TSTP Solution File: KLE008+1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : KLE008+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n016.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 13:11:26 EDT 2024
% Result : Theorem 4.15s 0.94s
% Output : Refutation 4.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 39
% Syntax : Number of formulae : 571 ( 268 unt; 0 def)
% Number of atoms : 1046 ( 573 equ)
% Maximal formula atoms : 14 ( 1 avg)
% Number of connectives : 833 ( 358 ~; 399 |; 35 &)
% ( 31 <=>; 9 =>; 0 <=; 1 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 25 ( 23 usr; 21 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 698 ( 681 !; 17 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f21445,plain,
$false,
inference(avatar_sat_refutation,[],[f77,f147,f179,f211,f222,f292,f813,f836,f838,f910,f1115,f1117,f1265,f1267,f4541,f11922,f11933,f12609,f20647,f20965,f20968,f21425,f21429,f21432]) ).
fof(f21432,plain,
( ~ spl4_1
| spl4_2 ),
inference(avatar_contradiction_clause,[],[f21431]) ).
fof(f21431,plain,
( $false
| ~ spl4_1
| spl4_2 ),
inference(subsumption_resolution,[],[f21430,f75]) ).
fof(f75,plain,
( ~ leq(sK0,sK1)
| spl4_2 ),
inference(avatar_component_clause,[],[f74]) ).
fof(f74,plain,
( spl4_2
<=> leq(sK0,sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_2])]) ).
fof(f21430,plain,
( leq(sK0,sK1)
| ~ spl4_1 ),
inference(forward_demodulation,[],[f21409,f49]) ).
fof(f49,plain,
! [X0] : addition(X0,X0) = X0,
inference(cnf_transformation,[],[f4]) ).
fof(f4,axiom,
! [X0] : addition(X0,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_idempotence) ).
fof(f21409,plain,
( leq(sK0,addition(sK1,sK1))
| ~ spl4_1 ),
inference(superposition,[],[f1229,f21291]) ).
fof(f21291,plain,
( sK1 = addition(sK0,sK1)
| ~ spl4_1 ),
inference(superposition,[],[f20893,f3512]) ).
fof(f3512,plain,
! [X0] : addition(multiplication(sK2,X0),X0) = X0,
inference(forward_demodulation,[],[f3431,f48]) ).
fof(f48,plain,
! [X0] : multiplication(one,X0) = X0,
inference(cnf_transformation,[],[f7]) ).
fof(f7,axiom,
! [X0] : multiplication(one,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_left_identity) ).
fof(f3431,plain,
! [X0] : multiplication(one,X0) = addition(multiplication(sK2,X0),X0),
inference(superposition,[],[f519,f869]) ).
fof(f869,plain,
one = addition(sK2,one),
inference(superposition,[],[f225,f134]) ).
fof(f134,plain,
one = addition(sK2,sK3(sK2)),
inference(resolution,[],[f90,f40]) ).
fof(f40,plain,
test(sK2),
inference(cnf_transformation,[],[f31]) ).
fof(f31,plain,
( ( ~ leq(multiplication(c(sK2),sK0),zero)
| ~ leq(sK0,sK1)
| ~ leq(sK0,multiplication(sK2,sK1)) )
& ( ( leq(multiplication(c(sK2),sK0),zero)
& leq(sK0,sK1) )
| leq(sK0,multiplication(sK2,sK1)) )
& test(sK2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f29,f30]) ).
fof(f30,plain,
( ? [X0,X1,X2] :
( ( ~ leq(multiplication(c(X2),X0),zero)
| ~ leq(X0,X1)
| ~ leq(X0,multiplication(X2,X1)) )
& ( ( leq(multiplication(c(X2),X0),zero)
& leq(X0,X1) )
| leq(X0,multiplication(X2,X1)) )
& test(X2) )
=> ( ( ~ leq(multiplication(c(sK2),sK0),zero)
| ~ leq(sK0,sK1)
| ~ leq(sK0,multiplication(sK2,sK1)) )
& ( ( leq(multiplication(c(sK2),sK0),zero)
& leq(sK0,sK1) )
| leq(sK0,multiplication(sK2,sK1)) )
& test(sK2) ) ),
introduced(choice_axiom,[]) ).
fof(f29,plain,
? [X0,X1,X2] :
( ( ~ leq(multiplication(c(X2),X0),zero)
| ~ leq(X0,X1)
| ~ leq(X0,multiplication(X2,X1)) )
& ( ( leq(multiplication(c(X2),X0),zero)
& leq(X0,X1) )
| leq(X0,multiplication(X2,X1)) )
& test(X2) ),
inference(flattening,[],[f28]) ).
fof(f28,plain,
? [X0,X1,X2] :
( ( ~ leq(multiplication(c(X2),X0),zero)
| ~ leq(X0,X1)
| ~ leq(X0,multiplication(X2,X1)) )
& ( ( leq(multiplication(c(X2),X0),zero)
& leq(X0,X1) )
| leq(X0,multiplication(X2,X1)) )
& test(X2) ),
inference(nnf_transformation,[],[f25]) ).
fof(f25,plain,
? [X0,X1,X2] :
( ( leq(X0,multiplication(X2,X1))
<~> ( leq(multiplication(c(X2),X0),zero)
& leq(X0,X1) ) )
& test(X2) ),
inference(ennf_transformation,[],[f19]) ).
fof(f19,plain,
~ ! [X0,X1,X2] :
( test(X2)
=> ( leq(X0,multiplication(X2,X1))
<=> ( leq(multiplication(c(X2),X0),zero)
& leq(X0,X1) ) ) ),
inference(rectify,[],[f18]) ).
fof(f18,negated_conjecture,
~ ! [X3,X4,X5] :
( test(X5)
=> ( leq(X3,multiplication(X5,X4))
<=> ( leq(multiplication(c(X5),X3),zero)
& leq(X3,X4) ) ) ),
inference(negated_conjecture,[],[f17]) ).
fof(f17,conjecture,
! [X3,X4,X5] :
( test(X5)
=> ( leq(X3,multiplication(X5,X4))
<=> ( leq(multiplication(c(X5),X3),zero)
& leq(X3,X4) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f90,plain,
! [X0] :
( ~ test(X0)
| one = addition(X0,sK3(X0)) ),
inference(resolution,[],[f58,f51]) ).
fof(f51,plain,
! [X0] :
( complement(sK3(X0),X0)
| ~ test(X0) ),
inference(cnf_transformation,[],[f35]) ).
fof(f35,plain,
! [X0] :
( ( test(X0)
| ! [X1] : ~ complement(X1,X0) )
& ( complement(sK3(X0),X0)
| ~ test(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f33,f34]) ).
fof(f34,plain,
! [X0] :
( ? [X2] : complement(X2,X0)
=> complement(sK3(X0),X0) ),
introduced(choice_axiom,[]) ).
fof(f33,plain,
! [X0] :
( ( test(X0)
| ! [X1] : ~ complement(X1,X0) )
& ( ? [X2] : complement(X2,X0)
| ~ test(X0) ) ),
inference(rectify,[],[f32]) ).
fof(f32,plain,
! [X0] :
( ( test(X0)
| ! [X1] : ~ complement(X1,X0) )
& ( ? [X1] : complement(X1,X0)
| ~ test(X0) ) ),
inference(nnf_transformation,[],[f21]) ).
fof(f21,plain,
! [X0] :
( test(X0)
<=> ? [X1] : complement(X1,X0) ),
inference(rectify,[],[f13]) ).
fof(f13,axiom,
! [X3] :
( test(X3)
<=> ? [X4] : complement(X4,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',test_1) ).
fof(f58,plain,
! [X0,X1] :
( ~ complement(X1,X0)
| addition(X0,X1) = one ),
inference(cnf_transformation,[],[f38]) ).
fof(f38,plain,
! [X0,X1] :
( ( complement(X1,X0)
| addition(X0,X1) != one
| zero != multiplication(X1,X0)
| zero != multiplication(X0,X1) )
& ( ( addition(X0,X1) = one
& zero = multiplication(X1,X0)
& zero = multiplication(X0,X1) )
| ~ complement(X1,X0) ) ),
inference(flattening,[],[f37]) ).
fof(f37,plain,
! [X0,X1] :
( ( complement(X1,X0)
| addition(X0,X1) != one
| zero != multiplication(X1,X0)
| zero != multiplication(X0,X1) )
& ( ( addition(X0,X1) = one
& zero = multiplication(X1,X0)
& zero = multiplication(X0,X1) )
| ~ complement(X1,X0) ) ),
inference(nnf_transformation,[],[f23]) ).
fof(f23,plain,
! [X0,X1] :
( complement(X1,X0)
<=> ( addition(X0,X1) = one
& zero = multiplication(X1,X0)
& zero = multiplication(X0,X1) ) ),
inference(rectify,[],[f14]) ).
fof(f14,axiom,
! [X3,X4] :
( complement(X4,X3)
<=> ( one = addition(X3,X4)
& zero = multiplication(X4,X3)
& zero = multiplication(X3,X4) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',test_2) ).
fof(f225,plain,
! [X0,X1] : addition(X0,X1) = addition(X0,addition(X0,X1)),
inference(superposition,[],[f62,f49]) ).
fof(f62,plain,
! [X2,X0,X1] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
inference(cnf_transformation,[],[f24]) ).
fof(f24,plain,
! [X0,X1,X2] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
inference(rectify,[],[f2]) ).
fof(f2,axiom,
! [X2,X1,X0] : addition(X0,addition(X1,X2)) = addition(addition(X0,X1),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_associativity) ).
fof(f519,plain,
! [X0,X1] : multiplication(addition(X1,one),X0) = addition(multiplication(X1,X0),X0),
inference(superposition,[],[f65,f48]) ).
fof(f65,plain,
! [X2,X0,X1] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
inference(cnf_transformation,[],[f9]) ).
fof(f9,axiom,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_distributivity) ).
fof(f20893,plain,
( ! [X0] : addition(multiplication(sK2,sK1),X0) = addition(sK0,addition(multiplication(sK2,sK1),X0))
| ~ spl4_1 ),
inference(superposition,[],[f62,f20679]) ).
fof(f20679,plain,
( multiplication(sK2,sK1) = addition(sK0,multiplication(sK2,sK1))
| ~ spl4_1 ),
inference(resolution,[],[f72,f60]) ).
fof(f60,plain,
! [X0,X1] :
( ~ leq(X0,X1)
| addition(X0,X1) = X1 ),
inference(cnf_transformation,[],[f39]) ).
fof(f39,plain,
! [X0,X1] :
( ( leq(X0,X1)
| addition(X0,X1) != X1 )
& ( addition(X0,X1) = X1
| ~ leq(X0,X1) ) ),
inference(nnf_transformation,[],[f12]) ).
fof(f12,axiom,
! [X0,X1] :
( leq(X0,X1)
<=> addition(X0,X1) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',order) ).
fof(f72,plain,
( leq(sK0,multiplication(sK2,sK1))
| ~ spl4_1 ),
inference(avatar_component_clause,[],[f70]) ).
fof(f70,plain,
( spl4_1
<=> leq(sK0,multiplication(sK2,sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_1])]) ).
fof(f1229,plain,
! [X0,X1] : leq(X0,addition(X1,addition(X0,X1))),
inference(global_subsumption,[],[f43,f42,f40,f44,f45,f46,f47,f48,f49,f52,f50,f51,f66,f68,f41,f53,f79,f80,f81,f78,f56,f57,f58,f60,f61,f97,f102,f101,f94,f86,f108,f106,f87,f110,f111,f109,f88,f113,f114,f112,f89,f116,f117,f115,f90,f135,f136,f134,f137,f138,f55,f92,f152,f153,f151,f154,f96,f164,f165,f170,f169,f105,f182,f186,f187,f181,f148,f200,f107,f202,f201,f62,f247,f227,f250,f233,f234,f238,f239,f242,f243,f244,f245,f246,f63,f312,f307,f310,f64,f386,f417,f421,f423,f425,f426,f427,f397,f429,f433,f435,f437,f438,f439,f408,f409,f411,f412,f413,f414,f415,f316,f487,f488,f65,f541,f505,f506,f543,f545,f547,f548,f549,f553,f518,f519,f555,f557,f559,f560,f561,f529,f530,f533,f534,f535,f536,f537,f318,f574,f575,f576,f577,f319,f593,f594,f595,f596,f320,f612,f613,f614,f615,f59,f723,f724,f725,f695,f729,f733,f743,f745,f749,f731,f750,f738,f756,f759,f768,f762,f763,f764,f765,f766,f767,f741,f773,f774,f775,f776,f777,f778,f779,f747,f785,f760,f800,f801,f721,f810,f806,f809,f820,f770,f823,f727,f829,f832,f834,f225,f854,f855,f859,f863,f864,f870,f896,f882,f899,f869,f901,f903,f906,f907,f908,f824,f911,f912,f155,f913,f900,f916,f226,f976,f977,f978,f979,f980,f931,f932,f933,f934,f984,f939,f940,f941,f985,f943,f944,f987,f988,f948,f990,f952,f953,f954,f956,f957,f994,f995,f865,f998,f999,f1000,f1002,f1005,f1006,f997,f1009,f1012,f895,f1017,f1021,f1022,f1026,f1027,f1016,f1038,f1045,f1046,f1050,f1051,f237,f1185,f1186,f1126,f1127,f1203,f1204,f1147,f1148,f1223,f1224,f1226,f1163]) ).
fof(f1163,plain,
! [X0,X1] :
( addition(X0,X1) != addition(X1,addition(X0,X1))
| leq(X0,addition(X1,addition(X0,X1))) ),
inference(superposition,[],[f61,f237]) ).
fof(f1226,plain,
! [X0] :
( zero != addition(X0,X0)
| zero = X0 ),
inference(forward_demodulation,[],[f1225,f78]) ).
fof(f1225,plain,
! [X0] :
( zero = X0
| zero != addition(X0,addition(zero,X0)) ),
inference(forward_demodulation,[],[f1154,f78]) ).
