TSTP Solution File: KLE052+1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : KLE052+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 : n023.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 13:11:48 EDT 2024
% Result : Theorem 0.22s 0.48s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 67
% Syntax : Number of formulae : 210 ( 61 unt; 0 def)
% Number of atoms : 455 ( 159 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 447 ( 202 ~; 195 |; 0 &)
% ( 49 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 51 ( 49 usr; 50 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 296 ( 294 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2063,plain,
$false,
inference(avatar_sat_refutation,[],[f50,f55,f59,f63,f67,f71,f75,f79,f83,f88,f100,f104,f118,f132,f136,f140,f186,f190,f224,f269,f273,f292,f315,f319,f323,f373,f377,f382,f386,f390,f394,f398,f402,f822,f826,f981,f985,f989,f993,f1286,f1291,f1338,f1342,f1346,f1740,f1848,f1854,f1858,f1863,f2027]) ).
fof(f2027,plain,
( spl1_1
| ~ spl1_47 ),
inference(avatar_contradiction_clause,[],[f2026]) ).
fof(f2026,plain,
( $false
| spl1_1
| ~ spl1_47 ),
inference(trivial_inequality_removal,[],[f1989]) ).
fof(f1989,plain,
( sK0 != sK0
| spl1_1
| ~ spl1_47 ),
inference(superposition,[],[f49,f1853]) ).
fof(f1853,plain,
( ! [X0] : multiplication(domain(X0),X0) = X0
| ~ spl1_47 ),
inference(avatar_component_clause,[],[f1852]) ).
fof(f1852,plain,
( spl1_47
<=> ! [X0] : multiplication(domain(X0),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl1_47])]) ).
fof(f49,plain,
( sK0 != multiplication(domain(sK0),sK0)
| spl1_1 ),
inference(avatar_component_clause,[],[f47]) ).
fof(f47,plain,
( spl1_1
<=> sK0 = multiplication(domain(sK0),sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_1])]) ).
fof(f1863,plain,
( spl1_49
| ~ spl1_7
| ~ spl1_20
| ~ spl1_31
| ~ spl1_48 ),
inference(avatar_split_clause,[],[f1859,f1856,f392,f267,f73,f1861]) ).
fof(f1861,plain,
( spl1_49
<=> ! [X0,X1] : multiplication(X0,domain(X1)) = multiplication(domain(multiplication(X0,X1)),multiplication(X0,domain(X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_49])]) ).
fof(f73,plain,
( spl1_7
<=> ! [X0] : multiplication(one,X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl1_7])]) ).
fof(f267,plain,
( spl1_20
<=> ! [X0] : one = addition(one,domain(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_20])]) ).
fof(f392,plain,
( spl1_31
<=> ! [X0,X1] : multiplication(addition(one,X1),X0) = addition(X0,multiplication(X1,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_31])]) ).
fof(f1856,plain,
( spl1_48
<=> ! [X0,X1] : multiplication(domain(multiplication(X0,X1)),multiplication(X0,domain(X1))) = addition(multiplication(X0,domain(X1)),multiplication(domain(multiplication(X0,X1)),multiplication(X0,domain(X1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_48])]) ).
fof(f1859,plain,
( ! [X0,X1] : multiplication(X0,domain(X1)) = multiplication(domain(multiplication(X0,X1)),multiplication(X0,domain(X1)))
| ~ spl1_7
| ~ spl1_20
| ~ spl1_31
| ~ spl1_48 ),
inference(forward_demodulation,[],[f1857,f721]) ).
fof(f721,plain,
( ! [X0,X1] : addition(X1,multiplication(domain(X0),X1)) = X1
| ~ spl1_7
| ~ spl1_20
| ~ spl1_31 ),
inference(forward_demodulation,[],[f680,f74]) ).
fof(f74,plain,
( ! [X0] : multiplication(one,X0) = X0
| ~ spl1_7 ),
inference(avatar_component_clause,[],[f73]) ).
fof(f680,plain,
( ! [X0,X1] : multiplication(one,X1) = addition(X1,multiplication(domain(X0),X1))
| ~ spl1_20
| ~ spl1_31 ),
inference(superposition,[],[f393,f268]) ).
fof(f268,plain,
( ! [X0] : one = addition(one,domain(X0))
| ~ spl1_20 ),
inference(avatar_component_clause,[],[f267]) ).
fof(f393,plain,
( ! [X0,X1] : multiplication(addition(one,X1),X0) = addition(X0,multiplication(X1,X0))
| ~ spl1_31 ),
inference(avatar_component_clause,[],[f392]) ).
