TSTP Solution File: KLE129+1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : KLE129+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 : n029.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 13:11:59 EDT 2024
% Result : Theorem 0.13s 0.40s
% Output : Refutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 58
% Syntax : Number of formulae : 172 ( 75 unt; 0 def)
% Number of atoms : 324 ( 165 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 263 ( 111 ~; 104 |; 4 &)
% ( 35 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of predicates : 37 ( 35 usr; 36 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 3 con; 0-2 aty)
% Number of variables : 192 ( 190 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f529,plain,
$false,
inference(avatar_sat_refutation,[],[f95,f99,f103,f107,f111,f115,f119,f123,f127,f135,f139,f147,f152,f156,f168,f172,f176,f226,f231,f235,f313,f317,f359,f393,f402,f408,f424,f428,f432,f437,f441,f445,f449,f520,f525,f528]) ).
fof(f528,plain,
( ~ spl1_7
| spl1_30 ),
inference(avatar_contradiction_clause,[],[f527]) ).
fof(f527,plain,
( $false
| ~ spl1_7
| spl1_30 ),
inference(trivial_inequality_removal,[],[f526]) ).
fof(f526,plain,
( divergence(sK0) != divergence(sK0)
| ~ spl1_7
| spl1_30 ),
inference(superposition,[],[f436,f118]) ).
fof(f118,plain,
( ! [X0] : addition(X0,X0) = X0
| ~ spl1_7 ),
inference(avatar_component_clause,[],[f117]) ).
fof(f117,plain,
( spl1_7
<=> ! [X0] : addition(X0,X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl1_7])]) ).
fof(f436,plain,
( divergence(sK0) != addition(divergence(sK0),divergence(sK0))
| spl1_30 ),
inference(avatar_component_clause,[],[f434]) ).
fof(f434,plain,
( spl1_30
<=> divergence(sK0) = addition(divergence(sK0),divergence(sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_30])]) ).
fof(f525,plain,
( spl1_35
| ~ spl1_6
| ~ spl1_17 ),
inference(avatar_split_clause,[],[f217,f174,f113,f522]) ).
fof(f522,plain,
( spl1_35
<=> divergence(one) = antidomain(antidomain(antidomain(antidomain(divergence(one))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_35])]) ).
fof(f113,plain,
( spl1_6
<=> ! [X0] : multiplication(one,X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl1_6])]) ).
fof(f174,plain,
( spl1_17
<=> ! [X0] : divergence(X0) = antidomain(antidomain(multiplication(X0,antidomain(antidomain(divergence(X0)))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_17])]) ).
fof(f217,plain,
( divergence(one) = antidomain(antidomain(antidomain(antidomain(divergence(one)))))
| ~ spl1_6
| ~ spl1_17 ),
inference(superposition,[],[f175,f114]) ).
fof(f114,plain,
( ! [X0] : multiplication(one,X0) = X0
| ~ spl1_6 ),
inference(avatar_component_clause,[],[f113]) ).
fof(f175,plain,
( ! [X0] : divergence(X0) = antidomain(antidomain(multiplication(X0,antidomain(antidomain(divergence(X0))))))
| ~ spl1_17 ),
inference(avatar_component_clause,[],[f174]) ).
fof(f520,plain,
( spl1_34
| ~ spl1_7
| ~ spl1_15 ),
inference(avatar_split_clause,[],[f178,f166,f117,f518]) ).
fof(f518,plain,
( spl1_34
<=> ! [X0,X1] : addition(X0,X1) = addition(X0,addition(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_34])]) ).
fof(f166,plain,
( spl1_15
<=> ! [X2,X0,X1] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_15])]) ).
fof(f178,plain,
( ! [X0,X1] : addition(X0,X1) = addition(X0,addition(X0,X1))
| ~ spl1_7
| ~ spl1_15 ),
inference(superposition,[],[f167,f118]) ).
fof(f167,plain,
( ! [X2,X0,X1] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0)
| ~ spl1_15 ),
inference(avatar_component_clause,[],[f166]) ).
fof(f449,plain,
( spl1_33
| ~ spl1_14
| ~ spl1_17 ),
inference(avatar_split_clause,[],[f220,f174,f154,f447]) ).
fof(f447,plain,
( spl1_33
<=> ! [X0] : one = addition(antidomain(divergence(X0)),divergence(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_33])]) ).