fof(f1154,plain,
! [X0] :
( zero = addition(zero,X0)
| zero != addition(X0,addition(zero,X0)) ),
inference(superposition,[],[f237,f181]) ).
fof(f1224,plain,
! [X2,X0,X1] : addition(X0,addition(X1,X2)) = addition(X0,addition(X1,addition(X2,addition(X0,addition(X1,X2))))),
inference(forward_demodulation,[],[f1153,f62]) ).
fof(f1153,plain,
! [X2,X0,X1] : addition(addition(X0,X1),X2) = addition(X0,addition(X1,addition(X2,addition(addition(X0,X1),X2)))),
inference(superposition,[],[f237,f62]) ).
fof(f1223,plain,
! [X2,X0,X1] : addition(X0,addition(X1,X2)) = addition(X1,addition(X0,addition(X2,addition(X0,addition(X1,X2))))),
inference(forward_demodulation,[],[f1152,f62]) ).
fof(f1152,plain,
! [X2,X0,X1] : addition(addition(X0,X1),X2) = addition(X1,addition(X0,addition(X2,addition(addition(X0,X1),X2)))),
inference(superposition,[],[f237,f226]) ).
fof(f1148,plain,
! [X2,X0,X1] : addition(X2,addition(X0,X1)) = addition(X2,addition(X0,addition(X1,addition(X2,addition(X0,X1))))),
inference(superposition,[],[f237,f62]) ).
fof(f1147,plain,
! [X2,X0,X1] : addition(X2,addition(X0,X1)) = addition(X2,addition(X1,addition(X0,addition(X2,addition(X0,X1))))),
inference(superposition,[],[f237,f226]) ).
fof(f1204,plain,
! [X2,X0,X1] : multiplication(addition(X0,X2),X1) = addition(multiplication(X0,X1),multiplication(addition(X2,addition(X0,X2)),X1)),
inference(forward_demodulation,[],[f1134,f65]) ).
fof(f1134,plain,
! [X2,X0,X1] : multiplication(addition(X0,X2),X1) = addition(multiplication(X0,X1),addition(multiplication(X2,X1),multiplication(addition(X0,X2),X1))),
inference(superposition,[],[f237,f65]) ).
fof(f1203,plain,
! [X2,X0,X1] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,addition(X2,addition(X1,X2)))),
inference(forward_demodulation,[],[f1133,f64]) ).
fof(f1133,plain,
! [X2,X0,X1] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),addition(multiplication(X0,X2),multiplication(X0,addition(X1,X2)))),
inference(superposition,[],[f237,f64]) ).
fof(f1127,plain,
! [X2,X0,X1] : addition(X0,addition(X1,X2)) = addition(addition(X0,X1),addition(X2,addition(X0,addition(X1,X2)))),
inference(superposition,[],[f237,f62]) ).
fof(f1126,plain,
! [X2,X0,X1] : addition(X1,addition(X0,X2)) = addition(addition(X0,X1),addition(X2,addition(X1,addition(X0,X2)))),
inference(superposition,[],[f237,f226]) ).
fof(f1186,plain,
! [X0,X1] : addition(X1,X0) = addition(X0,addition(X1,X0)),
inference(forward_demodulation,[],[f1121,f225]) ).
fof(f1121,plain,
! [X0,X1] : addition(X1,X0) = addition(X0,addition(X1,addition(X1,X0))),
inference(superposition,[],[f237,f53]) ).
fof(f1185,plain,
! [X0,X1] : addition(X1,X0) = addition(X0,addition(X1,X0)),
inference(forward_demodulation,[],[f1120,f225]) ).
fof(f1120,plain,
! [X0,X1] : addition(X1,X0) = addition(X0,addition(X1,addition(X1,X0))),
inference(superposition,[],[f237,f53]) ).
fof(f237,plain,
! [X0,X1] : addition(X0,X1) = addition(X0,addition(X1,addition(X0,X1))),
inference(superposition,[],[f62,f49]) ).
fof(f1051,plain,
! [X2,X0,X1] : leq(multiplication(X2,X1),multiplication(addition(X0,X2),X1)),
inference(superposition,[],[f1016,f65]) ).
fof(f1050,plain,
! [X2,X0,X1] : leq(multiplication(X0,X2),multiplication(X0,addition(X1,X2))),
inference(superposition,[],[f1016,f64]) ).
fof(f1046,plain,
! [X2,X0,X1] : leq(X2,addition(X0,addition(X1,X2))),
inference(superposition,[],[f1016,f62]) ).
fof(f1045,plain,
! [X2,X0,X1] : leq(X2,addition(X1,addition(X0,X2))),
inference(superposition,[],[f1016,f226]) ).
fof(f1038,plain,
! [X0,X1] : addition(X1,X0) = addition(X0,addition(X1,X0)),
inference(resolution,[],[f1016,f60]) ).
fof(f1016,plain,
! [X0,X1] : leq(X0,addition(X1,X0)),
inference(superposition,[],[f895,f53]) ).
fof(f1027,plain,
! [X2,X0,X1] : leq(multiplication(X0,X1),multiplication(addition(X0,X2),X1)),
inference(superposition,[],[f895,f65]) ).
fof(f1026,plain,
! [X2,X0,X1] : leq(multiplication(X0,X1),multiplication(X0,addition(X1,X2))),
inference(superposition,[],[f895,f64]) ).
fof(f1022,plain,
! [X2,X0,X1] : leq(addition(X0,X1),addition(X0,addition(X1,X2))),
inference(superposition,[],[f895,f62]) ).
fof(f1021,plain,
! [X2,X0,X1] : leq(addition(X0,X1),addition(X1,addition(X0,X2))),
inference(superposition,[],[f895,f226]) ).
fof(f1017,plain,
! [X0,X1] : leq(X0,addition(X1,X0)),
inference(superposition,[],[f895,f53]) ).
fof(f895,plain,
! [X0,X1] : leq(X0,addition(X0,X1)),
inference(trivial_inequality_removal,[],[f883]) ).
fof(f883,plain,
! [X0,X1] :
( addition(X0,X1) != addition(X0,X1)
| leq(X0,addition(X0,X1)) ),
inference(superposition,[],[f61,f225]) ).
fof(f1012,plain,
! [X0] : addition(one,X0) = addition(c(sK2),addition(one,X0)),
inference(superposition,[],[f226,f997]) ).
fof(f1009,plain,
! [X0] : addition(one,X0) = addition(one,addition(c(sK2),X0)),
inference(superposition,[],[f62,f997]) ).
fof(f997,plain,
one = addition(one,c(sK2)),
inference(superposition,[],[f865,f53]) ).
fof(f1006,plain,
leq(c(sK2),one),
inference(trivial_inequality_removal,[],[f1001]) ).
fof(f1001,plain,
( one != one
| leq(c(sK2),one) ),
inference(superposition,[],[f61,f865]) ).
fof(f1005,plain,
! [X0] : addition(one,X0) = addition(one,addition(c(sK2),X0)),
inference(superposition,[],[f226,f865]) ).
fof(f1002,plain,
! [X0] : addition(one,X0) = addition(c(sK2),addition(one,X0)),
inference(superposition,[],[f62,f865]) ).
fof(f1000,plain,
one = addition(one,c(sK2)),
inference(superposition,[],[f53,f865]) ).
fof(f999,plain,
one = addition(one,c(sK2)),
inference(superposition,[],[f53,f865]) ).
fof(f998,plain,
one = addition(one,c(sK2)),
inference(superposition,[],[f865,f53]) ).
fof(f865,plain,
one = addition(c(sK2),one),
inference(superposition,[],[f225,f770]) ).
fof(f995,plain,
! [X0,X1] :
( addition(X1,X0) = zero
| addition(X0,X1) != zero ),
inference(forward_demodulation,[],[f967,f46]) ).
fof(f967,plain,
! [X0,X1] :
( zero = addition(X1,addition(X0,zero))
| addition(X0,X1) != zero ),
inference(superposition,[],[f105,f226]) ).
fof(f994,plain,
! [X2,X0,X1] : addition(X0,addition(X1,X2)) = addition(X1,addition(X0,addition(X1,X2))),
inference(forward_demodulation,[],[f993,f225]) ).
fof(f993,plain,
! [X2,X0,X1] : addition(X0,addition(X1,X2)) = addition(X1,addition(X0,addition(X0,addition(X1,X2)))),
inference(forward_demodulation,[],[f966,f62]) ).
fof(f966,plain,
! [X2,X0,X1] : addition(addition(X0,X1),X2) = addition(X1,addition(X0,addition(addition(X0,X1),X2))),
inference(superposition,[],[f225,f226]) ).
fof(f957,plain,
! [X2,X0,X1] : addition(X1,addition(X0,X2)) = addition(addition(X0,X1),addition(X1,addition(X0,X2))),
inference(superposition,[],[f225,f226]) ).
fof(f956,plain,
! [X2,X0,X1] :
( addition(X0,X1) != addition(X1,addition(X0,X2))
| leq(X2,addition(X0,X1)) ),
inference(superposition,[],[f96,f226]) ).
fof(f954,plain,
! [X2,X0,X1] :
( addition(X1,addition(X0,X2)) != X2
| leq(addition(X0,X1),X2) ),
inference(superposition,[],[f61,f226]) ).
fof(f953,plain,
! [X2,X0,X1] : addition(X2,addition(X0,X1)) = addition(X1,addition(X0,X2)),
inference(superposition,[],[f53,f226]) ).
fof(f952,plain,
! [X2,X0,X1] : addition(X2,addition(X0,X1)) = addition(X1,addition(X0,X2)),
inference(superposition,[],[f53,f226]) ).
fof(f990,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,addition(X0,X1)),
inference(forward_demodulation,[],[f951,f225]) ).
fof(f951,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,addition(X0,addition(X0,X1))),
inference(superposition,[],[f49,f226]) ).
fof(f948,plain,
! [X2,X0,X1] : addition(X0,addition(X1,X2)) = addition(X1,addition(X0,X2)),
inference(superposition,[],[f62,f226]) ).
fof(f988,plain,
! [X0,X1] :
( addition(X1,X0) = zero
| addition(X0,X1) != zero ),
inference(forward_demodulation,[],[f946,f46]) ).
fof(f946,plain,
! [X0,X1] :
( zero = addition(X1,addition(X0,zero))
| addition(X0,X1) != zero ),
inference(superposition,[],[f226,f105]) ).
fof(f987,plain,
! [X2,X0,X1] : addition(X0,addition(X1,X2)) = addition(X1,addition(X0,addition(X1,X2))),
inference(forward_demodulation,[],[f986,f225]) ).
fof(f986,plain,
! [X2,X0,X1] : addition(X0,addition(X1,X2)) = addition(X1,addition(X0,addition(X0,addition(X1,X2)))),
inference(forward_demodulation,[],[f945,f62]) ).
fof(f945,plain,
! [X2,X0,X1] : addition(addition(X0,X1),X2) = addition(X1,addition(X0,addition(addition(X0,X1),X2))),
inference(superposition,[],[f226,f225]) ).
fof(f944,plain,
! [X2,X0,X1] : addition(X2,addition(X0,X1)) = addition(X1,addition(X0,X2)),
inference(superposition,[],[f226,f53]) ).
fof(f943,plain,
! [X2,X0,X1] : addition(X2,addition(X0,X1)) = addition(X1,addition(X0,X2)),
inference(superposition,[],[f226,f53]) ).
fof(f985,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,addition(X0,X1)),
inference(forward_demodulation,[],[f942,f225]) ).
fof(f942,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,addition(X0,addition(X0,X1))),
inference(superposition,[],[f226,f49]) ).
fof(f941,plain,
! [X2,X0,X1] : addition(X0,addition(X1,X2)) = addition(X1,addition(X0,X2)),
inference(superposition,[],[f226,f62]) ).
fof(f940,plain,
! [X0] : addition(one,X0) = addition(one,addition(sK2,X0)),
inference(superposition,[],[f226,f869]) ).
fof(f939,plain,
! [X0] : addition(one,X0) = addition(c(sK2),addition(sK2,X0)),
inference(superposition,[],[f226,f151]) ).
fof(f984,plain,
! [X0] : addition(one,X0) = addition(c(sK2),addition(sK2,X0)),
inference(forward_demodulation,[],[f938,f760]) ).
fof(f938,plain,
! [X0] : addition(one,X0) = addition(sK3(sK2),addition(sK2,X0)),
inference(superposition,[],[f226,f134]) ).
fof(f934,plain,
! [X0] : addition(one,X0) = addition(sK2,addition(c(sK2),X0)),
inference(superposition,[],[f226,f770]) ).
fof(f933,plain,
! [X0] : addition(one,X0) = addition(sK2,addition(one,X0)),
inference(superposition,[],[f226,f900]) ).
fof(f932,plain,
! [X2,X3,X0,X1] : addition(multiplication(addition(X0,X2),X1),X3) = addition(multiplication(X2,X1),addition(multiplication(X0,X1),X3)),
inference(superposition,[],[f226,f65]) ).
fof(f931,plain,
! [X2,X3,X0,X1] : addition(multiplication(X0,addition(X1,X2)),X3) = addition(multiplication(X0,X2),addition(multiplication(X0,X1),X3)),
inference(superposition,[],[f226,f64]) ).
fof(f980,plain,
! [X0,X1] :
( addition(X0,X1) = X1
| zero != X0 ),
inference(forward_demodulation,[],[f928,f78]) ).
fof(f928,plain,
! [X0,X1] :
( addition(zero,X1) = addition(X0,addition(zero,X1))
| zero != X0 ),
inference(superposition,[],[f226,f181]) ).
fof(f979,plain,
! [X2,X3,X0,X1] : addition(addition(X0,addition(X1,X2)),X3) = addition(X2,addition(X0,addition(X1,X3))),
inference(forward_demodulation,[],[f927,f62]) ).
fof(f927,plain,
! [X2,X3,X0,X1] : addition(addition(X0,addition(X1,X2)),X3) = addition(X2,addition(addition(X0,X1),X3)),
inference(superposition,[],[f226,f62]) ).