fof(f1857,plain,
( ! [X0,X1] : multiplication(domain(multiplication(X0,X1)),multiplication(X0,domain(X1))) = addition(multiplication(X0,domain(X1)),multiplication(domain(multiplication(X0,X1)),multiplication(X0,domain(X1))))
| ~ spl1_48 ),
inference(avatar_component_clause,[],[f1856]) ).
fof(f1858,plain,
( spl1_48
| ~ spl1_12
| ~ spl1_14 ),
inference(avatar_split_clause,[],[f142,f130,f102,f1856]) ).
fof(f102,plain,
( spl1_12
<=> ! [X0,X1] : domain(multiplication(X0,X1)) = domain(multiplication(X0,domain(X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_12])]) ).
fof(f130,plain,
( spl1_14
<=> ! [X0] : multiplication(domain(X0),X0) = addition(X0,multiplication(domain(X0),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_14])]) ).
fof(f142,plain,
( ! [X0,X1] : multiplication(domain(multiplication(X0,X1)),multiplication(X0,domain(X1))) = addition(multiplication(X0,domain(X1)),multiplication(domain(multiplication(X0,X1)),multiplication(X0,domain(X1))))
| ~ spl1_12
| ~ spl1_14 ),
inference(superposition,[],[f131,f103]) ).
fof(f103,plain,
( ! [X0,X1] : domain(multiplication(X0,X1)) = domain(multiplication(X0,domain(X1)))
| ~ spl1_12 ),
inference(avatar_component_clause,[],[f102]) ).
fof(f131,plain,
( ! [X0] : multiplication(domain(X0),X0) = addition(X0,multiplication(domain(X0),X0))
| ~ spl1_14 ),
inference(avatar_component_clause,[],[f130]) ).
fof(f1854,plain,
( spl1_47
| ~ spl1_7
| ~ spl1_14
| ~ spl1_20
| ~ spl1_31 ),
inference(avatar_split_clause,[],[f737,f392,f267,f130,f73,f1852]) ).
fof(f737,plain,
( ! [X0] : multiplication(domain(X0),X0) = X0
| ~ spl1_7
| ~ spl1_14
| ~ spl1_20
| ~ spl1_31 ),
inference(forward_demodulation,[],[f736,f74]) ).
fof(f736,plain,
( ! [X0] : multiplication(one,X0) = multiplication(domain(X0),X0)
| ~ spl1_14
| ~ spl1_20
| ~ spl1_31 ),
inference(forward_demodulation,[],[f697,f268]) ).
fof(f697,plain,
( ! [X0] : multiplication(domain(X0),X0) = multiplication(addition(one,domain(X0)),X0)
| ~ spl1_14
| ~ spl1_31 ),
inference(superposition,[],[f393,f131]) ).
fof(f1848,plain,
( spl1_46
| ~ spl1_14
| ~ spl1_15 ),
inference(avatar_split_clause,[],[f158,f134,f130,f1846]) ).
fof(f1846,plain,
( spl1_46
<=> ! [X0,X1] : multiplication(domain(addition(X0,X1)),addition(X0,X1)) = addition(X0,addition(X1,multiplication(domain(addition(X0,X1)),addition(X0,X1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_46])]) ).
fof(f134,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(f158,plain,
( ! [X0,X1] : multiplication(domain(addition(X0,X1)),addition(X0,X1)) = addition(X0,addition(X1,multiplication(domain(addition(X0,X1)),addition(X0,X1))))
| ~ spl1_14
| ~ spl1_15 ),
inference(superposition,[],[f135,f131]) ).
fof(f135,plain,
( ! [X2,X0,X1] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0)
| ~ spl1_15 ),
inference(avatar_component_clause,[],[f134]) ).
fof(f1740,plain,
( spl1_45
| ~ spl1_16
| ~ spl1_17 ),
inference(avatar_split_clause,[],[f212,f184,f138,f1738]) ).
fof(f1738,plain,
( spl1_45
<=> ! [X0,X3,X2,X1] : addition(multiplication(X0,multiplication(X1,X2)),multiplication(X0,multiplication(X1,X3))) = multiplication(X0,multiplication(X1,addition(X2,X3))) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_45])]) ).
fof(f138,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(f184,plain,
( spl1_17
<=> ! [X2,X0,X1] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_17])]) ).
fof(f212,plain,
( ! [X2,X3,X0,X1] : addition(multiplication(X0,multiplication(X1,X2)),multiplication(X0,multiplication(X1,X3))) = multiplication(X0,multiplication(X1,addition(X2,X3)))
| ~ spl1_16
| ~ spl1_17 ),
inference(forward_demodulation,[],[f211,f139]) ).
fof(f139,plain,
( ! [X2,X0,X1] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2)
| ~ spl1_16 ),
inference(avatar_component_clause,[],[f138]) ).
