition(X0,X1)) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f24,f22]) ).
fof(f92,plain,
one != addition(addition(addition(multiplication(sk0_2,sk0_1),multiplication(c(sk0_2),sk0_1)),multiplication(sk0_1,sk0_2)),addition(multiplication(c(sk0_1),sk0_2),multiplication(c(sk0_1),c(sk0_2)))),
inference(paramodulation,[status(thm)],[f22,f62]) ).
fof(f93,plain,
one != addition(addition(addition(multiplication(c(sk0_2),sk0_1),multiplication(sk0_2,sk0_1)),multiplication(sk0_1,sk0_2)),addition(multiplication(c(sk0_1),sk0_2),multiplication(c(sk0_1),c(sk0_2)))),
inference(forward_demodulation,[status(thm)],[f21,f92]) ).
fof(f94,plain,
one != addition(addition(addition(multiplication(c(sk0_2),sk0_1),multiplication(sk0_2,sk0_1)),multiplication(sk0_1,sk0_2)),addition(multiplication(c(sk0_1),c(sk0_2)),multiplication(c(sk0_1),sk0_2))),
inference(forward_demodulation,[status(thm)],[f21,f93]) ).
fof(f264,plain,
! [X0] : addition(zero,X0) = X0,
inference(paramodulation,[status(thm)],[f21,f23]) ).
fof(f349,plain,
complement(sk0_0(sk0_2),sk0_2),
inference(resolution,[status(thm)],[f39,f60]) ).
fof(f358,plain,
addition(sk0_2,sk0_0(sk0_2)) = one,
inference(resolution,[status(thm)],[f349,f45]) ).
fof(f473,plain,
addition(sk0_2,one) = addition(sk0_2,sk0_0(sk0_2)),
inference(paramodulation,[status(thm)],[f358,f85]) ).
fof(f474,plain,
addition(sk0_2,one) = one,
inference(forward_demodulation,[status(thm)],[f358,f473]) ).
fof(f684,plain,
( spl0_29
<=> multiplication(zero,one) = zero ),
introduced(split_symbol_definition) ).
fof(f686,plain,
( multiplication(zero,one) != zero
| spl0_29 ),
inference(component_clause,[status(thm)],[f684]) ).
fof(f687,plain,
( spl0_30
<=> multiplication(one,zero) = zero ),
introduced(split_symbol_definition) ).
fof(f689,plain,
( multiplication(one,zero) != zero
| spl0_30 ),
inference(component_clause,[status(thm)],[f687]) ).
fof(f692,plain,
( spl0_31
<=> complement(zero,one) ),
introduced(split_symbol_definition) ).
fof(f693,plain,
( complement(zero,one)
| ~ spl0_31 ),
inference(component_clause,[status(thm)],[f692]) ).
fof(f695,plain,
( complement(zero,one)
| multiplication(one,zero) != zero
| multiplication(zero,one) != zero ),
inference(resolution,[status(thm)],[f46,f23]) ).
fof(f696,plain,
( spl0_31
| ~ spl0_30
| ~ spl0_29 ),
inference(split_clause,[status(thm)],[f695,f692,f687,f684]) ).
fof(f785,plain,
( $false
| spl0_29 ),
inference(forward_subsumption_resolution,[status(thm)],[f686,f31]) ).
fof(f786,plain,
spl0_29,
inference(contradiction_clause,[status(thm)],[f785]) ).
fof(f787,plain,
( $false
| spl0_30 ),
inference(forward_subsumption_resolution,[status(thm)],[f689,f27]) ).
fof(f788,plain,
spl0_30,
inference(contradiction_clause,[status(thm)],[f787]) ).
fof(f852,plain,
! [X0] :
( c(sk0_1) != X0
| complement(sk0_1,X0) ),
inference(resolution,[status(thm)],[f50,f61]) ).
fof(f853,plain,
! [X0] :
( c(sk0_2) != X0
| complement(sk0_2,X0) ),
inference(resolution,[status(thm)],[f50,f60]) ).
fof(f900,plain,
( test(one)
| ~ spl0_31 ),
inference(resolution,[status(thm)],[f693,f40]) ).