fof(f154,plain,
( spl1_14
<=> ! [X0] : one = addition(antidomain(antidomain(X0)),antidomain(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_14])]) ).
fof(f220,plain,
( ! [X0] : one = addition(antidomain(divergence(X0)),divergence(X0))
| ~ spl1_14
| ~ spl1_17 ),
inference(superposition,[],[f155,f175]) ).
fof(f155,plain,
( ! [X0] : one = addition(antidomain(antidomain(X0)),antidomain(X0))
| ~ spl1_14 ),
inference(avatar_component_clause,[],[f154]) ).
fof(f445,plain,
( spl1_32
| ~ spl1_3
| ~ spl1_9
| ~ spl1_16 ),
inference(avatar_split_clause,[],[f212,f170,f125,f101,f443]) ).
fof(f443,plain,
( spl1_32
<=> ! [X0,X1] : zero = multiplication(antidomain(X0),multiplication(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_32])]) ).
fof(f101,plain,
( spl1_3
<=> ! [X0] : zero = multiplication(zero,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_3])]) ).
fof(f125,plain,
( spl1_9
<=> ! [X0] : zero = multiplication(antidomain(X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_9])]) ).
fof(f170,plain,
( spl1_16
<=> ! [X2,X0,X1] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_16])]) ).
fof(f212,plain,
( ! [X0,X1] : zero = multiplication(antidomain(X0),multiplication(X0,X1))
| ~ spl1_3
| ~ spl1_9
| ~ spl1_16 ),
inference(forward_demodulation,[],[f200,f102]) ).
fof(f102,plain,
( ! [X0] : zero = multiplication(zero,X0)
| ~ spl1_3 ),
inference(avatar_component_clause,[],[f101]) ).
fof(f200,plain,
( ! [X0,X1] : multiplication(zero,X1) = multiplication(antidomain(X0),multiplication(X0,X1))
| ~ spl1_9
| ~ spl1_16 ),
inference(superposition,[],[f171,f126]) ).
fof(f126,plain,
( ! [X0] : zero = multiplication(antidomain(X0),X0)
| ~ spl1_9 ),
inference(avatar_component_clause,[],[f125]) ).
fof(f171,plain,
( ! [X2,X0,X1] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2)
| ~ spl1_16 ),
inference(avatar_component_clause,[],[f170]) ).
fof(f441,plain,
( spl1_31
| ~ spl1_3
| ~ spl1_8
| ~ spl1_16 ),
inference(avatar_split_clause,[],[f208,f170,f121,f101,f439]) ).
fof(f439,plain,
( spl1_31
<=> ! [X0,X1] : zero = multiplication(X0,multiplication(coantidomain(X0),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_31])]) ).
fof(f121,plain,
( spl1_8
<=> ! [X0] : zero = multiplication(X0,coantidomain(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_8])]) ).
fof(f208,plain,
( ! [X0,X1] : zero = multiplication(X0,multiplication(coantidomain(X0),X1))
| ~ spl1_3
| ~ spl1_8
| ~ spl1_16 ),
inference(forward_demodulation,[],[f196,f102]) ).
fof(f196,plain,
( ! [X0,X1] : multiplication(zero,X1) = multiplication(X0,multiplication(coantidomain(X0),X1))
| ~ spl1_8
| ~ spl1_16 ),
inference(superposition,[],[f171,f122]) ).
fof(f122,plain,
( ! [X0] : zero = multiplication(X0,coantidomain(X0))
| ~ spl1_8 ),
inference(avatar_component_clause,[],[f121]) ).
fof(f437,plain,
( spl1_1
| ~ spl1_30
| ~ spl1_17
| ~ spl1_25 ),
inference(avatar_split_clause,[],[f403,f400,f174,f434,f92]) ).
fof(f92,plain,
( spl1_1
<=> zero = divergence(sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_1])]) ).
fof(f400,plain,
( spl1_25
<=> ! [X0] :
( antidomain(antidomain(multiplication(sK0,antidomain(antidomain(divergence(X0)))))) != addition(divergence(X0),antidomain(antidomain(multiplication(sK0,antidomain(antidomain(divergence(X0)))))))
| zero = divergence(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_25])]) ).
