TSTP Solution File: KLE137+1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : KLE137+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% Computer : n024.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 1 17:09:21 EDT 2023
% Result : Theorem 0.18s 0.48s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 32
% Syntax : Number of formulae : 209 ( 78 unt; 0 def)
% Number of atoms : 360 ( 211 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 291 ( 140 ~; 133 |; 1 &)
% ( 13 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 15 ( 13 usr; 13 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 249 (; 247 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f621,plain,
$false,
inference(avatar_smt_refutation,[],[f54,f124,f129,f138,f145,f158,f176,f184,f185,f186,f187,f280,f289,f339,f340,f620]) ).
fof(f620,plain,
spl1_1,
inference(avatar_contradiction_clause,[],[f618]) ).
fof(f618,plain,
( $false
| spl1_1 ),
inference(resolution,[],[f617,f53]) ).
fof(f53,plain,
( ~ leq(sK0,strong_iteration(one))
| spl1_1 ),
inference(avatar_component_clause,[],[f51]) ).
fof(f51,plain,
( spl1_1
<=> leq(sK0,strong_iteration(one)) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_1])]) ).
fof(f617,plain,
! [X0] : leq(X0,strong_iteration(one)),
inference(superposition,[],[f613,f33]) ).
fof(f33,plain,
! [X0] : multiplication(X0,one) = X0,
inference(cnf_transformation,[],[f6]) ).
fof(f6,axiom,
! [X0] : multiplication(X0,one) = X0,
file('/export/starexec/sandbox/tmp/tmp.kXLOdSrYtg/Vampire---4.8_2105',multiplicative_right_identity) ).
fof(f613,plain,
! [X8,X9] : leq(X8,multiplication(strong_iteration(one),X9)),
inference(subsumption_resolution,[],[f598,f369]) ).
fof(f369,plain,
! [X4,X5] : leq(X4,addition(X4,X5)),
inference(trivial_inequality_removal,[],[f363]) ).
fof(f363,plain,
! [X4,X5] :
( addition(X4,X5) != addition(X4,X5)
| leq(X4,addition(X4,X5)) ),
inference(superposition,[],[f42,f214]) ).
fof(f214,plain,
! [X4,X5] : addition(X4,X5) = addition(X4,addition(X4,X5)),
inference(superposition,[],[f43,f35]) ).
fof(f35,plain,
! [X0] : addition(X0,X0) = X0,
inference(cnf_transformation,[],[f4]) ).
fof(f4,axiom,
! [X0] : addition(X0,X0) = X0,
file('/export/starexec/sandbox/tmp/tmp.kXLOdSrYtg/Vampire---4.8_2105',idempotence) ).
fof(f43,plain,
! [X2,X0,X1] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
inference(cnf_transformation,[],[f22]) ).
fof(f22,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/sandbox/tmp/tmp.kXLOdSrYtg/Vampire---4.8_2105',additive_associativity) ).
fof(f42,plain,
! [X0,X1] :
( addition(X0,X1) != X1
| leq(X0,X1) ),
inference(cnf_transformation,[],[f29]) ).
fof(f29,plain,
! [X0,X1] :
( ( leq(X0,X1)
| addition(X0,X1) != X1 )
& ( addition(X0,X1) = X1
| ~ leq(X0,X1) ) ),
inference(nnf_transformation,[],[f18]) ).
fof(f18,axiom,
! [X0,X1] :
( leq(X0,X1)
<=> addition(X0,X1) = X1 ),
file('/export/starexec/sandbox/tmp/tmp.kXLOdSrYtg/Vampire---4.8_2105',order) ).
fof(f598,plain,
! [X8,X9] :
( ~ leq(X8,addition(X8,X9))
| leq(X8,multiplication(strong_iteration(one),X9)) ),
inference(superposition,[],[f47,f34]) ).
fof(f34,plain,
! [X0] : multiplication(one,X0) = X0,
inference(cnf_transformation,[],[f7]) ).
fof(f7,axiom,
! [X0] : multiplication(one,X0) = X0,
file('/export/starexec/sandbox/tmp/tmp.kXLOdSrYtg/Vampire---4.8_2105',multiplicative_left_identity) ).
fof(f47,plain,
! [X2,X0,X1] :
( ~ leq(X2,addition(multiplication(X0,X2),X1))
| leq(X2,multiplication(strong_iteration(X0),X1)) ),
inference(cnf_transformation,[],[f24]) ).
fof(f24,plain,
! [X0,X1,X2] :
( leq(X2,multiplication(strong_iteration(X0),X1))
| ~ leq(X2,addition(multiplication(X0,X2),X1)) ),
inference(ennf_transformation,[],[f16]) ).
fof(f16,axiom,
! [X0,X1,X2] :
( leq(X2,addition(multiplication(X0,X2),X1))
=> leq(X2,multiplication(strong_iteration(X0),X1)) ),
file('/export/starexec/sandbox/tmp/tmp.kXLOdSrYtg/Vampire---4.8_2105',infty_coinduction) ).
