TSTP Solution File: HAL002+1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : HAL002+1 : TPTP v8.1.2. Released v2.6.0.
% 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 : n008.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 15:58:37 EDT 2023
% Result : Theorem 0.21s 0.71s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 131
% Syntax : Number of formulae : 998 ( 4 unt; 0 def)
% Number of atoms : 4088 ( 783 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 5480 (2390 ~;2774 |; 147 &)
% ( 114 <=>; 52 =>; 0 <=; 3 <~>)
% Maximal formula depth : 17 ( 6 avg)
% Maximal term depth : 7 ( 1 avg)
% Number of predicates : 115 ( 113 usr; 107 prp; 0-4 aty)
% Number of functors : 15 ( 15 usr; 3 con; 0-5 aty)
% Number of variables : 1422 (;1376 !; 46 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2822,plain,
$false,
inference(avatar_smt_refutation,[],[f124,f129,f135,f142,f148,f150,f153,f155,f157,f159,f175,f189,f200,f212,f222,f226,f237,f251,f257,f259,f261,f264,f266,f268,f270,f272,f274,f276,f278,f280,f283,f300,f309,f316,f323,f330,f331,f349,f355,f361,f390,f397,f410,f420,f433,f440,f446,f489,f503,f517,f537,f553,f590,f604,f659,f665,f670,f701,f737,f765,f770,f801,f806,f850,f866,f873,f905,f910,f917,f918,f973,f1005,f1091,f1097,f1102,f1103,f1112,f1121,f1230,f1278,f1309,f1336,f1347,f1351,f1371,f1466,f1473,f1491,f1502,f1513,f1514,f1605,f1616,f1620,f1680,f1775,f1790,f1795,f1839,f1844,f1902,f2010,f2016,f2022,f2029,f2035,f2097,f2108,f2111,f2163,f2189,f2198,f2205,f2206,f2250,f2276,f2277,f2387,f2402,f2489,f2492,f2557,f2559,f2561,f2563,f2565,f2567,f2569,f2571,f2573,f2575,f2577,f2579,f2581,f2583,f2585,f2587,f2589,f2591,f2593,f2595,f2597,f2628,f2636,f2641,f2649,f2650,f2651,f2652,f2653,f2676,f2677,f2685,f2690,f2695,f2715,f2721,f2741,f2748,f2777,f2779,f2805,f2806,f2821]) ).
fof(f2821,plain,
( spl9_2
| ~ spl9_3
| ~ spl9_106 ),
inference(avatar_contradiction_clause,[],[f2820]) ).
fof(f2820,plain,
( $false
| spl9_2
| ~ spl9_3
| ~ spl9_106 ),
inference(subsumption_resolution,[],[f2819,f128]) ).
fof(f128,plain,
( morphism(x,any1,any2)
| ~ spl9_3 ),
inference(avatar_component_clause,[],[f126]) ).
fof(f126,plain,
( spl9_3
<=> morphism(x,any1,any2) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_3])]) ).
fof(f2819,plain,
( ~ morphism(x,any1,any2)
| spl9_2
| ~ spl9_106 ),
inference(subsumption_resolution,[],[f2816,f122]) ).
fof(f122,plain,
( ~ injection_2(x)
| spl9_2 ),
inference(avatar_component_clause,[],[f121]) ).
fof(f121,plain,
( spl9_2
<=> injection_2(x) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_2])]) ).
fof(f2816,plain,
( injection_2(x)
| ~ morphism(x,any1,any2)
| ~ spl9_106 ),
inference(trivial_inequality_removal,[],[f2814]) ).
fof(f2814,plain,
( zero(any1) != zero(any1)
| injection_2(x)
| ~ morphism(x,any1,any2)
| ~ spl9_106 ),
inference(superposition,[],[f99,f2804]) ).
fof(f2804,plain,
( zero(any1) = sK2(x,any1,any2)
| ~ spl9_106 ),
inference(avatar_component_clause,[],[f2802]) ).
fof(f2802,plain,
( spl9_106
<=> zero(any1) = sK2(x,any1,any2) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_106])]) ).
fof(f99,plain,
! [X2,X0,X1] :
( zero(X1) != sK2(X0,X1,X2)
| injection_2(X0)
| ~ morphism(X0,X1,X2) ),
inference(cnf_transformation,[],[f66]) ).
fof(f66,plain,
! [X0,X1,X2] :
( injection_2(X0)
| ( zero(X1) != sK2(X0,X1,X2)
& zero(X2) = apply(X0,sK2(X0,X1,X2))
& element(sK2(X0,X1,X2),X1) )
| ~ morphism(X0,X1,X2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f49,f65]) ).
fof(f65,plain,
! [X0,X1,X2] :
( ? [X3] :
( zero(X1) != X3
& apply(X0,X3) = zero(X2)
& element(X3,X1) )
=> ( zero(X1) != sK2(X0,X1,X2)
& zero(X2) = apply(X0,sK2(X0,X1,X2))
& element(sK2(X0,X1,X2),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f49,plain,
! [X0,X1,X2] :
( injection_2(X0)
| ? [X3] :
( zero(X1) != X3
& apply(X0,X3) = zero(X2)
& element(X3,X1) )
| ~ morphism(X0,X1,X2) ),
inference(flattening,[],[f48]) ).
fof(f48,plain,
! [X0,X1,X2] :
( injection_2(X0)
| ? [X3] :
( zero(X1) != X3
& apply(X0,X3) = zero(X2)
& element(X3,X1) )
| ~ morphism(X0,X1,X2) ),
inference(ennf_transformation,[],[f15]) ).
fof(f15,axiom,
! [X0,X1,X2] :
( ( ! [X3] :
( ( apply(X0,X3) = zero(X2)
& element(X3,X1) )
=> zero(X1) = X3 )
& morphism(X0,X1,X2) )
=> injection_2(X0) ),
file('/export/starexec/sandbox/tmp/tmp.YLPE9jctjB/Vampire---4.8_1232',properties_for_injection_2) ).
fof(f2806,plain,
( spl9_106
| ~ spl9_7
| ~ spl9_61
| ~ spl9_70
| ~ spl9_105 ),
inference(avatar_split_clause,[],[f2800,f2775,f1499,f1275,f168,f2802]) ).
fof(f168,plain,
( spl9_7
<=> element(zero(any1),any1) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_7])]) ).
fof(f1275,plain,
( spl9_61
<=> zero(any2) = apply(x,sK0(x,any1,zero(any2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_61])]) ).
fof(f1499,plain,
( spl9_70
<=> zero(any1) = sK0(x,any1,zero(any2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_70])]) ).
fof(f2775,plain,
( spl9_105
<=> ! [X2] :
( sK2(x,any1,any2) = X2
| zero(any2) != apply(x,X2)
| ~ element(X2,any1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_105])]) ).
fof(f2800,plain,
( zero(any1) = sK2(x,any1,any2)
| ~ spl9_7
| ~ spl9_61
| ~ spl9_70
| ~ spl9_105 ),
inference(subsumption_resolution,[],[f2799,f169]) ).
fof(f169,plain,
( element(zero(any1),any1)
| ~ spl9_7 ),
inference(avatar_component_clause,[],[f168]) ).
fof(f2799,plain,
( ~ element(zero(any1),any1)
| zero(any1) = sK2(x,any1,any2)
| ~ spl9_61
| ~ spl9_70
| ~ spl9_105 ),
inference(forward_demodulation,[],[f2798,f1501]) ).
fof(f1501,plain,
( zero(any1) = sK0(x,any1,zero(any2))
| ~ spl9_70 ),
inference(avatar_component_clause,[],[f1499]) ).
fof(f2798,plain,
( zero(any1) = sK2(x,any1,any2)
| ~ element(sK0(x,any1,zero(any2)),any1)
| ~ spl9_61
| ~ spl9_70
| ~ spl9_105 ),
inference(forward_demodulation,[],[f2791,f1501]) ).
fof(f2791,plain,
( sK2(x,any1,any2) = sK0(x,any1,zero(any2))
| ~ element(sK0(x,any1,zero(any2)),any1)
| ~ spl9_61
| ~ spl9_105 ),
inference(trivial_inequality_removal,[],[f2787]) ).
fof(f2787,plain,
( zero(any2) != zero(any2)
| sK2(x,any1,any2) = sK0(x,any1,zero(any2))
| ~ element(sK0(x,any1,zero(any2)),any1)
| ~ spl9_61
| ~ spl9_105 ),
inference(superposition,[],[f2776,f1277]) ).
fof(f1277,plain,
( zero(any2) = apply(x,sK0(x,any1,zero(any2)))
| ~ spl9_61 ),
inference(avatar_component_clause,[],[f1275]) ).
fof(f2776,plain,
( ! [X2] :
( zero(any2) != apply(x,X2)
| sK2(x,any1,any2) = X2
| ~ element(X2,any1) )
| ~ spl9_105 ),
inference(avatar_component_clause,[],[f2775]) ).
fof(f2805,plain,
( spl9_106
| ~ spl9_4
| ~ spl9_7
| ~ spl9_105 ),
inference(avatar_split_clause,[],[f2795,f2775,f168,f132,f2802]) ).
fof(f132,plain,
( spl9_4
<=> apply(x,zero(any1)) = zero(any2) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_4])]) ).
fof(f2795,plain,
( zero(any1) = sK2(x,any1,any2)
| ~ spl9_4
| ~ spl9_7
| ~ spl9_105 ),
inference(subsumption_resolution,[],[f2794,f169]) ).
fof(f2794,plain,
( zero(any1) = sK2(x,any1,any2)
| ~ element(zero(any1),any1)
| ~ spl9_4
| ~ spl9_105 ),
inference(trivial_inequality_removal,[],[f2780]) ).
fof(f2780,plain,
( zero(any2) != zero(any2)
| zero(any1) = sK2(x,any1,any2)
| ~ element(zero(any1),any1)
| ~ spl9_4
| ~ spl9_105 ),
inference(superposition,[],[f2776,f134]) ).
fof(f134,plain,
( apply(x,zero(any1)) = zero(any2)
| ~ spl9_4 ),
inference(avatar_component_clause,[],[f132]) ).
fof(f2779,plain,
( ~ spl9_3
| ~ spl9_104 ),
inference(avatar_contradiction_clause,[],[f2778]) ).
fof(f2778,plain,
( $false
| ~ spl9_3
| ~ spl9_104 ),
inference(resolution,[],[f2773,f128]) ).
fof(f2773,plain,
( ! [X3] : ~ morphism(x,any1,X3)
| ~ spl9_104 ),
inference(avatar_component_clause,[],[f2772]) ).
fof(f2772,plain,
( spl9_104
<=> ! [X3] : ~ morphism(x,any1,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_104])]) ).
fof(f2777,plain,
( spl9_104
| spl9_105
| ~ spl9_1
| ~ spl9_11
| ~ spl9_13 ),
inference(avatar_split_clause,[],[f2768,f219,f197,f117,f2775,f2772]) ).
fof(f117,plain,
( spl9_1
<=> injection(x) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_1])]) ).
fof(f197,plain,
( spl9_11
<=> zero(any2) = apply(x,sK2(x,any1,any2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_11])]) ).
fof(f219,plain,
( spl9_13
<=> element(sK2(x,any1,any2),any1) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_13])]) ).