fof(f403,plain,
( divergence(sK0) != addition(divergence(sK0),divergence(sK0))
| zero = divergence(sK0)
| ~ spl1_17
| ~ spl1_25 ),
inference(superposition,[],[f401,f175]) ).
fof(f401,plain,
( ! [X0] :
( antidomain(antidomain(multiplication(sK0,antidomain(antidomain(divergence(X0)))))) != addition(divergence(X0),antidomain(antidomain(multiplication(sK0,antidomain(antidomain(divergence(X0)))))))
| zero = divergence(X0) )
| ~ spl1_25 ),
inference(avatar_component_clause,[],[f400]) ).
fof(f432,plain,
( spl1_29
| ~ spl1_11
| ~ spl1_14 ),
inference(avatar_split_clause,[],[f161,f154,f137,f430]) ).
fof(f430,plain,
( spl1_29
<=> ! [X0] : one = addition(antidomain(X0),antidomain(antidomain(X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_29])]) ).
fof(f137,plain,
( spl1_11
<=> ! [X0,X1] : addition(X0,X1) = addition(X1,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_11])]) ).
fof(f161,plain,
( ! [X0] : one = addition(antidomain(X0),antidomain(antidomain(X0)))
| ~ spl1_11
| ~ spl1_14 ),
inference(superposition,[],[f155,f138]) ).
fof(f138,plain,
( ! [X0,X1] : addition(X0,X1) = addition(X1,X0)
| ~ spl1_11 ),
inference(avatar_component_clause,[],[f137]) ).
fof(f428,plain,
( spl1_28
| ~ spl1_11
| ~ spl1_12 ),
inference(avatar_split_clause,[],[f157,f145,f137,f426]) ).
fof(f426,plain,
( spl1_28
<=> ! [X0] : one = addition(coantidomain(X0),coantidomain(coantidomain(X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_28])]) ).
fof(f145,plain,
( spl1_12
<=> ! [X0] : one = addition(coantidomain(coantidomain(X0)),coantidomain(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_12])]) ).
fof(f157,plain,
( ! [X0] : one = addition(coantidomain(X0),coantidomain(coantidomain(X0)))
| ~ spl1_11
| ~ spl1_12 ),
inference(superposition,[],[f146,f138]) ).
fof(f146,plain,
( ! [X0] : one = addition(coantidomain(coantidomain(X0)),coantidomain(X0))
| ~ spl1_12 ),
inference(avatar_component_clause,[],[f145]) ).
fof(f424,plain,
( spl1_27
| ~ spl1_10
| ~ spl1_17 ),
inference(avatar_split_clause,[],[f221,f174,f133,f422]) ).
fof(f422,plain,
( spl1_27
<=> ! [X0] :
( antidomain(antidomain(multiplication(sK0,antidomain(antidomain(antidomain(divergence(X0))))))) != addition(antidomain(divergence(X0)),antidomain(antidomain(multiplication(sK0,antidomain(antidomain(antidomain(divergence(X0))))))))
| zero = antidomain(divergence(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_27])]) ).
fof(f133,plain,
( spl1_10
<=> ! [X1] :
( zero = antidomain(antidomain(X1))
| antidomain(antidomain(multiplication(sK0,antidomain(antidomain(antidomain(antidomain(X1))))))) != addition(antidomain(antidomain(X1)),antidomain(antidomain(multiplication(sK0,antidomain(antidomain(antidomain(antidomain(X1)))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_10])]) ).
fof(f221,plain,
( ! [X0] :
( antidomain(antidomain(multiplication(sK0,antidomain(antidomain(antidomain(divergence(X0))))))) != addition(antidomain(divergence(X0)),antidomain(antidomain(multiplication(sK0,antidomain(antidomain(antidomain(divergence(X0))))))))
| zero = antidomain(divergence(X0)) )
| ~ spl1_10
| ~ spl1_17 ),
inference(superposition,[],[f134,f175]) ).
fof(f134,plain,
( ! [X1] :
( antidomain(antidomain(multiplication(sK0,antidomain(antidomain(antidomain(antidomain(X1))))))) != addition(antidomain(antidomain(X1)),antidomain(antidomain(multiplication(sK0,antidomain(antidomain(antidomain(antidomain(X1))))))))
| zero = antidomain(antidomain(X1)) )
| ~ spl1_10 ),
inference(avatar_component_clause,[],[f133]) ).
