TSTP Solution File: KLE018+1 by Drodi---3.5.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : KLE018+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n022.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 86.60s 11.32s
% Output : CNFRefutation 87.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 42
% Number of leaves : 19
% Syntax : Number of formulae : 163 ( 85 unt; 0 def)
% Number of atoms : 307 ( 163 equ)
% Maximal formula atoms : 8 ( 1 avg)
% Number of connectives : 254 ( 110 ~; 102 |; 27 &)
% ( 9 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 9 ( 7 usr; 5 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 184 (; 178 !; 6 ?)
% 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(f10,axiom,
! [A] : multiplication(A,zero) = zero,
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(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(f16,axiom,
! [X0] :
( ~ test(X0)
=> c(X0) = zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,conjecture,
! [X0,X1,X2] :
( ( test(X0)
& test(X1)
& test(X2) )
=> ( leq(multiplication(X0,c(X1)),X2)
=> leq(X0,addition(X1,X2)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
~ ! [X0,X1,X2] :
( ( test(X0)
& test(X1)
& test(X2) )
=> ( leq(multiplication(X0,c(X1)),X2)
=> leq(X0,addition(X1,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(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(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(f28,plain,
! [X0] : multiplication(X0,zero) = zero,
inference(cnf_transformation,[status(esa)],[f10]) ).
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(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(f38,plain,
! [X0,X1] :
( test(X0)
| ~ complement(X1,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(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(f48,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,
? [X0,X1,X2] :
( test(X0)
& test(X1)
& test(X2)
& leq(multiplication(X0,c(X1)),X2)
& ~ leq(X0,addition(X1,X2)) ),
inference(pre_NNF_transformation,[status(esa)],[f18]) ).
fof(f53,plain,
( test(sk0_1)
& test(sk0_2)
& test(sk0_3)
& leq(multiplication(sk0_1,c(sk0_2)),sk0_3)
& ~ leq(sk0_1,addition(sk0_2,sk0_3)) ),
inference(skolemization,[status(esa)],[f52]) ).
fof(f54,plain,
test(sk0_1),
inference(cnf_transformation,[status(esa)],[f53]) ).
fof(f55,plain,
test(sk0_2),
inference(cnf_transformation,[status(esa)],[f53]) ).
fof(f56,plain,
test(sk0_3),
inference(cnf_transformation,[status(esa)],[f53]) ).
fof(f57,plain,
leq(multiplication(sk0_1,c(sk0_2)),sk0_3),
inference(cnf_transformation,[status(esa)],[f53]) ).
fof(f58,plain,
~ leq(sk0_1,addition(sk0_2,sk0_3)),
inference(cnf_transformation,[status(esa)],[f53]) ).
fof(f59,plain,
! [X0] :
( ~ test(X0)
| complement(X0,c(X0)) ),
inference(destructive_equality_resolution,[status(esa)],[f48]) ).
fof(f60,plain,
addition(multiplication(sk0_1,c(sk0_2)),sk0_3) = sk0_3,
inference(resolution,[status(thm)],[f32,f57]) ).
fof(f61,plain,
addition(sk0_3,multiplication(sk0_1,c(sk0_2))) = sk0_3,
inference(forward_demodulation,[status(thm)],[f19,f60]) ).
fof(f65,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X2,addition(X0,X1)),
inference(paramodulation,[status(thm)],[f19,f20]) ).
fof(f70,plain,
! [X0,X1] : addition(X0,addition(X0,X1)) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f22,f20]) ).
fof(f71,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(addition(X1,X0),X2),
inference(paramodulation,[status(thm)],[f19,f20]) ).
fof(f72,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X1,addition(X0,X2)),
inference(forward_demodulation,[status(thm)],[f20,f71]) ).
fof(f84,plain,
! [X0,X1] : addition(X0,addition(X1,X0)) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f19,f70]) ).
fof(f118,plain,
! [X0] : addition(zero,X0) = X0,
inference(paramodulation,[status(thm)],[f19,f21]) ).
fof(f162,plain,
! [X0] :
( multiplication(sk0_0(X0),X0) = zero
| ~ test(X0) ),
inference(resolution,[status(thm)],[f42,f37]) ).
fof(f164,plain,
! [X0] :
( addition(X0,sk0_0(X0)) = one
| ~ test(X0) ),
inference(resolution,[status(thm)],[f43,f37]) ).