fof(f2768,plain,
( ! [X2,X3] :
( sK2(x,any1,any2) = X2
| ~ element(X2,any1)
| zero(any2) != apply(x,X2)
| ~ morphism(x,any1,X3) )
| ~ spl9_1
| ~ spl9_11
| ~ spl9_13 ),
inference(resolution,[],[f2625,f220]) ).
fof(f220,plain,
( element(sK2(x,any1,any2),any1)
| ~ spl9_13 ),
inference(avatar_component_clause,[],[f219]) ).
fof(f2625,plain,
( ! [X2,X3,X4] :
( ~ element(sK2(x,any1,any2),X3)
| sK2(x,any1,any2) = X2
| ~ element(X2,X3)
| zero(any2) != apply(x,X2)
| ~ morphism(x,X3,X4) )
| ~ spl9_1
| ~ spl9_11 ),
inference(subsumption_resolution,[],[f2618,f119]) ).
fof(f119,plain,
( injection(x)
| ~ spl9_1 ),
inference(avatar_component_clause,[],[f117]) ).
fof(f2618,plain,
( ! [X2,X3,X4] :
( zero(any2) != apply(x,X2)
| sK2(x,any1,any2) = X2
| ~ element(X2,X3)
| ~ element(sK2(x,any1,any2),X3)
| ~ morphism(x,X3,X4)
| ~ injection(x) )
| ~ spl9_11 ),
inference(superposition,[],[f92,f199]) ).
fof(f199,plain,
( zero(any2) = apply(x,sK2(x,any1,any2))
| ~ spl9_11 ),
inference(avatar_component_clause,[],[f197]) ).
fof(f92,plain,
! [X2,X3,X0,X1,X4] :
( apply(X0,X3) != apply(X0,X4)
| X3 = X4
| ~ element(X4,X1)
| ~ element(X3,X1)
| ~ morphism(X0,X1,X2)
| ~ injection(X0) ),
inference(cnf_transformation,[],[f41]) ).
fof(f41,plain,
! [X0,X1,X2] :
( ! [X3,X4] :
( X3 = X4
| apply(X0,X3) != apply(X0,X4)
| ~ element(X4,X1)
| ~ element(X3,X1) )
| ~ morphism(X0,X1,X2)
| ~ injection(X0) ),
inference(flattening,[],[f40]) ).
fof(f40,plain,
! [X0,X1,X2] :
( ! [X3,X4] :
( X3 = X4
| apply(X0,X3) != apply(X0,X4)
| ~ element(X4,X1)
| ~ element(X3,X1) )
| ~ morphism(X0,X1,X2)
| ~ injection(X0) ),
inference(ennf_transformation,[],[f22]) ).
fof(f22,plain,
! [X0,X1,X2] :
( ( morphism(X0,X1,X2)
& injection(X0) )
=> ! [X3,X4] :
( ( apply(X0,X3) = apply(X0,X4)
& element(X4,X1)
& element(X3,X1) )
=> X3 = X4 ) ),
inference(rectify,[],[f2]) ).
fof(f2,axiom,
! [X0,X1,X2] :
( ( morphism(X0,X1,X2)
& injection(X0) )
=> ! [X4,X5] :
( ( apply(X0,X4) = apply(X0,X5)
& element(X5,X1)
& element(X4,X1) )
=> X4 = X5 ) ),
file('/export/starexec/sandbox/tmp/tmp.YLPE9jctjB/Vampire---4.8_1232',injection_properties) ).
fof(f2748,plain,
( ~ spl9_103
| spl9_16
| ~ spl9_55
| ~ spl9_65 ),
inference(avatar_split_clause,[],[f2743,f1344,f1088,f306,f2745]) ).
fof(f2745,plain,
( spl9_103
<=> element(subtract(any2,sK1(x,any1,any2),apply(x,sK3(x,any1))),any2) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_103])]) ).
fof(f306,plain,
( spl9_16
<=> element(apply(x,sK3(x,any1)),any2) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_16])]) ).
fof(f1088,plain,
( spl9_55
<=> apply(x,sK3(x,any1)) = subtract(any2,sK1(x,any1,any2),subtract(any2,sK1(x,any1,any2),apply(x,sK3(x,any1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_55])]) ).
fof(f1344,plain,
( spl9_65
<=> element(sK1(x,any1,any2),any2) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_65])]) ).
fof(f2743,plain,
( ~ element(subtract(any2,sK1(x,any1,any2),apply(x,sK3(x,any1))),any2)
| spl9_16
| ~ spl9_55
| ~ spl9_65 ),
inference(subsumption_resolution,[],[f2544,f307]) ).
fof(f307,plain,
( ~ element(apply(x,sK3(x,any1)),any2)
| spl9_16 ),
inference(avatar_component_clause,[],[f306]) ).
fof(f2544,plain,
( element(apply(x,sK3(x,any1)),any2)
| ~ element(subtract(any2,sK1(x,any1,any2),apply(x,sK3(x,any1))),any2)
| ~ spl9_55
| ~ spl9_65 ),
inference(subsumption_resolution,[],[f1092,f1346]) ).
fof(f1346,plain,
( element(sK1(x,any1,any2),any2)
| ~ spl9_65 ),
inference(avatar_component_clause,[],[f1344]) ).
fof(f1092,plain,
( element(apply(x,sK3(x,any1)),any2)
| ~ element(subtract(any2,sK1(x,any1,any2),apply(x,sK3(x,any1))),any2)
| ~ element(sK1(x,any1,any2),any2)
| ~ spl9_55 ),
inference(superposition,[],[f93,f1090]) ).
fof(f1090,plain,
( apply(x,sK3(x,any1)) = subtract(any2,sK1(x,any1,any2),subtract(any2,sK1(x,any1,any2),apply(x,sK3(x,any1))))
| ~ spl9_55 ),
inference(avatar_component_clause,[],[f1088]) ).
fof(f93,plain,
! [X2,X0,X1] :
( element(subtract(X0,X1,X2),X0)
| ~ element(X2,X0)
| ~ element(X1,X0) ),
inference(cnf_transformation,[],[f43]) ).
fof(f43,plain,
! [X0,X1,X2] :
( element(subtract(X0,X1,X2),X0)
| ~ element(X2,X0)
| ~ element(X1,X0) ),
inference(flattening,[],[f42]) ).
fof(f42,plain,
! [X0,X1,X2] :
( element(subtract(X0,X1,X2),X0)
| ~ element(X2,X0)
| ~ element(X1,X0) ),
inference(ennf_transformation,[],[f23]) ).
fof(f23,plain,
! [X0,X1,X2] :
( ( element(X2,X0)
& element(X1,X0) )
=> element(subtract(X0,X1,X2),X0) ),
inference(rectify,[],[f10]) ).
fof(f10,axiom,
! [X1,X4,X5] :
( ( element(X5,X1)
& element(X4,X1) )
=> element(subtract(X1,X4,X5),X1) ),
file('/export/starexec/sandbox/tmp/tmp.YLPE9jctjB/Vampire---4.8_1232',subtract_in_domain) ).
fof(f2741,plain,
( spl9_52
| spl9_53
| ~ spl9_3
| ~ spl9_11
| ~ spl9_13 ),
inference(avatar_split_clause,[],[f2740,f219,f197,f126,f971,f968]) ).
fof(f968,plain,
( spl9_52
<=> ! [X2,X1] :
( ~ morphism(X1,any2,X2)
| ~ exact(x,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_52])]) ).
fof(f971,plain,
( spl9_53
<=> ! [X0] :
( zero(any2) != X0
| element(X0,any2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_53])]) ).
fof(f2740,plain,
( ! [X2,X0,X1] :
( zero(any2) != X0
| ~ morphism(X1,any2,X2)
| element(X0,any2)
| ~ exact(x,X1) )
| ~ spl9_3
| ~ spl9_11
| ~ spl9_13 ),
inference(resolution,[],[f2737,f128]) ).
fof(f2737,plain,
( ! [X6,X7,X4,X5] :
( ~ morphism(x,any1,X5)
| zero(any2) != X4
| ~ morphism(X6,X5,X7)
| element(X4,X5)
| ~ exact(x,X6) )
| ~ spl9_11
| ~ spl9_13 ),
inference(resolution,[],[f2623,f220]) ).
fof(f2623,plain,
( ! [X21,X18,X19,X22,X20] :
( ~ element(sK2(x,any1,any2),X20)
| element(X18,X19)
| zero(any2) != X18
| ~ morphism(X21,X19,X22)
| ~ morphism(x,X20,X19)
| ~ exact(x,X21) )
| ~ spl9_11 ),
inference(superposition,[],[f106,f199]) ).
fof(f106,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( apply(X0,X6) != X5
| element(X5,X3)
| ~ element(X6,X2)
| ~ morphism(X1,X3,X4)
| ~ morphism(X0,X2,X3)
| ~ exact(X0,X1) ),
inference(cnf_transformation,[],[f73]) ).
fof(f73,plain,
! [X0,X1,X2,X3,X4] :
( ! [X5] :
( ( ( zero(X4) = apply(X1,X5)
& element(X5,X3) )
| ! [X6] :
( apply(X0,X6) != X5
| ~ element(X6,X2) ) )
& ( ( apply(X0,sK5(X0,X2,X5)) = X5
& element(sK5(X0,X2,X5),X2) )
| zero(X4) != apply(X1,X5)
| ~ element(X5,X3) ) )
| ~ morphism(X1,X3,X4)
| ~ morphism(X0,X2,X3)
| ~ exact(X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f71,f72]) ).
fof(f72,plain,
! [X0,X2,X5] :
( ? [X7] :
( apply(X0,X7) = X5
& element(X7,X2) )
=> ( apply(X0,sK5(X0,X2,X5)) = X5
& element(sK5(X0,X2,X5),X2) ) ),
introduced(choice_axiom,[]) ).
fof(f71,plain,
! [X0,X1,X2,X3,X4] :
( ! [X5] :
( ( ( zero(X4) = apply(X1,X5)
& element(X5,X3) )
| ! [X6] :
( apply(X0,X6) != X5
| ~ element(X6,X2) ) )
& ( ? [X7] :
( apply(X0,X7) = X5
& element(X7,X2) )
| zero(X4) != apply(X1,X5)
| ~ element(X5,X3) ) )
| ~ morphism(X1,X3,X4)
| ~ morphism(X0,X2,X3)
| ~ exact(X0,X1) ),
inference(rectify,[],[f70]) ).
fof(f70,plain,
! [X0,X1,X2,X3,X4] :
( ! [X5] :
( ( ( zero(X4) = apply(X1,X5)
& element(X5,X3) )
| ! [X6] :
( apply(X0,X6) != X5
| ~ element(X6,X2) ) )
& ( ? [X6] :
( apply(X0,X6) = X5
& element(X6,X2) )
| zero(X4) != apply(X1,X5)
| ~ element(X5,X3) ) )
| ~ morphism(X1,X3,X4)
| ~ morphism(X0,X2,X3)
| ~ exact(X0,X1) ),
inference(flattening,[],[f69]) ).
fof(f69,plain,
! [X0,X1,X2,X3,X4] :
( ! [X5] :
( ( ( zero(X4) = apply(X1,X5)
& element(X5,X3) )
| ! [X6] :
( apply(X0,X6) != X5
| ~ element(X6,X2) ) )
& ( ? [X6] :
( apply(X0,X6) = X5
& element(X6,X2) )
| zero(X4) != apply(X1,X5)
| ~ element(X5,X3) ) )
| ~ morphism(X1,X3,X4)
| ~ morphism(X0,X2,X3)
| ~ exact(X0,X1) ),
inference(nnf_transformation,[],[f53]) ).