fof(f408,plain,
( spl1_26
| ~ spl1_3
| ~ spl1_17 ),
inference(avatar_split_clause,[],[f215,f174,f101,f405]) ).
fof(f405,plain,
( spl1_26
<=> divergence(zero) = antidomain(antidomain(zero)) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_26])]) ).
fof(f215,plain,
( divergence(zero) = antidomain(antidomain(zero))
| ~ spl1_3
| ~ spl1_17 ),
inference(superposition,[],[f175,f102]) ).
fof(f402,plain,
( spl1_25
| ~ spl1_10
| ~ spl1_17 ),
inference(avatar_split_clause,[],[f219,f174,f133,f400]) ).
fof(f219,plain,
( ! [X0] :
( antidomain(antidomain(multiplication(sK0,antidomain(antidomain(divergence(X0)))))) != addition(divergence(X0),antidomain(antidomain(multiplication(sK0,antidomain(antidomain(divergence(X0)))))))
| zero = divergence(X0) )
| ~ spl1_10
| ~ spl1_17 ),
inference(superposition,[],[f134,f175]) ).
fof(f393,plain,
( spl1_24
| ~ spl1_4
| ~ spl1_11 ),
inference(avatar_split_clause,[],[f140,f137,f105,f391]) ).
fof(f391,plain,
( spl1_24
<=> ! [X0] : addition(zero,X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl1_24])]) ).
fof(f105,plain,
( spl1_4
<=> ! [X0] : addition(X0,zero) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl1_4])]) ).
fof(f140,plain,
( ! [X0] : addition(zero,X0) = X0
| ~ spl1_4
| ~ spl1_11 ),
inference(superposition,[],[f138,f106]) ).
fof(f106,plain,
( ! [X0] : addition(X0,zero) = X0
| ~ spl1_4 ),
inference(avatar_component_clause,[],[f105]) ).
fof(f359,plain,
spl1_23,
inference(avatar_split_clause,[],[f90,f357]) ).
fof(f357,plain,
( spl1_23
<=> ! [X2,X0,X1] :
( addition(divergence(X1),antidomain(antidomain(multiplication(star(X1),antidomain(antidomain(antidomain(antidomain(X2)))))))) = addition(antidomain(antidomain(X0)),addition(divergence(X1),antidomain(antidomain(multiplication(star(X1),antidomain(antidomain(antidomain(antidomain(X2)))))))))
| addition(antidomain(antidomain(multiplication(X1,antidomain(antidomain(antidomain(antidomain(X0))))))),antidomain(antidomain(X2))) != addition(antidomain(antidomain(X0)),addition(antidomain(antidomain(multiplication(X1,antidomain(antidomain(antidomain(antidomain(X0))))))),antidomain(antidomain(X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_23])]) ).
fof(f90,plain,
! [X2,X0,X1] :
( addition(divergence(X1),antidomain(antidomain(multiplication(star(X1),antidomain(antidomain(antidomain(antidomain(X2)))))))) = addition(antidomain(antidomain(X0)),addition(divergence(X1),antidomain(antidomain(multiplication(star(X1),antidomain(antidomain(antidomain(antidomain(X2)))))))))
| addition(antidomain(antidomain(multiplication(X1,antidomain(antidomain(antidomain(antidomain(X0))))))),antidomain(antidomain(X2))) != addition(antidomain(antidomain(X0)),addition(antidomain(antidomain(multiplication(X1,antidomain(antidomain(antidomain(antidomain(X0))))))),antidomain(antidomain(X2)))) ),
inference(definition_unfolding,[],[f81,f86,f65,f65,f86,f65,f86,f65,f65,f65,f86,f65,f65]) ).
fof(f65,plain,
! [X0] : domain(X0) = antidomain(antidomain(X0)),
inference(cnf_transformation,[],[f36]) ).
fof(f36,plain,
! [X0] : domain(X0) = antidomain(antidomain(X0)),
inference(rectify,[],[f16]) ).
fof(f16,axiom,
! [X3] : antidomain(antidomain(X3)) = domain(X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain4) ).
fof(f86,plain,
! [X0,X1] : forward_diamond(X0,X1) = antidomain(antidomain(multiplication(X0,antidomain(antidomain(X1))))),
inference(definition_unfolding,[],[f74,f65,f65]) ).
