TSTP Solution File: KLE010+2 by Drodi---3.5.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : KLE010+2 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n010.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 12:15:27 EDT 2023
% Result : Theorem 0.20s 0.56s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 14
% Syntax : Number of formulae : 143 ( 58 unt; 0 def)
% Number of atoms : 266 ( 85 equ)
% Maximal formula atoms : 8 ( 1 avg)
% Number of connectives : 218 ( 95 ~; 93 |; 20 &)
% ( 7 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 8 ( 6 usr; 4 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 104 (; 102 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B] : addition(A,B) = addition(B,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [C,B,A] : addition(A,addition(B,C)) = addition(addition(A,B),C),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A] : addition(A,A) = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [A] : multiplication(A,one) = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [A] : multiplication(one,A) = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [A,B,C] : multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [A,B,C] : multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [A,B] :
( leq(A,B)
<=> addition(A,B) = B ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [X0,X1] :
( test(X0)
=> ( c(X0) = X1
<=> complement(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,conjecture,
! [X0,X1] :
( ( test(X1)
& test(X0) )
=> ( leq(one,addition(addition(addition(addition(multiplication(X1,X0),multiplication(c(X1),X0)),multiplication(X0,X1)),multiplication(c(X0),X1)),multiplication(c(X0),c(X1))))
& leq(addition(addition(addition(addition(multiplication(X1,X0),multiplication(c(X1),X0)),multiplication(X0,X1)),multiplication(c(X0),X1)),multiplication(c(X0),c(X1))),one) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
~ ! [X0,X1] :
( ( test(X1)
& test(X0) )
=> ( leq(one,addition(addition(addition(addition(multiplication(X1,X0),multiplication(c(X1),X0)),multiplication(X0,X1)),multiplication(c(X0),X1)),multiplication(c(X0),c(X1))))
& leq(addition(addition(addition(addition(multiplication(X1,X0),multiplication(c(X1),X0)),multiplication(X0,X1)),multiplication(c(X0),X1)),multiplication(c(X0),c(X1))),one) ) ),
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(f22,plain,
! [X0] : addition(X0,X0) = X0,
inference(cnf_transformation,[status(esa)],[f4]) ).
fof(f24,plain,
! [X0] : multiplication(X0,one) = X0,
inference(cnf_transformation,[status(esa)],[f6]) ).
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(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)
& ( ~ leq(one,addition(addition(addition(addition(multiplication(X1,X0),multiplication(c(X1),X0)),multiplication(X0,X1)),multiplication(c(X0),X1)),multiplication(c(X0),c(X1))))
| ~ leq(addition(addition(addition(addition(multiplication(X1,X0),multiplication(c(X1),X0)),multiplication(X0,X1)),multiplication(c(X0),X1)),multiplication(c(X0),c(X1))),one) ) ),
inference(pre_NNF_transformation,[status(esa)],[f18]) ).
fof(f53,plain,
( test(sk0_2)
& test(sk0_1)
& ( ~ leq(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))))
| ~ leq(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))),one) ) ),
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,
( ~ leq(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))))
| ~ leq(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))),one) ),
inference(cnf_transformation,[status(esa)],[f53]) ).
fof(f57,plain,
( spl0_0
<=> leq(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)))) ),
introduced(split_symbol_definition) ).
fof(f58,plain,
( leq(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))))
| ~ spl0_0 ),
inference(component_clause,[status(thm)],[f57]) ).
fof(f59,plain,
( ~ leq(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))))
| spl0_0 ),
inference(component_clause,[status(thm)],[f57]) ).
fof(f60,plain,
( spl0_1
<=> leq(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))),one) ),
introduced(split_symbol_definition) ).
fof(f62,plain,
( ~ leq(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))),one)
| spl0_1 ),
inference(component_clause,[status(thm)],[f60]) ).
fof(f63,plain,
( ~ spl0_0
| ~ spl0_1 ),
inference(split_clause,[status(thm)],[f56,f57,f60]) ).
fof(f64,plain,
! [X0] :
( ~ test(X0)
| complement(X0,c(X0)) ),
inference(destructive_equality_resolution,[status(esa)],[f48]) ).