fof(f165,plain,
! [X0] :
( addition(c(X0),X0) = one
| ~ test(X0) ),
inference(resolution,[status(thm)],[f43,f59]) ).
fof(f166,plain,
! [X0] :
( addition(X0,c(X0)) = one
| ~ test(X0) ),
inference(forward_demodulation,[status(thm)],[f19,f165]) ).
fof(f207,plain,
! [X0,X1] : multiplication(addition(one,X0),X1) = addition(X1,multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f25,f27]) ).
fof(f239,plain,
! [X0,X1] :
( multiplication(X0,X1) != zero
| multiplication(X1,X0) != zero
| addition(X0,X1) != one
| test(X0) ),
inference(resolution,[status(thm)],[f44,f38]) ).
fof(f242,plain,
! [X0] : addition(sk0_3,addition(multiplication(sk0_1,c(sk0_2)),X0)) = addition(sk0_3,X0),
inference(paramodulation,[status(thm)],[f61,f20]) ).
fof(f249,plain,
! [X0] : addition(sk0_3,addition(multiplication(sk0_1,c(sk0_2)),X0)) = addition(sk0_3,addition(X0,multiplication(sk0_1,c(sk0_2)))),
inference(paramodulation,[status(thm)],[f84,f242]) ).
fof(f250,plain,
! [X0] : addition(sk0_3,X0) = addition(sk0_3,addition(X0,multiplication(sk0_1,c(sk0_2)))),
inference(forward_demodulation,[status(thm)],[f242,f249]) ).
fof(f268,plain,
! [X0] : addition(sk0_3,multiplication(sk0_1,X0)) = addition(sk0_3,multiplication(sk0_1,addition(X0,c(sk0_2)))),
inference(paramodulation,[status(thm)],[f26,f250]) ).
fof(f274,plain,
! [X0] : addition(addition(X0,multiplication(sk0_1,c(sk0_2))),addition(sk0_3,X0)) = addition(addition(X0,multiplication(sk0_1,c(sk0_2))),sk0_3),
inference(paramodulation,[status(thm)],[f250,f84]) ).
fof(f275,plain,
! [X0] : addition(X0,addition(multiplication(sk0_1,c(sk0_2)),addition(sk0_3,X0))) = addition(addition(X0,multiplication(sk0_1,c(sk0_2))),sk0_3),
inference(forward_demodulation,[status(thm)],[f20,f274]) ).
fof(f276,plain,
! [X0] : addition(X0,addition(multiplication(sk0_1,c(sk0_2)),addition(sk0_3,X0))) = addition(X0,addition(multiplication(sk0_1,c(sk0_2)),sk0_3)),
inference(forward_demodulation,[status(thm)],[f20,f275]) ).
fof(f277,plain,
! [X0] : addition(X0,addition(multiplication(sk0_1,c(sk0_2)),addition(sk0_3,X0))) = addition(X0,addition(sk0_3,multiplication(sk0_1,c(sk0_2)))),
inference(forward_demodulation,[status(thm)],[f19,f276]) ).
fof(f278,plain,
! [X0] : addition(X0,addition(multiplication(sk0_1,c(sk0_2)),addition(sk0_3,X0))) = addition(X0,sk0_3),
inference(forward_demodulation,[status(thm)],[f61,f277]) ).
fof(f281,plain,
! [X0,X1] : addition(sk0_3,addition(addition(X0,multiplication(sk0_1,c(sk0_2))),X1)) = addition(addition(sk0_3,X0),X1),
inference(paramodulation,[status(thm)],[f250,f20]) ).
fof(f282,plain,
! [X0,X1] : addition(sk0_3,addition(X0,addition(multiplication(sk0_1,c(sk0_2)),X1))) = addition(addition(sk0_3,X0),X1),
inference(forward_demodulation,[status(thm)],[f20,f281]) ).
fof(f283,plain,
! [X0,X1] : addition(sk0_3,addition(X0,addition(multiplication(sk0_1,c(sk0_2)),X1))) = addition(sk0_3,addition(X0,X1)),
inference(forward_demodulation,[status(thm)],[f20,f282]) ).
fof(f628,plain,
! [X0,X1] : addition(sk0_3,addition(addition(multiplication(sk0_1,c(sk0_2)),X0),X1)) = addition(sk0_3,addition(X1,X0)),
inference(paramodulation,[status(thm)],[f19,f283]) ).