fof(f340,plain,
( ~ spl1_12
| ~ spl1_5
| spl1_11 ),
inference(avatar_split_clause,[],[f334,f286,f142,f336]) ).
fof(f336,plain,
( spl1_12
<=> zero = star(one) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_12])]) ).
fof(f142,plain,
( spl1_5
<=> star(one) = addition(one,star(one)) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_5])]) ).
fof(f286,plain,
( spl1_11
<=> zero = one ),
introduced(avatar_definition,[new_symbols(naming,[spl1_11])]) ).
fof(f334,plain,
( zero != star(one)
| ~ spl1_5
| spl1_11 ),
inference(global_subsumption,[],[f45,f46,f47,f48,f49,f30,f31,f32,f33,f34,f35,f40,f56,f57,f58,f55,f41,f42,f66,f69,f68,f63,f65,f72,f82,f86,f87,f81,f36,f103,f104,f109,f105,f106,f107,f37,f114,f115,f119,f108,f116,f101,f111,f113,f144,f160,f38,f166,f170,f167,f171,f162,f118,f102,f195,f196,f201,f39,f204,f210,f205,f211,f43,f214,f215,f216,f243,f220,f221,f222,f223,f224,f226,f230,f231,f232,f235,f236,f237,f238,f239,f240,f248,f249,f251,f252,f253,f254,f255,f259,f261,f262,f263,f265,f266,f267,f268,f269,f271,f287,f44,f296,f297,f298,f247,f303,f306,f309,f310,f311,f312,f333,f314,f318,f319,f321,f322,f325,f326,f327,f328]) ).
fof(f328,plain,
( one = star(one)
| zero != star(one)
| ~ spl1_5 ),
inference(superposition,[],[f144,f247]) ).
fof(f327,plain,
! [X24] :
( one = star(X24)
| zero != multiplication(star(X24),X24) ),
inference(superposition,[],[f38,f247]) ).
fof(f326,plain,
! [X23] :
( one = strong_iteration(X23)
| zero != multiplication(X23,strong_iteration(X23)) ),
inference(superposition,[],[f102,f247]) ).
fof(f325,plain,
! [X22] :
( one = star(X22)
| zero != multiplication(X22,star(X22)) ),
inference(superposition,[],[f37,f247]) ).
fof(f322,plain,
! [X18,X16,X17] :
( addition(X16,X17) = addition(X16,addition(X17,X18))
| zero != X18 ),
inference(superposition,[],[f43,f247]) ).
fof(f321,plain,
! [X14,X15] :
( X14 = X15
| zero != X14
| zero != X15 ),
inference(superposition,[],[f240,f247]) ).
fof(f319,plain,
! [X10,X11,X9] :
( addition(X9,addition(X10,X11)) = addition(X9,X11)
| zero != X10 ),
inference(superposition,[],[f43,f247]) ).
fof(f318,plain,
! [X8,X7] :
( X7 != X8
| leq(X7,X8)
| zero != X8 ),
inference(superposition,[],[f42,f247]) ).
fof(f314,plain,
! [X20] :
( strong_iteration(X20) = star(X20)
| zero != multiplication(strong_iteration(X20),zero) ),
inference(superposition,[],[f247,f39]) ).
fof(f333,plain,
( zero != star(one)
| ~ spl1_5
| spl1_11 ),
inference(subsumption_resolution,[],[f332,f287]) ).
fof(f332,plain,
( zero = one
| zero != star(one)
| ~ spl1_5 ),
inference(inner_rewriting,[],[f312]) ).
fof(f312,plain,
( one = star(one)
| zero != star(one)
| ~ spl1_5 ),
inference(superposition,[],[f247,f144]) ).
fof(f311,plain,
! [X19] :
( one = star(X19)
| zero != multiplication(star(X19),X19) ),
inference(superposition,[],[f247,f38]) ).
fof(f310,plain,
! [X18] :
( one = strong_iteration(X18)
| zero != multiplication(X18,strong_iteration(X18)) ),
inference(superposition,[],[f247,f102]) ).
fof(f309,plain,
! [X17] :
( one = star(X17)
| zero != multiplication(X17,star(X17)) ),
inference(superposition,[],[f247,f37]) ).
fof(f306,plain,
! [X11,X12,X13] :
( addition(X11,X12) = addition(X11,addition(X12,X13))
| zero != X13 ),
inference(superposition,[],[f247,f43]) ).
fof(f303,plain,
! [X6,X5] :
( X5 = X6
| zero != X6
| zero != X5 ),
inference(superposition,[],[f247,f240]) ).
fof(f247,plain,
! [X6,X5] :
( addition(X6,X5) = X6
| zero != X5 ),
inference(superposition,[],[f240,f40]) ).