fof(f74,plain,
! [X0,X1] : forward_diamond(X0,X1) = domain(multiplication(X0,domain(X1))),
inference(cnf_transformation,[],[f44]) ).
fof(f44,plain,
! [X0,X1] : forward_diamond(X0,X1) = domain(multiplication(X0,domain(X1))),
inference(rectify,[],[f23]) ).
fof(f23,axiom,
! [X3,X4] : forward_diamond(X3,X4) = domain(multiplication(X3,domain(X4))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',forward_diamond) ).
fof(f81,plain,
! [X2,X0,X1] :
( addition(divergence(X1),forward_diamond(star(X1),domain(X2))) = addition(domain(X0),addition(divergence(X1),forward_diamond(star(X1),domain(X2))))
| addition(forward_diamond(X1,domain(X0)),domain(X2)) != addition(domain(X0),addition(forward_diamond(X1,domain(X0)),domain(X2))) ),
inference(cnf_transformation,[],[f50]) ).
fof(f50,plain,
! [X0,X1,X2] :
( addition(divergence(X1),forward_diamond(star(X1),domain(X2))) = addition(domain(X0),addition(divergence(X1),forward_diamond(star(X1),domain(X2))))
| addition(forward_diamond(X1,domain(X0)),domain(X2)) != addition(domain(X0),addition(forward_diamond(X1,domain(X0)),domain(X2))) ),
inference(ennf_transformation,[],[f48]) ).
fof(f48,plain,
! [X0,X1,X2] :
( addition(forward_diamond(X1,domain(X0)),domain(X2)) = addition(domain(X0),addition(forward_diamond(X1,domain(X0)),domain(X2)))
=> addition(divergence(X1),forward_diamond(star(X1),domain(X2))) = addition(domain(X0),addition(divergence(X1),forward_diamond(star(X1),domain(X2)))) ),
inference(rectify,[],[f28]) ).
fof(f28,axiom,
! [X3,X4,X5] :
( addition(forward_diamond(X4,domain(X3)),domain(X5)) = addition(domain(X3),addition(forward_diamond(X4,domain(X3)),domain(X5)))
=> addition(divergence(X4),forward_diamond(star(X4),domain(X5))) = addition(domain(X3),addition(divergence(X4),forward_diamond(star(X4),domain(X5)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',divergence2) ).
fof(f317,plain,
spl1_22,
inference(avatar_split_clause,[],[f76,f315]) ).
fof(f315,plain,
( spl1_22
<=> ! [X0,X1] : antidomain(multiplication(X0,antidomain(antidomain(X1)))) = addition(antidomain(multiplication(X0,X1)),antidomain(multiplication(X0,antidomain(antidomain(X1))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_22])]) ).
fof(f76,plain,
! [X0,X1] : antidomain(multiplication(X0,antidomain(antidomain(X1)))) = addition(antidomain(multiplication(X0,X1)),antidomain(multiplication(X0,antidomain(antidomain(X1))))),
inference(cnf_transformation,[],[f46]) ).
fof(f46,plain,
! [X0,X1] : antidomain(multiplication(X0,antidomain(antidomain(X1)))) = addition(antidomain(multiplication(X0,X1)),antidomain(multiplication(X0,antidomain(antidomain(X1))))),
inference(rectify,[],[f14]) ).
fof(f14,axiom,
! [X3,X4] : antidomain(multiplication(X3,antidomain(antidomain(X4)))) = addition(antidomain(multiplication(X3,X4)),antidomain(multiplication(X3,antidomain(antidomain(X4))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain2) ).
fof(f313,plain,
spl1_21,
inference(avatar_split_clause,[],[f75,f311]) ).
fof(f311,plain,
( spl1_21
<=> ! [X0,X1] : coantidomain(multiplication(coantidomain(coantidomain(X0)),X1)) = addition(coantidomain(multiplication(X0,X1)),coantidomain(multiplication(coantidomain(coantidomain(X0)),X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_21])]) ).
fof(f75,plain,
! [X0,X1] : coantidomain(multiplication(coantidomain(coantidomain(X0)),X1)) = addition(coantidomain(multiplication(X0,X1)),coantidomain(multiplication(coantidomain(coantidomain(X0)),X1))),
inference(cnf_transformation,[],[f45]) ).