fof(f65,plain,
( ~ leq(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)))))
| spl0_0 ),
inference(forward_demodulation,[status(thm)],[f20,f59]) ).
fof(f66,plain,
( ~ leq(one,addition(addition(multiplication(sk0_2,sk0_1),multiplication(c(sk0_2),sk0_1)),addition(multiplication(sk0_1,sk0_2),addition(multiplication(c(sk0_1),sk0_2),multiplication(c(sk0_1),c(sk0_2))))))
| spl0_0 ),
inference(forward_demodulation,[status(thm)],[f20,f65]) ).
fof(f67,plain,
( ~ leq(one,addition(multiplication(sk0_2,sk0_1),addition(multiplication(c(sk0_2),sk0_1),addition(multiplication(sk0_1,sk0_2),addition(multiplication(c(sk0_1),sk0_2),multiplication(c(sk0_1),c(sk0_2)))))))
| spl0_0 ),
inference(forward_demodulation,[status(thm)],[f20,f66]) ).
fof(f68,plain,
( ~ leq(one,addition(multiplication(sk0_2,sk0_1),addition(multiplication(c(sk0_2),sk0_1),addition(multiplication(sk0_1,sk0_2),multiplication(c(sk0_1),addition(sk0_2,c(sk0_2)))))))
| spl0_0 ),
inference(forward_demodulation,[status(thm)],[f26,f67]) ).
fof(f70,plain,
! [X0,X1] :
( leq(X0,X1)
| addition(X1,X0) != X1 ),
inference(paramodulation,[status(thm)],[f19,f33]) ).
fof(f75,plain,
complement(sk0_1,c(sk0_1)),
inference(resolution,[status(thm)],[f64,f55]) ).
fof(f76,plain,
complement(sk0_2,c(sk0_2)),
inference(resolution,[status(thm)],[f64,f54]) ).
fof(f82,plain,
addition(c(sk0_2),sk0_2) = one,
inference(resolution,[status(thm)],[f43,f76]) ).
fof(f83,plain,
addition(sk0_2,c(sk0_2)) = one,
inference(forward_demodulation,[status(thm)],[f19,f82]) ).
fof(f84,plain,
addition(c(sk0_1),sk0_1) = one,
inference(resolution,[status(thm)],[f43,f75]) ).
fof(f85,plain,
addition(sk0_1,c(sk0_1)) = one,
inference(forward_demodulation,[status(thm)],[f19,f84]) ).
fof(f86,plain,
( ~ leq(one,addition(multiplication(sk0_2,sk0_1),addition(multiplication(c(sk0_2),sk0_1),addition(multiplication(sk0_1,sk0_2),multiplication(c(sk0_1),one)))))
| spl0_0 ),
inference(backward_demodulation,[status(thm)],[f83,f68]) ).
fof(f87,plain,
( ~ leq(one,addition(multiplication(sk0_2,sk0_1),addition(multiplication(c(sk0_2),sk0_1),addition(multiplication(sk0_1,sk0_2),c(sk0_1)))))
| spl0_0 ),
inference(forward_demodulation,[status(thm)],[f24,f86]) ).
fof(f88,plain,
( ~ leq(one,addition(multiplication(sk0_2,sk0_1),addition(multiplication(c(sk0_2),sk0_1),addition(c(sk0_1),multiplication(sk0_1,sk0_2)))))
| spl0_0 ),
inference(forward_demodulation,[status(thm)],[f19,f87]) ).
fof(f121,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X2,addition(X0,X1)),
inference(paramodulation,[status(thm)],[f19,f20]) ).
fof(f127,plain,
! [X0] : addition(sk0_1,addition(c(sk0_1),X0)) = addition(one,X0),
inference(paramodulation,[status(thm)],[f85,f20]) ).
fof(f129,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(addition(X1,X0),X2),
inference(paramodulation,[status(thm)],[f19,f20]) ).
fof(f130,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X1,addition(X0,X2)),
inference(forward_demodulation,[status(thm)],[f20,f129]) ).