fof(f53,plain,
! [X0,X1,X2,X3,X4] :
( ! [X5] :
( ( zero(X4) = apply(X1,X5)
& element(X5,X3) )
<=> ? [X6] :
( apply(X0,X6) = X5
& element(X6,X2) ) )
| ~ morphism(X1,X3,X4)
| ~ morphism(X0,X2,X3)
| ~ exact(X0,X1) ),
inference(flattening,[],[f52]) ).
fof(f52,plain,
! [X0,X1,X2,X3,X4] :
( ! [X5] :
( ( zero(X4) = apply(X1,X5)
& element(X5,X3) )
<=> ? [X6] :
( apply(X0,X6) = X5
& element(X6,X2) ) )
| ~ morphism(X1,X3,X4)
| ~ morphism(X0,X2,X3)
| ~ exact(X0,X1) ),
inference(ennf_transformation,[],[f27]) ).
fof(f27,plain,
! [X0,X1,X2,X3,X4] :
( ( morphism(X1,X3,X4)
& morphism(X0,X2,X3)
& exact(X0,X1) )
=> ! [X5] :
( ( zero(X4) = apply(X1,X5)
& element(X5,X3) )
<=> ? [X6] :
( apply(X0,X6) = X5
& element(X6,X2) ) ) ),
inference(rectify,[],[f6]) ).
fof(f6,axiom,
! [X8,X9,X1,X10,X2] :
( ( morphism(X9,X10,X2)
& morphism(X8,X1,X10)
& exact(X8,X9) )
=> ! [X11] :
( ( zero(X2) = apply(X9,X11)
& element(X11,X10) )
<=> ? [X7] :
( apply(X8,X7) = X11
& element(X7,X1) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.YLPE9jctjB/Vampire---4.8_1232',exact_properties) ).
fof(f2721,plain,
( spl9_102
| ~ spl9_7
| ~ spl9_13 ),
inference(avatar_split_clause,[],[f2699,f219,f168,f2718]) ).
fof(f2718,plain,
( spl9_102
<=> sK2(x,any1,any2) = subtract(any1,zero(any1),subtract(any1,zero(any1),sK2(x,any1,any2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_102])]) ).
fof(f2699,plain,
( sK2(x,any1,any2) = subtract(any1,zero(any1),subtract(any1,zero(any1),sK2(x,any1,any2)))
| ~ spl9_7
| ~ spl9_13 ),
inference(resolution,[],[f2613,f169]) ).
fof(f2613,plain,
( ! [X7] :
( ~ element(X7,any1)
| sK2(x,any1,any2) = subtract(any1,X7,subtract(any1,X7,sK2(x,any1,any2))) )
| ~ spl9_13 ),
inference(resolution,[],[f220,f94]) ).
fof(f94,plain,
! [X2,X0,X1] :
( ~ element(X2,X0)
| subtract(X0,X1,subtract(X0,X1,X2)) = X2
| ~ element(X1,X0) ),
inference(cnf_transformation,[],[f45]) ).
fof(f45,plain,
! [X0,X1,X2] :
( subtract(X0,X1,subtract(X0,X1,X2)) = X2
| ~ element(X2,X0)
| ~ element(X1,X0) ),
inference(flattening,[],[f44]) ).
fof(f44,plain,
! [X0,X1,X2] :
( subtract(X0,X1,subtract(X0,X1,X2)) = X2
| ~ element(X2,X0)
| ~ element(X1,X0) ),
inference(ennf_transformation,[],[f24]) ).
fof(f24,plain,
! [X0,X1,X2] :
( ( element(X2,X0)
& element(X1,X0) )
=> subtract(X0,X1,subtract(X0,X1,X2)) = X2 ),
inference(rectify,[],[f12]) ).
fof(f12,axiom,
! [X1,X4,X5] :
( ( element(X5,X1)
& element(X4,X1) )
=> subtract(X1,X4,subtract(X1,X4,X5)) = X5 ),
file('/export/starexec/sandbox/tmp/tmp.YLPE9jctjB/Vampire---4.8_1232',subtract_cancellation) ).
fof(f2715,plain,
( spl9_101
| ~ spl9_13
| ~ spl9_97 ),
inference(avatar_split_clause,[],[f2710,f2633,f219,f2712]) ).
fof(f2712,plain,
( spl9_101
<=> sK2(x,any1,any2) = subtract(any1,sK2(x,any1,any2),zero(any1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_101])]) ).
fof(f2633,plain,
( spl9_97
<=> zero(any1) = subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_97])]) ).
fof(f2710,plain,
( sK2(x,any1,any2) = subtract(any1,sK2(x,any1,any2),zero(any1))
| ~ spl9_13
| ~ spl9_97 ),
inference(forward_demodulation,[],[f2702,f2635]) ).
fof(f2635,plain,
( zero(any1) = subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2))
| ~ spl9_97 ),
inference(avatar_component_clause,[],[f2633]) ).
fof(f2702,plain,
( sK2(x,any1,any2) = subtract(any1,sK2(x,any1,any2),subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2)))
| ~ spl9_13 ),
inference(resolution,[],[f2613,f220]) ).
fof(f2695,plain,
( ~ spl9_100
| ~ spl9_3
| spl9_45
| ~ spl9_78 ),
inference(avatar_split_clause,[],[f2601,f1836,f798,f126,f2692]) ).
fof(f2692,plain,
( spl9_100
<=> element(subtract(any1,subtract(any1,sK4(x,any1),sK3(x,any1)),sK3(x,any1)),any1) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_100])]) ).
fof(f798,plain,
( spl9_45
<=> element(subtract(any2,zero(any2),apply(x,sK3(x,any1))),any2) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_45])]) ).
fof(f1836,plain,
( spl9_78
<=> subtract(any2,zero(any2),apply(x,sK3(x,any1))) = apply(x,subtract(any1,subtract(any1,sK4(x,any1),sK3(x,any1)),sK3(x,any1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_78])]) ).
fof(f2601,plain,
( ~ element(subtract(any1,subtract(any1,sK4(x,any1),sK3(x,any1)),sK3(x,any1)),any1)
| ~ spl9_3
| spl9_45
| ~ spl9_78 ),
inference(global_subsumption,[],[f82,f84,f128,f85,f87,f130,f100,f101,f86,f93,f163,f95,f97,f99,f103,f165,f89,f181,f94,f98,f90,f96,f102,f91,f92,f106,f88,f164,f472,f473,f474,f107,f176,f177,f190,f542,f543,f544,f104,f108,f613,f616,f617,f634,f637,f638,f457,f674,f675,f676,f679,f680,f105,f799,f113,f109,f875,f878,f879,f886,f110,f939,f942,f943,f950,f522,f1008,f115,f111,f114,f1113,f1114,f1116,f468,f1128,f1129,f1130,f1133,f1134,f1135,f1136,f178,f1142,f1143,f1144,f1147,f1148,f1149,f1150,f179,f112,f180,f191,f1279,f1283,f1287,f1288,f1291,f1292,f1293,f1294,f192,f193,f802,f1069,f615,f1719,f1720,f1721,f1722,f1723,f1724,f1725,f1732,f1733,f636,f1845,f1846,f1847,f1848,f1849,f1850,f1851,f1858,f1859,f1838,f1908,f1909,f1910,f1911,f877,f2017,f614,f2077,f1907,f240,f1315,f635,f2158,f941,f2191,f876,f2253,f940,f2302,f1906,f1905,f294,f1904,f1425,f1184,f540,f136,f162,f194,f83,f1903]) ).
fof(f1903,plain,
( element(subtract(any2,zero(any2),apply(x,sK3(x,any1))),any2)
| ~ element(subtract(any1,subtract(any1,sK4(x,any1),sK3(x,any1)),sK3(x,any1)),any1)
| ~ spl9_3
| ~ spl9_78 ),
inference(superposition,[],[f163,f1838]) ).
fof(f83,plain,
( ~ injection_2(x)
| ~ injection(x) ),
inference(cnf_transformation,[],[f60]) ).
fof(f60,plain,
( ( ~ injection_2(x)
| ~ injection(x) )
& ( injection_2(x)
| injection(x) ) ),
inference(nnf_transformation,[],[f31]) ).
fof(f31,plain,
( injection(x)
<~> injection_2(x) ),
inference(ennf_transformation,[],[f18]) ).
fof(f18,negated_conjecture,
~ ( injection(x)
<=> injection_2(x) ),
inference(negated_conjecture,[],[f17]) ).
fof(f17,conjecture,
( injection(x)
<=> injection_2(x) ),
file('/export/starexec/sandbox/tmp/tmp.YLPE9jctjB/Vampire---4.8_1232',my) ).
fof(f194,plain,
( zero(any2) = apply(x,sK2(x,any1,any2))
| injection_2(x)
| ~ spl9_3 ),
inference(resolution,[],[f98,f128]) ).
fof(f162,plain,
( element(sK4(x,any1),any1)
| injection(x)
| ~ spl9_3 ),
inference(resolution,[],[f101,f128]) ).
fof(f136,plain,
( element(sK3(x,any1),any1)
| injection(x)
| ~ spl9_3 ),
inference(resolution,[],[f100,f128]) ).
fof(f540,plain,
( injection_2(x)
| zero(any1) = subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2))
| ~ spl9_3 ),
inference(resolution,[],[f177,f128]) ).
fof(f1184,plain,
( injection_2(x)
| zero(any2) = subtract(any2,apply(x,sK2(x,any1,any2)),apply(x,sK2(x,any1,any2)))
| ~ spl9_3 ),
inference(resolution,[],[f180,f128]) ).
fof(f1425,plain,
( ! [X0] :
( ~ element(X0,any1)
| injection_2(x)
| sK2(x,any1,any2) = subtract(any1,X0,subtract(any1,X0,sK2(x,any1,any2))) )
| ~ spl9_3 ),
inference(resolution,[],[f193,f128]) ).
fof(f1904,plain,
( ! [X0,X1] :
( zero(X0) != subtract(any2,zero(any2),apply(x,sK3(x,any1)))
| zero(X1) = subtract(any1,subtract(any1,sK4(x,any1),sK3(x,any1)),sK3(x,any1))
| ~ element(subtract(any1,subtract(any1,sK4(x,any1),sK3(x,any1)),sK3(x,any1)),X1)
| ~ morphism(x,X1,X0)
| ~ injection_2(x) )
| ~ spl9_78 ),
inference(superposition,[],[f91,f1838]) ).
fof(f294,plain,
( apply(x,sK3(x,any1)) = apply(x,sK4(x,any1))
| injection(x)
| ~ spl9_3 ),
inference(resolution,[],[f102,f128]) ).
fof(f1905,plain,
( ! [X2,X3,X4] :
( subtract(any2,zero(any2),apply(x,sK3(x,any1))) != apply(x,X2)
| subtract(any1,subtract(any1,sK4(x,any1),sK3(x,any1)),sK3(x,any1)) = X2
| ~ element(X2,X3)
| ~ element(subtract(any1,subtract(any1,sK4(x,any1),sK3(x,any1)),sK3(x,any1)),X3)
| ~ morphism(x,X3,X4)
| ~ injection(x) )
| ~ spl9_78 ),
inference(superposition,[],[f92,f1838]) ).