fof(f978,plain,
! [X2,X3,X0,X1] : addition(addition(X1,addition(X0,X2)),X3) = addition(X2,addition(X0,addition(X1,X3))),
inference(forward_demodulation,[],[f926,f62]) ).
fof(f926,plain,
! [X2,X3,X0,X1] : addition(X2,addition(addition(X0,X1),X3)) = addition(addition(X1,addition(X0,X2)),X3),
inference(superposition,[],[f226,f226]) ).
fof(f977,plain,
! [X0,X1] :
( addition(zero,addition(X0,X1)) = X1
| zero != X0 ),
inference(forward_demodulation,[],[f924,f78]) ).
fof(f924,plain,
! [X0,X1] :
( addition(zero,X1) = addition(zero,addition(X0,X1))
| zero != X0 ),
inference(superposition,[],[f226,f105]) ).
fof(f976,plain,
! [X2,X0,X1] : addition(X0,addition(X1,X2)) = addition(addition(X0,X1),addition(X0,X2)),
inference(forward_demodulation,[],[f923,f62]) ).
fof(f923,plain,
! [X2,X0,X1] : addition(addition(X0,X1),X2) = addition(addition(X0,X1),addition(X0,X2)),
inference(superposition,[],[f226,f225]) ).
fof(f226,plain,
! [X2,X0,X1] : addition(X0,addition(X1,X2)) = addition(addition(X1,X0),X2),
inference(superposition,[],[f62,f53]) ).
fof(f916,plain,
! [X0] : addition(one,X0) = addition(one,addition(sK2,X0)),
inference(superposition,[],[f62,f900]) ).
fof(f900,plain,
one = addition(one,sK2),
inference(superposition,[],[f869,f53]) ).
fof(f913,plain,
leq(sK2,one),
inference(global_subsumption,[],[f43,f42,f40,f44,f45,f46,f47,f48,f49,f52,f50,f51,f66,f68,f41,f53,f79,f80,f81,f78,f56,f57,f58,f60,f61,f97,f102,f101,f94,f86,f108,f106,f87,f110,f111,f109,f88,f113,f114,f112,f89,f116,f117,f115,f90,f135,f136,f134,f137,f138,f55,f92,f152,f153,f151,f154,f96,f164,f165,f170,f169,f105,f182,f186,f187,f181,f148,f200,f107,f202,f201,f62,f247,f226,f227,f250,f233,f234,f237,f238,f239,f242,f243,f244,f245,f246,f63,f312,f307,f310,f64,f386,f417,f421,f423,f425,f426,f427,f397,f429,f433,f435,f437,f438,f439,f408,f409,f411,f412,f413,f414,f415,f316,f487,f488,f65,f541,f505,f506,f543,f545,f547,f548,f549,f553,f518,f519,f555,f557,f559,f560,f561,f529,f530,f533,f534,f535,f536,f537,f318,f574,f575,f576,f577,f319,f593,f594,f595,f596,f320,f612,f613,f614,f615,f59,f723,f724,f725,f695,f729,f733,f743,f745,f749,f731,f750,f738,f756,f759,f768,f762,f763,f764,f765,f766,f767,f741,f773,f774,f775,f776,f777,f778,f779,f747,f785,f760,f800,f801,f721,f810,f806,f809,f820,f770,f823,f727,f829,f832,f834,f225,f854,f855,f859,f863,f864,f865,f870,f896,f882,f895,f899,f869,f900,f901,f903,f906,f907,f908,f824,f911,f912,f155]) ).
fof(f155,plain,
( one != c(sK2)
| leq(sK2,one) ),
inference(inner_rewriting,[],[f154]) ).
fof(f912,plain,
leq(sK2,one),
inference(global_subsumption,[],[f43,f42,f40,f44,f45,f46,f47,f48,f49,f52,f50,f51,f66,f68,f41,f53,f79,f80,f81,f78,f56,f57,f58,f60,f61,f97,f102,f101,f94,f86,f108,f106,f87,f110,f111,f109,f88,f113,f114,f112,f89,f116,f117,f115,f90,f135,f136,f134,f137,f138,f55,f92,f152,f153,f151,f154,f96,f164,f165,f170,f169,f105,f182,f186,f187,f181,f148,f200,f107,f202,f201,f62,f247,f226,f227,f250,f233,f234,f237,f238,f239,f242,f243,f244,f245,f246,f63,f312,f307,f310,f64,f386,f417,f421,f423,f425,f426,f427,f397,f429,f433,f435,f437,f438,f439,f408,f409,f411,f412,f413,f414,f415,f316,f487,f488,f65,f541,f505,f506,f543,f545,f547,f548,f549,f553,f518,f519,f555,f557,f559,f560,f561,f529,f530,f533,f534,f535,f536,f537,f318,f574,f575,f576,f577,f319,f593,f594,f595,f596,f320,f612,f613,f614,f615,f59,f723,f724,f725,f695,f729,f733,f743,f745,f749,f731,f750,f738,f756,f759,f768,f762,f763,f764,f765,f766,f767,f741,f773,f774,f775,f776,f777,f778,f779,f747,f785,f760,f800,f801,f721,f810,f806,f809,f820,f770,f823,f727,f829,f832,f834,f225,f854,f855,f859,f863,f864,f865,f870,f896,f882,f895,f899,f869,f900,f901,f903,f906,f907,f908,f824,f911]) ).
fof(f911,plain,
( one != c(sK2)
| leq(sK2,one) ),
inference(inner_rewriting,[],[f824]) ).
fof(f824,plain,
( one != c(sK2)
| leq(sK2,c(sK2)) ),
inference(superposition,[],[f96,f770]) ).
fof(f908,plain,
leq(sK2,one),
inference(trivial_inequality_removal,[],[f905]) ).
fof(f905,plain,
( one != one
| leq(sK2,one) ),
inference(superposition,[],[f61,f869]) ).
fof(f907,plain,
one = addition(one,sK2),
inference(superposition,[],[f53,f869]) ).
fof(f906,plain,
one = addition(one,sK2),
inference(superposition,[],[f53,f869]) ).
fof(f903,plain,
! [X0] : addition(one,X0) = addition(sK2,addition(one,X0)),
inference(superposition,[],[f62,f869]) ).
fof(f901,plain,
one = addition(one,sK2),
inference(superposition,[],[f869,f53]) ).
fof(f899,plain,
! [X2,X0,X1] : addition(X0,addition(X1,X2)) = addition(X0,addition(X1,addition(X0,addition(X1,X2)))),
inference(forward_demodulation,[],[f884,f62]) ).
fof(f884,plain,
! [X2,X0,X1] : addition(addition(X0,X1),X2) = addition(X0,addition(X1,addition(addition(X0,X1),X2))),
inference(superposition,[],[f62,f225]) ).
fof(f882,plain,
! [X0,X1] :
( addition(X0,X1) != X0
| leq(addition(X0,X1),X0) ),
inference(superposition,[],[f96,f225]) ).
fof(f896,plain,
! [X2,X0,X1] : addition(X0,addition(X1,X2)) = addition(X0,addition(X1,addition(X0,addition(X1,X2)))),
inference(forward_demodulation,[],[f871,f62]) ).
fof(f871,plain,
! [X2,X0,X1] : addition(addition(X0,X1),X2) = addition(X0,addition(X1,addition(addition(X0,X1),X2))),
inference(superposition,[],[f225,f62]) ).
fof(f870,plain,
one = addition(sK2,one),
inference(superposition,[],[f225,f151]) ).
fof(f864,plain,
! [X2,X0,X1] : multiplication(addition(X0,X2),X1) = addition(multiplication(X0,X1),multiplication(addition(X0,X2),X1)),
inference(superposition,[],[f225,f65]) ).
fof(f863,plain,
! [X2,X0,X1] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,addition(X1,X2))),
inference(superposition,[],[f225,f64]) ).
fof(f859,plain,
! [X2,X0,X1] : addition(X0,addition(X1,X2)) = addition(addition(X0,X1),addition(X0,addition(X1,X2))),
inference(superposition,[],[f225,f62]) ).
fof(f855,plain,
! [X0,X1] : addition(X1,X0) = addition(X0,addition(X1,X0)),
inference(superposition,[],[f225,f53]) ).
fof(f854,plain,
! [X0,X1] : addition(X1,X0) = addition(X0,addition(X1,X0)),
inference(superposition,[],[f225,f53]) ).
fof(f834,plain,
test(one),
inference(equality_resolution,[],[f832]) ).
fof(f832,plain,
! [X0] :
( one != X0
| test(X0) ),
inference(resolution,[],[f727,f52]) ).
fof(f829,plain,
! [X0] :
( addition(X0,zero) = one
| one != X0 ),
inference(resolution,[],[f727,f58]) ).
fof(f727,plain,
! [X0] :
( complement(zero,X0)
| one != X0 ),
inference(forward_demodulation,[],[f726,f46]) ).
fof(f726,plain,
! [X0] :
( addition(X0,zero) != one
| complement(zero,X0) ),
inference(subsumption_resolution,[],[f717,f44]) ).
fof(f717,plain,
! [X0] :
( addition(X0,zero) != one
| complement(zero,X0)
| zero != multiplication(X0,zero) ),
inference(trivial_inequality_removal,[],[f694]) ).
fof(f694,plain,
! [X0] :
( zero != zero
| addition(X0,zero) != one
| complement(zero,X0)
| zero != multiplication(X0,zero) ),
inference(superposition,[],[f59,f45]) ).
fof(f823,plain,
! [X0] : addition(one,X0) = addition(c(sK2),addition(sK2,X0)),
inference(superposition,[],[f62,f770]) ).
fof(f770,plain,
one = addition(c(sK2),sK2),
inference(resolution,[],[f741,f58]) ).
fof(f820,plain,
one = addition(c(sK2),sK2),
inference(forward_demodulation,[],[f756,f760]) ).
fof(f809,plain,
! [X0] :
( one != X0
| test(zero) ),
inference(resolution,[],[f721,f52]) ).
fof(f806,plain,
! [X0] :
( one = addition(zero,X0)
| one != X0 ),
inference(resolution,[],[f721,f58]) ).
fof(f810,plain,
! [X0] :
( zero = c(X0)
| one != X0 ),
inference(subsumption_resolution,[],[f805,f50]) ).
fof(f805,plain,
! [X0] :
( one != X0
| zero = c(X0)
| ~ test(X0) ),
inference(resolution,[],[f721,f55]) ).
fof(f721,plain,
! [X0] :
( complement(X0,zero)
| one != X0 ),
inference(forward_demodulation,[],[f720,f78]) ).
fof(f720,plain,
! [X0] :
( one != addition(zero,X0)
| complement(X0,zero) ),
inference(subsumption_resolution,[],[f719,f45]) ).
fof(f719,plain,
! [X0] :
( one != addition(zero,X0)
| complement(X0,zero)
| zero != multiplication(zero,X0) ),
inference(trivial_inequality_removal,[],[f691]) ).
fof(f691,plain,
! [X0] :
( zero != zero
| one != addition(zero,X0)
| complement(X0,zero)
| zero != multiplication(zero,X0) ),
inference(superposition,[],[f59,f44]) ).
fof(f801,plain,
sK2 = c(c(sK2)),
inference(forward_demodulation,[],[f785,f760]) ).
fof(f800,plain,
sK2 = c(c(sK2)),
inference(forward_demodulation,[],[f799,f760]) ).
fof(f799,plain,
sK2 = c(sK3(sK2)),
inference(subsumption_resolution,[],[f798,f40]) ).
fof(f798,plain,
( sK2 = c(sK3(sK2))
| ~ test(sK2) ),
inference(subsumption_resolution,[],[f796,f773]) ).
fof(f796,plain,
( ~ test(c(sK2))
| sK2 = c(sK3(sK2))
| ~ test(sK2) ),
inference(superposition,[],[f148,f760]) ).
fof(f760,plain,
c(sK2) = sK3(sK2),
inference(subsumption_resolution,[],[f755,f40]) ).
fof(f755,plain,
( c(sK2) = sK3(sK2)
| ~ test(sK2) ),
inference(resolution,[],[f738,f55]) ).
fof(f785,plain,
sK2 = c(sK3(sK2)),
inference(subsumption_resolution,[],[f780,f759]) ).
fof(f780,plain,
( sK2 = c(sK3(sK2))
| ~ test(sK3(sK2)) ),
inference(resolution,[],[f747,f55]) ).
fof(f747,plain,
complement(sK3(sK2),sK2),
inference(subsumption_resolution,[],[f746,f106]) ).
fof(f746,plain,
( complement(sK3(sK2),sK2)
| zero != multiplication(sK2,sK3(sK2)) ),
inference(subsumption_resolution,[],[f708,f134]) ).
fof(f708,plain,
( one != addition(sK2,sK3(sK2))
| complement(sK3(sK2),sK2)
| zero != multiplication(sK2,sK3(sK2)) ),
inference(trivial_inequality_removal,[],[f705]) ).
fof(f705,plain,
( zero != zero
| one != addition(sK2,sK3(sK2))
| complement(sK3(sK2),sK2)
| zero != multiplication(sK2,sK3(sK2)) ),
inference(superposition,[],[f59,f112]) ).
fof(f779,plain,
zero = multiplication(c(sK2),sK3(c(sK2))),
inference(resolution,[],[f773,f86]) ).
fof(f778,plain,
zero = multiplication(c(c(sK2)),c(sK2)),
inference(resolution,[],[f773,f87]) ).
fof(f777,plain,
zero = multiplication(sK3(c(sK2)),c(sK2)),
inference(resolution,[],[f773,f88]) ).
fof(f776,plain,
zero = multiplication(c(sK2),c(c(sK2))),
inference(resolution,[],[f773,f89]) ).
fof(f775,plain,
one = addition(c(sK2),sK3(c(sK2))),
inference(resolution,[],[f773,f90]) ).
fof(f774,plain,
one = addition(c(sK2),c(c(sK2))),
inference(resolution,[],[f773,f92]) ).