fof(f211,plain,
( ! [X2,X3,X0,X1] : multiplication(multiplication(X0,X1),addition(X2,X3)) = addition(multiplication(X0,multiplication(X1,X2)),multiplication(X0,multiplication(X1,X3)))
| ~ spl1_16
| ~ spl1_17 ),
inference(forward_demodulation,[],[f194,f139]) ).
fof(f194,plain,
( ! [X2,X3,X0,X1] : multiplication(multiplication(X0,X1),addition(X2,X3)) = addition(multiplication(X0,multiplication(X1,X2)),multiplication(multiplication(X0,X1),X3))
| ~ spl1_16
| ~ spl1_17 ),
inference(superposition,[],[f185,f139]) ).
fof(f185,plain,
( ! [X2,X0,X1] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2))
| ~ spl1_17 ),
inference(avatar_component_clause,[],[f184]) ).
fof(f1346,plain,
( spl1_44
| ~ spl1_15
| ~ spl1_18 ),
inference(avatar_split_clause,[],[f241,f188,f134,f1344]) ).
fof(f1344,plain,
( spl1_44
<=> ! [X0,X3,X2,X1] : addition(multiplication(X0,X1),addition(multiplication(X2,X1),X3)) = addition(multiplication(addition(X0,X2),X1),X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_44])]) ).
fof(f188,plain,
( spl1_18
<=> ! [X2,X0,X1] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_18])]) ).
fof(f241,plain,
( ! [X2,X3,X0,X1] : addition(multiplication(X0,X1),addition(multiplication(X2,X1),X3)) = addition(multiplication(addition(X0,X2),X1),X3)
| ~ spl1_15
| ~ spl1_18 ),
inference(superposition,[],[f135,f189]) ).
fof(f189,plain,
( ! [X2,X0,X1] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2))
| ~ spl1_18 ),
inference(avatar_component_clause,[],[f188]) ).
fof(f1342,plain,
( spl1_43
| ~ spl1_16
| ~ spl1_18 ),
inference(avatar_split_clause,[],[f233,f188,f138,f1340]) ).
fof(f1340,plain,
( spl1_43
<=> ! [X0,X3,X2,X1] : multiplication(addition(X3,multiplication(X0,X1)),X2) = addition(multiplication(X3,X2),multiplication(X0,multiplication(X1,X2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_43])]) ).
fof(f233,plain,
( ! [X2,X3,X0,X1] : multiplication(addition(X3,multiplication(X0,X1)),X2) = addition(multiplication(X3,X2),multiplication(X0,multiplication(X1,X2)))
| ~ spl1_16
| ~ spl1_18 ),
inference(superposition,[],[f189,f139]) ).
fof(f1338,plain,
( spl1_42
| ~ spl1_16
| ~ spl1_18 ),
inference(avatar_split_clause,[],[f228,f188,f138,f1336]) ).
fof(f1336,plain,
( spl1_42
<=> ! [X0,X3,X2,X1] : multiplication(addition(multiplication(X0,X1),X3),X2) = addition(multiplication(X0,multiplication(X1,X2)),multiplication(X3,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_42])]) ).
fof(f228,plain,
( ! [X2,X3,X0,X1] : multiplication(addition(multiplication(X0,X1),X3),X2) = addition(multiplication(X0,multiplication(X1,X2)),multiplication(X3,X2))
| ~ spl1_16
| ~ spl1_18 ),
inference(superposition,[],[f189,f139]) ).
fof(f1291,plain,
( spl1_41
| ~ spl1_15
| ~ spl1_17 ),
inference(avatar_split_clause,[],[f205,f184,f134,f1289]) ).
fof(f1289,plain,
( spl1_41
<=> ! [X0,X3,X2,X1] : addition(multiplication(X0,X1),addition(multiplication(X0,X2),X3)) = addition(multiplication(X0,addition(X1,X2)),X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_41])]) ).
fof(f205,plain,
( ! [X2,X3,X0,X1] : addition(multiplication(X0,X1),addition(multiplication(X0,X2),X3)) = addition(multiplication(X0,addition(X1,X2)),X3)
| ~ spl1_15
| ~ spl1_17 ),
inference(superposition,[],[f135,f185]) ).
fof(f1286,plain,
( spl1_40
| ~ spl1_14
| ~ spl1_15 ),
inference(avatar_split_clause,[],[f150,f134,f130,f1284]) ).
fof(f1284,plain,
( spl1_40
<=> ! [X0,X1] : addition(multiplication(domain(X0),X0),X1) = addition(X0,addition(multiplication(domain(X0),X0),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_40])]) ).
fof(f150,plain,
( ! [X0,X1] : addition(multiplication(domain(X0),X0),X1) = addition(X0,addition(multiplication(domain(X0),X0),X1))
| ~ spl1_14
| ~ spl1_15 ),
inference(superposition,[],[f135,f131]) ).