fof(f133,plain,
! [X0,X1] : addition(X0,addition(X0,X1)) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f22,f20]) ).
fof(f146,plain,
! [X0,X1] : leq(X0,addition(X0,X1)),
inference(resolution,[status(thm)],[f133,f33]) ).
fof(f153,plain,
addition(sk0_1,one) = addition(sk0_1,c(sk0_1)),
inference(paramodulation,[status(thm)],[f85,f133]) ).
fof(f154,plain,
addition(one,sk0_1) = addition(sk0_1,c(sk0_1)),
inference(forward_demodulation,[status(thm)],[f19,f153]) ).
fof(f155,plain,
addition(one,sk0_1) = one,
inference(forward_demodulation,[status(thm)],[f85,f154]) ).
fof(f156,plain,
addition(sk0_2,one) = addition(sk0_2,c(sk0_2)),
inference(paramodulation,[status(thm)],[f83,f133]) ).
fof(f157,plain,
addition(one,sk0_2) = addition(sk0_2,c(sk0_2)),
inference(forward_demodulation,[status(thm)],[f19,f156]) ).
fof(f158,plain,
addition(one,sk0_2) = one,
inference(forward_demodulation,[status(thm)],[f83,f157]) ).
fof(f159,plain,
! [X0,X1] : addition(X0,addition(X1,X0)) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f19,f133]) ).
fof(f167,plain,
! [X0,X1] :
( leq(addition(X0,X1),X0)
| addition(X0,X1) != X0 ),
inference(paramodulation,[status(thm)],[f133,f70]) ).
fof(f176,plain,
! [X0,X1] : leq(X0,addition(X1,X0)),
inference(paramodulation,[status(thm)],[f19,f146]) ).
fof(f197,plain,
! [X0] : addition(one,addition(sk0_1,X0)) = addition(one,X0),
inference(paramodulation,[status(thm)],[f155,f20]) ).
fof(f218,plain,
! [X0] : addition(one,addition(sk0_2,X0)) = addition(one,X0),
inference(paramodulation,[status(thm)],[f158,f20]) ).
fof(f302,plain,
addition(c(sk0_1),one) = addition(c(sk0_1),sk0_1),
inference(paramodulation,[status(thm)],[f85,f159]) ).
fof(f303,plain,
addition(one,c(sk0_1)) = addition(c(sk0_1),sk0_1),
inference(forward_demodulation,[status(thm)],[f19,f302]) ).
fof(f304,plain,
addition(one,c(sk0_1)) = addition(sk0_1,c(sk0_1)),
inference(forward_demodulation,[status(thm)],[f19,f303]) ).
fof(f305,plain,
addition(one,c(sk0_1)) = one,
inference(forward_demodulation,[status(thm)],[f85,f304]) ).
fof(f306,plain,
addition(c(sk0_2),one) = addition(c(sk0_2),sk0_2),
inference(paramodulation,[status(thm)],[f83,f159]) ).
fof(f307,plain,
addition(one,c(sk0_2)) = addition(c(sk0_2),sk0_2),
inference(forward_demodulation,[status(thm)],[f19,f306]) ).
fof(f308,plain,
addition(one,c(sk0_2)) = addition(sk0_2,c(sk0_2)),
inference(forward_demodulation,[status(thm)],[f19,f307]) ).
fof(f309,plain,
addition(one,c(sk0_2)) = one,
inference(forward_demodulation,[status(thm)],[f83,f308]) ).
fof(f446,plain,
! [X0,X1,X2] : leq(multiplication(X0,X1),multiplication(addition(X2,X0),X1)),
inference(paramodulation,[status(thm)],[f27,f176]) ).
fof(f451,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),addition(multiplication(X2,X1),X3)) = addition(multiplication(addition(X0,X2),X1),X3),
inference(paramodulation,[status(thm)],[f27,f20]) ).
fof(f459,plain,
( ~ leq(one,addition(multiplication(addition(sk0_2,c(sk0_2)),sk0_1),addition(c(sk0_1),multiplication(sk0_1,sk0_2))))
| spl0_0 ),
inference(backward_demodulation,[status(thm)],[f451,f88]) ).