fof(f298,plain,
! [X6,X7] : strong_iteration(multiplication(X6,X7)) = addition(multiplication(X6,multiplication(X7,strong_iteration(multiplication(X6,X7)))),one),
inference(superposition,[],[f36,f44]) ).
fof(f297,plain,
! [X4,X5] : strong_iteration(multiplication(X4,X5)) = addition(one,multiplication(X4,multiplication(X5,strong_iteration(multiplication(X4,X5))))),
inference(superposition,[],[f102,f44]) ).
fof(f296,plain,
! [X2,X3] : star(multiplication(X2,X3)) = addition(one,multiplication(X2,multiplication(X3,star(multiplication(X2,X3))))),
inference(superposition,[],[f37,f44]) ).
fof(f44,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/sandbox/tmp/tmp.kXLOdSrYtg/Vampire---4.8_2105',multiplicative_associativity) ).
fof(f287,plain,
( zero != one
| spl1_11 ),
inference(avatar_component_clause,[],[f286]) ).
fof(f271,plain,
! [X8,X9] :
( leq(X8,X9)
| zero != X8 ),
inference(trivial_inequality_removal,[],[f260]) ).
fof(f260,plain,
! [X8,X9] :
( X9 != X9
| leq(X8,X9)
| zero != X8 ),
inference(superposition,[],[f42,f240]) ).
fof(f269,plain,
! [X23] :
( strong_iteration(X23) = multiplication(strong_iteration(X23),zero)
| zero != star(X23) ),
inference(superposition,[],[f39,f240]) ).
fof(f268,plain,
! [X22] :
( star(X22) = multiplication(star(X22),X22)
| zero != one ),
inference(superposition,[],[f38,f240]) ).
fof(f267,plain,
! [X21] :
( strong_iteration(X21) = multiplication(X21,strong_iteration(X21))
| zero != one ),
inference(superposition,[],[f102,f240]) ).
fof(f266,plain,
! [X20] :
( star(X20) = multiplication(X20,star(X20))
| zero != one ),
inference(superposition,[],[f37,f240]) ).
fof(f265,plain,
! [X19] :
( one = strong_iteration(X19)
| zero != multiplication(X19,strong_iteration(X19)) ),
inference(superposition,[],[f36,f240]) ).
fof(f263,plain,
! [X16,X14,X15] :
( addition(X14,addition(X15,X16)) = X16
| zero != addition(X14,X15) ),
inference(superposition,[],[f43,f240]) ).
fof(f262,plain,
! [X12,X13] :
( addition(X13,X12) = X13
| zero != X12 ),
inference(superposition,[],[f40,f240]) ).
fof(f261,plain,
! [X10,X11] :
( addition(X11,X10) = X11
| zero != X10 ),
inference(superposition,[],[f40,f240]) ).
fof(f259,plain,
! [X6,X7] :
( X6 != X7
| leq(X7,X6)
| zero != X6 ),
inference(superposition,[],[f65,f240]) ).
fof(f255,plain,
! [X18] :
( strong_iteration(X18) = multiplication(strong_iteration(X18),zero)
| zero != star(X18) ),
inference(superposition,[],[f240,f39]) ).
fof(f254,plain,
! [X17] :
( star(X17) = multiplication(star(X17),X17)
| zero != one ),
inference(superposition,[],[f240,f38]) ).
fof(f253,plain,
! [X16] :
( strong_iteration(X16) = multiplication(X16,strong_iteration(X16))
| zero != one ),
inference(superposition,[],[f240,f102]) ).
fof(f252,plain,
! [X15] :
( star(X15) = multiplication(X15,star(X15))
| zero != one ),
inference(superposition,[],[f240,f37]) ).
fof(f251,plain,
! [X14] :
( one = strong_iteration(X14)
| zero != multiplication(X14,strong_iteration(X14)) ),
inference(superposition,[],[f240,f36]) ).
fof(f249,plain,
! [X10,X11,X9] :
( addition(X9,addition(X10,X11)) = X11
| zero != addition(X9,X10) ),
inference(superposition,[],[f240,f43]) ).
fof(f248,plain,
! [X8,X7] :
( addition(X8,X7) = X8
| zero != X7 ),
inference(superposition,[],[f240,f40]) ).
fof(f240,plain,
! [X0,X1] :
( addition(X0,X1) = X1
| zero != X0 ),
inference(forward_demodulation,[],[f212,f55]) ).
fof(f212,plain,
! [X0,X1] :
( addition(zero,X1) = addition(X0,addition(zero,X1))
| zero != X0 ),
inference(superposition,[],[f43,f72]) ).
fof(f239,plain,
! [X16,X17,X15] : addition(X15,addition(X16,X17)) = addition(X17,addition(X15,X16)),
inference(superposition,[],[f40,f43]) ).
fof(f238,plain,
! [X14,X12,X13] : addition(X12,addition(X13,X14)) = addition(X14,addition(X12,X13)),
inference(superposition,[],[f40,f43]) ).