fof(f993,plain,
( spl1_39
| ~ spl1_11
| ~ spl1_15 ),
inference(avatar_split_clause,[],[f152,f134,f98,f991]) ).
fof(f991,plain,
( spl1_39
<=> ! [X2,X0,X1] : addition(domain(X0),addition(domain(X1),X2)) = addition(domain(addition(X0,X1)),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_39])]) ).
fof(f98,plain,
( spl1_11
<=> ! [X0,X1] : domain(addition(X0,X1)) = addition(domain(X0),domain(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_11])]) ).
fof(f152,plain,
( ! [X2,X0,X1] : addition(domain(X0),addition(domain(X1),X2)) = addition(domain(addition(X0,X1)),X2)
| ~ spl1_11
| ~ spl1_15 ),
inference(superposition,[],[f135,f99]) ).
fof(f99,plain,
( ! [X0,X1] : domain(addition(X0,X1)) = addition(domain(X0),domain(X1))
| ~ spl1_11 ),
inference(avatar_component_clause,[],[f98]) ).
fof(f989,plain,
( spl1_38
| ~ spl1_11
| ~ spl1_12 ),
inference(avatar_split_clause,[],[f128,f102,f98,f987]) ).
fof(f987,plain,
( spl1_38
<=> ! [X2,X0,X1] : domain(addition(multiplication(X0,domain(X1)),X2)) = domain(addition(multiplication(X0,X1),X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_38])]) ).
fof(f128,plain,
( ! [X2,X0,X1] : domain(addition(multiplication(X0,domain(X1)),X2)) = domain(addition(multiplication(X0,X1),X2))
| ~ spl1_11
| ~ spl1_12 ),
inference(forward_demodulation,[],[f123,f99]) ).
fof(f123,plain,
( ! [X2,X0,X1] : domain(addition(multiplication(X0,domain(X1)),X2)) = addition(domain(multiplication(X0,X1)),domain(X2))
| ~ spl1_11
| ~ spl1_12 ),
inference(superposition,[],[f99,f103]) ).
fof(f985,plain,
( spl1_37
| ~ spl1_11
| ~ spl1_12 ),
inference(avatar_split_clause,[],[f127,f102,f98,f983]) ).
fof(f983,plain,
( spl1_37
<=> ! [X2,X0,X1] : domain(addition(X2,multiplication(X0,domain(X1)))) = domain(addition(X2,multiplication(X0,X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_37])]) ).
fof(f127,plain,
( ! [X2,X0,X1] : domain(addition(X2,multiplication(X0,domain(X1)))) = domain(addition(X2,multiplication(X0,X1)))
| ~ spl1_11
| ~ spl1_12 ),
inference(forward_demodulation,[],[f122,f99]) ).
fof(f122,plain,
( ! [X2,X0,X1] : domain(addition(X2,multiplication(X0,domain(X1)))) = addition(domain(X2),domain(multiplication(X0,X1)))
| ~ spl1_11
| ~ spl1_12 ),
inference(superposition,[],[f99,f103]) ).
fof(f981,plain,
( spl1_36
| ~ spl1_12 ),
inference(avatar_split_clause,[],[f125,f102,f979]) ).
fof(f979,plain,
( spl1_36
<=> ! [X2,X0,X1] : domain(multiplication(X2,multiplication(X0,domain(X1)))) = domain(multiplication(X2,multiplication(X0,X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_36])]) ).
fof(f125,plain,
( ! [X2,X0,X1] : domain(multiplication(X2,multiplication(X0,domain(X1)))) = domain(multiplication(X2,multiplication(X0,X1)))
| ~ spl1_12 ),
inference(forward_demodulation,[],[f119,f103]) ).
fof(f119,plain,
( ! [X2,X0,X1] : domain(multiplication(X2,multiplication(X0,domain(X1)))) = domain(multiplication(X2,domain(multiplication(X0,X1))))
| ~ spl1_12 ),
inference(superposition,[],[f103,f103]) ).
fof(f826,plain,
( spl1_35
| ~ spl1_10
| ~ spl1_18 ),
inference(avatar_split_clause,[],[f237,f188,f86,f824]) ).
fof(f824,plain,
( spl1_35
<=> ! [X2,X0,X1] : multiplication(addition(X0,X2),X1) = addition(multiplication(X2,X1),multiplication(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_35])]) ).
fof(f86,plain,
( spl1_10
<=> ! [X0,X1] : addition(X0,X1) = addition(X1,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_10])]) ).
fof(f237,plain,
( ! [X2,X0,X1] : multiplication(addition(X0,X2),X1) = addition(multiplication(X2,X1),multiplication(X0,X1))
| ~ spl1_10
| ~ spl1_18 ),
inference(superposition,[],[f189,f87]) ).