fof(f773,plain,
test(c(sK2)),
inference(resolution,[],[f741,f52]) ).
fof(f741,plain,
complement(sK2,c(sK2)),
inference(subsumption_resolution,[],[f740,f151]) ).
fof(f740,plain,
( one != addition(sK2,c(sK2))
| complement(sK2,c(sK2)) ),
inference(forward_demodulation,[],[f739,f53]) ).
fof(f739,plain,
( one != addition(c(sK2),sK2)
| complement(sK2,c(sK2)) ),
inference(subsumption_resolution,[],[f711,f109]) ).
fof(f711,plain,
( one != addition(c(sK2),sK2)
| complement(sK2,c(sK2))
| zero != multiplication(c(sK2),sK2) ),
inference(trivial_inequality_removal,[],[f702]) ).
fof(f702,plain,
( zero != zero
| one != addition(c(sK2),sK2)
| complement(sK2,c(sK2))
| zero != multiplication(c(sK2),sK2) ),
inference(superposition,[],[f59,f115]) ).
fof(f767,plain,
zero = multiplication(sK3(sK2),sK3(sK3(sK2))),
inference(resolution,[],[f759,f86]) ).
fof(f766,plain,
zero = multiplication(c(sK3(sK2)),sK3(sK2)),
inference(resolution,[],[f759,f87]) ).
fof(f765,plain,
zero = multiplication(sK3(sK3(sK2)),sK3(sK2)),
inference(resolution,[],[f759,f88]) ).
fof(f764,plain,
zero = multiplication(sK3(sK2),c(sK3(sK2))),
inference(resolution,[],[f759,f89]) ).
fof(f763,plain,
one = addition(sK3(sK2),sK3(sK3(sK2))),
inference(resolution,[],[f759,f90]) ).
fof(f762,plain,
one = addition(sK3(sK2),c(sK3(sK2))),
inference(resolution,[],[f759,f92]) ).
fof(f768,plain,
sK2 = c(sK3(sK2)),
inference(subsumption_resolution,[],[f761,f40]) ).
fof(f761,plain,
( sK2 = c(sK3(sK2))
| ~ test(sK2) ),
inference(resolution,[],[f759,f148]) ).
fof(f759,plain,
test(sK3(sK2)),
inference(resolution,[],[f738,f52]) ).
fof(f756,plain,
one = addition(sK3(sK2),sK2),
inference(resolution,[],[f738,f58]) ).
fof(f738,plain,
complement(sK2,sK3(sK2)),
inference(subsumption_resolution,[],[f737,f134]) ).
fof(f737,plain,
( one != addition(sK2,sK3(sK2))
| complement(sK2,sK3(sK2)) ),
inference(forward_demodulation,[],[f736,f53]) ).
fof(f736,plain,
( one != addition(sK3(sK2),sK2)
| complement(sK2,sK3(sK2)) ),
inference(subsumption_resolution,[],[f712,f112]) ).
fof(f712,plain,
( one != addition(sK3(sK2),sK2)
| complement(sK2,sK3(sK2))
| zero != multiplication(sK3(sK2),sK2) ),
inference(trivial_inequality_removal,[],[f701]) ).
fof(f701,plain,
( zero != zero
| one != addition(sK3(sK2),sK2)
| complement(sK2,sK3(sK2))
| zero != multiplication(sK3(sK2),sK2) ),
inference(superposition,[],[f59,f106]) ).
fof(f750,plain,
( sK2 = c(c(sK2))
| ~ test(c(sK2)) ),
inference(resolution,[],[f731,f55]) ).
fof(f731,plain,
complement(c(sK2),sK2),
inference(subsumption_resolution,[],[f730,f115]) ).
fof(f730,plain,
( complement(c(sK2),sK2)
| zero != multiplication(sK2,c(sK2)) ),
inference(subsumption_resolution,[],[f716,f151]) ).
fof(f716,plain,
( one != addition(sK2,c(sK2))
| complement(c(sK2),sK2)
| zero != multiplication(sK2,c(sK2)) ),
inference(trivial_inequality_removal,[],[f697]) ).
fof(f697,plain,
( zero != zero
| one != addition(sK2,c(sK2))
| complement(c(sK2),sK2)
| zero != multiplication(sK2,c(sK2)) ),
inference(superposition,[],[f59,f109]) ).
fof(f749,plain,
! [X0] :
( zero != multiplication(sK2,multiplication(X0,sK3(sK2)))
| one != addition(sK3(sK2),multiplication(sK2,X0))
| complement(sK3(sK2),multiplication(sK2,X0)) ),
inference(forward_demodulation,[],[f748,f63]) ).
fof(f748,plain,
! [X0] :
( one != addition(sK3(sK2),multiplication(sK2,X0))
| complement(sK3(sK2),multiplication(sK2,X0))
| zero != multiplication(multiplication(sK2,X0),sK3(sK2)) ),
inference(forward_demodulation,[],[f707,f53]) ).
fof(f707,plain,
! [X0] :
( one != addition(multiplication(sK2,X0),sK3(sK2))
| complement(sK3(sK2),multiplication(sK2,X0))
| zero != multiplication(multiplication(sK2,X0),sK3(sK2)) ),
inference(trivial_inequality_removal,[],[f706]) ).
fof(f706,plain,
! [X0] :
( zero != zero
| one != addition(multiplication(sK2,X0),sK3(sK2))
| complement(sK3(sK2),multiplication(sK2,X0))
| zero != multiplication(multiplication(sK2,X0),sK3(sK2)) ),
inference(superposition,[],[f59,f320]) ).
fof(f745,plain,
! [X0] :
( zero != multiplication(c(sK2),multiplication(X0,sK2))
| one != addition(sK2,multiplication(c(sK2),X0))
| complement(sK2,multiplication(c(sK2),X0)) ),
inference(forward_demodulation,[],[f744,f63]) ).
fof(f744,plain,
! [X0] :
( one != addition(sK2,multiplication(c(sK2),X0))
| complement(sK2,multiplication(c(sK2),X0))
| zero != multiplication(multiplication(c(sK2),X0),sK2) ),
inference(forward_demodulation,[],[f709,f53]) ).
fof(f709,plain,
! [X0] :
( one != addition(multiplication(c(sK2),X0),sK2)
| complement(sK2,multiplication(c(sK2),X0))
| zero != multiplication(multiplication(c(sK2),X0),sK2) ),
inference(trivial_inequality_removal,[],[f704]) ).
fof(f704,plain,
! [X0] :
( zero != zero
| one != addition(multiplication(c(sK2),X0),sK2)
| complement(sK2,multiplication(c(sK2),X0))
| zero != multiplication(multiplication(c(sK2),X0),sK2) ),
inference(superposition,[],[f59,f319]) ).
fof(f743,plain,
! [X0] :
( zero != multiplication(sK3(sK2),multiplication(X0,sK2))
| one != addition(sK2,multiplication(sK3(sK2),X0))
| complement(sK2,multiplication(sK3(sK2),X0)) ),
inference(forward_demodulation,[],[f742,f63]) ).
fof(f742,plain,
! [X0] :
( one != addition(sK2,multiplication(sK3(sK2),X0))
| complement(sK2,multiplication(sK3(sK2),X0))
| zero != multiplication(multiplication(sK3(sK2),X0),sK2) ),
inference(forward_demodulation,[],[f710,f53]) ).
fof(f710,plain,
! [X0] :
( one != addition(multiplication(sK3(sK2),X0),sK2)
| complement(sK2,multiplication(sK3(sK2),X0))
| zero != multiplication(multiplication(sK3(sK2),X0),sK2) ),
inference(trivial_inequality_removal,[],[f703]) ).
fof(f703,plain,
! [X0] :
( zero != zero
| one != addition(multiplication(sK3(sK2),X0),sK2)
| complement(sK2,multiplication(sK3(sK2),X0))
| zero != multiplication(multiplication(sK3(sK2),X0),sK2) ),
inference(superposition,[],[f59,f318]) ).
fof(f733,plain,
! [X0] :
( zero != multiplication(sK2,multiplication(X0,c(sK2)))
| one != addition(c(sK2),multiplication(sK2,X0))
| complement(c(sK2),multiplication(sK2,X0)) ),
inference(forward_demodulation,[],[f732,f63]) ).
fof(f732,plain,
! [X0] :
( one != addition(c(sK2),multiplication(sK2,X0))
| complement(c(sK2),multiplication(sK2,X0))
| zero != multiplication(multiplication(sK2,X0),c(sK2)) ),
inference(forward_demodulation,[],[f714,f53]) ).
fof(f714,plain,
! [X0] :
( one != addition(multiplication(sK2,X0),c(sK2))
| complement(c(sK2),multiplication(sK2,X0))
| zero != multiplication(multiplication(sK2,X0),c(sK2)) ),
inference(trivial_inequality_removal,[],[f699]) ).
fof(f699,plain,
! [X0] :
( zero != zero
| one != addition(multiplication(sK2,X0),c(sK2))
| complement(c(sK2),multiplication(sK2,X0))
| zero != multiplication(multiplication(sK2,X0),c(sK2)) ),
inference(superposition,[],[f59,f316]) ).
fof(f729,plain,
! [X0] :
( one != addition(X0,one)
| zero != X0
| complement(one,X0) ),
inference(duplicate_literal_removal,[],[f728]) ).
fof(f728,plain,
! [X0] :
( zero != X0
| zero != X0
| one != addition(X0,one)
| complement(one,X0) ),
inference(forward_demodulation,[],[f696,f47]) ).
fof(f696,plain,
! [X0] :
( zero != X0
| one != addition(X0,one)
| complement(one,X0)
| zero != multiplication(X0,one) ),
inference(superposition,[],[f59,f48]) ).
fof(f695,plain,
! [X2,X0,X1] :
( one != addition(X2,multiplication(X0,X1))
| zero != multiplication(X0,multiplication(X1,X2))
| complement(multiplication(X0,X1),X2)
| zero != multiplication(X2,multiplication(X0,X1)) ),
inference(superposition,[],[f59,f63]) ).
fof(f725,plain,
! [X0] :
( complement(X0,sK3(X0))
| zero = c(X0) ),
inference(global_subsumption,[],[f43,f42,f40,f44,f45,f46,f47,f48,f49,f52,f50,f51,f66,f68,f41,f53,f79,f80,f81,f78,f56,f57,f58,f60,f61,f97,f102,f101,f94,f86,f108,f106,f87,f110,f111,f109,f88,f113,f114,f112,f89,f116,f117,f115,f90,f135,f136,f134,f137,f138,f55,f92,f152,f153,f151,f154,f96,f164,f165,f170,f169,f105,f182,f186,f187,f181,f148,f200,f107,f202,f201,f62,f247,f225,f226,f227,f250,f233,f234,f237,f238,f239,f242,f243,f244,f245,f246,f63,f312,f307,f310,f64,f386,f417,f421,f423,f425,f426,f427,f397,f429,f433,f435,f437,f438,f439,f408,f409,f411,f412,f413,f414,f415,f316,f487,f488,f65,f541,f505,f506,f543,f545,f547,f548,f549,f553,f518,f519,f555,f557,f559,f560,f561,f529,f530,f533,f534,f535,f536,f537,f318,f574,f575,f576,f577,f319,f593,f594,f595,f596,f320,f612,f613,f614,f615,f59,f721,f723,f724]) ).
fof(f724,plain,
! [X0] :
( one != addition(X0,sK3(X0))
| complement(X0,sK3(X0))
| zero != multiplication(sK3(X0),X0)
| zero = c(X0) ),
inference(forward_demodulation,[],[f718,f53]) ).
fof(f718,plain,
! [X0] :
( one != addition(sK3(X0),X0)
| complement(X0,sK3(X0))
| zero != multiplication(sK3(X0),X0)
| zero = c(X0) ),
inference(trivial_inequality_removal,[],[f693]) ).
fof(f693,plain,
! [X0] :
( zero != zero
| one != addition(sK3(X0),X0)
| complement(X0,sK3(X0))
| zero != multiplication(sK3(X0),X0)
| zero = c(X0) ),
inference(superposition,[],[f59,f107]) ).
fof(f723,plain,
! [X0] :
( one != addition(one,X0)
| zero != X0
| complement(X0,one) ),
inference(duplicate_literal_removal,[],[f722]) ).
fof(f722,plain,
! [X0] :
( zero != X0
| zero != X0
| one != addition(one,X0)
| complement(X0,one) ),
inference(forward_demodulation,[],[f692,f48]) ).
fof(f692,plain,
! [X0] :
( zero != X0
| one != addition(one,X0)
| complement(X0,one)
| zero != multiplication(one,X0) ),
inference(superposition,[],[f59,f47]) ).
fof(f59,plain,
! [X0,X1] :
( zero != multiplication(X1,X0)
| addition(X0,X1) != one
| complement(X1,X0)
| zero != multiplication(X0,X1) ),
inference(cnf_transformation,[],[f38]) ).
fof(f615,plain,
! [X0,X1] : multiplication(sK3(sK2),X1) = multiplication(sK3(sK2),addition(multiplication(sK2,X0),X1)),
inference(forward_demodulation,[],[f610,f78]) ).
fof(f610,plain,
! [X0,X1] : multiplication(sK3(sK2),addition(multiplication(sK2,X0),X1)) = addition(zero,multiplication(sK3(sK2),X1)),
inference(superposition,[],[f64,f320]) ).
fof(f614,plain,
! [X0,X1] : multiplication(sK3(sK2),X1) = multiplication(sK3(sK2),addition(X1,multiplication(sK2,X0))),
inference(forward_demodulation,[],[f609,f46]) ).
fof(f609,plain,
! [X0,X1] : multiplication(sK3(sK2),addition(X1,multiplication(sK2,X0))) = addition(multiplication(sK3(sK2),X1),zero),
inference(superposition,[],[f64,f320]) ).
fof(f613,plain,
! [X0,X1] : multiplication(X1,multiplication(sK2,X0)) = multiplication(addition(sK3(sK2),X1),multiplication(sK2,X0)),
inference(forward_demodulation,[],[f608,f78]) ).