fof(f460,plain,
( ~ leq(one,addition(addition(c(sk0_1),multiplication(sk0_1,sk0_2)),multiplication(addition(sk0_2,c(sk0_2)),sk0_1)))
| spl0_0 ),
inference(forward_demodulation,[status(thm)],[f19,f459]) ).
fof(f461,plain,
( ~ leq(one,addition(c(sk0_1),addition(multiplication(sk0_1,sk0_2),multiplication(addition(sk0_2,c(sk0_2)),sk0_1))))
| spl0_0 ),
inference(forward_demodulation,[status(thm)],[f20,f460]) ).
fof(f462,plain,
( ~ leq(one,addition(c(sk0_1),addition(multiplication(sk0_1,sk0_2),multiplication(one,sk0_1))))
| spl0_0 ),
inference(forward_demodulation,[status(thm)],[f83,f461]) ).
fof(f463,plain,
( ~ leq(one,addition(c(sk0_1),addition(multiplication(one,sk0_1),multiplication(sk0_1,sk0_2))))
| spl0_0 ),
inference(forward_demodulation,[status(thm)],[f19,f462]) ).
fof(f464,plain,
( ~ leq(one,addition(c(sk0_1),addition(sk0_1,multiplication(sk0_1,sk0_2))))
| spl0_0 ),
inference(forward_demodulation,[status(thm)],[f25,f463]) ).
fof(f465,plain,
( ~ leq(one,addition(sk0_1,addition(c(sk0_1),multiplication(sk0_1,sk0_2))))
| spl0_0 ),
inference(forward_demodulation,[status(thm)],[f130,f464]) ).
fof(f466,plain,
( ~ leq(one,addition(one,multiplication(sk0_1,sk0_2)))
| spl0_0 ),
inference(forward_demodulation,[status(thm)],[f127,f465]) ).
fof(f467,plain,
( $false
| spl0_0 ),
inference(forward_subsumption_resolution,[status(thm)],[f466,f146]) ).
fof(f468,plain,
spl0_0,
inference(contradiction_clause,[status(thm)],[f467]) ).
fof(f469,plain,
( ~ leq(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)))),one)
| spl0_1 ),
inference(forward_demodulation,[status(thm)],[f20,f62]) ).
fof(f470,plain,
( ~ leq(addition(addition(multiplication(sk0_2,sk0_1),multiplication(c(sk0_2),sk0_1)),addition(multiplication(sk0_1,sk0_2),addition(multiplication(c(sk0_1),sk0_2),multiplication(c(sk0_1),c(sk0_2))))),one)
| spl0_1 ),
inference(forward_demodulation,[status(thm)],[f20,f469]) ).
fof(f471,plain,
( ~ leq(addition(multiplication(sk0_2,sk0_1),addition(multiplication(c(sk0_2),sk0_1),addition(multiplication(sk0_1,sk0_2),addition(multiplication(c(sk0_1),sk0_2),multiplication(c(sk0_1),c(sk0_2)))))),one)
| spl0_1 ),
inference(forward_demodulation,[status(thm)],[f20,f470]) ).
fof(f472,plain,
( ~ leq(addition(multiplication(addition(sk0_2,c(sk0_2)),sk0_1),addition(multiplication(sk0_1,sk0_2),addition(multiplication(c(sk0_1),sk0_2),multiplication(c(sk0_1),c(sk0_2))))),one)
| spl0_1 ),
inference(forward_demodulation,[status(thm)],[f451,f471]) ).
fof(f473,plain,
( ~ leq(addition(multiplication(sk0_1,sk0_2),addition(multiplication(addition(sk0_2,c(sk0_2)),sk0_1),addition(multiplication(c(sk0_1),sk0_2),multiplication(c(sk0_1),c(sk0_2))))),one)
| spl0_1 ),
inference(forward_demodulation,[status(thm)],[f130,f472]) ).