fof(f45,plain,
! [X0,X1] : coantidomain(multiplication(coantidomain(coantidomain(X0)),X1)) = addition(coantidomain(multiplication(X0,X1)),coantidomain(multiplication(coantidomain(coantidomain(X0)),X1))),
inference(rectify,[],[f18]) ).
fof(f18,axiom,
! [X3,X4] : coantidomain(multiplication(coantidomain(coantidomain(X3)),X4)) = addition(coantidomain(multiplication(X3,X4)),coantidomain(multiplication(coantidomain(coantidomain(X3)),X4))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',codomain2) ).
fof(f235,plain,
spl1_20,
inference(avatar_split_clause,[],[f80,f233]) ).
fof(f233,plain,
( spl1_20
<=> ! [X2,X0,X1] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_20])]) ).
fof(f80,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/benchmark/theBenchmark.p',left_distributivity) ).
fof(f231,plain,
( spl1_19
| ~ spl1_5
| ~ spl1_9 ),
inference(avatar_split_clause,[],[f130,f125,f109,f228]) ).
fof(f228,plain,
( spl1_19
<=> zero = antidomain(one) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_19])]) ).
fof(f109,plain,
( spl1_5
<=> ! [X0] : multiplication(X0,one) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl1_5])]) ).
fof(f130,plain,
( zero = antidomain(one)
| ~ spl1_5
| ~ spl1_9 ),
inference(superposition,[],[f126,f110]) ).
fof(f110,plain,
( ! [X0] : multiplication(X0,one) = X0
| ~ spl1_5 ),
inference(avatar_component_clause,[],[f109]) ).
fof(f226,plain,
spl1_18,
inference(avatar_split_clause,[],[f79,f224]) ).
fof(f224,plain,
( spl1_18
<=> ! [X2,X0,X1] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_18])]) ).
fof(f79,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/benchmark/theBenchmark.p',right_distributivity) ).
fof(f176,plain,
spl1_17,
inference(avatar_split_clause,[],[f89,f174]) ).
fof(f89,plain,
! [X0] : divergence(X0) = antidomain(antidomain(multiplication(X0,antidomain(antidomain(divergence(X0)))))),
inference(definition_unfolding,[],[f66,f86]) ).
fof(f66,plain,
! [X0] : divergence(X0) = forward_diamond(X0,divergence(X0)),
inference(cnf_transformation,[],[f37]) ).
fof(f37,plain,
! [X0] : divergence(X0) = forward_diamond(X0,divergence(X0)),
inference(rectify,[],[f27]) ).
fof(f27,axiom,
! [X3] : divergence(X3) = forward_diamond(X3,divergence(X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',divergence1) ).
fof(f172,plain,
spl1_16,
inference(avatar_split_clause,[],[f78,f170]) ).
fof(f78,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/benchmark/theBenchmark.p',multiplicative_associativity) ).
fof(f168,plain,
spl1_15,
inference(avatar_split_clause,[],[f77,f166]) ).
fof(f77,plain,
! [X2,X0,X1] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
inference(cnf_transformation,[],[f47]) ).
fof(f47,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/benchmark/theBenchmark.p',additive_associativity) ).
fof(f156,plain,
spl1_14,
inference(avatar_split_clause,[],[f68,f154]) ).
fof(f68,plain,
! [X0] : one = addition(antidomain(antidomain(X0)),antidomain(X0)),
inference(cnf_transformation,[],[f39]) ).
fof(f39,plain,
! [X0] : one = addition(antidomain(antidomain(X0)),antidomain(X0)),
inference(rectify,[],[f15]) ).
fof(f15,axiom,
! [X3] : one = addition(antidomain(antidomain(X3)),antidomain(X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain3) ).
fof(f152,plain,
( spl1_13
| ~ spl1_6
| ~ spl1_8 ),
inference(avatar_split_clause,[],[f128,f121,f113,f149]) ).
fof(f149,plain,
( spl1_13
<=> zero = coantidomain(one) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_13])]) ).
fof(f128,plain,
( zero = coantidomain(one)
| ~ spl1_6
| ~ spl1_8 ),
inference(superposition,[],[f122,f114]) ).
fof(f147,plain,
spl1_12,
inference(avatar_split_clause,[],[f67,f145]) ).