fof(f1906,plain,
( ! [X6,X7,X5] :
( subtract(any2,zero(any2),apply(x,sK3(x,any1))) != apply(x,X5)
| subtract(any1,subtract(any1,sK4(x,any1),sK3(x,any1)),sK3(x,any1)) = X5
| ~ element(subtract(any1,subtract(any1,sK4(x,any1),sK3(x,any1)),sK3(x,any1)),X6)
| ~ element(X5,X6)
| ~ morphism(x,X6,X7)
| ~ injection(x) )
| ~ spl9_78 ),
inference(superposition,[],[f92,f1838]) ).
fof(f2302,plain,
( ! [X2,X0,X1] :
( exact(X0,x)
| sK6(X0,x,X1,any1,any2) = apply(X0,sK7(X0,x,X1,any1,any2))
| ~ morphism(X0,X1,any1)
| sK6(X0,x,X1,any1,any2) = subtract(any1,X2,subtract(any1,X2,sK6(X0,x,X1,any1,any2)))
| ~ element(X2,any1) )
| ~ spl9_3 ),
inference(resolution,[],[f940,f128]) ).
fof(f940,plain,
! [X10,X11,X8,X6,X9,X7] :
( ~ morphism(X7,X9,X10)
| exact(X6,X7)
| sK6(X6,X7,X8,X9,X10) = apply(X6,sK7(X6,X7,X8,X9,X10))
| ~ morphism(X6,X8,X9)
| sK6(X6,X7,X8,X9,X10) = subtract(X9,X11,subtract(X9,X11,sK6(X6,X7,X8,X9,X10)))
| ~ element(X11,X9) ),
inference(resolution,[],[f110,f94]) ).
fof(f2253,plain,
( ! [X2,X0,X1] :
( zero(any2) = apply(x,sK6(X0,x,X1,any1,any2))
| exact(X0,x)
| ~ morphism(X0,X1,any1)
| sK7(X0,x,X1,any1,any2) = subtract(X1,X2,subtract(X1,X2,sK7(X0,x,X1,any1,any2)))
| ~ element(X2,X1) )
| ~ spl9_3 ),
inference(resolution,[],[f876,f128]) ).
fof(f876,plain,
! [X10,X11,X8,X6,X9,X7] :
( ~ morphism(X7,X10,X8)
| zero(X8) = apply(X7,sK6(X6,X7,X9,X10,X8))
| exact(X6,X7)
| ~ morphism(X6,X9,X10)
| sK7(X6,X7,X9,X10,X8) = subtract(X9,X11,subtract(X9,X11,sK7(X6,X7,X9,X10,X8)))
| ~ element(X11,X9) ),
inference(resolution,[],[f109,f94]) ).
fof(f2191,plain,
( ! [X0,X1] :
( exact(X0,x)
| sK6(X0,x,X1,any1,any2) = apply(X0,sK7(X0,x,X1,any1,any2))
| ~ morphism(X0,X1,any1)
| zero(any1) = subtract(any1,sK6(X0,x,X1,any1,any2),sK6(X0,x,X1,any1,any2)) )
| ~ spl9_3 ),
inference(resolution,[],[f941,f128]) ).
fof(f941,plain,
! [X16,X14,X15,X12,X13] :
( ~ morphism(X13,X15,X16)
| exact(X12,X13)
| sK6(X12,X13,X14,X15,X16) = apply(X12,sK7(X12,X13,X14,X15,X16))
| ~ morphism(X12,X14,X15)
| zero(X15) = subtract(X15,sK6(X12,X13,X14,X15,X16),sK6(X12,X13,X14,X15,X16)) ),
inference(resolution,[],[f110,f85]) ).
fof(f2158,plain,
( ! [X2,X0,X1] :
( exact(X0,x)
| element(sK7(X0,x,X1,any1,any2),X1)
| ~ morphism(X0,X1,any1)
| sK6(X0,x,X1,any1,any2) = subtract(any1,X2,subtract(any1,X2,sK6(X0,x,X1,any1,any2)))
| ~ element(X2,any1) )
| ~ spl9_3 ),
inference(resolution,[],[f635,f128]) ).
fof(f635,plain,
! [X10,X11,X8,X6,X9,X7] :
( ~ morphism(X7,X9,X10)
| exact(X6,X7)
| element(sK7(X6,X7,X8,X9,X10),X8)
| ~ morphism(X6,X8,X9)
| sK6(X6,X7,X8,X9,X10) = subtract(X9,X11,subtract(X9,X11,sK6(X6,X7,X8,X9,X10)))
| ~ element(X11,X9) ),
inference(resolution,[],[f108,f94]) ).
fof(f1315,plain,
( ! [X0] :
( ~ element(X0,any2)
| surjection(x)
| sK1(x,any1,any2) = subtract(any2,X0,subtract(any2,X0,sK1(x,any1,any2))) )
| ~ spl9_3 ),
inference(resolution,[],[f192,f128]) ).
fof(f240,plain,
( ! [X0] :
( ~ element(X0,any2)
| apply(x,sK0(x,any1,X0)) = X0
| ~ surjection(x) )
| ~ spl9_3 ),
inference(resolution,[],[f90,f128]) ).
fof(f1907,plain,
( ! [X8,X9] :
( subtract(any2,zero(any2),apply(x,sK3(x,any1))) != sK1(x,X8,X9)
| surjection(x)
| ~ element(subtract(any1,subtract(any1,sK4(x,any1),sK3(x,any1)),sK3(x,any1)),X8)
| ~ morphism(x,X8,X9) )
| ~ spl9_78 ),
inference(superposition,[],[f96,f1838]) ).
fof(f2077,plain,
( ! [X2,X0,X1] :
( exact(X0,x)
| element(sK6(X0,x,X1,any1,any2),any1)
| ~ morphism(X0,X1,any1)
| sK7(X0,x,X1,any1,any2) = subtract(X1,X2,subtract(X1,X2,sK7(X0,x,X1,any1,any2)))
| ~ element(X2,X1) )
| ~ spl9_3 ),
inference(resolution,[],[f614,f128]) ).
fof(f614,plain,
! [X10,X11,X8,X6,X9,X7] :
( ~ morphism(X7,X9,X10)
| exact(X6,X7)
| element(sK6(X6,X7,X8,X9,X10),X9)
| ~ morphism(X6,X8,X9)
| sK7(X6,X7,X8,X9,X10) = subtract(X8,X11,subtract(X8,X11,sK7(X6,X7,X8,X9,X10)))
| ~ element(X11,X8) ),
inference(resolution,[],[f108,f94]) ).
fof(f2017,plain,
( ! [X0,X1] :
( zero(any2) = apply(x,sK6(X0,x,X1,any1,any2))
| exact(X0,x)
| ~ morphism(X0,X1,any1)
| zero(X1) = subtract(X1,sK7(X0,x,X1,any1,any2),sK7(X0,x,X1,any1,any2)) )
| ~ spl9_3 ),
inference(resolution,[],[f877,f128]) ).
fof(f877,plain,
! [X16,X14,X15,X12,X13] :
( ~ morphism(X13,X16,X14)
| zero(X14) = apply(X13,sK6(X12,X13,X15,X16,X14))
| exact(X12,X13)
| ~ morphism(X12,X15,X16)
| zero(X15) = subtract(X15,sK7(X12,X13,X15,X16,X14),sK7(X12,X13,X15,X16,X14)) ),
inference(resolution,[],[f109,f85]) ).
fof(f1911,plain,
( ! [X26,X27,X24,X25,X23] :
( subtract(any2,zero(any2),apply(x,sK3(x,any1))) != X23
| zero(X24) = apply(X25,X23)
| ~ element(subtract(any1,subtract(any1,sK4(x,any1),sK3(x,any1)),sK3(x,any1)),X26)
| ~ morphism(X25,X27,X24)
| ~ morphism(x,X26,X27)
| ~ exact(x,X25) )
| ~ spl9_78 ),
inference(superposition,[],[f107,f1838]) ).
fof(f1910,plain,
( ! [X21,X18,X19,X22,X20] :
( subtract(any2,zero(any2),apply(x,sK3(x,any1))) != X18
| element(X18,X19)
| ~ element(subtract(any1,subtract(any1,sK4(x,any1),sK3(x,any1)),sK3(x,any1)),X20)
| ~ morphism(X21,X19,X22)
| ~ morphism(x,X20,X19)
| ~ exact(x,X21) )
| ~ spl9_78 ),
inference(superposition,[],[f106,f1838]) ).
fof(f1909,plain,
( ! [X16,X14,X17,X15] :
( subtract(any2,zero(any2),apply(x,sK3(x,any1))) != zero(X14)
| subtract(any1,subtract(any1,sK4(x,any1),sK3(x,any1)),sK3(x,any1)) = apply(X15,sK5(X15,X16,subtract(any1,subtract(any1,sK4(x,any1),sK3(x,any1)),sK3(x,any1))))
| ~ element(subtract(any1,subtract(any1,sK4(x,any1),sK3(x,any1)),sK3(x,any1)),X17)
| ~ morphism(x,X17,X14)
| ~ morphism(X15,X16,X17)
| ~ exact(X15,x) )
| ~ spl9_78 ),
inference(superposition,[],[f105,f1838]) ).
fof(f1908,plain,
( ! [X10,X11,X12,X13] :
( subtract(any2,zero(any2),apply(x,sK3(x,any1))) != zero(X10)
| element(sK5(X11,X12,subtract(any1,subtract(any1,sK4(x,any1),sK3(x,any1)),sK3(x,any1))),X12)
| ~ element(subtract(any1,subtract(any1,sK4(x,any1),sK3(x,any1)),sK3(x,any1)),X13)
| ~ morphism(x,X13,X10)
| ~ morphism(X11,X12,X13)
| ~ exact(X11,x) )
| ~ spl9_78 ),
inference(superposition,[],[f104,f1838]) ).
fof(f1838,plain,
( subtract(any2,zero(any2),apply(x,sK3(x,any1))) = apply(x,subtract(any1,subtract(any1,sK4(x,any1),sK3(x,any1)),sK3(x,any1)))
| ~ spl9_78 ),
inference(avatar_component_clause,[],[f1836]) ).
fof(f1859,plain,
( ! [X72,X70,X71,X68,X69] :
( exact(X68,X69)
| ~ morphism(X69,X70,X71)
| ~ morphism(X68,any1,X70)
| zero(X70) = subtract(X70,sK6(X68,X69,any1,X70,X71),sK6(X68,X69,any1,X70,X71))
| zero(any2) = subtract(any2,subtract(any2,apply(x,sK7(X68,X69,any1,X70,X71)),X72),subtract(any2,apply(x,sK7(X68,X69,any1,X70,X71)),X72))
| ~ element(X72,any2) )
| ~ spl9_3 ),
inference(resolution,[],[f636,f468]) ).
fof(f1858,plain,
( ! [X65,X63,X66,X67,X64] :
( exact(X63,X64)
| ~ morphism(X64,X65,X66)
| ~ morphism(X63,any1,X65)
| zero(X65) = subtract(X65,sK6(X63,X64,any1,X65,X66),sK6(X63,X64,any1,X65,X66))
| ~ element(X67,any1)
| apply(x,subtract(any1,sK7(X63,X64,any1,X65,X66),X67)) = subtract(any2,apply(x,sK7(X63,X64,any1,X65,X66)),apply(x,X67)) )
| ~ spl9_3 ),
inference(resolution,[],[f636,f457]) ).