fof(f474,plain,
( ~ leq(addition(multiplication(sk0_1,sk0_2),addition(multiplication(c(sk0_1),sk0_2),addition(multiplication(addition(sk0_2,c(sk0_2)),sk0_1),multiplication(c(sk0_1),c(sk0_2))))),one)
| spl0_1 ),
inference(forward_demodulation,[status(thm)],[f130,f473]) ).
fof(f475,plain,
( ~ leq(addition(multiplication(addition(sk0_1,c(sk0_1)),sk0_2),addition(multiplication(addition(sk0_2,c(sk0_2)),sk0_1),multiplication(c(sk0_1),c(sk0_2)))),one)
| spl0_1 ),
inference(forward_demodulation,[status(thm)],[f451,f474]) ).
fof(f476,plain,
( ~ leq(addition(multiplication(c(sk0_1),c(sk0_2)),addition(multiplication(addition(sk0_1,c(sk0_1)),sk0_2),multiplication(addition(sk0_2,c(sk0_2)),sk0_1))),one)
| spl0_1 ),
inference(forward_demodulation,[status(thm)],[f121,f475]) ).
fof(f477,plain,
( ~ leq(addition(multiplication(c(sk0_1),c(sk0_2)),addition(multiplication(one,sk0_2),multiplication(addition(sk0_2,c(sk0_2)),sk0_1))),one)
| spl0_1 ),
inference(forward_demodulation,[status(thm)],[f85,f476]) ).
fof(f478,plain,
( ~ leq(addition(multiplication(one,sk0_2),addition(multiplication(c(sk0_1),c(sk0_2)),multiplication(addition(sk0_2,c(sk0_2)),sk0_1))),one)
| spl0_1 ),
inference(forward_demodulation,[status(thm)],[f130,f477]) ).
fof(f479,plain,
( ~ leq(addition(sk0_2,addition(multiplication(c(sk0_1),c(sk0_2)),multiplication(addition(sk0_2,c(sk0_2)),sk0_1))),one)
| spl0_1 ),
inference(forward_demodulation,[status(thm)],[f25,f478]) ).
fof(f480,plain,
( ~ leq(addition(sk0_2,addition(multiplication(c(sk0_1),c(sk0_2)),multiplication(one,sk0_1))),one)
| spl0_1 ),
inference(forward_demodulation,[status(thm)],[f83,f479]) ).
fof(f481,plain,
( ~ leq(addition(sk0_2,addition(multiplication(one,sk0_1),multiplication(c(sk0_1),c(sk0_2)))),one)
| spl0_1 ),
inference(forward_demodulation,[status(thm)],[f19,f480]) ).
fof(f482,plain,
( ~ leq(addition(sk0_2,addition(sk0_1,multiplication(c(sk0_1),c(sk0_2)))),one)
| spl0_1 ),
inference(forward_demodulation,[status(thm)],[f25,f481]) ).
fof(f483,plain,
( ~ leq(addition(sk0_1,addition(sk0_2,multiplication(c(sk0_1),c(sk0_2)))),one)
| spl0_1 ),
inference(forward_demodulation,[status(thm)],[f130,f482]) ).
fof(f484,plain,
( leq(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)))))
| ~ spl0_0 ),
inference(forward_demodulation,[status(thm)],[f20,f58]) ).
fof(f485,plain,
( leq(one,addition(addition(multiplication(sk0_2,sk0_1),multiplication(c(sk0_2),sk0_1)),addition(multiplication(sk0_1,sk0_2),addition(multiplication(c(sk0_1),sk0_2),multiplication(c(sk0_1),c(sk0_2))))))
| ~ spl0_0 ),
inference(forward_demodulation,[status(thm)],[f20,f484]) ).
fof(f486,plain,
( leq(one,addition(multiplication(sk0_2,sk0_1),addition(multiplication(c(sk0_2),sk0_1),addition(multiplication(sk0_1,sk0_2),addition(multiplication(c(sk0_1),sk0_2),multiplication(c(sk0_1),c(sk0_2)))))))
| ~ spl0_0 ),
inference(forward_demodulation,[status(thm)],[f20,f485]) ).