fof(f608,plain,
! [X0,X1] : addition(zero,multiplication(X1,multiplication(sK2,X0))) = multiplication(addition(sK3(sK2),X1),multiplication(sK2,X0)),
inference(superposition,[],[f65,f320]) ).
fof(f612,plain,
! [X0,X1] : multiplication(X1,multiplication(sK2,X0)) = multiplication(addition(X1,sK3(sK2)),multiplication(sK2,X0)),
inference(forward_demodulation,[],[f607,f46]) ).
fof(f607,plain,
! [X0,X1] : addition(multiplication(X1,multiplication(sK2,X0)),zero) = multiplication(addition(X1,sK3(sK2)),multiplication(sK2,X0)),
inference(superposition,[],[f65,f320]) ).
fof(f320,plain,
! [X0] : zero = multiplication(sK3(sK2),multiplication(sK2,X0)),
inference(forward_demodulation,[],[f304,f45]) ).
fof(f304,plain,
! [X0] : multiplication(zero,X0) = multiplication(sK3(sK2),multiplication(sK2,X0)),
inference(superposition,[],[f63,f112]) ).
fof(f596,plain,
! [X0,X1] : multiplication(sK2,X1) = multiplication(sK2,addition(multiplication(c(sK2),X0),X1)),
inference(forward_demodulation,[],[f591,f78]) ).
fof(f591,plain,
! [X0,X1] : addition(zero,multiplication(sK2,X1)) = multiplication(sK2,addition(multiplication(c(sK2),X0),X1)),
inference(superposition,[],[f64,f319]) ).
fof(f595,plain,
! [X0,X1] : multiplication(sK2,X1) = multiplication(sK2,addition(X1,multiplication(c(sK2),X0))),
inference(forward_demodulation,[],[f590,f46]) ).
fof(f590,plain,
! [X0,X1] : addition(multiplication(sK2,X1),zero) = multiplication(sK2,addition(X1,multiplication(c(sK2),X0))),
inference(superposition,[],[f64,f319]) ).
fof(f594,plain,
! [X0,X1] : multiplication(X1,multiplication(c(sK2),X0)) = multiplication(addition(sK2,X1),multiplication(c(sK2),X0)),
inference(forward_demodulation,[],[f589,f78]) ).
fof(f589,plain,
! [X0,X1] : multiplication(addition(sK2,X1),multiplication(c(sK2),X0)) = addition(zero,multiplication(X1,multiplication(c(sK2),X0))),
inference(superposition,[],[f65,f319]) ).
fof(f593,plain,
! [X0,X1] : multiplication(addition(X1,sK2),multiplication(c(sK2),X0)) = multiplication(X1,multiplication(c(sK2),X0)),
inference(forward_demodulation,[],[f588,f46]) ).
fof(f588,plain,
! [X0,X1] : multiplication(addition(X1,sK2),multiplication(c(sK2),X0)) = addition(multiplication(X1,multiplication(c(sK2),X0)),zero),
inference(superposition,[],[f65,f319]) ).
fof(f319,plain,
! [X0] : zero = multiplication(sK2,multiplication(c(sK2),X0)),
inference(forward_demodulation,[],[f303,f45]) ).
fof(f303,plain,
! [X0] : multiplication(zero,X0) = multiplication(sK2,multiplication(c(sK2),X0)),
inference(superposition,[],[f63,f115]) ).
fof(f577,plain,
! [X0,X1] : multiplication(sK2,X1) = multiplication(sK2,addition(multiplication(sK3(sK2),X0),X1)),
inference(forward_demodulation,[],[f572,f78]) ).
fof(f572,plain,
! [X0,X1] : multiplication(sK2,addition(multiplication(sK3(sK2),X0),X1)) = addition(zero,multiplication(sK2,X1)),
inference(superposition,[],[f64,f318]) ).
fof(f576,plain,
! [X0,X1] : multiplication(sK2,X1) = multiplication(sK2,addition(X1,multiplication(sK3(sK2),X0))),
inference(forward_demodulation,[],[f571,f46]) ).
fof(f571,plain,
! [X0,X1] : multiplication(sK2,addition(X1,multiplication(sK3(sK2),X0))) = addition(multiplication(sK2,X1),zero),
inference(superposition,[],[f64,f318]) ).
fof(f575,plain,
! [X0,X1] : multiplication(X1,multiplication(sK3(sK2),X0)) = multiplication(addition(sK2,X1),multiplication(sK3(sK2),X0)),
inference(forward_demodulation,[],[f570,f78]) ).
fof(f570,plain,
! [X0,X1] : multiplication(addition(sK2,X1),multiplication(sK3(sK2),X0)) = addition(zero,multiplication(X1,multiplication(sK3(sK2),X0))),
inference(superposition,[],[f65,f318]) ).
fof(f574,plain,
! [X0,X1] : multiplication(addition(X1,sK2),multiplication(sK3(sK2),X0)) = multiplication(X1,multiplication(sK3(sK2),X0)),
inference(forward_demodulation,[],[f569,f46]) ).
fof(f569,plain,
! [X0,X1] : multiplication(addition(X1,sK2),multiplication(sK3(sK2),X0)) = addition(multiplication(X1,multiplication(sK3(sK2),X0)),zero),
inference(superposition,[],[f65,f318]) ).
fof(f318,plain,
! [X0] : zero = multiplication(sK2,multiplication(sK3(sK2),X0)),
inference(forward_demodulation,[],[f302,f45]) ).
fof(f302,plain,
! [X0] : multiplication(zero,X0) = multiplication(sK2,multiplication(sK3(sK2),X0)),
inference(superposition,[],[f63,f106]) ).
fof(f537,plain,
! [X2,X0,X1] : multiplication(addition(X0,X2),X1) = addition(multiplication(X2,X1),multiplication(X0,X1)),
inference(superposition,[],[f53,f65]) ).
fof(f536,plain,
! [X2,X0,X1] : multiplication(addition(X0,X2),X1) = addition(multiplication(X2,X1),multiplication(X0,X1)),
inference(superposition,[],[f53,f65]) ).
fof(f535,plain,
! [X2,X0,X1] :
( multiplication(X2,X1) != multiplication(addition(X0,X2),X1)
| leq(multiplication(X0,X1),multiplication(X2,X1)) ),
inference(superposition,[],[f61,f65]) ).
fof(f534,plain,
! [X2,X0,X1] :
( multiplication(X0,X1) != multiplication(addition(X0,X2),X1)
| leq(multiplication(X2,X1),multiplication(X0,X1)) ),
inference(superposition,[],[f96,f65]) ).
fof(f533,plain,
! [X2,X3,X0,X1] : addition(multiplication(X0,X1),addition(multiplication(X2,X1),X3)) = addition(multiplication(addition(X0,X2),X1),X3),
inference(superposition,[],[f62,f65]) ).
fof(f530,plain,
! [X2,X0,X1] : multiplication(addition(X0,X2),X1) = addition(multiplication(X2,X1),multiplication(X0,X1)),
inference(superposition,[],[f65,f53]) ).
fof(f529,plain,
! [X2,X0,X1] : multiplication(addition(X0,X2),X1) = addition(multiplication(X2,X1),multiplication(X0,X1)),
inference(superposition,[],[f65,f53]) ).
fof(f561,plain,
! [X0] : multiplication(X0,sK2) = multiplication(addition(X0,sK3(sK2)),sK2),
inference(forward_demodulation,[],[f526,f46]) ).
fof(f526,plain,
! [X0] : addition(multiplication(X0,sK2),zero) = multiplication(addition(X0,sK3(sK2)),sK2),
inference(superposition,[],[f65,f112]) ).
fof(f560,plain,
! [X0] : multiplication(X0,c(sK2)) = multiplication(addition(X0,sK2),c(sK2)),
inference(forward_demodulation,[],[f525,f46]) ).
fof(f525,plain,
! [X0] : multiplication(addition(X0,sK2),c(sK2)) = addition(multiplication(X0,c(sK2)),zero),
inference(superposition,[],[f65,f115]) ).
fof(f559,plain,
! [X0] : multiplication(X0,sK3(sK2)) = multiplication(addition(X0,sK2),sK3(sK2)),
inference(forward_demodulation,[],[f524,f46]) ).
fof(f524,plain,
! [X0] : multiplication(addition(X0,sK2),sK3(sK2)) = addition(multiplication(X0,sK3(sK2)),zero),
inference(superposition,[],[f65,f106]) ).
fof(f557,plain,
! [X0,X1] : multiplication(X1,multiplication(sK2,X0)) = multiplication(addition(X1,c(sK2)),multiplication(sK2,X0)),
inference(forward_demodulation,[],[f522,f46]) ).
fof(f522,plain,
! [X0,X1] : multiplication(addition(X1,c(sK2)),multiplication(sK2,X0)) = addition(multiplication(X1,multiplication(sK2,X0)),zero),
inference(superposition,[],[f65,f316]) ).
fof(f555,plain,
! [X0] : multiplication(X0,sK2) = multiplication(addition(X0,c(sK2)),sK2),
inference(forward_demodulation,[],[f520,f46]) ).
fof(f520,plain,
! [X0] : multiplication(addition(X0,c(sK2)),sK2) = addition(multiplication(X0,sK2),zero),
inference(superposition,[],[f65,f109]) ).
fof(f518,plain,
! [X2,X3,X0,X1] : multiplication(addition(X3,multiplication(X0,X1)),X2) = addition(multiplication(X3,X2),multiplication(X0,multiplication(X1,X2))),
inference(superposition,[],[f65,f63]) ).
fof(f553,plain,
! [X0,X1] :
( multiplication(X1,sK3(X0)) = multiplication(addition(X1,X0),sK3(X0))
| zero = c(X0) ),
inference(forward_demodulation,[],[f516,f46]) ).
fof(f516,plain,
! [X0,X1] :
( multiplication(addition(X1,X0),sK3(X0)) = addition(multiplication(X1,sK3(X0)),zero)
| zero = c(X0) ),
inference(superposition,[],[f65,f107]) ).
fof(f549,plain,
! [X0] : multiplication(X0,sK2) = multiplication(addition(sK3(sK2),X0),sK2),
inference(forward_demodulation,[],[f513,f78]) ).
fof(f513,plain,
! [X0] : addition(zero,multiplication(X0,sK2)) = multiplication(addition(sK3(sK2),X0),sK2),
inference(superposition,[],[f65,f112]) ).
fof(f548,plain,
! [X0] : multiplication(addition(sK2,X0),c(sK2)) = multiplication(X0,c(sK2)),
inference(forward_demodulation,[],[f512,f78]) ).
fof(f512,plain,
! [X0] : multiplication(addition(sK2,X0),c(sK2)) = addition(zero,multiplication(X0,c(sK2))),
inference(superposition,[],[f65,f115]) ).
fof(f547,plain,
! [X0] : multiplication(addition(sK2,X0),sK3(sK2)) = multiplication(X0,sK3(sK2)),
inference(forward_demodulation,[],[f511,f78]) ).
fof(f511,plain,
! [X0] : multiplication(addition(sK2,X0),sK3(sK2)) = addition(zero,multiplication(X0,sK3(sK2))),
inference(superposition,[],[f65,f106]) ).
fof(f545,plain,
! [X0,X1] : multiplication(addition(c(sK2),X1),multiplication(sK2,X0)) = multiplication(X1,multiplication(sK2,X0)),
inference(forward_demodulation,[],[f509,f78]) ).
fof(f509,plain,
! [X0,X1] : multiplication(addition(c(sK2),X1),multiplication(sK2,X0)) = addition(zero,multiplication(X1,multiplication(sK2,X0))),
inference(superposition,[],[f65,f316]) ).
fof(f543,plain,
! [X0] : multiplication(addition(c(sK2),X0),sK2) = multiplication(X0,sK2),
inference(forward_demodulation,[],[f507,f78]) ).
fof(f507,plain,
! [X0] : multiplication(addition(c(sK2),X0),sK2) = addition(zero,multiplication(X0,sK2)),
inference(superposition,[],[f65,f109]) ).
fof(f506,plain,
! [X0,X1] : multiplication(addition(one,X1),X0) = addition(X0,multiplication(X1,X0)),
inference(superposition,[],[f65,f48]) ).
fof(f505,plain,
! [X2,X3,X0,X1] : multiplication(addition(multiplication(X0,X1),X3),X2) = addition(multiplication(X0,multiplication(X1,X2)),multiplication(X3,X2)),
inference(superposition,[],[f65,f63]) ).
fof(f541,plain,
! [X0,X1] :
( multiplication(addition(X0,X1),sK3(X0)) = multiplication(X1,sK3(X0))
| zero = c(X0) ),
inference(forward_demodulation,[],[f503,f78]) ).
fof(f503,plain,
! [X0,X1] :
( multiplication(addition(X0,X1),sK3(X0)) = addition(zero,multiplication(X1,sK3(X0)))
| zero = c(X0) ),
inference(superposition,[],[f65,f107]) ).
fof(f488,plain,
! [X0,X1] : multiplication(c(sK2),X1) = multiplication(c(sK2),addition(multiplication(sK2,X0),X1)),
inference(forward_demodulation,[],[f485,f78]) ).
fof(f485,plain,
! [X0,X1] : multiplication(c(sK2),addition(multiplication(sK2,X0),X1)) = addition(zero,multiplication(c(sK2),X1)),
inference(superposition,[],[f64,f316]) ).
fof(f487,plain,
! [X0,X1] : multiplication(c(sK2),addition(X1,multiplication(sK2,X0))) = multiplication(c(sK2),X1),
inference(forward_demodulation,[],[f484,f46]) ).
fof(f484,plain,
! [X0,X1] : multiplication(c(sK2),addition(X1,multiplication(sK2,X0))) = addition(multiplication(c(sK2),X1),zero),
inference(superposition,[],[f64,f316]) ).
fof(f316,plain,
! [X0] : zero = multiplication(c(sK2),multiplication(sK2,X0)),
inference(forward_demodulation,[],[f300,f45]) ).