fof(f629,plain,
! [X0,X1] : addition(sk0_3,addition(multiplication(sk0_1,c(sk0_2)),addition(X0,X1))) = addition(sk0_3,addition(X1,X0)),
inference(forward_demodulation,[status(thm)],[f20,f628]) ).
fof(f630,plain,
! [X0,X1] : addition(sk0_3,addition(X0,X1)) = addition(sk0_3,addition(X1,X0)),
inference(forward_demodulation,[status(thm)],[f242,f629]) ).
fof(f694,plain,
! [X0,X1,X2] : addition(sk0_3,addition(X0,addition(X1,X2))) = addition(sk0_3,addition(X2,addition(X0,X1))),
inference(paramodulation,[status(thm)],[f20,f630]) ).
fof(f907,plain,
! [X0,X1] : addition(sk0_3,addition(X0,X1)) = addition(sk0_3,addition(X1,addition(sk0_3,X0))),
inference(paramodulation,[status(thm)],[f70,f694]) ).
fof(f1378,plain,
! [X0,X1] : addition(addition(X0,addition(sk0_3,X1)),addition(multiplication(sk0_1,c(sk0_2)),addition(sk0_3,addition(X1,X0)))) = addition(addition(X0,addition(sk0_3,X1)),sk0_3),
inference(paramodulation,[status(thm)],[f907,f278]) ).
fof(f1379,plain,
! [X0,X1] : addition(X0,addition(addition(sk0_3,X1),addition(multiplication(sk0_1,c(sk0_2)),addition(sk0_3,addition(X1,X0))))) = addition(addition(X0,addition(sk0_3,X1)),sk0_3),
inference(forward_demodulation,[status(thm)],[f20,f1378]) ).
fof(f1380,plain,
! [X0,X1] : addition(X0,addition(sk0_3,addition(X1,addition(multiplication(sk0_1,c(sk0_2)),addition(sk0_3,addition(X1,X0)))))) = addition(addition(X0,addition(sk0_3,X1)),sk0_3),
inference(forward_demodulation,[status(thm)],[f20,f1379]) ).
fof(f1381,plain,
! [X0,X1] : addition(X0,addition(sk0_3,addition(X1,addition(sk0_3,addition(X1,X0))))) = addition(addition(X0,addition(sk0_3,X1)),sk0_3),
inference(forward_demodulation,[status(thm)],[f283,f1380]) ).
fof(f1382,plain,
! [X0,X1] : addition(X0,addition(sk0_3,addition(addition(X1,X0),X1))) = addition(addition(X0,addition(sk0_3,X1)),sk0_3),
inference(forward_demodulation,[status(thm)],[f907,f1381]) ).
fof(f1383,plain,
! [X0,X1] : addition(X0,addition(sk0_3,addition(X1,addition(X1,X0)))) = addition(addition(X0,addition(sk0_3,X1)),sk0_3),
inference(forward_demodulation,[status(thm)],[f630,f1382]) ).
fof(f1384,plain,
! [X0,X1] : addition(X0,addition(sk0_3,addition(X1,X0))) = addition(addition(X0,addition(sk0_3,X1)),sk0_3),
inference(forward_demodulation,[status(thm)],[f70,f1383]) ).
fof(f1385,plain,
! [X0,X1] : addition(X0,addition(sk0_3,addition(X1,X0))) = addition(X0,addition(addition(sk0_3,X1),sk0_3)),
inference(forward_demodulation,[status(thm)],[f20,f1384]) ).
fof(f1386,plain,
! [X0,X1] : addition(X0,addition(sk0_3,addition(X1,X0))) = addition(X0,addition(sk0_3,addition(X1,sk0_3))),
inference(forward_demodulation,[status(thm)],[f20,f1385]) ).
fof(f1387,plain,
! [X0,X1] : addition(X0,addition(sk0_3,addition(X1,X0))) = addition(X0,addition(sk0_3,X1)),
inference(forward_demodulation,[status(thm)],[f84,f1386]) ).
fof(f1472,plain,
! [X0,X1] : addition(X0,addition(sk0_3,addition(X0,X1))) = addition(X0,addition(sk0_3,X1)),
inference(paramodulation,[status(thm)],[f630,f1387]) ).
fof(f2769,plain,
addition(sk0_3,c(sk0_3)) = one,
inference(resolution,[status(thm)],[f166,f56]) ).