fof(f910,plain,
( complement(sk0_0(one),one)
| ~ spl0_31 ),
inference(resolution,[status(thm)],[f900,f39]) ).
fof(f929,plain,
( multiplication(sk0_0(one),one) = zero
| ~ spl0_31 ),
inference(resolution,[status(thm)],[f910,f44]) ).
fof(f974,plain,
( sk0_0(one) = zero
| ~ spl0_31 ),
inference(paramodulation,[status(thm)],[f26,f929]) ).
fof(f976,plain,
! [X0] :
( multiplication(addition(X0,sk0_0(one)),one) = addition(multiplication(X0,one),zero)
| ~ spl0_31 ),
inference(paramodulation,[status(thm)],[f929,f29]) ).
fof(f977,plain,
! [X0] :
( multiplication(addition(X0,sk0_0(one)),one) = addition(X0,zero)
| ~ spl0_31 ),
inference(forward_demodulation,[status(thm)],[f26,f976]) ).
fof(f978,plain,
! [X0] :
( multiplication(addition(sk0_0(one),X0),one) = addition(zero,multiplication(X0,one))
| ~ spl0_31 ),
inference(paramodulation,[status(thm)],[f929,f29]) ).
fof(f979,plain,
! [X0] :
( multiplication(addition(sk0_0(one),X0),one) = addition(zero,X0)
| ~ spl0_31 ),
inference(forward_demodulation,[status(thm)],[f26,f978]) ).
fof(f1577,plain,
! [X0] :
( multiplication(addition(X0,zero),one) = addition(X0,zero)
| ~ spl0_31 ),
inference(forward_demodulation,[status(thm)],[f974,f977]) ).
fof(f1578,plain,
! [X0] :
( multiplication(X0,one) = addition(X0,zero)
| ~ spl0_31 ),
inference(forward_demodulation,[status(thm)],[f23,f1577]) ).
fof(f1607,plain,
! [X0,X1] :
( multiplication(X0,addition(X1,one)) = addition(multiplication(X0,X1),addition(X0,zero))
| ~ spl0_31 ),
inference(paramodulation,[status(thm)],[f1578,f28]) ).
fof(f1608,plain,
! [X0,X1] :
( multiplication(X0,addition(X1,one)) = addition(multiplication(X0,X1),X0)
| ~ spl0_31 ),
inference(forward_demodulation,[status(thm)],[f23,f1607]) ).
fof(f1654,plain,
! [X0] :
( multiplication(addition(zero,X0),one) = addition(zero,X0)
| ~ spl0_31 ),
inference(forward_demodulation,[status(thm)],[f974,f979]) ).
fof(f1655,plain,
! [X0] :
( multiplication(X0,one) = addition(zero,X0)
| ~ spl0_31 ),
inference(forward_demodulation,[status(thm)],[f264,f1654]) ).
fof(f2096,plain,
complement(sk0_1,multiplication(one,c(sk0_1))),
inference(resolution,[status(thm)],[f852,f27]) ).
fof(f2097,plain,
complement(sk0_1,c(sk0_1)),
inference(forward_demodulation,[status(thm)],[f27,f2096]) ).
fof(f2111,plain,
addition(c(sk0_1),sk0_1) = one,
inference(resolution,[status(thm)],[f2097,f45]) ).
fof(f2152,plain,
complement(sk0_2,multiplication(one,c(sk0_2))),
inference(resolution,[status(thm)],[f853,f27]) ).
fof(f2153,plain,
complement(sk0_2,c(sk0_2)),
inference(forward_demodulation,[status(thm)],[f27,f2152]) ).
fof(f2168,plain,
addition(c(sk0_2),sk0_2) = one,
inference(resolution,[status(thm)],[f2153,f45]) ).
fof(f2540,plain,
! [X0] :
( multiplication(X0,one) = addition(multiplication(X0,sk0_2),X0)
| ~ spl0_31 ),
inference(paramodulation,[status(thm)],[f474,f1608]) ).