fof(f1851,plain,
( ! [X36,X37,X34,X35,X33] :
( exact(X33,X34)
| ~ morphism(X34,X35,X36)
| ~ morphism(X33,any1,X35)
| zero(X35) = subtract(X35,sK6(X33,X34,any1,X35,X36),sK6(X33,X34,any1,X35,X36))
| ~ element(X37,any2)
| apply(x,sK7(X33,X34,any1,X35,X36)) = subtract(any2,X37,subtract(any2,X37,apply(x,sK7(X33,X34,any1,X35,X36)))) )
| ~ spl9_3 ),
inference(resolution,[],[f636,f190]) ).
fof(f1850,plain,
( ! [X31,X28,X29,X32,X30] :
( exact(X28,X29)
| ~ morphism(X29,X30,X31)
| ~ morphism(X28,any1,X30)
| zero(X30) = subtract(X30,sK6(X28,X29,any1,X30,X31),sK6(X28,X29,any1,X30,X31))
| zero(any2) = subtract(any2,apply(x,subtract(any1,X32,sK7(X28,X29,any1,X30,X31))),apply(x,subtract(any1,X32,sK7(X28,X29,any1,X30,X31))))
| ~ element(X32,any1) )
| ~ spl9_3 ),
inference(resolution,[],[f636,f178]) ).
fof(f1849,plain,
( ! [X26,X27,X24,X25] :
( exact(X24,X25)
| ~ morphism(X25,X26,X27)
| ~ morphism(X24,any1,X26)
| zero(X26) = subtract(X26,sK6(X24,X25,any1,X26,X27),sK6(X24,X25,any1,X26,X27))
| zero(any2) = subtract(any2,apply(x,sK7(X24,X25,any1,X26,X27)),apply(x,sK7(X24,X25,any1,X26,X27))) )
| ~ spl9_3 ),
inference(resolution,[],[f636,f165]) ).
fof(f1848,plain,
! [X21,X19,X22,X23,X20] :
( exact(X19,X20)
| ~ morphism(X20,X21,X22)
| ~ morphism(X19,X23,X21)
| zero(X21) = subtract(X21,sK6(X19,X20,X23,X21,X22),sK6(X19,X20,X23,X21,X22))
| zero(X23) = subtract(X23,sK7(X19,X20,X23,X21,X22),sK7(X19,X20,X23,X21,X22)) ),
inference(resolution,[],[f636,f85]) ).
fof(f1847,plain,
! [X18,X16,X14,X17,X15,X13] :
( exact(X13,X14)
| ~ morphism(X14,X15,X16)
| ~ morphism(X13,X17,X15)
| zero(X15) = subtract(X15,sK6(X13,X14,X17,X15,X16),sK6(X13,X14,X17,X15,X16))
| sK7(X13,X14,X17,X15,X16) = subtract(X17,X18,subtract(X17,X18,sK7(X13,X14,X17,X15,X16)))
| ~ element(X18,X17) ),
inference(resolution,[],[f636,f94]) ).
fof(f1846,plain,
! [X10,X11,X8,X9,X7,X12] :
( exact(X7,X8)
| ~ morphism(X8,X9,X10)
| ~ morphism(X7,X11,X9)
| zero(X9) = subtract(X9,sK6(X7,X8,X11,X9,X10),sK6(X7,X8,X11,X9,X10))
| ~ element(X12,X11)
| zero(X11) = subtract(X11,subtract(X11,sK7(X7,X8,X11,X9,X10),X12),subtract(X11,sK7(X7,X8,X11,X9,X10),X12)) ),
inference(resolution,[],[f636,f164]) ).
fof(f1845,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( exact(X0,X1)
| ~ morphism(X1,X2,X3)
| ~ morphism(X0,X4,X2)
| zero(X2) = subtract(X2,sK6(X0,X1,X4,X2,X3),sK6(X0,X1,X4,X2,X3))
| ~ element(X5,X4)
| subtract(X4,X6,sK7(X0,X1,X4,X2,X3)) = subtract(X4,X5,subtract(X4,X5,subtract(X4,X6,sK7(X0,X1,X4,X2,X3))))
| ~ element(X6,X4) ),
inference(resolution,[],[f636,f191]) ).
fof(f636,plain,
! [X16,X14,X15,X12,X13] :
( element(sK7(X12,X13,X14,X15,X16),X14)
| exact(X12,X13)
| ~ morphism(X13,X15,X16)
| ~ morphism(X12,X14,X15)
| zero(X15) = subtract(X15,sK6(X12,X13,X14,X15,X16),sK6(X12,X13,X14,X15,X16)) ),
inference(resolution,[],[f108,f85]) ).
fof(f1733,plain,
( ! [X72,X70,X71,X68,X69] :
( exact(X68,X69)
| ~ morphism(X69,any1,X70)
| ~ morphism(X68,X71,any1)
| zero(X71) = subtract(X71,sK7(X68,X69,X71,any1,X70),sK7(X68,X69,X71,any1,X70))
| zero(any2) = subtract(any2,subtract(any2,apply(x,sK6(X68,X69,X71,any1,X70)),X72),subtract(any2,apply(x,sK6(X68,X69,X71,any1,X70)),X72))
| ~ element(X72,any2) )
| ~ spl9_3 ),
inference(resolution,[],[f615,f468]) ).
fof(f1732,plain,
( ! [X65,X63,X66,X67,X64] :
( exact(X63,X64)
| ~ morphism(X64,any1,X65)
| ~ morphism(X63,X66,any1)
| zero(X66) = subtract(X66,sK7(X63,X64,X66,any1,X65),sK7(X63,X64,X66,any1,X65))
| ~ element(X67,any1)
| apply(x,subtract(any1,sK6(X63,X64,X66,any1,X65),X67)) = subtract(any2,apply(x,sK6(X63,X64,X66,any1,X65)),apply(x,X67)) )
| ~ spl9_3 ),
inference(resolution,[],[f615,f457]) ).
fof(f1725,plain,
( ! [X36,X37,X34,X35,X33] :
( exact(X33,X34)
| ~ morphism(X34,any1,X35)
| ~ morphism(X33,X36,any1)
| zero(X36) = subtract(X36,sK7(X33,X34,X36,any1,X35),sK7(X33,X34,X36,any1,X35))
| ~ element(X37,any2)
| apply(x,sK6(X33,X34,X36,any1,X35)) = subtract(any2,X37,subtract(any2,X37,apply(x,sK6(X33,X34,X36,any1,X35)))) )
| ~ spl9_3 ),
inference(resolution,[],[f615,f190]) ).
fof(f1724,plain,
( ! [X31,X28,X29,X32,X30] :
( exact(X28,X29)
| ~ morphism(X29,any1,X30)
| ~ morphism(X28,X31,any1)
| zero(X31) = subtract(X31,sK7(X28,X29,X31,any1,X30),sK7(X28,X29,X31,any1,X30))
| zero(any2) = subtract(any2,apply(x,subtract(any1,X32,sK6(X28,X29,X31,any1,X30))),apply(x,subtract(any1,X32,sK6(X28,X29,X31,any1,X30))))
| ~ element(X32,any1) )
| ~ spl9_3 ),
inference(resolution,[],[f615,f178]) ).
fof(f1723,plain,
( ! [X26,X27,X24,X25] :
( exact(X24,X25)
| ~ morphism(X25,any1,X26)
| ~ morphism(X24,X27,any1)
| zero(X27) = subtract(X27,sK7(X24,X25,X27,any1,X26),sK7(X24,X25,X27,any1,X26))
| zero(any2) = subtract(any2,apply(x,sK6(X24,X25,X27,any1,X26)),apply(x,sK6(X24,X25,X27,any1,X26))) )
| ~ spl9_3 ),
inference(resolution,[],[f615,f165]) ).
fof(f1722,plain,
! [X21,X19,X22,X23,X20] :
( exact(X19,X20)
| ~ morphism(X20,X21,X22)
| ~ morphism(X19,X23,X21)
| zero(X23) = subtract(X23,sK7(X19,X20,X23,X21,X22),sK7(X19,X20,X23,X21,X22))
| zero(X21) = subtract(X21,sK6(X19,X20,X23,X21,X22),sK6(X19,X20,X23,X21,X22)) ),
inference(resolution,[],[f615,f85]) ).
fof(f1721,plain,
! [X18,X16,X14,X17,X15,X13] :
( exact(X13,X14)
| ~ morphism(X14,X15,X16)
| ~ morphism(X13,X17,X15)
| zero(X17) = subtract(X17,sK7(X13,X14,X17,X15,X16),sK7(X13,X14,X17,X15,X16))
| sK6(X13,X14,X17,X15,X16) = subtract(X15,X18,subtract(X15,X18,sK6(X13,X14,X17,X15,X16)))
| ~ element(X18,X15) ),
inference(resolution,[],[f615,f94]) ).
fof(f1720,plain,
! [X10,X11,X8,X9,X7,X12] :
( exact(X7,X8)
| ~ morphism(X8,X9,X10)
| ~ morphism(X7,X11,X9)
| zero(X11) = subtract(X11,sK7(X7,X8,X11,X9,X10),sK7(X7,X8,X11,X9,X10))
| ~ element(X12,X9)
| zero(X9) = subtract(X9,subtract(X9,sK6(X7,X8,X11,X9,X10),X12),subtract(X9,sK6(X7,X8,X11,X9,X10),X12)) ),
inference(resolution,[],[f615,f164]) ).
fof(f1719,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( exact(X0,X1)
| ~ morphism(X1,X2,X3)
| ~ morphism(X0,X4,X2)
| zero(X4) = subtract(X4,sK7(X0,X1,X4,X2,X3),sK7(X0,X1,X4,X2,X3))
| ~ element(X5,X2)
| subtract(X2,X6,sK6(X0,X1,X4,X2,X3)) = subtract(X2,X5,subtract(X2,X5,subtract(X2,X6,sK6(X0,X1,X4,X2,X3))))
| ~ element(X6,X2) ),
inference(resolution,[],[f615,f191]) ).
fof(f615,plain,
! [X16,X14,X15,X12,X13] :
( element(sK6(X12,X13,X14,X15,X16),X15)
| exact(X12,X13)
| ~ morphism(X13,X15,X16)
| ~ morphism(X12,X14,X15)
| zero(X14) = subtract(X14,sK7(X12,X13,X14,X15,X16),sK7(X12,X13,X14,X15,X16)) ),
inference(resolution,[],[f108,f85]) ).
fof(f1069,plain,
( ! [X0,X1] :
( ~ morphism(X0,X1,any1)
| zero(any2) = apply(x,sK6(X0,x,X1,any1,any2))
| exact(X0,x)
| sK6(X0,x,X1,any1,any2) = apply(X0,sK7(X0,x,X1,any1,any2)) )
| ~ spl9_3 ),
inference(resolution,[],[f111,f128]) ).
fof(f802,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ morphism(X2,X3,any1)
| commute(X0,X1,X2,x)
| element(sK8(X0,X1,X2,x,X3),X3)
| ~ morphism(X1,X4,any2)
| ~ morphism(X0,X3,X4) )
| ~ spl9_3 ),
inference(resolution,[],[f113,f128]) ).