fof(f300,plain,
! [X0] : multiplication(zero,X0) = multiplication(c(sK2),multiplication(sK2,X0)),
inference(superposition,[],[f63,f109]) ).
fof(f415,plain,
! [X2,X0,X1] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X2),multiplication(X0,X1)),
inference(superposition,[],[f53,f64]) ).
fof(f414,plain,
! [X2,X0,X1] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X2),multiplication(X0,X1)),
inference(superposition,[],[f53,f64]) ).
fof(f413,plain,
! [X2,X0,X1] :
( multiplication(X0,addition(X1,X2)) != multiplication(X0,X2)
| leq(multiplication(X0,X1),multiplication(X0,X2)) ),
inference(superposition,[],[f61,f64]) ).
fof(f412,plain,
! [X2,X0,X1] :
( multiplication(X0,X1) != multiplication(X0,addition(X1,X2))
| leq(multiplication(X0,X2),multiplication(X0,X1)) ),
inference(superposition,[],[f96,f64]) ).
fof(f411,plain,
! [X2,X3,X0,X1] : addition(multiplication(X0,X1),addition(multiplication(X0,X2),X3)) = addition(multiplication(X0,addition(X1,X2)),X3),
inference(superposition,[],[f62,f64]) ).
fof(f409,plain,
! [X2,X0,X1] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X2),multiplication(X0,X1)),
inference(superposition,[],[f64,f53]) ).
fof(f408,plain,
! [X2,X0,X1] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X2),multiplication(X0,X1)),
inference(superposition,[],[f64,f53]) ).
fof(f439,plain,
! [X0] : multiplication(sK3(sK2),X0) = multiplication(sK3(sK2),addition(X0,sK2)),
inference(forward_demodulation,[],[f406,f46]) ).
fof(f406,plain,
! [X0] : multiplication(sK3(sK2),addition(X0,sK2)) = addition(multiplication(sK3(sK2),X0),zero),
inference(superposition,[],[f64,f112]) ).
fof(f438,plain,
! [X0] : multiplication(sK2,X0) = multiplication(sK2,addition(X0,c(sK2))),
inference(forward_demodulation,[],[f405,f46]) ).
fof(f405,plain,
! [X0] : addition(multiplication(sK2,X0),zero) = multiplication(sK2,addition(X0,c(sK2))),
inference(superposition,[],[f64,f115]) ).
fof(f437,plain,
! [X0] : multiplication(sK2,X0) = multiplication(sK2,addition(X0,sK3(sK2))),
inference(forward_demodulation,[],[f404,f46]) ).
fof(f404,plain,
! [X0] : multiplication(sK2,addition(X0,sK3(sK2))) = addition(multiplication(sK2,X0),zero),
inference(superposition,[],[f64,f106]) ).
fof(f435,plain,
! [X0] : multiplication(c(sK2),X0) = multiplication(c(sK2),addition(X0,sK2)),
inference(forward_demodulation,[],[f402,f46]) ).
fof(f402,plain,
! [X0] : multiplication(c(sK2),addition(X0,sK2)) = addition(multiplication(c(sK2),X0),zero),
inference(superposition,[],[f64,f109]) ).
fof(f433,plain,
! [X2,X3,X0,X1] : addition(multiplication(X0,multiplication(X1,X3)),multiplication(X0,multiplication(X1,X2))) = multiplication(X0,multiplication(X1,addition(X3,X2))),
inference(forward_demodulation,[],[f432,f63]) ).
fof(f432,plain,
! [X2,X3,X0,X1] : multiplication(multiplication(X0,X1),addition(X3,X2)) = addition(multiplication(X0,multiplication(X1,X3)),multiplication(X0,multiplication(X1,X2))),
inference(forward_demodulation,[],[f400,f63]) ).
fof(f400,plain,
! [X2,X3,X0,X1] : multiplication(multiplication(X0,X1),addition(X3,X2)) = addition(multiplication(multiplication(X0,X1),X3),multiplication(X0,multiplication(X1,X2))),
inference(superposition,[],[f64,f63]) ).
fof(f429,plain,
! [X0,X1] :
( multiplication(X0,X1) = multiplication(X0,addition(X1,sK3(X0)))
| zero = c(X0) ),
inference(forward_demodulation,[],[f398,f46]) ).
fof(f398,plain,
! [X0,X1] :
( addition(multiplication(X0,X1),zero) = multiplication(X0,addition(X1,sK3(X0)))
| zero = c(X0) ),
inference(superposition,[],[f64,f107]) ).
fof(f397,plain,
! [X0,X1] : multiplication(X0,addition(X1,one)) = addition(multiplication(X0,X1),X0),
inference(superposition,[],[f64,f47]) ).
fof(f427,plain,
! [X0] : multiplication(sK3(sK2),X0) = multiplication(sK3(sK2),addition(sK2,X0)),
inference(forward_demodulation,[],[f395,f78]) ).
fof(f395,plain,
! [X0] : multiplication(sK3(sK2),addition(sK2,X0)) = addition(zero,multiplication(sK3(sK2),X0)),
inference(superposition,[],[f64,f112]) ).
fof(f426,plain,
! [X0] : multiplication(sK2,X0) = multiplication(sK2,addition(c(sK2),X0)),
inference(forward_demodulation,[],[f394,f78]) ).
fof(f394,plain,
! [X0] : addition(zero,multiplication(sK2,X0)) = multiplication(sK2,addition(c(sK2),X0)),
inference(superposition,[],[f64,f115]) ).
fof(f425,plain,
! [X0] : multiplication(sK2,X0) = multiplication(sK2,addition(sK3(sK2),X0)),
inference(forward_demodulation,[],[f393,f78]) ).
fof(f393,plain,
! [X0] : multiplication(sK2,addition(sK3(sK2),X0)) = addition(zero,multiplication(sK2,X0)),
inference(superposition,[],[f64,f106]) ).
fof(f423,plain,
! [X0] : multiplication(c(sK2),X0) = multiplication(c(sK2),addition(sK2,X0)),
inference(forward_demodulation,[],[f391,f78]) ).
fof(f391,plain,
! [X0] : multiplication(c(sK2),addition(sK2,X0)) = addition(zero,multiplication(c(sK2),X0)),
inference(superposition,[],[f64,f109]) ).
fof(f421,plain,
! [X2,X3,X0,X1] : addition(multiplication(X0,multiplication(X1,X2)),multiplication(X0,multiplication(X1,X3))) = multiplication(X0,multiplication(X1,addition(X2,X3))),
inference(forward_demodulation,[],[f420,f63]) ).
fof(f420,plain,
! [X2,X3,X0,X1] : multiplication(multiplication(X0,X1),addition(X2,X3)) = addition(multiplication(X0,multiplication(X1,X2)),multiplication(X0,multiplication(X1,X3))),
inference(forward_demodulation,[],[f389,f63]) ).
fof(f389,plain,
! [X2,X3,X0,X1] : multiplication(multiplication(X0,X1),addition(X2,X3)) = addition(multiplication(X0,multiplication(X1,X2)),multiplication(multiplication(X0,X1),X3)),
inference(superposition,[],[f64,f63]) ).
fof(f417,plain,
! [X0,X1] :
( multiplication(X0,X1) = multiplication(X0,addition(sK3(X0),X1))
| zero = c(X0) ),
inference(forward_demodulation,[],[f387,f78]) ).
fof(f387,plain,
! [X0,X1] :
( addition(zero,multiplication(X0,X1)) = multiplication(X0,addition(sK3(X0),X1))
| zero = c(X0) ),
inference(superposition,[],[f64,f107]) ).
fof(f386,plain,
! [X0,X1] : multiplication(X0,addition(one,X1)) = addition(X0,multiplication(X0,X1)),
inference(superposition,[],[f64,f47]) ).
fof(f64,plain,
! [X2,X0,X1] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
inference(cnf_transformation,[],[f8]) ).
fof(f8,axiom,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_distributivity) ).
fof(f310,plain,
! [X0,X1] :
( zero = multiplication(X0,multiplication(X1,sK3(multiplication(X0,X1))))
| zero = c(multiplication(X0,X1)) ),
inference(superposition,[],[f107,f63]) ).
fof(f307,plain,
! [X0,X1] :
( zero = multiplication(X0,multiplication(X1,sK3(multiplication(X0,X1))))
| zero = c(multiplication(X0,X1)) ),
inference(superposition,[],[f63,f107]) ).
fof(f312,plain,
! [X0,X1] :
( zero = multiplication(X0,multiplication(sK3(X0),X1))
| zero = c(X0) ),
inference(forward_demodulation,[],[f296,f45]) ).
fof(f296,plain,
! [X0,X1] :
( multiplication(zero,X1) = multiplication(X0,multiplication(sK3(X0),X1))
| zero = c(X0) ),
inference(superposition,[],[f63,f107]) ).
fof(f63,plain,
! [X2,X0,X1] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
inference(cnf_transformation,[],[f5]) ).
fof(f5,axiom,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_associativity) ).
fof(f246,plain,
! [X2,X0,X1] : addition(X0,addition(X1,X2)) = addition(X2,addition(X0,X1)),
inference(superposition,[],[f53,f62]) ).
fof(f245,plain,
! [X2,X0,X1] : addition(X0,addition(X1,X2)) = addition(X2,addition(X0,X1)),
inference(superposition,[],[f53,f62]) ).
fof(f244,plain,
! [X2,X0,X1] :
( addition(X0,addition(X1,X2)) != X2
| leq(addition(X0,X1),X2) ),
inference(superposition,[],[f61,f62]) ).
fof(f243,plain,
! [X2,X0,X1] :
( addition(X0,X1) != addition(X0,addition(X1,X2))
| leq(X2,addition(X0,X1)) ),
inference(superposition,[],[f96,f62]) ).
fof(f242,plain,
! [X0,X1] : addition(X0,X1) = addition(X0,addition(X1,addition(X0,X1))),
inference(superposition,[],[f49,f62]) ).
fof(f239,plain,
! [X2,X0,X1] : addition(X0,addition(X1,X2)) = addition(X2,addition(X0,X1)),
inference(superposition,[],[f62,f53]) ).
fof(f238,plain,
! [X2,X0,X1] : addition(X0,addition(X1,X2)) = addition(X2,addition(X0,X1)),
inference(superposition,[],[f62,f53]) ).
fof(f234,plain,
! [X0] : addition(one,X0) = addition(sK2,addition(c(sK2),X0)),
inference(superposition,[],[f62,f151]) ).
fof(f233,plain,
! [X0] : addition(sK2,addition(sK3(sK2),X0)) = addition(one,X0),
inference(superposition,[],[f62,f134]) ).
fof(f250,plain,
! [X0,X1] :
( addition(zero,addition(X0,X1)) = X1
| zero != X0 ),
inference(forward_demodulation,[],[f229,f78]) ).
fof(f229,plain,
! [X0,X1] :
( addition(zero,X1) = addition(zero,addition(X0,X1))
| zero != X0 ),
inference(superposition,[],[f62,f181]) ).
fof(f227,plain,
! [X2,X0,X1] : addition(X0,addition(X1,X2)) = addition(addition(X1,X0),X2),
inference(superposition,[],[f62,f53]) ).
fof(f247,plain,
! [X0,X1] :
( addition(X0,X1) = X1
| zero != X0 ),
inference(forward_demodulation,[],[f223,f78]) ).
fof(f223,plain,
! [X0,X1] :
( addition(zero,X1) = addition(X0,addition(zero,X1))
| zero != X0 ),
inference(superposition,[],[f62,f105]) ).
fof(f201,plain,
( zero = sK3(one)
| zero = c(one) ),
inference(superposition,[],[f107,f48]) ).
fof(f202,plain,
( zero = sK3(one)
| zero = c(one) ),
inference(superposition,[],[f48,f107]) ).
fof(f107,plain,
! [X0] :
( zero = multiplication(X0,sK3(X0))
| zero = c(X0) ),
inference(resolution,[],[f86,f50]) ).
fof(f200,plain,
! [X0] :
( c(sK3(X0)) = X0
| ~ test(X0)
| zero = c(sK3(X0)) ),
inference(resolution,[],[f148,f50]) ).
fof(f148,plain,
! [X0] :
( ~ test(sK3(X0))
| c(sK3(X0)) = X0
| ~ test(X0) ),
inference(resolution,[],[f55,f51]) ).
fof(f181,plain,
! [X0] :
( zero = addition(zero,X0)
| zero != X0 ),
inference(superposition,[],[f105,f53]) ).
fof(f187,plain,
! [X0] :
( zero = addition(zero,X0)
| zero != X0 ),
inference(superposition,[],[f53,f105]) ).
fof(f186,plain,
! [X0] :
( zero = addition(zero,X0)
| zero != X0 ),
inference(superposition,[],[f53,f105]) ).
fof(f182,plain,
! [X0] :
( zero = addition(zero,X0)
| zero != X0 ),
inference(superposition,[],[f105,f53]) ).
fof(f105,plain,
! [X0] :
( zero = addition(X0,zero)
| zero != X0 ),
inference(resolution,[],[f94,f60]) ).
fof(f169,plain,
( one != sK2
| leq(sK3(one),one) ),
inference(inner_rewriting,[],[f164]) ).
fof(f170,plain,
( one != sK2
| leq(c(one),one) ),
inference(inner_rewriting,[],[f165]) ).
fof(f165,plain,
( one != sK2
| leq(c(sK2),sK2) ),
inference(superposition,[],[f96,f151]) ).
fof(f164,plain,
( one != sK2
| leq(sK3(sK2),sK2) ),
inference(superposition,[],[f96,f134]) ).
fof(f96,plain,
! [X0,X1] :
( addition(X1,X0) != X1
| leq(X0,X1) ),
inference(superposition,[],[f61,f53]) ).
fof(f154,plain,
( one != c(sK2)
| leq(sK2,c(sK2)) ),
inference(superposition,[],[f61,f151]) ).
fof(f151,plain,
one = addition(sK2,c(sK2)),
inference(resolution,[],[f92,f40]) ).