fof(f2770,plain,
addition(sk0_2,c(sk0_2)) = one,
inference(resolution,[status(thm)],[f166,f55]) ).
fof(f2771,plain,
addition(sk0_1,c(sk0_1)) = one,
inference(resolution,[status(thm)],[f166,f54]) ).
fof(f2772,plain,
! [X0] :
( addition(X0,c(X0)) = one
| c(X0) = zero ),
inference(resolution,[status(thm)],[f166,f51]) ).
fof(f2775,plain,
addition(sk0_3,addition(sk0_3,one)) = addition(sk0_3,addition(sk0_3,c(sk0_3))),
inference(paramodulation,[status(thm)],[f2769,f1472]) ).
fof(f2776,plain,
addition(sk0_3,addition(one,sk0_3)) = addition(sk0_3,addition(sk0_3,c(sk0_3))),
inference(forward_demodulation,[status(thm)],[f630,f2775]) ).
fof(f2777,plain,
addition(sk0_3,one) = addition(sk0_3,addition(sk0_3,c(sk0_3))),
inference(forward_demodulation,[status(thm)],[f84,f2776]) ).
fof(f2778,plain,
addition(one,sk0_3) = addition(sk0_3,addition(sk0_3,c(sk0_3))),
inference(forward_demodulation,[status(thm)],[f19,f2777]) ).
fof(f2779,plain,
addition(one,sk0_3) = addition(sk0_3,c(sk0_3)),
inference(forward_demodulation,[status(thm)],[f70,f2778]) ).
fof(f2780,plain,
addition(one,sk0_3) = one,
inference(forward_demodulation,[status(thm)],[f2769,f2779]) ).
fof(f3209,plain,
! [X0] : addition(one,addition(sk0_3,X0)) = addition(X0,one),
inference(paramodulation,[status(thm)],[f2780,f65]) ).
fof(f3306,plain,
addition(sk0_1,one) = addition(sk0_1,c(sk0_1)),
inference(paramodulation,[status(thm)],[f2771,f70]) ).
fof(f3307,plain,
addition(one,sk0_1) = addition(sk0_1,c(sk0_1)),
inference(forward_demodulation,[status(thm)],[f19,f3306]) ).
fof(f3308,plain,
addition(one,sk0_1) = one,
inference(forward_demodulation,[status(thm)],[f2771,f3307]) ).
fof(f3476,plain,
! [X0,X1,X2] : addition(addition(X0,X1),X2) = addition(X0,addition(X2,X1)),
inference(paramodulation,[status(thm)],[f19,f72]) ).
fof(f3477,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X0,addition(X2,X1)),
inference(forward_demodulation,[status(thm)],[f20,f3476]) ).
fof(f5389,plain,
( spl0_2
<=> c(sk0_2) = zero ),
introduced(split_symbol_definition) ).
fof(f5390,plain,
( c(sk0_2) = zero
| ~ spl0_2 ),
inference(component_clause,[status(thm)],[f5389]) ).
fof(f5481,plain,
( spl0_13
<=> multiplication(c(sk0_2),zero) = zero ),
introduced(split_symbol_definition) ).
fof(f5483,plain,
( multiplication(c(sk0_2),zero) != zero
| spl0_13 ),
inference(component_clause,[status(thm)],[f5481]) ).
fof(f5641,plain,
( spl0_38
<=> addition(sk0_3,multiplication(sk0_1,sk0_2)) = addition(sk0_3,multiplication(sk0_1,one)) ),
introduced(split_symbol_definition) ).
fof(f5642,plain,
( addition(sk0_3,multiplication(sk0_1,sk0_2)) = addition(sk0_3,multiplication(sk0_1,one))
| ~ spl0_38 ),
inference(component_clause,[status(thm)],[f5641]) ).
fof(f5644,plain,
( addition(sk0_3,multiplication(sk0_1,sk0_2)) = addition(sk0_3,multiplication(sk0_1,one))
| c(sk0_2) = zero ),
inference(paramodulation,[status(thm)],[f2772,f268]) ).
fof(f5645,plain,
( spl0_38
| spl0_2 ),
inference(split_clause,[status(thm)],[f5644,f5641,f5389]) ).
fof(f5907,plain,
addition(sk0_2,sk0_0(sk0_2)) = one,
inference(resolution,[status(thm)],[f164,f55]) ).