fof(f87,plain,
( ! [X0,X1] : addition(X0,X1) = addition(X1,X0)
| ~ spl1_10 ),
inference(avatar_component_clause,[],[f86]) ).
fof(f822,plain,
( spl1_34
| ~ spl1_10
| ~ spl1_17 ),
inference(avatar_split_clause,[],[f202,f184,f86,f820]) ).
fof(f820,plain,
( spl1_34
<=> ! [X2,X0,X1] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X2),multiplication(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_34])]) ).
fof(f202,plain,
( ! [X2,X0,X1] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X2),multiplication(X0,X1))
| ~ spl1_10
| ~ spl1_17 ),
inference(superposition,[],[f185,f87]) ).
fof(f402,plain,
( spl1_33
| ~ spl1_9
| ~ spl1_10
| ~ spl1_11
| ~ spl1_19 ),
inference(avatar_split_clause,[],[f260,f221,f98,f86,f81,f400]) ).
fof(f400,plain,
( spl1_33
<=> ! [X0] : one = domain(addition(one,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_33])]) ).
fof(f81,plain,
( spl1_9
<=> ! [X0] : one = addition(domain(X0),one) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_9])]) ).
fof(f221,plain,
( spl1_19
<=> one = domain(one) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_19])]) ).
fof(f260,plain,
( ! [X0] : one = domain(addition(one,X0))
| ~ spl1_9
| ~ spl1_10
| ~ spl1_11
| ~ spl1_19 ),
inference(forward_demodulation,[],[f256,f90]) ).
fof(f90,plain,
( ! [X0] : one = addition(one,domain(X0))
| ~ spl1_9
| ~ spl1_10 ),
inference(superposition,[],[f87,f82]) ).
fof(f82,plain,
( ! [X0] : one = addition(domain(X0),one)
| ~ spl1_9 ),
inference(avatar_component_clause,[],[f81]) ).
fof(f256,plain,
( ! [X0] : addition(one,domain(X0)) = domain(addition(one,X0))
| ~ spl1_11
| ~ spl1_19 ),
inference(superposition,[],[f99,f223]) ).
fof(f223,plain,
( one = domain(one)
| ~ spl1_19 ),
inference(avatar_component_clause,[],[f221]) ).
fof(f398,plain,
( spl1_32
| ~ spl1_7
| ~ spl1_18 ),
inference(avatar_split_clause,[],[f234,f188,f73,f396]) ).
fof(f396,plain,
( spl1_32
<=> ! [X0,X1] : multiplication(addition(X1,one),X0) = addition(multiplication(X1,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_32])]) ).
fof(f234,plain,
( ! [X0,X1] : multiplication(addition(X1,one),X0) = addition(multiplication(X1,X0),X0)
| ~ spl1_7
| ~ spl1_18 ),
inference(superposition,[],[f189,f74]) ).
fof(f394,plain,
( spl1_31
| ~ spl1_7
| ~ spl1_18 ),
inference(avatar_split_clause,[],[f229,f188,f73,f392]) ).
fof(f229,plain,
( ! [X0,X1] : multiplication(addition(one,X1),X0) = addition(X0,multiplication(X1,X0))
| ~ spl1_7
| ~ spl1_18 ),
inference(superposition,[],[f189,f74]) ).
fof(f390,plain,
( spl1_30
| ~ spl1_6
| ~ spl1_17 ),
inference(avatar_split_clause,[],[f197,f184,f69,f388]) ).
fof(f388,plain,
( spl1_30
<=> ! [X0,X1] : multiplication(X0,addition(X1,one)) = addition(multiplication(X0,X1),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_30])]) ).
fof(f69,plain,
( spl1_6
<=> ! [X0] : multiplication(X0,one) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl1_6])]) ).
fof(f197,plain,
( ! [X0,X1] : multiplication(X0,addition(X1,one)) = addition(multiplication(X0,X1),X0)
| ~ spl1_6
| ~ spl1_17 ),
inference(superposition,[],[f185,f70]) ).
fof(f70,plain,
( ! [X0] : multiplication(X0,one) = X0
| ~ spl1_6 ),
inference(avatar_component_clause,[],[f69]) ).
fof(f386,plain,
( spl1_29
| ~ spl1_6
| ~ spl1_17 ),
inference(avatar_split_clause,[],[f192,f184,f69,f384]) ).
fof(f384,plain,
( spl1_29
<=> ! [X0,X1] : multiplication(X0,addition(one,X1)) = addition(X0,multiplication(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_29])]) ).
fof(f192,plain,
( ! [X0,X1] : multiplication(X0,addition(one,X1)) = addition(X0,multiplication(X0,X1))
| ~ spl1_6
| ~ spl1_17 ),
inference(superposition,[],[f185,f70]) ).