fof(f153,plain,
! [X0] :
( one = addition(c(X0),c(c(X0)))
| ~ test(X0) ),
inference(resolution,[],[f92,f68]) ).
fof(f152,plain,
! [X0] :
( one = addition(X0,c(X0))
| zero = c(X0) ),
inference(resolution,[],[f92,f50]) ).
fof(f92,plain,
! [X0] :
( ~ test(X0)
| one = addition(X0,c(X0)) ),
inference(forward_demodulation,[],[f91,f53]) ).
fof(f91,plain,
! [X0] :
( one = addition(c(X0),X0)
| ~ test(X0) ),
inference(resolution,[],[f58,f66]) ).
fof(f55,plain,
! [X0,X1] :
( ~ complement(X0,X1)
| c(X0) = X1
| ~ test(X0) ),
inference(cnf_transformation,[],[f36]) ).
fof(f36,plain,
! [X0,X1] :
( ( ( c(X0) = X1
| ~ complement(X0,X1) )
& ( complement(X0,X1)
| c(X0) != X1 ) )
| ~ test(X0) ),
inference(nnf_transformation,[],[f27]) ).
fof(f27,plain,
! [X0,X1] :
( ( c(X0) = X1
<=> complement(X0,X1) )
| ~ test(X0) ),
inference(ennf_transformation,[],[f22]) ).
fof(f22,plain,
! [X0,X1] :
( test(X0)
=> ( c(X0) = X1
<=> complement(X0,X1) ) ),
inference(rectify,[],[f15]) ).
fof(f15,axiom,
! [X3,X4] :
( test(X3)
=> ( c(X3) = X4
<=> complement(X3,X4) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',test_3) ).
fof(f138,plain,
( one != sK3(sK2)
| leq(sK2,one) ),
inference(inner_rewriting,[],[f137]) ).
fof(f137,plain,
( one != sK3(sK2)
| leq(sK2,sK3(sK2)) ),
inference(superposition,[],[f61,f134]) ).
fof(f136,plain,
! [X0] :
( one = addition(c(X0),sK3(c(X0)))
| ~ test(X0) ),
inference(resolution,[],[f90,f68]) ).
fof(f135,plain,
! [X0] :
( one = addition(X0,sK3(X0))
| zero = c(X0) ),
inference(resolution,[],[f90,f50]) ).
fof(f115,plain,
zero = multiplication(sK2,c(sK2)),
inference(resolution,[],[f89,f40]) ).
fof(f117,plain,
! [X0] :
( zero = multiplication(c(X0),c(c(X0)))
| ~ test(X0) ),
inference(resolution,[],[f89,f68]) ).
fof(f116,plain,
! [X0] :
( zero = multiplication(X0,c(X0))
| zero = c(X0) ),
inference(resolution,[],[f89,f50]) ).
fof(f89,plain,
! [X0] :
( ~ test(X0)
| zero = multiplication(X0,c(X0)) ),
inference(resolution,[],[f57,f66]) ).
fof(f112,plain,
zero = multiplication(sK3(sK2),sK2),
inference(resolution,[],[f88,f40]) ).
fof(f114,plain,
! [X0] :
( zero = multiplication(sK3(c(X0)),c(X0))
| ~ test(X0) ),
inference(resolution,[],[f88,f68]) ).
fof(f113,plain,
! [X0] :
( zero = multiplication(sK3(X0),X0)
| zero = c(X0) ),
inference(resolution,[],[f88,f50]) ).
fof(f88,plain,
! [X0] :
( ~ test(X0)
| zero = multiplication(sK3(X0),X0) ),
inference(resolution,[],[f57,f51]) ).
fof(f109,plain,
zero = multiplication(c(sK2),sK2),
inference(resolution,[],[f87,f40]) ).
fof(f111,plain,
! [X0] :
( zero = multiplication(c(c(X0)),c(X0))
| ~ test(X0) ),
inference(resolution,[],[f87,f68]) ).
fof(f110,plain,
! [X0] :
( zero = multiplication(c(X0),X0)
| zero = c(X0) ),
inference(resolution,[],[f87,f50]) ).
fof(f87,plain,
! [X0] :
( ~ test(X0)
| zero = multiplication(c(X0),X0) ),
inference(resolution,[],[f56,f66]) ).
fof(f106,plain,
zero = multiplication(sK2,sK3(sK2)),
inference(resolution,[],[f86,f40]) ).
fof(f108,plain,
! [X0] :
( zero = multiplication(c(X0),sK3(c(X0)))
| ~ test(X0) ),
inference(resolution,[],[f86,f68]) ).
fof(f86,plain,
! [X0] :
( ~ test(X0)
| zero = multiplication(X0,sK3(X0)) ),
inference(resolution,[],[f56,f51]) ).
fof(f94,plain,
! [X0] :
( leq(X0,zero)
| zero != X0 ),
inference(superposition,[],[f61,f46]) ).
fof(f101,plain,
! [X0] : leq(zero,X0),
inference(trivial_inequality_removal,[],[f98]) ).
fof(f98,plain,
! [X0] :
( X0 != X0
| leq(zero,X0) ),
inference(superposition,[],[f61,f78]) ).
fof(f102,plain,
! [X0] : leq(X0,X0),
inference(trivial_inequality_removal,[],[f95]) ).
fof(f95,plain,
! [X0] :
( X0 != X0
| leq(X0,X0) ),
inference(superposition,[],[f61,f49]) ).
fof(f97,plain,
! [X0,X1] :
( addition(X1,X0) != X1
| leq(X0,X1) ),
inference(superposition,[],[f61,f53]) ).
fof(f61,plain,
! [X0,X1] :
( addition(X0,X1) != X1
| leq(X0,X1) ),
inference(cnf_transformation,[],[f39]) ).
fof(f57,plain,
! [X0,X1] :
( ~ complement(X1,X0)
| zero = multiplication(X1,X0) ),
inference(cnf_transformation,[],[f38]) ).
fof(f56,plain,
! [X0,X1] :
( ~ complement(X1,X0)
| zero = multiplication(X0,X1) ),
inference(cnf_transformation,[],[f38]) ).
fof(f78,plain,
! [X0] : addition(zero,X0) = X0,
inference(superposition,[],[f53,f46]) ).
fof(f81,plain,
! [X0] : addition(zero,X0) = X0,
inference(superposition,[],[f46,f53]) ).
fof(f80,plain,
! [X0] : addition(zero,X0) = X0,
inference(superposition,[],[f46,f53]) ).
fof(f79,plain,
! [X0] : addition(zero,X0) = X0,
inference(superposition,[],[f53,f46]) ).
fof(f53,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f1,axiom,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_commutativity) ).
fof(f41,plain,
( leq(sK0,sK1)
| leq(sK0,multiplication(sK2,sK1)) ),
inference(cnf_transformation,[],[f31]) ).
fof(f68,plain,
! [X0] :
( test(c(X0))
| ~ test(X0) ),
inference(resolution,[],[f66,f52]) ).
fof(f66,plain,
! [X0] :
( complement(X0,c(X0))
| ~ test(X0) ),
inference(equality_resolution,[],[f54]) ).
fof(f54,plain,
! [X0,X1] :
( complement(X0,X1)
| c(X0) != X1
| ~ test(X0) ),
inference(cnf_transformation,[],[f36]) ).
fof(f50,plain,
! [X0] :
( test(X0)
| zero = c(X0) ),
inference(cnf_transformation,[],[f26]) ).
fof(f26,plain,
! [X0] :
( zero = c(X0)
| test(X0) ),
inference(ennf_transformation,[],[f20]) ).
fof(f20,plain,
! [X0] :
( ~ test(X0)
=> zero = c(X0) ),
inference(rectify,[],[f16]) ).
fof(f16,axiom,
! [X3] :
( ~ test(X3)
=> zero = c(X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',test_4) ).
fof(f52,plain,
! [X0,X1] :
( ~ complement(X1,X0)
| test(X0) ),
inference(cnf_transformation,[],[f35]) ).
fof(f47,plain,
! [X0] : multiplication(X0,one) = X0,
inference(cnf_transformation,[],[f6]) ).
fof(f6,axiom,
! [X0] : multiplication(X0,one) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_right_identity) ).
fof(f46,plain,
! [X0] : addition(X0,zero) = X0,
inference(cnf_transformation,[],[f3]) ).
fof(f3,axiom,
! [X0] : addition(X0,zero) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_identity) ).
fof(f45,plain,
! [X0] : zero = multiplication(zero,X0),
inference(cnf_transformation,[],[f11]) ).
fof(f11,axiom,
! [X0] : zero = multiplication(zero,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_annihilation) ).
fof(f44,plain,
! [X0] : zero = multiplication(X0,zero),
inference(cnf_transformation,[],[f10]) ).
fof(f10,axiom,
! [X0] : zero = multiplication(X0,zero),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_annihilation) ).
fof(f42,plain,
( leq(multiplication(c(sK2),sK0),zero)
| leq(sK0,multiplication(sK2,sK1)) ),
inference(cnf_transformation,[],[f31]) ).
fof(f43,plain,
( ~ leq(multiplication(c(sK2),sK0),zero)
| ~ leq(sK0,sK1)
| ~ leq(sK0,multiplication(sK2,sK1)) ),
inference(cnf_transformation,[],[f31]) ).
fof(f21429,plain,
( ~ spl4_1
| spl4_2 ),
inference(avatar_contradiction_clause,[],[f21428]) ).
fof(f21428,plain,
( $false
| ~ spl4_1
| spl4_2 ),
inference(subsumption_resolution,[],[f21407,f75]) ).
fof(f21407,plain,
( leq(sK0,sK1)
| ~ spl4_1 ),
inference(superposition,[],[f895,f21291]) ).
fof(f21425,plain,
( ~ spl4_1
| spl4_2 ),
inference(avatar_contradiction_clause,[],[f21424]) ).
fof(f21424,plain,
( $false
| ~ spl4_1
| spl4_2 ),
inference(subsumption_resolution,[],[f21423,f75]) ).
fof(f21423,plain,
( leq(sK0,sK1)
| ~ spl4_1 ),
inference(trivial_inequality_removal,[],[f21395]) ).
fof(f21395,plain,
( sK1 != sK1
| leq(sK0,sK1)
| ~ spl4_1 ),
inference(superposition,[],[f61,f21291]) ).
fof(f20968,plain,
( ~ spl4_1
| ~ spl4_2 ),
inference(avatar_contradiction_clause,[],[f20967]) ).
fof(f20967,plain,
( $false
| ~ spl4_1
| ~ spl4_2 ),
inference(subsumption_resolution,[],[f20966,f20876]) ).
fof(f20876,plain,
( ~ leq(multiplication(c(sK2),sK0),zero)
| ~ spl4_1
| ~ spl4_2 ),
inference(subsumption_resolution,[],[f20678,f72]) ).
fof(f20678,plain,
( ~ leq(multiplication(c(sK2),sK0),zero)
| ~ leq(sK0,multiplication(sK2,sK1))
| ~ spl4_2 ),
inference(subsumption_resolution,[],[f43,f76]) ).
fof(f76,plain,
( leq(sK0,sK1)
| ~ spl4_2 ),
inference(avatar_component_clause,[],[f74]) ).
fof(f20966,plain,
( leq(multiplication(c(sK2),sK0),zero)
| ~ spl4_1 ),
inference(forward_demodulation,[],[f20955,f760]) ).
fof(f20955,plain,
( leq(multiplication(sK3(sK2),sK0),zero)
| ~ spl4_1 ),
inference(superposition,[],[f20919,f320]) ).
fof(f20919,plain,
( ! [X0] : leq(multiplication(X0,sK0),multiplication(X0,multiplication(sK2,sK1)))
| ~ spl4_1 ),
inference(trivial_inequality_removal,[],[f20901]) ).
fof(f20901,plain,
( ! [X0] :
( multiplication(X0,multiplication(sK2,sK1)) != multiplication(X0,multiplication(sK2,sK1))
| leq(multiplication(X0,sK0),multiplication(X0,multiplication(sK2,sK1))) )
| ~ spl4_1 ),
inference(superposition,[],[f413,f20679]) ).
fof(f20965,plain,
( ~ spl4_1
| ~ spl4_2 ),
inference(avatar_contradiction_clause,[],[f20964]) ).
fof(f20964,plain,
( $false
| ~ spl4_1
| ~ spl4_2 ),
inference(subsumption_resolution,[],[f20954,f20876]) ).
fof(f20954,plain,
( leq(multiplication(c(sK2),sK0),zero)
| ~ spl4_1 ),
inference(superposition,[],[f20919,f316]) ).
fof(f20647,plain,
( spl4_1
| ~ spl4_2 ),
inference(avatar_contradiction_clause,[],[f20646]) ).
fof(f20646,plain,
( $false
| spl4_1
| ~ spl4_2 ),
inference(subsumption_resolution,[],[f20617,f71]) ).
fof(f71,plain,
( ~ leq(sK0,multiplication(sK2,sK1))
| spl4_1 ),
inference(avatar_component_clause,[],[f70]) ).
fof(f20617,plain,
( leq(sK0,multiplication(sK2,sK1))
| spl4_1
| ~ spl4_2 ),
inference(superposition,[],[f6365,f20561]) ).
fof(f20561,plain,
( sK0 = multiplication(sK2,sK0)
| spl4_1 ),
inference(forward_demodulation,[],[f20560,f48]) ).
fof(f20560,plain,
( multiplication(sK2,sK0) = multiplication(one,sK0)
| spl4_1 ),
inference(forward_demodulation,[],[f20497,f46]) ).
fof(f20497,plain,
( multiplication(sK2,sK0) = addition(multiplication(one,sK0),zero)
| spl4_1 ),
inference(superposition,[],[f8838,f151]) ).
fof(f8838,plain,
( ! [X0] : multiplication(X0,sK0) = addition(multiplication(addition(X0,c(sK2)),sK0),zero)
| spl4_1 ),
inference(forward_demodulation,[],[f8676,f46]) ).