fof(f2826,plain,
one != addition(addition(multiplication(addition(c(sk0_2),sk0_2),sk0_1),multiplication(sk0_1,sk0_2)),addition(multiplication(c(sk0_1),c(sk0_2)),multiplication(c(sk0_1),sk0_2))),
inference(forward_demodulation,[status(thm)],[f29,f94]) ).
fof(f2827,plain,
one != addition(addition(multiplication(addition(c(sk0_2),sk0_2),sk0_1),multiplication(sk0_1,sk0_2)),multiplication(c(sk0_1),addition(c(sk0_2),sk0_2))),
inference(forward_demodulation,[status(thm)],[f28,f2826]) ).
fof(f2968,plain,
one != addition(addition(multiplication(addition(c(sk0_2),sk0_2),sk0_1),multiplication(sk0_1,sk0_2)),multiplication(c(sk0_1),one)),
inference(backward_demodulation,[status(thm)],[f2168,f2827]) ).
fof(f2969,plain,
one != addition(addition(multiplication(one,sk0_1),multiplication(sk0_1,sk0_2)),multiplication(c(sk0_1),one)),
inference(forward_demodulation,[status(thm)],[f2168,f2968]) ).
fof(f2970,plain,
one != addition(addition(sk0_1,multiplication(sk0_1,sk0_2)),multiplication(c(sk0_1),one)),
inference(forward_demodulation,[status(thm)],[f27,f2969]) ).
fof(f2971,plain,
one != addition(addition(multiplication(sk0_1,sk0_2),sk0_1),multiplication(c(sk0_1),one)),
inference(forward_demodulation,[status(thm)],[f21,f2970]) ).
fof(f2972,plain,
( one != addition(addition(multiplication(sk0_1,sk0_2),sk0_1),addition(zero,c(sk0_1)))
| ~ spl0_31 ),
inference(forward_demodulation,[status(thm)],[f1655,f2971]) ).
fof(f2973,plain,
( one != addition(addition(multiplication(sk0_1,sk0_2),sk0_1),c(sk0_1))
| ~ spl0_31 ),
inference(forward_demodulation,[status(thm)],[f264,f2972]) ).
fof(f3248,plain,
( one != addition(c(sk0_1),addition(multiplication(sk0_1,sk0_2),sk0_1))
| ~ spl0_31 ),
inference(paramodulation,[status(thm)],[f21,f2973]) ).
fof(f4160,plain,
( one != addition(c(sk0_1),multiplication(sk0_1,one))
| ~ spl0_31 ),
inference(backward_demodulation,[status(thm)],[f2540,f3248]) ).
fof(f4161,plain,
( one != addition(c(sk0_1),addition(zero,sk0_1))
| ~ spl0_31 ),
inference(forward_demodulation,[status(thm)],[f1655,f4160]) ).
fof(f4162,plain,
( one != addition(c(sk0_1),sk0_1)
| ~ spl0_31 ),
inference(forward_demodulation,[status(thm)],[f264,f4161]) ).
fof(f4163,plain,
( one != one
| ~ spl0_31 ),
inference(forward_demodulation,[status(thm)],[f2111,f4162]) ).
fof(f4164,plain,
( $false
| ~ spl0_31 ),
inference(trivial_equality_resolution,[status(esa)],[f4163]) ).
fof(f4165,plain,
~ spl0_31,
inference(contradiction_clause,[status(thm)],[f4164]) ).
fof(f4166,plain,
$false,
inference(sat_refutation,[status(thm)],[f696,f786,f788,f4165]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : KLE010+3 : TPTP v8.1.2. Released v4.0.0.
% 0.12/0.14 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.35 % Computer : n024.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Tue May 30 11:47:03 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.13/0.36 % Drodi V3.5.1
% 3.16/0.81 % Refutation found
% 3.16/0.81 % SZS status Theorem for theBenchmark: Theorem is valid
% 3.16/0.81 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 3.53/0.84 % Elapsed time: 0.476744 seconds
% 3.53/0.84 % CPU time: 3.590156 seconds
% 3.53/0.84 % Memory used: 95.630 MB
%------------------------------------------------------------------------------