fof(f382,plain,
( spl1_28
| ~ spl1_10
| ~ spl1_15 ),
inference(avatar_split_clause,[],[f155,f134,f86,f380]) ).
fof(f380,plain,
( spl1_28
<=> ! [X2,X0,X1] : addition(X0,addition(X1,X2)) = addition(X2,addition(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_28])]) ).
fof(f155,plain,
( ! [X2,X0,X1] : addition(X0,addition(X1,X2)) = addition(X2,addition(X0,X1))
| ~ spl1_10
| ~ spl1_15 ),
inference(superposition,[],[f135,f87]) ).
fof(f377,plain,
( spl1_27
| ~ spl1_8
| ~ spl1_15 ),
inference(avatar_split_clause,[],[f154,f134,f77,f375]) ).
fof(f375,plain,
( spl1_27
<=> ! [X0,X1] : addition(X0,X1) = addition(X0,addition(X1,addition(X0,X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_27])]) ).
fof(f77,plain,
( spl1_8
<=> ! [X0] : addition(X0,X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl1_8])]) ).
fof(f154,plain,
( ! [X0,X1] : addition(X0,X1) = addition(X0,addition(X1,addition(X0,X1)))
| ~ spl1_8
| ~ spl1_15 ),
inference(superposition,[],[f135,f78]) ).
fof(f78,plain,
( ! [X0] : addition(X0,X0) = X0
| ~ spl1_8 ),
inference(avatar_component_clause,[],[f77]) ).
fof(f373,plain,
( spl1_26
| ~ spl1_10
| ~ spl1_15 ),
inference(avatar_split_clause,[],[f147,f134,f86,f371]) ).
fof(f371,plain,
( spl1_26
<=> ! [X2,X0,X1] : addition(X0,addition(X1,X2)) = addition(addition(X1,X0),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_26])]) ).
fof(f147,plain,
( ! [X2,X0,X1] : addition(X0,addition(X1,X2)) = addition(addition(X1,X0),X2)
| ~ spl1_10
| ~ spl1_15 ),
inference(superposition,[],[f135,f87]) ).
fof(f323,plain,
( spl1_25
| ~ spl1_9
| ~ spl1_15 ),
inference(avatar_split_clause,[],[f151,f134,f81,f321]) ).
fof(f321,plain,
( spl1_25
<=> ! [X0,X1] : addition(one,X1) = addition(domain(X0),addition(one,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_25])]) ).
fof(f151,plain,
( ! [X0,X1] : addition(one,X1) = addition(domain(X0),addition(one,X1))
| ~ spl1_9
| ~ spl1_15 ),
inference(superposition,[],[f135,f82]) ).
fof(f319,plain,
( spl1_24
| ~ spl1_9
| ~ spl1_11
| ~ spl1_19 ),
inference(avatar_split_clause,[],[f259,f221,f98,f81,f317]) ).
fof(f317,plain,
( spl1_24
<=> ! [X0] : one = domain(addition(X0,one)) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_24])]) ).
fof(f259,plain,
( ! [X0] : one = domain(addition(X0,one))
| ~ spl1_9
| ~ spl1_11
| ~ spl1_19 ),
inference(forward_demodulation,[],[f255,f82]) ).
fof(f255,plain,
( ! [X0] : addition(domain(X0),one) = domain(addition(X0,one))
| ~ spl1_11
| ~ spl1_19 ),
inference(superposition,[],[f99,f223]) ).
fof(f315,plain,
( spl1_23
| ~ spl1_10
| ~ spl1_11 ),
inference(avatar_split_clause,[],[f108,f98,f86,f313]) ).
fof(f313,plain,
( spl1_23
<=> ! [X0,X1] : domain(addition(X0,X1)) = addition(domain(X1),domain(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_23])]) ).
fof(f108,plain,
( ! [X0,X1] : domain(addition(X0,X1)) = addition(domain(X1),domain(X0))
| ~ spl1_10
| ~ spl1_11 ),
inference(superposition,[],[f99,f87]) ).
fof(f292,plain,
( spl1_22
| ~ spl1_8
| ~ spl1_15 ),
inference(avatar_split_clause,[],[f146,f134,f77,f290]) ).
fof(f290,plain,
( spl1_22
<=> ! [X0,X1] : addition(X0,X1) = addition(X0,addition(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_22])]) ).
fof(f146,plain,
( ! [X0,X1] : addition(X0,X1) = addition(X0,addition(X0,X1))
| ~ spl1_8
| ~ spl1_15 ),
inference(superposition,[],[f135,f78]) ).
fof(f273,plain,
( spl1_21
| ~ spl1_7
| ~ spl1_12 ),
inference(avatar_split_clause,[],[f126,f102,f73,f271]) ).