fof(f237,plain,
! [X10,X11,X9] :
( addition(X9,addition(X10,X11)) != X11
| leq(addition(X9,X10),X11) ),
inference(superposition,[],[f42,f43]) ).
fof(f236,plain,
! [X8,X6,X7] :
( addition(X6,X7) != addition(X6,addition(X7,X8))
| leq(X8,addition(X6,X7)) ),
inference(superposition,[],[f65,f43]) ).
fof(f235,plain,
! [X4,X5] : addition(X4,X5) = addition(X4,addition(X5,addition(X4,X5))),
inference(superposition,[],[f35,f43]) ).
fof(f232,plain,
! [X14,X12,X13] : addition(X12,addition(X13,X14)) = addition(X14,addition(X12,X13)),
inference(superposition,[],[f43,f40]) ).
fof(f231,plain,
! [X10,X11,X9] : addition(X9,addition(X10,X11)) = addition(X11,addition(X9,X10)),
inference(superposition,[],[f43,f40]) ).
fof(f230,plain,
! [X8,X7] : addition(X7,X8) = addition(X7,addition(X8,addition(X7,X8))),
inference(superposition,[],[f43,f35]) ).
fof(f226,plain,
! [X31,X30] : addition(star(X30),addition(multiplication(strong_iteration(X30),zero),X31)) = addition(strong_iteration(X30),X31),
inference(superposition,[],[f43,f39]) ).
fof(f224,plain,
( ! [X28] : addition(star(one),X28) = addition(one,addition(star(one),X28))
| ~ spl1_5 ),
inference(superposition,[],[f43,f144]) ).
fof(f223,plain,
! [X26,X27] : addition(one,addition(multiplication(star(X26),X26),X27)) = addition(star(X26),X27),
inference(superposition,[],[f43,f38]) ).
fof(f222,plain,
! [X24,X25] : addition(one,addition(multiplication(X24,strong_iteration(X24)),X25)) = addition(strong_iteration(X24),X25),
inference(superposition,[],[f43,f102]) ).
fof(f221,plain,
! [X22,X23] : addition(one,addition(multiplication(X22,star(X22)),X23)) = addition(star(X22),X23),
inference(superposition,[],[f43,f37]) ).
fof(f220,plain,
! [X21,X20] : addition(multiplication(X20,strong_iteration(X20)),addition(one,X21)) = addition(strong_iteration(X20),X21),
inference(superposition,[],[f43,f36]) ).
fof(f243,plain,
! [X16,X17] :
( addition(zero,addition(X16,X17)) = X17
| zero != X16 ),
inference(forward_demodulation,[],[f218,f55]) ).
fof(f218,plain,
! [X16,X17] :
( addition(zero,addition(X16,X17)) = addition(zero,X17)
| zero != X16 ),
inference(superposition,[],[f43,f81]) ).
fof(f216,plain,
! [X10,X11,X9] : addition(X9,addition(X10,X11)) = addition(addition(X10,X9),X11),
inference(superposition,[],[f43,f40]) ).
fof(f215,plain,
! [X8,X6,X7] : addition(X6,addition(X7,X8)) = addition(addition(X7,X6),X8),
inference(superposition,[],[f43,f40]) ).
fof(f211,plain,
! [X1] :
( strong_iteration(X1) != multiplication(strong_iteration(X1),zero)
| leq(star(X1),strong_iteration(X1)) ),
inference(inner_rewriting,[],[f205]) ).
fof(f205,plain,
! [X1] :
( strong_iteration(X1) != multiplication(strong_iteration(X1),zero)
| leq(star(X1),multiplication(strong_iteration(X1),zero)) ),
inference(superposition,[],[f42,f39]) ).
fof(f210,plain,
! [X0] :
( star(X0) != strong_iteration(X0)
| leq(multiplication(star(X0),zero),star(X0)) ),
inference(inner_rewriting,[],[f204]) ).
fof(f204,plain,
! [X0] :
( star(X0) != strong_iteration(X0)
| leq(multiplication(strong_iteration(X0),zero),star(X0)) ),
inference(superposition,[],[f65,f39]) ).
fof(f39,plain,
! [X0] : strong_iteration(X0) = addition(star(X0),multiplication(strong_iteration(X0),zero)),
inference(cnf_transformation,[],[f17]) ).
fof(f17,axiom,
! [X0] : strong_iteration(X0) = addition(star(X0),multiplication(strong_iteration(X0),zero)),
file('/export/starexec/sandbox/tmp/tmp.kXLOdSrYtg/Vampire---4.8_2105',isolation) ).
fof(f201,plain,
! [X1] :
( strong_iteration(X1) != multiplication(X1,strong_iteration(X1))
| leq(one,strong_iteration(X1)) ),
inference(inner_rewriting,[],[f196]) ).