fof(f193,plain,
! [X10,X11,X12,X13] :
( ~ morphism(X12,X10,X13)
| ~ element(X11,X10)
| injection_2(X12)
| sK2(X12,X10,X13) = subtract(X10,X11,subtract(X10,X11,sK2(X12,X10,X13))) ),
inference(resolution,[],[f94,f97]) ).
fof(f192,plain,
! [X8,X6,X9,X7] :
( ~ morphism(X8,X9,X6)
| ~ element(X7,X6)
| surjection(X8)
| sK1(X8,X9,X6) = subtract(X6,X7,subtract(X6,X7,sK1(X8,X9,X6))) ),
inference(resolution,[],[f94,f95]) ).
fof(f1294,plain,
! [X58,X59,X56,X57,X62,X60,X61] :
( ~ element(X56,X57)
| subtract(X57,X58,sK7(X59,X60,X57,X61,X62)) = subtract(X57,X56,subtract(X57,X56,subtract(X57,X58,sK7(X59,X60,X57,X61,X62))))
| ~ element(X58,X57)
| element(sK6(X59,X60,X57,X61,X62),X61)
| exact(X59,X60)
| ~ morphism(X60,X61,X62)
| ~ morphism(X59,X57,X61) ),
inference(resolution,[],[f191,f108]) ).
fof(f1293,plain,
! [X50,X51,X49,X54,X55,X52,X53] :
( ~ element(X49,X50)
| subtract(X50,X51,sK7(X52,X53,X50,X54,X55)) = subtract(X50,X49,subtract(X50,X49,subtract(X50,X51,sK7(X52,X53,X50,X54,X55))))
| ~ element(X51,X50)
| exact(X52,X53)
| zero(X55) = apply(X53,sK6(X52,X53,X50,X54,X55))
| ~ morphism(X53,X54,X55)
| ~ morphism(X52,X50,X54) ),
inference(resolution,[],[f191,f109]) ).
fof(f1292,plain,
! [X48,X46,X47,X44,X45,X42,X43] :
( ~ element(X42,X43)
| subtract(X43,X44,sK6(X45,X46,X47,X43,X48)) = subtract(X43,X42,subtract(X43,X42,subtract(X43,X44,sK6(X45,X46,X47,X43,X48))))
| ~ element(X44,X43)
| element(sK7(X45,X46,X47,X43,X48),X47)
| exact(X45,X46)
| ~ morphism(X46,X43,X48)
| ~ morphism(X45,X47,X43) ),
inference(resolution,[],[f191,f108]) ).
fof(f1291,plain,
! [X40,X38,X41,X39,X36,X37,X35] :
( ~ element(X35,X36)
| subtract(X36,X37,sK6(X38,X39,X40,X36,X41)) = subtract(X36,X35,subtract(X36,X35,subtract(X36,X37,sK6(X38,X39,X40,X36,X41))))
| ~ element(X37,X36)
| sK6(X38,X39,X40,X36,X41) = apply(X38,sK7(X38,X39,X40,X36,X41))
| exact(X38,X39)
| ~ morphism(X39,X36,X41)
| ~ morphism(X38,X40,X36) ),
inference(resolution,[],[f191,f110]) ).
fof(f1288,plain,
! [X28,X29,X26,X27,X30] :
( ~ element(X26,X27)
| subtract(X27,X28,sK2(X29,X27,X30)) = subtract(X27,X26,subtract(X27,X26,subtract(X27,X28,sK2(X29,X27,X30))))
| ~ element(X28,X27)
| injection_2(X29)
| ~ morphism(X29,X27,X30) ),
inference(resolution,[],[f191,f97]) ).
fof(f1287,plain,
! [X21,X24,X22,X25,X23] :
( ~ element(X21,X22)
| subtract(X22,X23,sK1(X24,X25,X22)) = subtract(X22,X21,subtract(X22,X21,subtract(X22,X23,sK1(X24,X25,X22))))
| ~ element(X23,X22)
| surjection(X24)
| ~ morphism(X24,X25,X22) ),
inference(resolution,[],[f191,f95]) ).
fof(f1283,plain,
! [X10,X11,X9,X12,X13] :
( ~ element(X9,X10)
| subtract(X10,X11,subtract(X10,X12,X13)) = subtract(X10,X9,subtract(X10,X9,subtract(X10,X11,subtract(X10,X12,X13))))
| ~ element(X11,X10)
| ~ element(X13,X10)
| ~ element(X12,X10) ),
inference(resolution,[],[f191,f93]) ).
fof(f1279,plain,
( ! [X2,X0,X1] :
( ~ element(X0,any2)
| subtract(any2,X1,apply(x,X2)) = subtract(any2,X0,subtract(any2,X0,subtract(any2,X1,apply(x,X2))))
| ~ element(X1,any2)
| ~ element(X2,any1) )
| ~ spl9_3 ),
inference(resolution,[],[f191,f163]) ).
fof(f191,plain,
! [X2,X3,X4,X5] :
( ~ element(X5,X2)
| ~ element(X3,X2)
| subtract(X2,X4,X5) = subtract(X2,X3,subtract(X2,X3,subtract(X2,X4,X5)))
| ~ element(X4,X2) ),
inference(resolution,[],[f94,f93]) ).
fof(f180,plain,
( ! [X4,X5] :
( ~ morphism(X4,any1,X5)
| injection_2(X4)
| zero(any2) = subtract(any2,apply(x,sK2(X4,any1,X5)),apply(x,sK2(X4,any1,X5))) )
| ~ spl9_3 ),
inference(resolution,[],[f165,f97]) ).
fof(f112,plain,
! [X2,X3,X0,X1,X6,X4] :
( zero(X4) != apply(X1,sK6(X0,X1,X2,X3,X4))
| apply(X0,X6) != sK6(X0,X1,X2,X3,X4)
| ~ element(X6,X2)
| exact(X0,X1)
| ~ element(sK6(X0,X1,X2,X3,X4),X3)
| ~ morphism(X1,X3,X4)
| ~ morphism(X0,X2,X3) ),
inference(cnf_transformation,[],[f79]) ).
fof(f79,plain,
! [X0,X1,X2,X3,X4] :
( exact(X0,X1)
| ( ( ! [X6] :
( apply(X0,X6) != sK6(X0,X1,X2,X3,X4)
| ~ element(X6,X2) )
| zero(X4) != apply(X1,sK6(X0,X1,X2,X3,X4))
| ~ element(sK6(X0,X1,X2,X3,X4),X3) )
& ( ( sK6(X0,X1,X2,X3,X4) = apply(X0,sK7(X0,X1,X2,X3,X4))
& element(sK7(X0,X1,X2,X3,X4),X2) )
| ( zero(X4) = apply(X1,sK6(X0,X1,X2,X3,X4))
& element(sK6(X0,X1,X2,X3,X4),X3) ) ) )
| ~ morphism(X1,X3,X4)
| ~ morphism(X0,X2,X3) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6,sK7])],[f76,f78,f77]) ).
fof(f77,plain,
! [X0,X1,X2,X3,X4] :
( ? [X5] :
( ( ! [X6] :
( apply(X0,X6) != X5
| ~ element(X6,X2) )
| zero(X4) != apply(X1,X5)
| ~ element(X5,X3) )
& ( ? [X7] :
( apply(X0,X7) = X5
& element(X7,X2) )
| ( zero(X4) = apply(X1,X5)
& element(X5,X3) ) ) )
=> ( ( ! [X6] :
( apply(X0,X6) != sK6(X0,X1,X2,X3,X4)
| ~ element(X6,X2) )
| zero(X4) != apply(X1,sK6(X0,X1,X2,X3,X4))
| ~ element(sK6(X0,X1,X2,X3,X4),X3) )
& ( ? [X7] :
( apply(X0,X7) = sK6(X0,X1,X2,X3,X4)
& element(X7,X2) )
| ( zero(X4) = apply(X1,sK6(X0,X1,X2,X3,X4))
& element(sK6(X0,X1,X2,X3,X4),X3) ) ) ) ),
introduced(choice_axiom,[]) ).
fof(f78,plain,
! [X0,X1,X2,X3,X4] :
( ? [X7] :
( apply(X0,X7) = sK6(X0,X1,X2,X3,X4)
& element(X7,X2) )
=> ( sK6(X0,X1,X2,X3,X4) = apply(X0,sK7(X0,X1,X2,X3,X4))
& element(sK7(X0,X1,X2,X3,X4),X2) ) ),
introduced(choice_axiom,[]) ).
fof(f76,plain,
! [X0,X1,X2,X3,X4] :
( exact(X0,X1)
| ? [X5] :
( ( ! [X6] :
( apply(X0,X6) != X5
| ~ element(X6,X2) )
| zero(X4) != apply(X1,X5)
| ~ element(X5,X3) )
& ( ? [X7] :
( apply(X0,X7) = X5
& element(X7,X2) )
| ( zero(X4) = apply(X1,X5)
& element(X5,X3) ) ) )
| ~ morphism(X1,X3,X4)
| ~ morphism(X0,X2,X3) ),
inference(rectify,[],[f75]) ).
fof(f75,plain,
! [X0,X1,X2,X3,X4] :
( exact(X0,X1)
| ? [X5] :
( ( ! [X6] :
( apply(X0,X6) != X5
| ~ element(X6,X2) )
| zero(X4) != apply(X1,X5)
| ~ element(X5,X3) )
& ( ? [X6] :
( apply(X0,X6) = X5
& element(X6,X2) )
| ( zero(X4) = apply(X1,X5)
& element(X5,X3) ) ) )
| ~ morphism(X1,X3,X4)
| ~ morphism(X0,X2,X3) ),
inference(flattening,[],[f74]) ).
fof(f74,plain,
! [X0,X1,X2,X3,X4] :
( exact(X0,X1)
| ? [X5] :
( ( ! [X6] :
( apply(X0,X6) != X5
| ~ element(X6,X2) )
| zero(X4) != apply(X1,X5)
| ~ element(X5,X3) )
& ( ? [X6] :
( apply(X0,X6) = X5
& element(X6,X2) )
| ( zero(X4) = apply(X1,X5)
& element(X5,X3) ) ) )
| ~ morphism(X1,X3,X4)
| ~ morphism(X0,X2,X3) ),
inference(nnf_transformation,[],[f55]) ).
fof(f55,plain,
! [X0,X1,X2,X3,X4] :
( exact(X0,X1)
| ? [X5] :
( ( zero(X4) = apply(X1,X5)
& element(X5,X3) )
<~> ? [X6] :
( apply(X0,X6) = X5
& element(X6,X2) ) )
| ~ morphism(X1,X3,X4)
| ~ morphism(X0,X2,X3) ),
inference(flattening,[],[f54]) ).
fof(f54,plain,
! [X0,X1,X2,X3,X4] :
( exact(X0,X1)
| ? [X5] :
( ( zero(X4) = apply(X1,X5)
& element(X5,X3) )
<~> ? [X6] :
( apply(X0,X6) = X5
& element(X6,X2) ) )
| ~ morphism(X1,X3,X4)
| ~ morphism(X0,X2,X3) ),
inference(ennf_transformation,[],[f28]) ).
fof(f28,plain,
! [X0,X1,X2,X3,X4] :
( ( ! [X5] :
( ( zero(X4) = apply(X1,X5)
& element(X5,X3) )
<=> ? [X6] :
( apply(X0,X6) = X5
& element(X6,X2) ) )
& morphism(X1,X3,X4)
& morphism(X0,X2,X3) )
=> exact(X0,X1) ),
inference(rectify,[],[f7]) ).