fof(f271,plain,
( spl1_21
<=> ! [X0] : domain(X0) = domain(domain(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_21])]) ).
fof(f126,plain,
( ! [X0] : domain(X0) = domain(domain(X0))
| ~ spl1_7
| ~ spl1_12 ),
inference(forward_demodulation,[],[f121,f74]) ).
fof(f121,plain,
( ! [X0] : domain(multiplication(one,X0)) = domain(domain(X0))
| ~ spl1_7
| ~ spl1_12 ),
inference(superposition,[],[f103,f74]) ).
fof(f269,plain,
( spl1_20
| ~ spl1_9
| ~ spl1_10 ),
inference(avatar_split_clause,[],[f90,f86,f81,f267]) ).
fof(f224,plain,
( spl1_19
| ~ spl1_6
| ~ spl1_9
| ~ spl1_10
| ~ spl1_14 ),
inference(avatar_split_clause,[],[f145,f130,f86,f81,f69,f221]) ).
fof(f145,plain,
( one = domain(one)
| ~ spl1_6
| ~ spl1_9
| ~ spl1_10
| ~ spl1_14 ),
inference(forward_demodulation,[],[f144,f90]) ).
fof(f144,plain,
( domain(one) = addition(one,domain(one))
| ~ spl1_6
| ~ spl1_14 ),
inference(superposition,[],[f131,f70]) ).
fof(f190,plain,
spl1_18,
inference(avatar_split_clause,[],[f45,f188]) ).
fof(f45,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(f186,plain,
spl1_17,
inference(avatar_split_clause,[],[f44,f184]) ).
fof(f44,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(f140,plain,
spl1_16,
inference(avatar_split_clause,[],[f43,f138]) ).
fof(f43,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(f136,plain,
spl1_15,
inference(avatar_split_clause,[],[f42,f134]) ).
fof(f42,plain,
! [X2,X0,X1] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
inference(cnf_transformation,[],[f25]) ).
fof(f25,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(f132,plain,
spl1_14,
inference(avatar_split_clause,[],[f38,f130]) ).
fof(f38,plain,
! [X0] : multiplication(domain(X0),X0) = addition(X0,multiplication(domain(X0),X0)),
inference(cnf_transformation,[],[f22]) ).
fof(f22,plain,
! [X0] : multiplication(domain(X0),X0) = addition(X0,multiplication(domain(X0),X0)),
inference(rectify,[],[f13]) ).
fof(f13,axiom,
! [X3] : multiplication(domain(X3),X3) = addition(X3,multiplication(domain(X3),X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain1) ).
fof(f118,plain,
( spl1_13
| ~ spl1_5
| ~ spl1_10 ),
inference(avatar_split_clause,[],[f89,f86,f65,f116]) ).
fof(f116,plain,
( spl1_13
<=> ! [X0] : addition(zero,X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl1_13])]) ).
fof(f65,plain,
( spl1_5
<=> ! [X0] : addition(X0,zero) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl1_5])]) ).
fof(f89,plain,
( ! [X0] : addition(zero,X0) = X0
| ~ spl1_5
| ~ spl1_10 ),
inference(superposition,[],[f87,f66]) ).
fof(f66,plain,
( ! [X0] : addition(X0,zero) = X0
| ~ spl1_5 ),
inference(avatar_component_clause,[],[f65]) ).
fof(f104,plain,
spl1_12,
inference(avatar_split_clause,[],[f41,f102]) ).
fof(f41,plain,
! [X0,X1] : domain(multiplication(X0,X1)) = domain(multiplication(X0,domain(X1))),
inference(cnf_transformation,[],[f24]) ).
fof(f24,plain,
! [X0,X1] : domain(multiplication(X0,X1)) = domain(multiplication(X0,domain(X1))),
inference(rectify,[],[f14]) ).
fof(f14,axiom,
! [X3,X4] : domain(multiplication(X3,X4)) = domain(multiplication(X3,domain(X4))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain2) ).
fof(f100,plain,
spl1_11,
inference(avatar_split_clause,[],[f40,f98]) ).
fof(f40,plain,
! [X0,X1] : domain(addition(X0,X1)) = addition(domain(X0),domain(X1)),
inference(cnf_transformation,[],[f23]) ).
fof(f23,plain,
! [X0,X1] : domain(addition(X0,X1)) = addition(domain(X0),domain(X1)),
inference(rectify,[],[f17]) ).
fof(f17,axiom,
! [X3,X4] : domain(addition(X3,X4)) = addition(domain(X3),domain(X4)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain5) ).
fof(f88,plain,
spl1_10,
inference(avatar_split_clause,[],[f39,f86]) ).