fof(f196,plain,
! [X1] :
( strong_iteration(X1) != multiplication(X1,strong_iteration(X1))
| leq(one,multiplication(X1,strong_iteration(X1))) ),
inference(superposition,[],[f42,f102]) ).
fof(f195,plain,
! [X0] :
( one != strong_iteration(X0)
| leq(multiplication(X0,strong_iteration(X0)),one) ),
inference(superposition,[],[f65,f102]) ).
fof(f102,plain,
! [X1] : strong_iteration(X1) = addition(one,multiplication(X1,strong_iteration(X1))),
inference(superposition,[],[f36,f40]) ).
fof(f118,plain,
! [X0] :
( one != star(X0)
| leq(X0,one) ),
inference(forward_demodulation,[],[f117,f33]) ).
fof(f117,plain,
! [X0] :
( one != star(X0)
| leq(multiplication(X0,one),one) ),
inference(inner_rewriting,[],[f114]) ).
fof(f162,plain,
( leq(one,star(one))
| ~ spl1_5 ),
inference(trivial_inequality_removal,[],[f161]) ).
fof(f161,plain,
( star(one) != star(one)
| leq(one,star(one))
| ~ spl1_5 ),
inference(superposition,[],[f42,f144]) ).
fof(f171,plain,
! [X1] :
( star(X1) != multiplication(star(X1),X1)
| leq(one,star(X1)) ),
inference(inner_rewriting,[],[f167]) ).
fof(f167,plain,
! [X1] :
( star(X1) != multiplication(star(X1),X1)
| leq(one,multiplication(star(X1),X1)) ),
inference(superposition,[],[f42,f38]) ).
fof(f170,plain,
! [X0] :
( leq(X0,one)
| one != star(X0) ),
inference(forward_demodulation,[],[f169,f34]) ).
fof(f169,plain,
! [X0] :
( one != star(X0)
| leq(multiplication(one,X0),one) ),
inference(inner_rewriting,[],[f166]) ).
fof(f166,plain,
! [X0] :
( one != star(X0)
| leq(multiplication(star(X0),X0),one) ),
inference(superposition,[],[f65,f38]) ).
fof(f38,plain,
! [X0] : star(X0) = addition(one,multiplication(star(X0),X0)),
inference(cnf_transformation,[],[f12]) ).
fof(f12,axiom,
! [X0] : star(X0) = addition(one,multiplication(star(X0),X0)),
file('/export/starexec/sandbox/tmp/tmp.kXLOdSrYtg/Vampire---4.8_2105',star_unfold2) ).
fof(f160,plain,
( one != star(one)
| leq(star(one),one)
| ~ spl1_5 ),
inference(superposition,[],[f65,f144]) ).
fof(f144,plain,
( star(one) = addition(one,star(one))
| ~ spl1_5 ),
inference(avatar_component_clause,[],[f142]) ).
fof(f113,plain,
star(one) = addition(one,star(one)),
inference(superposition,[],[f37,f34]) ).
fof(f111,plain,
! [X1] :
( one != strong_iteration(X1)
| leq(X1,one) ),
inference(forward_demodulation,[],[f110,f33]) ).
fof(f110,plain,
! [X1] :
( one != strong_iteration(X1)
| leq(multiplication(X1,one),one) ),
inference(inner_rewriting,[],[f105]) ).
fof(f101,plain,
strong_iteration(one) = addition(strong_iteration(one),one),
inference(superposition,[],[f36,f34]) ).
fof(f116,plain,
one = star(zero),
inference(forward_demodulation,[],[f112,f32]) ).
fof(f112,plain,
addition(one,zero) = star(zero),
inference(superposition,[],[f37,f31]) ).
fof(f108,plain,
one = strong_iteration(zero),
inference(forward_demodulation,[],[f100,f55]) ).
fof(f100,plain,
strong_iteration(zero) = addition(zero,one),
inference(superposition,[],[f36,f31]) ).
fof(f119,plain,
! [X1] :
( star(X1) != multiplication(X1,star(X1))
| leq(one,star(X1)) ),
inference(inner_rewriting,[],[f115]) ).
fof(f115,plain,
! [X1] :
( star(X1) != multiplication(X1,star(X1))
| leq(one,multiplication(X1,star(X1))) ),
inference(superposition,[],[f42,f37]) ).
fof(f114,plain,
! [X0] :
( one != star(X0)
| leq(multiplication(X0,star(X0)),one) ),
inference(superposition,[],[f65,f37]) ).
fof(f37,plain,
! [X0] : star(X0) = addition(one,multiplication(X0,star(X0))),
inference(cnf_transformation,[],[f11]) ).
fof(f11,axiom,
! [X0] : star(X0) = addition(one,multiplication(X0,star(X0))),
file('/export/starexec/sandbox/tmp/tmp.kXLOdSrYtg/Vampire---4.8_2105',star_unfold1) ).