fof(f67,plain,
! [X0] : one = addition(coantidomain(coantidomain(X0)),coantidomain(X0)),
inference(cnf_transformation,[],[f38]) ).
fof(f38,plain,
! [X0] : one = addition(coantidomain(coantidomain(X0)),coantidomain(X0)),
inference(rectify,[],[f19]) ).
fof(f19,axiom,
! [X3] : one = addition(coantidomain(coantidomain(X3)),coantidomain(X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',codomain3) ).
fof(f139,plain,
spl1_11,
inference(avatar_split_clause,[],[f69,f137]) ).
fof(f69,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/benchmark/theBenchmark.p',additive_commutativity) ).
fof(f135,plain,
spl1_10,
inference(avatar_split_clause,[],[f88,f133]) ).
fof(f88,plain,
! [X1] :
( zero = antidomain(antidomain(X1))
| antidomain(antidomain(multiplication(sK0,antidomain(antidomain(antidomain(antidomain(X1))))))) != addition(antidomain(antidomain(X1)),antidomain(antidomain(multiplication(sK0,antidomain(antidomain(antidomain(antidomain(X1)))))))) ),
inference(definition_unfolding,[],[f53,f65,f86,f65,f65,f86,f65]) ).
fof(f53,plain,
! [X1] :
( zero = domain(X1)
| forward_diamond(sK0,domain(X1)) != addition(domain(X1),forward_diamond(sK0,domain(X1))) ),
inference(cnf_transformation,[],[f52]) ).
fof(f52,plain,
( zero != divergence(sK0)
& ! [X1] :
( zero = domain(X1)
| forward_diamond(sK0,domain(X1)) != addition(domain(X1),forward_diamond(sK0,domain(X1))) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f49,f51]) ).
fof(f51,plain,
( ? [X0] :
( zero != divergence(X0)
& ! [X1] :
( zero = domain(X1)
| forward_diamond(X0,domain(X1)) != addition(domain(X1),forward_diamond(X0,domain(X1))) ) )
=> ( zero != divergence(sK0)
& ! [X1] :
( zero = domain(X1)
| forward_diamond(sK0,domain(X1)) != addition(domain(X1),forward_diamond(sK0,domain(X1))) ) ) ),
introduced(choice_axiom,[]) ).
fof(f49,plain,
? [X0] :
( zero != divergence(X0)
& ! [X1] :
( zero = domain(X1)
| forward_diamond(X0,domain(X1)) != addition(domain(X1),forward_diamond(X0,domain(X1))) ) ),
inference(ennf_transformation,[],[f31]) ).
fof(f31,plain,
~ ! [X0] :
( ! [X1] :
( forward_diamond(X0,domain(X1)) = addition(domain(X1),forward_diamond(X0,domain(X1)))
=> zero = domain(X1) )
=> zero = divergence(X0) ),
inference(rectify,[],[f30]) ).
fof(f30,negated_conjecture,
~ ! [X3] :
( ! [X4] :
( forward_diamond(X3,domain(X4)) = addition(domain(X4),forward_diamond(X3,domain(X4)))
=> zero = domain(X4) )
=> zero = divergence(X3) ),
inference(negated_conjecture,[],[f29]) ).
fof(f29,conjecture,
! [X3] :
( ! [X4] :
( forward_diamond(X3,domain(X4)) = addition(domain(X4),forward_diamond(X3,domain(X4)))
=> zero = domain(X4) )
=> zero = divergence(X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f127,plain,
spl1_9,
inference(avatar_split_clause,[],[f62,f125]) ).
fof(f62,plain,
! [X0] : zero = multiplication(antidomain(X0),X0),
inference(cnf_transformation,[],[f33]) ).
fof(f33,plain,
! [X0] : zero = multiplication(antidomain(X0),X0),
inference(rectify,[],[f13]) ).
fof(f13,axiom,
! [X3] : zero = multiplication(antidomain(X3),X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain1) ).
fof(f123,plain,
spl1_8,
inference(avatar_split_clause,[],[f61,f121]) ).
fof(f61,plain,
! [X0] : zero = multiplication(X0,coantidomain(X0)),
inference(cnf_transformation,[],[f32]) ).
fof(f32,plain,
! [X0] : zero = multiplication(X0,coantidomain(X0)),
inference(rectify,[],[f17]) ).