fof(f487,plain,
( leq(one,addition(multiplication(addition(sk0_2,c(sk0_2)),sk0_1),addition(multiplication(sk0_1,sk0_2),addition(multiplication(c(sk0_1),sk0_2),multiplication(c(sk0_1),c(sk0_2))))))
| ~ spl0_0 ),
inference(forward_demodulation,[status(thm)],[f451,f486]) ).
fof(f488,plain,
( leq(one,addition(multiplication(sk0_1,sk0_2),addition(multiplication(addition(sk0_2,c(sk0_2)),sk0_1),addition(multiplication(c(sk0_1),sk0_2),multiplication(c(sk0_1),c(sk0_2))))))
| ~ spl0_0 ),
inference(forward_demodulation,[status(thm)],[f130,f487]) ).
fof(f489,plain,
( leq(one,addition(multiplication(sk0_1,sk0_2),addition(multiplication(c(sk0_1),sk0_2),addition(multiplication(addition(sk0_2,c(sk0_2)),sk0_1),multiplication(c(sk0_1),c(sk0_2))))))
| ~ spl0_0 ),
inference(forward_demodulation,[status(thm)],[f130,f488]) ).
fof(f490,plain,
( leq(one,addition(multiplication(addition(sk0_1,c(sk0_1)),sk0_2),addition(multiplication(addition(sk0_2,c(sk0_2)),sk0_1),multiplication(c(sk0_1),c(sk0_2)))))
| ~ spl0_0 ),
inference(forward_demodulation,[status(thm)],[f451,f489]) ).
fof(f491,plain,
( leq(one,addition(multiplication(c(sk0_1),c(sk0_2)),addition(multiplication(addition(sk0_1,c(sk0_1)),sk0_2),multiplication(addition(sk0_2,c(sk0_2)),sk0_1))))
| ~ spl0_0 ),
inference(forward_demodulation,[status(thm)],[f121,f490]) ).
fof(f492,plain,
( leq(one,addition(multiplication(c(sk0_1),c(sk0_2)),addition(multiplication(one,sk0_2),multiplication(addition(sk0_2,c(sk0_2)),sk0_1))))
| ~ spl0_0 ),
inference(forward_demodulation,[status(thm)],[f85,f491]) ).
fof(f493,plain,
( leq(one,addition(multiplication(one,sk0_2),addition(multiplication(c(sk0_1),c(sk0_2)),multiplication(addition(sk0_2,c(sk0_2)),sk0_1))))
| ~ spl0_0 ),
inference(forward_demodulation,[status(thm)],[f130,f492]) ).
fof(f494,plain,
( leq(one,addition(sk0_2,addition(multiplication(c(sk0_1),c(sk0_2)),multiplication(addition(sk0_2,c(sk0_2)),sk0_1))))
| ~ spl0_0 ),
inference(forward_demodulation,[status(thm)],[f25,f493]) ).
fof(f495,plain,
( leq(one,addition(sk0_2,addition(multiplication(c(sk0_1),c(sk0_2)),multiplication(one,sk0_1))))
| ~ spl0_0 ),
inference(forward_demodulation,[status(thm)],[f83,f494]) ).
fof(f496,plain,
( leq(one,addition(sk0_2,addition(multiplication(one,sk0_1),multiplication(c(sk0_1),c(sk0_2)))))
| ~ spl0_0 ),
inference(forward_demodulation,[status(thm)],[f19,f495]) ).
fof(f497,plain,
( leq(one,addition(sk0_2,addition(sk0_1,multiplication(c(sk0_1),c(sk0_2)))))
| ~ spl0_0 ),
inference(forward_demodulation,[status(thm)],[f25,f496]) ).
fof(f498,plain,
( leq(one,addition(sk0_1,addition(sk0_2,multiplication(c(sk0_1),c(sk0_2)))))
| ~ spl0_0 ),
inference(forward_demodulation,[status(thm)],[f130,f497]) ).
fof(f499,plain,
( addition(one,addition(sk0_1,addition(sk0_2,multiplication(c(sk0_1),c(sk0_2))))) = addition(sk0_1,addition(sk0_2,multiplication(c(sk0_1),c(sk0_2))))
| ~ spl0_0 ),
inference(resolution,[status(thm)],[f498,f32]) ).