fof(f7,axiom,
! [X8,X9,X1,X10,X2] :
( ( ! [X11] :
( ( zero(X2) = apply(X9,X11)
& element(X11,X10) )
<=> ? [X7] :
( apply(X8,X7) = X11
& element(X7,X1) ) )
& morphism(X9,X10,X2)
& morphism(X8,X1,X10) )
=> exact(X8,X9) ),
file('/export/starexec/sandbox/tmp/tmp.YLPE9jctjB/Vampire---4.8_1232',properties_for_exact) ).
fof(f179,plain,
( ! [X2,X3] :
( ~ morphism(X2,X3,any1)
| surjection(X2)
| zero(any2) = subtract(any2,apply(x,sK1(X2,X3,any1)),apply(x,sK1(X2,X3,any1))) )
| ~ spl9_3 ),
inference(resolution,[],[f165,f95]) ).
fof(f1150,plain,
( ! [X31,X28,X29,X32,X30] :
( zero(any2) = subtract(any2,apply(x,subtract(any1,X28,sK7(X29,X30,any1,X31,X32))),apply(x,subtract(any1,X28,sK7(X29,X30,any1,X31,X32))))
| ~ element(X28,any1)
| element(sK6(X29,X30,any1,X31,X32),X31)
| exact(X29,X30)
| ~ morphism(X30,X31,X32)
| ~ morphism(X29,any1,X31) )
| ~ spl9_3 ),
inference(resolution,[],[f178,f108]) ).
fof(f1149,plain,
( ! [X26,X27,X24,X25,X23] :
( zero(any2) = subtract(any2,apply(x,subtract(any1,X23,sK7(X24,X25,any1,X26,X27))),apply(x,subtract(any1,X23,sK7(X24,X25,any1,X26,X27))))
| ~ element(X23,any1)
| exact(X24,X25)
| zero(X27) = apply(X25,sK6(X24,X25,any1,X26,X27))
| ~ morphism(X25,X26,X27)
| ~ morphism(X24,any1,X26) )
| ~ spl9_3 ),
inference(resolution,[],[f178,f109]) ).
fof(f1148,plain,
( ! [X21,X18,X19,X22,X20] :
( zero(any2) = subtract(any2,apply(x,subtract(any1,X18,sK6(X19,X20,X21,any1,X22))),apply(x,subtract(any1,X18,sK6(X19,X20,X21,any1,X22))))
| ~ element(X18,any1)
| element(sK7(X19,X20,X21,any1,X22),X21)
| exact(X19,X20)
| ~ morphism(X20,any1,X22)
| ~ morphism(X19,X21,any1) )
| ~ spl9_3 ),
inference(resolution,[],[f178,f108]) ).
fof(f1147,plain,
( ! [X16,X14,X17,X15,X13] :
( zero(any2) = subtract(any2,apply(x,subtract(any1,X13,sK6(X14,X15,X16,any1,X17))),apply(x,subtract(any1,X13,sK6(X14,X15,X16,any1,X17))))
| ~ element(X13,any1)
| sK6(X14,X15,X16,any1,X17) = apply(X14,sK7(X14,X15,X16,any1,X17))
| exact(X14,X15)
| ~ morphism(X15,any1,X17)
| ~ morphism(X14,X16,any1) )
| ~ spl9_3 ),
inference(resolution,[],[f178,f110]) ).
fof(f1144,plain,
( ! [X10,X8,X9] :
( zero(any2) = subtract(any2,apply(x,subtract(any1,X8,sK2(X9,any1,X10))),apply(x,subtract(any1,X8,sK2(X9,any1,X10))))
| ~ element(X8,any1)
| injection_2(X9)
| ~ morphism(X9,any1,X10) )
| ~ spl9_3 ),
inference(resolution,[],[f178,f97]) ).
fof(f1143,plain,
( ! [X6,X7,X5] :
( zero(any2) = subtract(any2,apply(x,subtract(any1,X5,sK1(X6,X7,any1))),apply(x,subtract(any1,X5,sK1(X6,X7,any1))))
| ~ element(X5,any1)
| surjection(X6)
| ~ morphism(X6,X7,any1) )
| ~ spl9_3 ),
inference(resolution,[],[f178,f95]) ).
fof(f1142,plain,
( ! [X2,X3,X4] :
( zero(any2) = subtract(any2,apply(x,subtract(any1,X2,subtract(any1,X3,X4))),apply(x,subtract(any1,X2,subtract(any1,X3,X4))))
| ~ element(X2,any1)
| ~ element(X4,any1)
| ~ element(X3,any1) )
| ~ spl9_3 ),
inference(resolution,[],[f178,f93]) ).
fof(f178,plain,
( ! [X0,X1] :
( ~ element(X1,any1)
| zero(any2) = subtract(any2,apply(x,subtract(any1,X0,X1)),apply(x,subtract(any1,X0,X1)))
| ~ element(X0,any1) )
| ~ spl9_3 ),
inference(resolution,[],[f165,f93]) ).
fof(f1136,plain,
( ! [X31,X28,X29,X32,X30] :
( zero(any2) = subtract(any2,subtract(any2,apply(x,sK7(X28,X29,any1,X30,X31)),X32),subtract(any2,apply(x,sK7(X28,X29,any1,X30,X31)),X32))
| ~ element(X32,any2)
| element(sK6(X28,X29,any1,X30,X31),X30)
| exact(X28,X29)
| ~ morphism(X29,X30,X31)
| ~ morphism(X28,any1,X30) )
| ~ spl9_3 ),
inference(resolution,[],[f468,f108]) ).
fof(f1135,plain,
( ! [X26,X27,X24,X25,X23] :
( zero(any2) = subtract(any2,subtract(any2,apply(x,sK7(X23,X24,any1,X25,X26)),X27),subtract(any2,apply(x,sK7(X23,X24,any1,X25,X26)),X27))
| ~ element(X27,any2)
| exact(X23,X24)
| zero(X26) = apply(X24,sK6(X23,X24,any1,X25,X26))
| ~ morphism(X24,X25,X26)
| ~ morphism(X23,any1,X25) )
| ~ spl9_3 ),
inference(resolution,[],[f468,f109]) ).
fof(f1134,plain,
( ! [X21,X18,X19,X22,X20] :
( zero(any2) = subtract(any2,subtract(any2,apply(x,sK6(X18,X19,X20,any1,X21)),X22),subtract(any2,apply(x,sK6(X18,X19,X20,any1,X21)),X22))
| ~ element(X22,any2)
| element(sK7(X18,X19,X20,any1,X21),X20)
| exact(X18,X19)
| ~ morphism(X19,any1,X21)
| ~ morphism(X18,X20,any1) )
| ~ spl9_3 ),
inference(resolution,[],[f468,f108]) ).
fof(f1133,plain,
( ! [X16,X14,X17,X15,X13] :
( zero(any2) = subtract(any2,subtract(any2,apply(x,sK6(X13,X14,X15,any1,X16)),X17),subtract(any2,apply(x,sK6(X13,X14,X15,any1,X16)),X17))
| ~ element(X17,any2)
| sK6(X13,X14,X15,any1,X16) = apply(X13,sK7(X13,X14,X15,any1,X16))
| exact(X13,X14)
| ~ morphism(X14,any1,X16)
| ~ morphism(X13,X15,any1) )
| ~ spl9_3 ),
inference(resolution,[],[f468,f110]) ).
fof(f1130,plain,
( ! [X10,X8,X9] :
( zero(any2) = subtract(any2,subtract(any2,apply(x,sK2(X8,any1,X9)),X10),subtract(any2,apply(x,sK2(X8,any1,X9)),X10))
| ~ element(X10,any2)
| injection_2(X8)
| ~ morphism(X8,any1,X9) )
| ~ spl9_3 ),
inference(resolution,[],[f468,f97]) ).
fof(f1129,plain,
( ! [X6,X7,X5] :
( zero(any2) = subtract(any2,subtract(any2,apply(x,sK1(X5,X6,any1)),X7),subtract(any2,apply(x,sK1(X5,X6,any1)),X7))
| ~ element(X7,any2)
| surjection(X5)
| ~ morphism(X5,X6,any1) )
| ~ spl9_3 ),
inference(resolution,[],[f468,f95]) ).
fof(f1128,plain,
( ! [X2,X3,X4] :
( zero(any2) = subtract(any2,subtract(any2,apply(x,subtract(any1,X2,X3)),X4),subtract(any2,apply(x,subtract(any1,X2,X3)),X4))
| ~ element(X4,any2)
| ~ element(X3,any1)
| ~ element(X2,any1) )
| ~ spl9_3 ),
inference(resolution,[],[f468,f93]) ).
fof(f468,plain,
( ! [X0,X1] :
( ~ element(X1,any1)
| zero(any2) = subtract(any2,subtract(any2,apply(x,X1),X0),subtract(any2,apply(x,X1),X0))
| ~ element(X0,any2) )
| ~ spl9_3 ),
inference(resolution,[],[f164,f163]) ).
fof(f1116,plain,
( ! [X0,X1] :
( ~ morphism(X0,X1,any1)
| commute(X0,x,X0,x) )
| ~ spl9_3 ),
inference(duplicate_literal_removal,[],[f1115]) ).
fof(f1115,plain,
( ! [X0,X1] :
( ~ morphism(X0,X1,any1)
| commute(X0,x,X0,x)
| ~ morphism(X0,X1,any1) )
| ~ spl9_3 ),
inference(resolution,[],[f1114,f128]) ).
fof(f1114,plain,
( ! [X2,X0,X1] :
( ~ morphism(x,X0,any2)
| ~ morphism(X1,X2,X0)
| commute(X1,x,X1,x)
| ~ morphism(X1,X2,any1) )
| ~ spl9_3 ),
inference(resolution,[],[f1113,f128]) ).
fof(f1113,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ morphism(X1,X5,X3)
| ~ morphism(X1,X2,X3)
| ~ morphism(X0,X4,X2)
| commute(X0,X1,X0,X1)
| ~ morphism(X0,X4,X5) ),
inference(equality_resolution,[],[f114]) ).
fof(f114,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( apply(X1,apply(X0,sK8(X0,X1,X2,X3,X4))) != apply(X3,apply(X2,sK8(X0,X1,X2,X3,X4)))
| commute(X0,X1,X2,X3)
| ~ morphism(X3,X6,X7)
| ~ morphism(X2,X4,X6)
| ~ morphism(X1,X5,X7)
| ~ morphism(X0,X4,X5) ),
inference(cnf_transformation,[],[f81]) ).
fof(f81,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( commute(X0,X1,X2,X3)
| ( apply(X1,apply(X0,sK8(X0,X1,X2,X3,X4))) != apply(X3,apply(X2,sK8(X0,X1,X2,X3,X4)))
& element(sK8(X0,X1,X2,X3,X4),X4) )
| ~ morphism(X3,X6,X7)
| ~ morphism(X2,X4,X6)
| ~ morphism(X1,X5,X7)
| ~ morphism(X0,X4,X5) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f57,f80]) ).
fof(f80,plain,
! [X0,X1,X2,X3,X4] :
( ? [X8] :
( apply(X1,apply(X0,X8)) != apply(X3,apply(X2,X8))
& element(X8,X4) )
=> ( apply(X1,apply(X0,sK8(X0,X1,X2,X3,X4))) != apply(X3,apply(X2,sK8(X0,X1,X2,X3,X4)))
& element(sK8(X0,X1,X2,X3,X4),X4) ) ),
introduced(choice_axiom,[]) ).