fof(f107,plain,
! [X3] : strong_iteration(X3) = addition(one,multiplication(X3,strong_iteration(X3))),
inference(superposition,[],[f40,f36]) ).
fof(f106,plain,
! [X2] : strong_iteration(X2) = addition(one,multiplication(X2,strong_iteration(X2))),
inference(superposition,[],[f40,f36]) ).
fof(f105,plain,
! [X1] :
( one != strong_iteration(X1)
| leq(multiplication(X1,strong_iteration(X1)),one) ),
inference(superposition,[],[f42,f36]) ).
fof(f109,plain,
! [X0] :
( strong_iteration(X0) != multiplication(X0,strong_iteration(X0))
| leq(one,strong_iteration(X0)) ),
inference(inner_rewriting,[],[f104]) ).
fof(f104,plain,
! [X0] :
( strong_iteration(X0) != multiplication(X0,strong_iteration(X0))
| leq(one,multiplication(X0,strong_iteration(X0))) ),
inference(superposition,[],[f65,f36]) ).
fof(f103,plain,
! [X2] : strong_iteration(X2) = addition(one,multiplication(X2,strong_iteration(X2))),
inference(superposition,[],[f36,f40]) ).
fof(f36,plain,
! [X0] : strong_iteration(X0) = addition(multiplication(X0,strong_iteration(X0)),one),
inference(cnf_transformation,[],[f15]) ).
fof(f15,axiom,
! [X0] : strong_iteration(X0) = addition(multiplication(X0,strong_iteration(X0)),one),
file('/export/starexec/sandbox/tmp/tmp.kXLOdSrYtg/Vampire---4.8_2105',infty_unfold1) ).
fof(f81,plain,
! [X2] :
( zero = addition(zero,X2)
| zero != X2 ),
inference(superposition,[],[f72,f40]) ).
fof(f87,plain,
! [X4] :
( zero = addition(zero,X4)
| zero != X4 ),
inference(superposition,[],[f40,f72]) ).
fof(f86,plain,
! [X3] :
( zero = addition(zero,X3)
| zero != X3 ),
inference(superposition,[],[f40,f72]) ).
fof(f82,plain,
! [X3] :
( zero = addition(zero,X3)
| zero != X3 ),
inference(superposition,[],[f72,f40]) ).
fof(f72,plain,
! [X0] :
( zero = addition(X0,zero)
| zero != X0 ),
inference(resolution,[],[f63,f41]) ).
fof(f65,plain,
! [X2,X3] :
( addition(X3,X2) != X3
| leq(X2,X3) ),
inference(superposition,[],[f42,f40]) ).
fof(f63,plain,
! [X0] :
( leq(X0,zero)
| zero != X0 ),
inference(superposition,[],[f42,f32]) ).
fof(f68,plain,
! [X6] : leq(zero,X6),
inference(trivial_inequality_removal,[],[f67]) ).
fof(f67,plain,
! [X6] :
( X6 != X6
| leq(zero,X6) ),
inference(superposition,[],[f42,f55]) ).
fof(f69,plain,
! [X1] : leq(X1,X1),
inference(trivial_inequality_removal,[],[f64]) ).
fof(f64,plain,
! [X1] :
( X1 != X1
| leq(X1,X1) ),
inference(superposition,[],[f42,f35]) ).
fof(f66,plain,
! [X4,X5] :
( addition(X5,X4) != X5
| leq(X4,X5) ),
inference(superposition,[],[f42,f40]) ).
fof(f41,plain,
! [X0,X1] :
( ~ leq(X0,X1)
| addition(X0,X1) = X1 ),
inference(cnf_transformation,[],[f29]) ).
fof(f55,plain,
! [X0] : addition(zero,X0) = X0,
inference(superposition,[],[f40,f32]) ).
fof(f58,plain,
! [X0] : addition(zero,X0) = X0,
inference(superposition,[],[f32,f40]) ).
fof(f57,plain,
! [X0] : addition(zero,X0) = X0,
inference(superposition,[],[f32,f40]) ).
fof(f56,plain,
! [X0] : addition(zero,X0) = X0,
inference(superposition,[],[f40,f32]) ).
fof(f40,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/sandbox/tmp/tmp.kXLOdSrYtg/Vampire---4.8_2105',additive_commutativity) ).
fof(f32,plain,
! [X0] : addition(X0,zero) = X0,
inference(cnf_transformation,[],[f3]) ).
fof(f3,axiom,
! [X0] : addition(X0,zero) = X0,
file('/export/starexec/sandbox/tmp/tmp.kXLOdSrYtg/Vampire---4.8_2105',additive_identity) ).
fof(f31,plain,
! [X0] : zero = multiplication(zero,X0),
inference(cnf_transformation,[],[f10]) ).
fof(f10,axiom,
! [X0] : zero = multiplication(zero,X0),
file('/export/starexec/sandbox/tmp/tmp.kXLOdSrYtg/Vampire---4.8_2105',left_annihilation) ).