fof(f500,plain,
( addition(one,addition(sk0_2,multiplication(c(sk0_1),c(sk0_2)))) = addition(sk0_1,addition(sk0_2,multiplication(c(sk0_1),c(sk0_2))))
| ~ spl0_0 ),
inference(forward_demodulation,[status(thm)],[f197,f499]) ).
fof(f501,plain,
( addition(one,multiplication(c(sk0_1),c(sk0_2))) = addition(sk0_1,addition(sk0_2,multiplication(c(sk0_1),c(sk0_2))))
| ~ spl0_0 ),
inference(forward_demodulation,[status(thm)],[f218,f500]) ).
fof(f503,plain,
( ~ leq(addition(one,multiplication(c(sk0_1),c(sk0_2))),one)
| ~ spl0_0
| spl0_1 ),
inference(backward_demodulation,[status(thm)],[f501,f483]) ).
fof(f1265,plain,
! [X0] : addition(one,addition(c(sk0_2),X0)) = addition(one,X0),
inference(paramodulation,[status(thm)],[f309,f20]) ).
fof(f1655,plain,
( addition(one,multiplication(c(sk0_1),c(sk0_2))) != one
| ~ spl0_0
| spl0_1 ),
inference(resolution,[status(thm)],[f167,f503]) ).
fof(f1684,plain,
( spl0_30
<=> addition(one,sk0_1) = one ),
introduced(split_symbol_definition) ).
fof(f1686,plain,
( addition(one,sk0_1) != one
| spl0_30 ),
inference(component_clause,[status(thm)],[f1684]) ).
fof(f1733,plain,
( one != one
| spl0_30 ),
inference(forward_demodulation,[status(thm)],[f155,f1686]) ).
fof(f1734,plain,
( $false
| spl0_30 ),
inference(trivial_equality_resolution,[status(esa)],[f1733]) ).
fof(f1735,plain,
spl0_30,
inference(contradiction_clause,[status(thm)],[f1734]) ).
fof(f1857,plain,
! [X0] : leq(multiplication(c(sk0_1),X0),multiplication(one,X0)),
inference(paramodulation,[status(thm)],[f305,f446]) ).
fof(f1858,plain,
! [X0] : leq(multiplication(c(sk0_1),X0),X0),
inference(forward_demodulation,[status(thm)],[f25,f1857]) ).
fof(f1885,plain,
! [X0] : addition(multiplication(c(sk0_1),X0),X0) = X0,
inference(resolution,[status(thm)],[f1858,f32]) ).
fof(f1886,plain,
! [X0] : addition(X0,multiplication(c(sk0_1),X0)) = X0,
inference(forward_demodulation,[status(thm)],[f19,f1885]) ).
fof(f1949,plain,
addition(one,c(sk0_2)) = addition(one,multiplication(c(sk0_1),c(sk0_2))),
inference(paramodulation,[status(thm)],[f1886,f1265]) ).
fof(f1950,plain,
one = addition(one,multiplication(c(sk0_1),c(sk0_2))),
inference(forward_demodulation,[status(thm)],[f309,f1949]) ).
fof(f1951,plain,
( $false
| ~ spl0_0
| spl0_1 ),
inference(forward_subsumption_resolution,[status(thm)],[f1950,f1655]) ).
fof(f1952,plain,
( ~ spl0_0
| spl0_1 ),
inference(contradiction_clause,[status(thm)],[f1951]) ).
fof(f1953,plain,
$false,
inference(sat_refutation,[status(thm)],[f63,f468,f1735,f1952]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : KLE010+2 : TPTP v8.1.2. Released v4.0.0.
% 0.11/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.34 % Computer : n010.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue May 30 11:37:07 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.13/0.35 % Drodi V3.5.1
% 0.20/0.56 % Refutation found
% 0.20/0.56 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.20/0.56 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.20/0.58 % Elapsed time: 0.230834 seconds
% 0.20/0.58 % CPU time: 1.720156 seconds
% 0.20/0.58 % Memory used: 81.742 MB
%------------------------------------------------------------------------------