fof(f7159,plain,
( addition(sk0_2,zero) = one
| ~ spl0_2 ),
inference(backward_demodulation,[status(thm)],[f5390,f2770]) ).
fof(f7160,plain,
( sk0_2 = one
| ~ spl0_2 ),
inference(forward_demodulation,[status(thm)],[f21,f7159]) ).
fof(f7221,plain,
( addition(sk0_3,multiplication(sk0_1,sk0_2)) = addition(sk0_3,sk0_1)
| ~ spl0_38 ),
inference(forward_demodulation,[status(thm)],[f24,f5642]) ).
fof(f7222,plain,
( addition(sk0_3,multiplication(sk0_1,sk0_2)) = addition(sk0_1,sk0_3)
| ~ spl0_38 ),
inference(forward_demodulation,[status(thm)],[f19,f7221]) ).
fof(f7280,plain,
( spl0_71
<=> test(one) ),
introduced(split_symbol_definition) ).
fof(f7281,plain,
( test(one)
| ~ spl0_71 ),
inference(component_clause,[status(thm)],[f7280]) ).
fof(f7282,plain,
( ~ test(one)
| spl0_71 ),
inference(component_clause,[status(thm)],[f7280]) ).
fof(f8903,plain,
! [X0] : multiplication(one,X0) = addition(X0,multiplication(sk0_1,X0)),
inference(paramodulation,[status(thm)],[f3308,f207]) ).
fof(f8904,plain,
! [X0] : X0 = addition(X0,multiplication(sk0_1,X0)),
inference(forward_demodulation,[status(thm)],[f25,f8903]) ).
fof(f9893,plain,
! [X0,X1] : addition(X0,addition(X1,multiplication(sk0_1,X0))) = addition(X1,X0),
inference(paramodulation,[status(thm)],[f8904,f72]) ).
fof(f28898,plain,
! [X0] : X0 = addition(X0,zero),
inference(paramodulation,[status(thm)],[f118,f19]) ).
fof(f29805,plain,
addition(sk0_1,addition(sk0_2,sk0_3)) != addition(sk0_2,sk0_3),
inference(resolution,[status(thm)],[f58,f33]) ).
fof(f33366,plain,
! [X0] :
( multiplication(one,X0) != zero
| multiplication(X0,one) != zero
| addition(one,X0) != one
| spl0_71 ),
inference(resolution,[status(thm)],[f7282,f239]) ).
fof(f33367,plain,
! [X0] :
( X0 != zero
| multiplication(X0,one) != zero
| addition(one,X0) != one
| spl0_71 ),
inference(forward_demodulation,[status(thm)],[f25,f33366]) ).
fof(f33368,plain,
! [X0] :
( X0 != zero
| X0 != zero
| addition(one,X0) != one
| spl0_71 ),
inference(forward_demodulation,[status(thm)],[f24,f33367]) ).
fof(f33369,plain,
! [X0] :
( X0 != zero
| addition(one,X0) != one
| spl0_71 ),
inference(duplicate_literals_removal,[status(esa)],[f33368]) ).
fof(f33370,plain,
( addition(one,zero) != one
| spl0_71 ),
inference(destructive_equality_resolution,[status(esa)],[f33369]) ).
fof(f33371,plain,
( $false
| spl0_71 ),
inference(forward_subsumption_resolution,[status(thm)],[f33370,f28898]) ).
fof(f33372,plain,
spl0_71,
inference(contradiction_clause,[status(thm)],[f33371]) ).
fof(f33455,plain,
( multiplication(sk0_0(one),one) = zero
| ~ spl0_71 ),
inference(resolution,[status(thm)],[f7281,f162]) ).
fof(f33456,plain,
( sk0_0(one) = zero
| ~ spl0_71 ),
inference(forward_demodulation,[status(thm)],[f24,f33455]) ).
fof(f62488,plain,
( addition(sk0_2,addition(sk0_1,sk0_3)) = addition(sk0_3,sk0_2)
| ~ spl0_38 ),
inference(paramodulation,[status(thm)],[f7222,f9893]) ).
fof(f62489,plain,
( addition(sk0_1,addition(sk0_3,sk0_2)) = addition(sk0_3,sk0_2)
| ~ spl0_38 ),
inference(forward_demodulation,[status(thm)],[f65,f62488]) ).