fof(f30,plain,
~ leq(sK0,strong_iteration(one)),
inference(cnf_transformation,[],[f28]) ).
fof(f28,plain,
~ leq(sK0,strong_iteration(one)),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f23,f27]) ).
fof(f27,plain,
( ? [X0] : ~ leq(X0,strong_iteration(one))
=> ~ leq(sK0,strong_iteration(one)) ),
introduced(choice_axiom,[]) ).
fof(f23,plain,
? [X0] : ~ leq(X0,strong_iteration(one)),
inference(ennf_transformation,[],[f21]) ).
fof(f21,plain,
~ ! [X0] : leq(X0,strong_iteration(one)),
inference(rectify,[],[f20]) ).
fof(f20,negated_conjecture,
~ ! [X3] : leq(X3,strong_iteration(one)),
inference(negated_conjecture,[],[f19]) ).
fof(f19,conjecture,
! [X3] : leq(X3,strong_iteration(one)),
file('/export/starexec/sandbox/tmp/tmp.kXLOdSrYtg/Vampire---4.8_2105',goals) ).
fof(f49,plain,
! [X2,X0,X1] :
( leq(multiplication(star(X0),X1),X2)
| ~ leq(addition(multiplication(X0,X2),X1),X2) ),
inference(cnf_transformation,[],[f26]) ).
fof(f26,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),X1),X2)
| ~ leq(addition(multiplication(X0,X2),X1),X2) ),
inference(ennf_transformation,[],[f13]) ).
fof(f13,axiom,
! [X0,X1,X2] :
( leq(addition(multiplication(X0,X2),X1),X2)
=> leq(multiplication(star(X0),X1),X2) ),
file('/export/starexec/sandbox/tmp/tmp.kXLOdSrYtg/Vampire---4.8_2105',star_induction1) ).
fof(f48,plain,
! [X2,X0,X1] :
( leq(multiplication(X1,star(X0)),X2)
| ~ leq(addition(multiplication(X2,X0),X1),X2) ),
inference(cnf_transformation,[],[f25]) ).
fof(f25,plain,
! [X0,X1,X2] :
( leq(multiplication(X1,star(X0)),X2)
| ~ leq(addition(multiplication(X2,X0),X1),X2) ),
inference(ennf_transformation,[],[f14]) ).
fof(f14,axiom,
! [X0,X1,X2] :
( leq(addition(multiplication(X2,X0),X1),X2)
=> leq(multiplication(X1,star(X0)),X2) ),
file('/export/starexec/sandbox/tmp/tmp.kXLOdSrYtg/Vampire---4.8_2105',star_induction2) ).
fof(f46,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/sandbox/tmp/tmp.kXLOdSrYtg/Vampire---4.8_2105',distributivity2) ).
fof(f45,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/sandbox/tmp/tmp.kXLOdSrYtg/Vampire---4.8_2105',distributivity1) ).
fof(f339,plain,
( ~ spl1_12
| ~ spl1_5
| spl1_11 ),
inference(avatar_split_clause,[],[f333,f286,f142,f336]) ).
fof(f289,plain,
( ~ spl1_10
| spl1_11
| ~ spl1_4 ),
inference(avatar_split_clause,[],[f272,f135,f286,f282]) ).
fof(f282,plain,
( spl1_10
<=> zero = strong_iteration(one) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_10])]) ).
fof(f135,plain,
( spl1_4
<=> strong_iteration(one) = addition(strong_iteration(one),one) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_4])]) ).
fof(f272,plain,
( zero = one
| zero != strong_iteration(one)
| ~ spl1_4 ),
inference(inner_rewriting,[],[f256]) ).
fof(f256,plain,
( one = strong_iteration(one)
| zero != strong_iteration(one)
| ~ spl1_4 ),
inference(superposition,[],[f240,f137]) ).
fof(f137,plain,
( strong_iteration(one) = addition(strong_iteration(one),one)
| ~ spl1_4 ),
inference(avatar_component_clause,[],[f135]) ).
fof(f280,plain,
( ~ spl1_9
| spl1_1 ),
inference(avatar_split_clause,[],[f274,f51,f277]) ).
fof(f277,plain,
( spl1_9
<=> zero = sK0 ),
introduced(avatar_definition,[new_symbols(naming,[spl1_9])]) ).
fof(f274,plain,
( zero != sK0
| spl1_1 ),
inference(resolution,[],[f271,f53]) ).
fof(f187,plain,
( spl1_8
| ~ spl1_4 ),
inference(avatar_split_clause,[],[f151,f135,f181]) ).
fof(f181,plain,
( spl1_8
<=> strong_iteration(one) = addition(one,strong_iteration(one)) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_8])]) ).
fof(f151,plain,
( strong_iteration(one) = addition(one,strong_iteration(one))
| ~ spl1_4 ),
inference(superposition,[],[f40,f137]) ).