fof(f8676,plain,
( ! [X0] : addition(multiplication(X0,sK0),zero) = addition(multiplication(addition(X0,c(sK2)),sK0),zero)
| spl4_1 ),
inference(superposition,[],[f533,f119]) ).
fof(f119,plain,
( zero = addition(multiplication(c(sK2),sK0),zero)
| spl4_1 ),
inference(resolution,[],[f118,f60]) ).
fof(f118,plain,
( leq(multiplication(c(sK2),sK0),zero)
| spl4_1 ),
inference(subsumption_resolution,[],[f42,f71]) ).
fof(f6365,plain,
( ! [X0] : leq(multiplication(X0,sK0),multiplication(X0,sK1))
| ~ spl4_2 ),
inference(trivial_inequality_removal,[],[f6327]) ).
fof(f6327,plain,
( ! [X0] :
( multiplication(X0,sK1) != multiplication(X0,sK1)
| leq(multiplication(X0,sK0),multiplication(X0,sK1)) )
| ~ spl4_2 ),
inference(superposition,[],[f413,f93]) ).
fof(f93,plain,
( sK1 = addition(sK0,sK1)
| ~ spl4_2 ),
inference(resolution,[],[f60,f76]) ).
fof(f12609,plain,
( ~ spl4_19
| spl4_20
| ~ spl4_2 ),
inference(avatar_split_clause,[],[f12600,f74,f12606,f12602]) ).
fof(f12602,plain,
( spl4_19
<=> one = sK0 ),
introduced(avatar_definition,[new_symbols(naming,[spl4_19])]) ).
fof(f12606,plain,
( spl4_20
<=> leq(one,sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_20])]) ).
fof(f12600,plain,
( leq(one,sK1)
| one != sK0
| ~ spl4_2 ),
inference(subsumption_resolution,[],[f12469,f78]) ).
fof(f12469,plain,
( leq(one,sK1)
| sK1 != addition(zero,sK1)
| one != sK0
| ~ spl4_2 ),
inference(superposition,[],[f4136,f806]) ).
fof(f4136,plain,
( ! [X0] :
( leq(addition(X0,sK0),sK1)
| sK1 != addition(X0,sK1) )
| ~ spl4_2 ),
inference(superposition,[],[f244,f93]) ).
fof(f11933,plain,
( ~ spl4_17
| ~ spl4_18
| spl4_1
| ~ spl4_10 ),
inference(avatar_split_clause,[],[f11807,f219,f70,f11930,f11926]) ).
fof(f11926,plain,
( spl4_17
<=> one = multiplication(sK2,sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_17])]) ).
fof(f11930,plain,
( spl4_18
<=> leq(sK0,one) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_18])]) ).
fof(f219,plain,
( spl4_10
<=> test(zero) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_10])]) ).
fof(f11807,plain,
( ~ leq(sK0,one)
| one != multiplication(sK2,sK1)
| spl4_1
| ~ spl4_10 ),
inference(forward_demodulation,[],[f11225,f1064]) ).
fof(f1064,plain,
( one = c(zero)
| ~ spl4_10 ),
inference(superposition,[],[f814,f78]) ).
fof(f814,plain,
( one = addition(zero,c(zero))
| ~ spl4_10 ),
inference(resolution,[],[f221,f92]) ).
fof(f221,plain,
( test(zero)
| ~ spl4_10 ),
inference(avatar_component_clause,[],[f219]) ).
fof(f11225,plain,
( ~ leq(sK0,c(zero))
| one != multiplication(sK2,sK1)
| spl4_1
| ~ spl4_10 ),
inference(superposition,[],[f71,f833]) ).
fof(f833,plain,
( ! [X0] :
( c(zero) = X0
| one != X0 )
| ~ spl4_10 ),
inference(subsumption_resolution,[],[f828,f221]) ).
fof(f828,plain,
! [X0] :
( one != X0
| c(zero) = X0
| ~ test(zero) ),
inference(resolution,[],[f727,f55]) ).
fof(f11922,plain,
( ~ spl4_15
| spl4_16
| ~ spl4_2
| ~ spl4_10 ),
inference(avatar_split_clause,[],[f11560,f219,f74,f11919,f11915]) ).
fof(f11915,plain,
( spl4_15
<=> one = addition(sK0,sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_15])]) ).
fof(f11919,plain,
( spl4_16
<=> one = sK1 ),
introduced(avatar_definition,[new_symbols(naming,[spl4_16])]) ).
fof(f11560,plain,
( one = sK1
| one != addition(sK0,sK1)
| ~ spl4_2
| ~ spl4_10 ),
inference(forward_demodulation,[],[f11043,f1064]) ).
fof(f11043,plain,
( sK1 = c(zero)
| one != addition(sK0,sK1)
| ~ spl4_2
| ~ spl4_10 ),
inference(superposition,[],[f93,f833]) ).
fof(f4541,plain,
( ~ spl4_13
| spl4_14 ),
inference(avatar_split_clause,[],[f4511,f4538,f4534]) ).
fof(f4534,plain,
( spl4_13
<=> zero = one ),
introduced(avatar_definition,[new_symbols(naming,[spl4_13])]) ).
fof(f4538,plain,
( spl4_14
<=> leq(sK2,zero) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_14])]) ).
fof(f4511,plain,
( leq(sK2,zero)
| zero != one ),
inference(superposition,[],[f4483,f105]) ).
fof(f4483,plain,
! [X0] : leq(sK2,addition(one,X0)),
inference(superposition,[],[f895,f903]) ).
fof(f1267,plain,
( spl4_8
| ~ spl4_9 ),
inference(avatar_contradiction_clause,[],[f1266]) ).
fof(f1266,plain,
( $false
| spl4_8
| ~ spl4_9 ),
inference(subsumption_resolution,[],[f1256,f209]) ).
fof(f209,plain,
( zero != sK3(one)
| spl4_8 ),
inference(avatar_component_clause,[],[f208]) ).
fof(f208,plain,
( spl4_8
<=> zero = sK3(one) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_8])]) ).
fof(f1256,plain,
( zero = sK3(one)
| ~ spl4_9 ),
inference(superposition,[],[f47,f842]) ).
fof(f842,plain,
( zero = multiplication(sK3(one),one)
| ~ spl4_9 ),
inference(resolution,[],[f216,f88]) ).
fof(f216,plain,
( test(one)
| ~ spl4_9 ),
inference(avatar_component_clause,[],[f215]) ).
fof(f215,plain,
( spl4_9
<=> test(one) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_9])]) ).
fof(f1265,plain,
( spl4_8
| ~ spl4_9 ),
inference(avatar_contradiction_clause,[],[f1264]) ).
fof(f1264,plain,
( $false
| spl4_8
| ~ spl4_9 ),
inference(subsumption_resolution,[],[f1255,f209]) ).
fof(f1255,plain,
( zero = sK3(one)
| ~ spl4_9 ),
inference(superposition,[],[f842,f47]) ).
fof(f1117,plain,
( spl4_5
| ~ spl4_9 ),
inference(avatar_contradiction_clause,[],[f1116]) ).
fof(f1116,plain,
( $false
| spl4_5
| ~ spl4_9 ),
inference(subsumption_resolution,[],[f1111,f173]) ).
fof(f173,plain,
( ~ leq(sK3(one),one)
| spl4_5 ),
inference(avatar_component_clause,[],[f172]) ).
fof(f172,plain,
( spl4_5
<=> leq(sK3(one),one) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_5])]) ).
fof(f1111,plain,
( leq(sK3(one),one)
| ~ spl4_9 ),
inference(superposition,[],[f1016,f840]) ).
fof(f840,plain,
( one = addition(one,sK3(one))
| ~ spl4_9 ),
inference(resolution,[],[f216,f90]) ).
fof(f1115,plain,
( spl4_5
| ~ spl4_9 ),
inference(avatar_contradiction_clause,[],[f1114]) ).
fof(f1114,plain,
( $false
| spl4_5
| ~ spl4_9 ),
inference(subsumption_resolution,[],[f1112,f173]) ).
fof(f1112,plain,
( leq(sK3(one),one)
| ~ spl4_9 ),
inference(trivial_inequality_removal,[],[f1107]) ).
fof(f1107,plain,
( one != one
| leq(sK3(one),one)
| ~ spl4_9 ),
inference(superposition,[],[f96,f840]) ).
fof(f910,plain,
spl4_3,
inference(avatar_contradiction_clause,[],[f909]) ).
fof(f909,plain,
( $false
| spl4_3 ),
inference(subsumption_resolution,[],[f908,f141]) ).
fof(f141,plain,
( ~ leq(sK2,one)
| spl4_3 ),
inference(avatar_component_clause,[],[f140]) ).
fof(f140,plain,
( spl4_3
<=> leq(sK2,one) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_3])]) ).
fof(f838,plain,
spl4_9,
inference(avatar_split_clause,[],[f834,f215]) ).
fof(f836,plain,
spl4_9,
inference(avatar_contradiction_clause,[],[f835]) ).
fof(f835,plain,
( $false
| spl4_9 ),
inference(subsumption_resolution,[],[f834,f217]) ).
fof(f217,plain,
( ~ test(one)
| spl4_9 ),
inference(avatar_component_clause,[],[f215]) ).
fof(f813,plain,
spl4_10,
inference(avatar_contradiction_clause,[],[f812]) ).
fof(f812,plain,
( $false
| spl4_10 ),
inference(equality_resolution,[],[f811]) ).
fof(f811,plain,
( ! [X0] : one != X0
| spl4_10 ),
inference(subsumption_resolution,[],[f809,f220]) ).
fof(f220,plain,
( ~ test(zero)
| spl4_10 ),
inference(avatar_component_clause,[],[f219]) ).
fof(f292,plain,
( ~ spl4_11
| spl4_12
| ~ spl4_2 ),
inference(avatar_split_clause,[],[f271,f74,f289,f285]) ).
fof(f285,plain,
( spl4_11
<=> zero = sK1 ),
introduced(avatar_definition,[new_symbols(naming,[spl4_11])]) ).
fof(f289,plain,
( spl4_12
<=> leq(sK0,zero) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_12])]) ).
fof(f271,plain,
( leq(sK0,zero)
| zero != sK1
| ~ spl4_2 ),
inference(superposition,[],[f267,f105]) ).
fof(f267,plain,
( ! [X0] : leq(sK0,addition(sK1,X0))
| ~ spl4_2 ),
inference(trivial_inequality_removal,[],[f266]) ).
fof(f266,plain,
( ! [X0] :
( addition(sK1,X0) != addition(sK1,X0)
| leq(sK0,addition(sK1,X0)) )
| ~ spl4_2 ),
inference(superposition,[],[f61,f232]) ).
fof(f232,plain,
( ! [X0] : addition(sK1,X0) = addition(sK0,addition(sK1,X0))
| ~ spl4_2 ),
inference(superposition,[],[f62,f93]) ).
fof(f222,plain,
( ~ spl4_9
| spl4_10
| ~ spl4_7 ),
inference(avatar_split_clause,[],[f212,f204,f219,f215]) ).
fof(f204,plain,
( spl4_7
<=> zero = c(one) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_7])]) ).
fof(f212,plain,
( test(zero)
| ~ test(one)
| ~ spl4_7 ),
inference(superposition,[],[f68,f206]) ).
fof(f206,plain,
( zero = c(one)
| ~ spl4_7 ),
inference(avatar_component_clause,[],[f204]) ).
fof(f211,plain,
( spl4_7
| spl4_8 ),
inference(avatar_split_clause,[],[f201,f208,f204]) ).
fof(f179,plain,
( spl4_5
| ~ spl4_6 ),
inference(avatar_split_clause,[],[f169,f176,f172]) ).
fof(f176,plain,
( spl4_6
<=> one = sK2 ),
introduced(avatar_definition,[new_symbols(naming,[spl4_6])]) ).
fof(f147,plain,
( spl4_3
| ~ spl4_4 ),
inference(avatar_split_clause,[],[f138,f144,f140]) ).
fof(f144,plain,
( spl4_4
<=> one = sK3(sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_4])]) ).
fof(f77,plain,
( spl4_1
| spl4_2 ),
inference(avatar_split_clause,[],[f41,f74,f70]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : KLE008+1 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.15 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.35 % Computer : n016.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Tue Apr 30 05:39:41 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.14/0.35 % (2854)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.37 % (2857)WARNING: value z3 for option sas not known
% 0.14/0.37 % (2856)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.37 % (2861)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.14/0.37 % (2857)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.14/0.37 % (2859)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.14/0.37 % (2858)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.37 % (2860)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.14/0.37 TRYING [1]
% 0.14/0.37 % (2855)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.37 TRYING [2]
% 0.14/0.37 TRYING [3]
% 0.14/0.38 TRYING [1]
% 0.14/0.38 TRYING [2]
% 0.14/0.38 TRYING [4]
% 0.14/0.39 TRYING [3]
% 0.19/0.41 TRYING [5]
% 0.19/0.43 TRYING [4]
% 0.19/0.48 TRYING [6]
% 0.19/0.51 TRYING [5]
% 2.05/0.69 TRYING [7]
% 3.11/0.81 TRYING [6]
% 3.95/0.93 % (2857)First to succeed.
% 4.15/0.94 % (2857)Refutation found. Thanks to Tanya!
% 4.15/0.94 % SZS status Theorem for theBenchmark
% 4.15/0.94 % SZS output start Proof for theBenchmark
% See solution above
% 4.15/0.94 % (2857)------------------------------
% 4.15/0.94 % (2857)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 4.15/0.94 % (2857)Termination reason: Refutation
% 4.15/0.94
% 4.15/0.94 % (2857)Memory used [KB]: 6750
% 4.15/0.94 % (2857)Time elapsed: 0.566 s
% 4.15/0.94 % (2857)Instructions burned: 1346 (million)
% 4.15/0.94 % (2857)------------------------------
% 4.15/0.94 % (2857)------------------------------
% 4.15/0.94 % (2854)Success in time 0.574 s
%------------------------------------------------------------------------------