fof(f62490,plain,
( addition(sk0_1,addition(sk0_2,sk0_3)) = addition(sk0_3,sk0_2)
| ~ spl0_38 ),
inference(forward_demodulation,[status(thm)],[f3477,f62489]) ).
fof(f62491,plain,
( addition(sk0_1,addition(sk0_2,sk0_3)) = addition(sk0_2,sk0_3)
| ~ spl0_38 ),
inference(forward_demodulation,[status(thm)],[f19,f62490]) ).
fof(f62492,plain,
( $false
| ~ spl0_38 ),
inference(forward_subsumption_resolution,[status(thm)],[f62491,f29805]) ).
fof(f62493,plain,
~ spl0_38,
inference(contradiction_clause,[status(thm)],[f62492]) ).
fof(f62517,plain,
( addition(sk0_2,sk0_0(one)) = one
| ~ spl0_2 ),
inference(backward_demodulation,[status(thm)],[f7160,f5907]) ).
fof(f62518,plain,
( addition(sk0_2,zero) = one
| ~ spl0_71
| ~ spl0_2 ),
inference(forward_demodulation,[status(thm)],[f33456,f62517]) ).
fof(f62519,plain,
( sk0_2 = one
| ~ spl0_71
| ~ spl0_2 ),
inference(forward_demodulation,[status(thm)],[f28898,f62518]) ).
fof(f62619,plain,
( zero != zero
| spl0_13 ),
inference(forward_demodulation,[status(thm)],[f28,f5483]) ).
fof(f62620,plain,
( $false
| spl0_13 ),
inference(trivial_equality_resolution,[status(esa)],[f62619]) ).
fof(f62621,plain,
spl0_13,
inference(contradiction_clause,[status(thm)],[f62620]) ).
fof(f62863,plain,
( addition(sk0_1,addition(sk0_2,sk0_3)) != addition(one,sk0_3)
| ~ spl0_71
| ~ spl0_2 ),
inference(backward_demodulation,[status(thm)],[f62519,f29805]) ).
fof(f62864,plain,
( addition(sk0_1,addition(one,sk0_3)) != addition(one,sk0_3)
| ~ spl0_71
| ~ spl0_2 ),
inference(forward_demodulation,[status(thm)],[f62519,f62863]) ).
fof(f62865,plain,
( addition(one,addition(sk0_3,sk0_1)) != addition(one,sk0_3)
| ~ spl0_71
| ~ spl0_2 ),
inference(forward_demodulation,[status(thm)],[f65,f62864]) ).
fof(f62866,plain,
( addition(sk0_1,one) != addition(one,sk0_3)
| ~ spl0_71
| ~ spl0_2 ),
inference(forward_demodulation,[status(thm)],[f3209,f62865]) ).
fof(f62867,plain,
( addition(one,sk0_1) != addition(one,sk0_3)
| ~ spl0_71
| ~ spl0_2 ),
inference(forward_demodulation,[status(thm)],[f19,f62866]) ).
fof(f62868,plain,
( one != addition(one,sk0_3)
| ~ spl0_71
| ~ spl0_2 ),
inference(forward_demodulation,[status(thm)],[f3308,f62867]) ).
fof(f62869,plain,
( one != one
| ~ spl0_71
| ~ spl0_2 ),
inference(forward_demodulation,[status(thm)],[f2780,f62868]) ).
fof(f62870,plain,
( $false
| ~ spl0_71
| ~ spl0_2 ),
inference(trivial_equality_resolution,[status(esa)],[f62869]) ).
fof(f62871,plain,
( ~ spl0_71
| ~ spl0_2 ),
inference(contradiction_clause,[status(thm)],[f62870]) ).
fof(f62872,plain,
$false,
inference(sat_refutation,[status(thm)],[f5645,f33372,f62493,f62621,f62871]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : KLE018+1 : TPTP v8.1.2. Released v4.0.0.
% 0.03/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.34 % Computer : n022.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 11:45:42 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.13/0.35 % Drodi V3.5.1
% 86.60/11.32 % Refutation found
% 86.60/11.32 % SZS status Theorem for theBenchmark: Theorem is valid
% 86.60/11.32 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 87.94/11.52 % Elapsed time: 11.155812 seconds
% 87.94/11.52 % CPU time: 87.929061 seconds
% 87.94/11.52 % Memory used: 574.859 MB
%------------------------------------------------------------------------------