fof(f186,plain,
( spl1_8
| ~ spl1_4 ),
inference(avatar_split_clause,[],[f150,f135,f181]) ).
fof(f150,plain,
( strong_iteration(one) = addition(one,strong_iteration(one))
| ~ spl1_4 ),
inference(superposition,[],[f40,f137]) ).
fof(f185,plain,
( spl1_8
| ~ spl1_4 ),
inference(avatar_split_clause,[],[f147,f135,f181]) ).
fof(f147,plain,
( strong_iteration(one) = addition(one,strong_iteration(one))
| ~ spl1_4 ),
inference(superposition,[],[f137,f40]) ).
fof(f184,plain,
( spl1_8
| ~ spl1_4 ),
inference(avatar_split_clause,[],[f146,f135,f181]) ).
fof(f146,plain,
( strong_iteration(one) = addition(one,strong_iteration(one))
| ~ spl1_4 ),
inference(superposition,[],[f137,f40]) ).
fof(f176,plain,
( spl1_7
| ~ spl1_5 ),
inference(avatar_split_clause,[],[f162,f142,f173]) ).
fof(f173,plain,
( spl1_7
<=> leq(one,star(one)) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_7])]) ).
fof(f158,plain,
( spl1_6
| ~ spl1_4 ),
inference(avatar_split_clause,[],[f152,f135,f155]) ).
fof(f155,plain,
( spl1_6
<=> leq(one,strong_iteration(one)) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_6])]) ).
fof(f152,plain,
( leq(one,strong_iteration(one))
| ~ spl1_4 ),
inference(trivial_inequality_removal,[],[f148]) ).
fof(f148,plain,
( strong_iteration(one) != strong_iteration(one)
| leq(one,strong_iteration(one))
| ~ spl1_4 ),
inference(superposition,[],[f65,f137]) ).
fof(f145,plain,
spl1_5,
inference(avatar_split_clause,[],[f113,f142]) ).
fof(f138,plain,
spl1_4,
inference(avatar_split_clause,[],[f101,f135]) ).
fof(f129,plain,
spl1_3,
inference(avatar_split_clause,[],[f116,f126]) ).
fof(f126,plain,
( spl1_3
<=> one = star(zero) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_3])]) ).
fof(f124,plain,
spl1_2,
inference(avatar_split_clause,[],[f108,f121]) ).
fof(f121,plain,
( spl1_2
<=> one = strong_iteration(zero) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_2])]) ).
fof(f54,plain,
~ spl1_1,
inference(avatar_split_clause,[],[f30,f51]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : KLE137+1 : TPTP v8.1.2. Released v4.0.0.
% 0.06/0.14 % Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.13/0.34 % Computer : n024.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 : Wed Aug 30 17:45:52 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.13/0.39 % (2216)Running in auto input_syntax mode. Trying TPTP
% 0.13/0.39 % (2218)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on Vampire---4 for (793ds/0Mi)
% 0.13/0.39 % (2223)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on Vampire---4 for (533ds/0Mi)
% 0.13/0.39 % (2226)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 Vampire---4 for (522ds/0Mi)
% 0.13/0.39 % (2225)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 Vampire---4 for (531ds/0Mi)
% 0.13/0.39 % (2220)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 Vampire---4 for (569ds/0Mi)
% 0.13/0.39 % (2227)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 Vampire---4 for (497ds/0Mi)
% 0.13/0.39 % (2217)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on Vampire---4 for (846ds/0Mi)
% 0.13/0.39 TRYING [1]
% 0.13/0.39 TRYING [2]
% 0.13/0.39 TRYING [3]
% 0.13/0.40 TRYING [1]
% 0.13/0.40 TRYING [2]
% 0.13/0.40 TRYING [4]
% 0.18/0.41 TRYING [3]
% 0.18/0.43 TRYING [1]
% 0.18/0.43 TRYING [2]
% 0.18/0.43 TRYING [3]
% 0.18/0.44 TRYING [4]
% 0.18/0.44 TRYING [5]
% 0.18/0.45 TRYING [4]
% 0.18/0.47 % (2220)First to succeed.
% 0.18/0.48 % (2220)Refutation found. Thanks to Tanya!
% 0.18/0.48 % SZS status Theorem for Vampire---4
% 0.18/0.48 % SZS output start Proof for Vampire---4
% See solution above
% 0.18/0.48 % (2220)------------------------------
% 0.18/0.48 % (2220)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.18/0.48 % (2220)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.18/0.48 % (2220)Termination reason: Refutation
% 0.18/0.48
% 0.18/0.48 % (2220)Memory used [KB]: 5884
% 0.18/0.48 % (2220)Time elapsed: 0.085 s
% 0.18/0.48 % (2220)------------------------------
% 0.18/0.48 % (2220)------------------------------
% 0.18/0.48 % (2216)Success in time 0.131 s
% 0.18/0.48 % Vampire---4.8 exiting
%------------------------------------------------------------------------------