fof(f17,axiom,
! [X3] : zero = multiplication(X3,coantidomain(X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',codomain1) ).
fof(f119,plain,
spl1_7,
inference(avatar_split_clause,[],[f60,f117]) ).
fof(f60,plain,
! [X0] : addition(X0,X0) = X0,
inference(cnf_transformation,[],[f4]) ).
fof(f4,axiom,
! [X0] : addition(X0,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_idempotence) ).
fof(f115,plain,
spl1_6,
inference(avatar_split_clause,[],[f59,f113]) ).
fof(f59,plain,
! [X0] : multiplication(one,X0) = X0,
inference(cnf_transformation,[],[f7]) ).
fof(f7,axiom,
! [X0] : multiplication(one,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_left_identity) ).
fof(f111,plain,
spl1_5,
inference(avatar_split_clause,[],[f58,f109]) ).
fof(f58,plain,
! [X0] : multiplication(X0,one) = X0,
inference(cnf_transformation,[],[f6]) ).
fof(f6,axiom,
! [X0] : multiplication(X0,one) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_right_identity) ).
fof(f107,plain,
spl1_4,
inference(avatar_split_clause,[],[f57,f105]) ).
fof(f57,plain,
! [X0] : addition(X0,zero) = X0,
inference(cnf_transformation,[],[f3]) ).
fof(f3,axiom,
! [X0] : addition(X0,zero) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_identity) ).
fof(f103,plain,
spl1_3,
inference(avatar_split_clause,[],[f56,f101]) ).
fof(f56,plain,
! [X0] : zero = multiplication(zero,X0),
inference(cnf_transformation,[],[f11]) ).
fof(f11,axiom,
! [X0] : zero = multiplication(zero,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_annihilation) ).
fof(f99,plain,
spl1_2,
inference(avatar_split_clause,[],[f55,f97]) ).
fof(f97,plain,
( spl1_2
<=> ! [X0] : zero = multiplication(X0,zero) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_2])]) ).
fof(f55,plain,
! [X0] : zero = multiplication(X0,zero),
inference(cnf_transformation,[],[f10]) ).
fof(f10,axiom,
! [X0] : zero = multiplication(X0,zero),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_annihilation) ).
fof(f95,plain,
~ spl1_1,
inference(avatar_split_clause,[],[f54,f92]) ).
fof(f54,plain,
zero != divergence(sK0),
inference(cnf_transformation,[],[f52]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.01/0.12 % Problem : KLE129+1 : TPTP v8.1.2. Released v4.0.0.
% 0.12/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.13/0.35 % Computer : n029.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Tue Apr 30 05:22:20 EDT 2024
% 0.13/0.35 % CPUTime :
% 0.13/0.36 % (23851)Running in auto input_syntax mode. Trying TPTP
% 0.13/0.37 % (23855)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.13/0.37 % (23854)WARNING: value z3 for option sas not known
% 0.13/0.38 % (23852)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.13/0.38 % (23854)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)
% 0.13/0.38 TRYING [1]
% 0.13/0.38 % (23856)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)
% 0.13/0.38 % (23857)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)
% 0.13/0.38 % (23853)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.13/0.38 % (23858)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)
% 0.13/0.38 TRYING [2]
% 0.13/0.38 TRYING [3]
% 0.13/0.39 TRYING [1]
% 0.13/0.39 TRYING [2]
% 0.13/0.39 % (23856)First to succeed.
% 0.13/0.40 % (23856)Refutation found. Thanks to Tanya!
% 0.13/0.40 % SZS status Theorem for theBenchmark
% 0.13/0.40 % SZS output start Proof for theBenchmark
% See solution above
% 0.13/0.40 % (23856)------------------------------
% 0.13/0.40 % (23856)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.13/0.40 % (23856)Termination reason: Refutation
% 0.13/0.40
% 0.13/0.40 % (23856)Memory used [KB]: 1162
% 0.13/0.40 % (23856)Time elapsed: 0.021 s
% 0.13/0.40 % (23856)Instructions burned: 32 (million)
% 0.13/0.40 % (23856)------------------------------
% 0.13/0.40 % (23856)------------------------------
% 0.13/0.40 % (23851)Success in time 0.038 s
%------------------------------------------------------------------------------