fof(f39,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(f83,plain,
spl1_9,
inference(avatar_split_clause,[],[f37,f81]) ).
fof(f37,plain,
! [X0] : one = addition(domain(X0),one),
inference(cnf_transformation,[],[f21]) ).
fof(f21,plain,
! [X0] : one = addition(domain(X0),one),
inference(rectify,[],[f15]) ).
fof(f15,axiom,
! [X3] : one = addition(domain(X3),one),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain3) ).
fof(f79,plain,
spl1_8,
inference(avatar_split_clause,[],[f36,f77]) ).
fof(f36,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(f75,plain,
spl1_7,
inference(avatar_split_clause,[],[f35,f73]) ).
fof(f35,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(f71,plain,
spl1_6,
inference(avatar_split_clause,[],[f34,f69]) ).
fof(f34,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(f67,plain,
spl1_5,
inference(avatar_split_clause,[],[f33,f65]) ).
fof(f33,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(f63,plain,
spl1_4,
inference(avatar_split_clause,[],[f32,f61]) ).
fof(f61,plain,
( spl1_4
<=> ! [X0] : zero = multiplication(zero,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_4])]) ).
fof(f32,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(f59,plain,
spl1_3,
inference(avatar_split_clause,[],[f31,f57]) ).
fof(f57,plain,
( spl1_3
<=> ! [X0] : zero = multiplication(X0,zero) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_3])]) ).
fof(f31,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(f55,plain,
spl1_2,
inference(avatar_split_clause,[],[f30,f52]) ).
fof(f52,plain,
( spl1_2
<=> zero = domain(zero) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_2])]) ).
fof(f30,plain,
zero = domain(zero),
inference(cnf_transformation,[],[f16]) ).
fof(f16,axiom,
zero = domain(zero),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain4) ).
fof(f50,plain,
~ spl1_1,
inference(avatar_split_clause,[],[f29,f47]) ).
fof(f29,plain,
sK0 != multiplication(domain(sK0),sK0),
inference(cnf_transformation,[],[f28]) ).
fof(f28,plain,
sK0 != multiplication(domain(sK0),sK0),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f26,f27]) ).
fof(f27,plain,
( ? [X0] : multiplication(domain(X0),X0) != X0
=> sK0 != multiplication(domain(sK0),sK0) ),
introduced(choice_axiom,[]) ).
fof(f26,plain,
? [X0] : multiplication(domain(X0),X0) != X0,
inference(ennf_transformation,[],[f20]) ).
fof(f20,plain,
~ ! [X0] : multiplication(domain(X0),X0) = X0,
inference(rectify,[],[f19]) ).
fof(f19,negated_conjecture,
~ ! [X3] : multiplication(domain(X3),X3) = X3,
inference(negated_conjecture,[],[f18]) ).
fof(f18,conjecture,
! [X3] : multiplication(domain(X3),X3) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : KLE052+1 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.35 % Computer : n023.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Tue Apr 30 05:18:40 EDT 2024
% 0.15/0.35 % CPUTime :
% 0.15/0.36 % (28493)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.37 % (28496)WARNING: value z3 for option sas not known
% 0.15/0.37 % (28494)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.37 % (28495)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.15/0.37 % (28497)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.37 % (28496)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)
% 0.15/0.37 % (28498)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)
% 0.15/0.37 % (28499)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)
% 0.15/0.37 % (28500)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)
% 0.15/0.37 TRYING [1]
% 0.15/0.38 TRYING [2]
% 0.15/0.38 TRYING [3]
% 0.15/0.38 TRYING [1]
% 0.15/0.38 TRYING [2]
% 0.15/0.39 TRYING [4]
% 0.22/0.39 TRYING [3]
% 0.22/0.42 TRYING [1]
% 0.22/0.42 TRYING [2]
% 0.22/0.42 TRYING [3]
% 0.22/0.42 TRYING [5]
% 0.22/0.43 TRYING [4]
% 0.22/0.43 TRYING [4]
% 0.22/0.47 % (28498)First to succeed.
% 0.22/0.48 % (28498)Refutation found. Thanks to Tanya!
% 0.22/0.48 % SZS status Theorem for theBenchmark
% 0.22/0.48 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.48 % (28498)------------------------------
% 0.22/0.48 % (28498)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.22/0.48 % (28498)Termination reason: Refutation
% 0.22/0.48
% 0.22/0.48 % (28498)Memory used [KB]: 2113
% 0.22/0.48 % (28498)Time elapsed: 0.105 s
% 0.22/0.48 % (28498)Instructions burned: 149 (million)
% 0.22/0.48 % (28498)------------------------------
% 0.22/0.48 % (28498)------------------------------
% 0.22/0.48 % (28493)Success in time 0.122 s
%------------------------------------------------------------------------------