fof(f57,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( commute(X0,X1,X2,X3)
| ? [X8] :
( apply(X1,apply(X0,X8)) != apply(X3,apply(X2,X8))
& element(X8,X4) )
| ~ morphism(X3,X6,X7)
| ~ morphism(X2,X4,X6)
| ~ morphism(X1,X5,X7)
| ~ morphism(X0,X4,X5) ),
inference(flattening,[],[f56]) ).
fof(f56,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( commute(X0,X1,X2,X3)
| ? [X8] :
( apply(X1,apply(X0,X8)) != apply(X3,apply(X2,X8))
& element(X8,X4) )
| ~ morphism(X3,X6,X7)
| ~ morphism(X2,X4,X6)
| ~ morphism(X1,X5,X7)
| ~ morphism(X0,X4,X5) ),
inference(ennf_transformation,[],[f29]) ).
fof(f29,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ( ! [X8] :
( element(X8,X4)
=> apply(X1,apply(X0,X8)) = apply(X3,apply(X2,X8)) )
& morphism(X3,X6,X7)
& morphism(X2,X4,X6)
& morphism(X1,X5,X7)
& morphism(X0,X4,X5) )
=> commute(X0,X1,X2,X3) ),
inference(rectify,[],[f9]) ).
fof(f9,axiom,
! [X12,X13,X14,X15,X1,X16,X17,X2] :
( ( ! [X7] :
( element(X7,X1)
=> apply(X13,apply(X12,X7)) = apply(X15,apply(X14,X7)) )
& morphism(X15,X17,X2)
& morphism(X14,X1,X17)
& morphism(X13,X16,X2)
& morphism(X12,X1,X16) )
=> commute(X12,X13,X14,X15) ),
file('/export/starexec/sandbox/tmp/tmp.YLPE9jctjB/Vampire---4.8_1232',properties_for_commute) ).
fof(f111,plain,
! [X2,X3,X0,X1,X4] :
( ~ morphism(X1,X3,X4)
| sK6(X0,X1,X2,X3,X4) = apply(X0,sK7(X0,X1,X2,X3,X4))
| zero(X4) = apply(X1,sK6(X0,X1,X2,X3,X4))
| exact(X0,X1)
| ~ morphism(X0,X2,X3) ),
inference(cnf_transformation,[],[f79]) ).
fof(f115,plain,
! [X2,X3,X0,X1,X8,X6,X7,X4,X5] :
( ~ commute(X0,X1,X2,X3)
| ~ element(X8,X4)
| ~ morphism(X3,X6,X7)
| ~ morphism(X2,X4,X6)
| ~ morphism(X1,X5,X7)
| ~ morphism(X0,X4,X5)
| apply(X1,apply(X0,X8)) = apply(X3,apply(X2,X8)) ),
inference(cnf_transformation,[],[f59]) ).
fof(f59,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ! [X8] :
( apply(X1,apply(X0,X8)) = apply(X3,apply(X2,X8))
| ~ element(X8,X4) )
| ~ morphism(X3,X6,X7)
| ~ morphism(X2,X4,X6)
| ~ morphism(X1,X5,X7)
| ~ morphism(X0,X4,X5)
| ~ commute(X0,X1,X2,X3) ),
inference(flattening,[],[f58]) ).
fof(f58,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ! [X8] :
( apply(X1,apply(X0,X8)) = apply(X3,apply(X2,X8))
| ~ element(X8,X4) )
| ~ morphism(X3,X6,X7)
| ~ morphism(X2,X4,X6)
| ~ morphism(X1,X5,X7)
| ~ morphism(X0,X4,X5)
| ~ commute(X0,X1,X2,X3) ),
inference(ennf_transformation,[],[f30]) ).
fof(f30,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ( morphism(X3,X6,X7)
& morphism(X2,X4,X6)
& morphism(X1,X5,X7)
& morphism(X0,X4,X5)
& commute(X0,X1,X2,X3) )
=> ! [X8] :
( element(X8,X4)
=> apply(X1,apply(X0,X8)) = apply(X3,apply(X2,X8)) ) ),
inference(rectify,[],[f8]) ).
fof(f8,axiom,
! [X12,X13,X14,X15,X1,X16,X17,X2] :
( ( morphism(X15,X17,X2)
& morphism(X14,X1,X17)
& morphism(X13,X16,X2)
& morphism(X12,X1,X16)
& commute(X12,X13,X14,X15) )
=> ! [X7] :
( element(X7,X1)
=> apply(X13,apply(X12,X7)) = apply(X15,apply(X14,X7)) ) ),
file('/export/starexec/sandbox/tmp/tmp.YLPE9jctjB/Vampire---4.8_1232',commute_properties) ).
fof(f1008,plain,
( ! [X2,X0,X1] :
( ~ morphism(X1,any2,X2)
| ~ element(X0,any1)
| zero(X2) = apply(X1,apply(x,X0))
| ~ exact(x,X1) )
| ~ spl9_3 ),
inference(resolution,[],[f522,f128]) ).
fof(f522,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ morphism(X2,X4,X5)
| ~ element(X3,X4)
| ~ morphism(X1,X5,X0)
| zero(X0) = apply(X1,apply(X2,X3))
| ~ exact(X2,X1) ),
inference(equality_resolution,[],[f107]) ).
fof(f950,plain,
( ! [X51,X54,X55,X52,X53] :
( sK6(X51,X52,X53,any1,X54) = apply(X51,sK7(X51,X52,X53,any1,X54))
| exact(X51,X52)
| ~ morphism(X52,any1,X54)
| ~ morphism(X51,X53,any1)
| ~ element(X55,any1)
| apply(x,subtract(any1,sK6(X51,X52,X53,any1,X54),X55)) = subtract(any2,apply(x,sK6(X51,X52,X53,any1,X54)),apply(x,X55)) )
| ~ spl9_3 ),
inference(resolution,[],[f110,f457]) ).
fof(f943,plain,
( ! [X21,X24,X22,X25,X23] :
( sK6(X21,X22,X23,any1,X24) = apply(X21,sK7(X21,X22,X23,any1,X24))
| exact(X21,X22)
| ~ morphism(X22,any1,X24)
| ~ morphism(X21,X23,any1)
| ~ element(X25,any2)
| apply(x,sK6(X21,X22,X23,any1,X24)) = subtract(any2,X25,subtract(any2,X25,apply(x,sK6(X21,X22,X23,any1,X24)))) )
| ~ spl9_3 ),
inference(resolution,[],[f110,f190]) ).
fof(f942,plain,
( ! [X18,X19,X17,X20] :
( sK6(X17,X18,X19,any1,X20) = apply(X17,sK7(X17,X18,X19,any1,X20))
| exact(X17,X18)
| ~ morphism(X18,any1,X20)
| ~ morphism(X17,X19,any1)
| zero(any2) = subtract(any2,apply(x,sK6(X17,X18,X19,any1,X20)),apply(x,sK6(X17,X18,X19,any1,X20))) )
| ~ spl9_3 ),
inference(resolution,[],[f110,f165]) ).
fof(f939,plain,
! [X2,X3,X0,X1,X4,X5] :
( sK6(X0,X1,X2,X3,X4) = apply(X0,sK7(X0,X1,X2,X3,X4))
| exact(X0,X1)
| ~ morphism(X1,X3,X4)
| ~ morphism(X0,X2,X3)
| ~ element(X5,X3)
| zero(X3) = subtract(X3,subtract(X3,sK6(X0,X1,X2,X3,X4),X5),subtract(X3,sK6(X0,X1,X2,X3,X4),X5)) ),
inference(resolution,[],[f110,f164]) ).
fof(f110,plain,
! [X2,X3,X0,X1,X4] :
( element(sK6(X0,X1,X2,X3,X4),X3)
| sK6(X0,X1,X2,X3,X4) = apply(X0,sK7(X0,X1,X2,X3,X4))
| exact(X0,X1)
| ~ morphism(X1,X3,X4)
| ~ morphism(X0,X2,X3) ),
inference(cnf_transformation,[],[f79]) ).
fof(f886,plain,
( ! [X51,X54,X55,X52,X53] :
( exact(X51,X52)
| zero(X53) = apply(X52,sK6(X51,X52,any1,X54,X53))
| ~ morphism(X52,X54,X53)
| ~ morphism(X51,any1,X54)
| ~ element(X55,any1)
| apply(x,subtract(any1,sK7(X51,X52,any1,X54,X53),X55)) = subtract(any2,apply(x,sK7(X51,X52,any1,X54,X53)),apply(x,X55)) )
| ~ spl9_3 ),
inference(resolution,[],[f109,f457]) ).
fof(f879,plain,
( ! [X21,X24,X22,X25,X23] :
( exact(X21,X22)
| zero(X23) = apply(X22,sK6(X21,X22,any1,X24,X23))
| ~ morphism(X22,X24,X23)
| ~ morphism(X21,any1,X24)
| ~ element(X25,any2)
| apply(x,sK7(X21,X22,any1,X24,X23)) = subtract(any2,X25,subtract(any2,X25,apply(x,sK7(X21,X22,any1,X24,X23)))) )
| ~ spl9_3 ),
inference(resolution,[],[f109,f190]) ).
fof(f878,plain,
( ! [X18,X19,X17,X20] :
( exact(X17,X18)
| zero(X19) = apply(X18,sK6(X17,X18,any1,X20,X19))
| ~ morphism(X18,X20,X19)
| ~ morphism(X17,any1,X20)
| zero(any2) = subtract(any2,apply(x,sK7(X17,X18,any1,X20,X19)),apply(x,sK7(X17,X18,any1,X20,X19))) )
| ~ spl9_3 ),
inference(resolution,[],[f109,f165]) ).
fof(f875,plain,
! [X2,X3,X0,X1,X4,X5] :
( exact(X0,X1)
| zero(X2) = apply(X1,sK6(X0,X1,X3,X4,X2))
| ~ morphism(X1,X4,X2)
| ~ morphism(X0,X3,X4)
| ~ element(X5,X3)
| zero(X3) = subtract(X3,subtract(X3,sK7(X0,X1,X3,X4,X2),X5),subtract(X3,sK7(X0,X1,X3,X4,X2),X5)) ),
inference(resolution,[],[f109,f164]) ).
fof(f109,plain,
! [X2,X3,X0,X1,X4] :
( element(sK7(X0,X1,X2,X3,X4),X2)
| exact(X0,X1)
| zero(X4) = apply(X1,sK6(X0,X1,X2,X3,X4))
| ~ morphism(X1,X3,X4)
| ~ morphism(X0,X2,X3) ),
inference(cnf_transformation,[],[f79]) ).
fof(f113,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( ~ morphism(X3,X6,X7)
| element(sK8(X0,X1,X2,X3,X4),X4)
| commute(X0,X1,X2,X3)
| ~ morphism(X2,X4,X6)
| ~ morphism(X1,X5,X7)
| ~ morphism(X0,X4,X5) ),
inference(cnf_transformation,[],[f81]) ).
fof(f799,plain,
( ~ element(subtract(any2,zero(any2),apply(x,sK3(x,any1))),any2)
| spl9_45 ),
inference(avatar_component_clause,[],[f798]) ).
fof(f105,plain,
! [X2,X3,X0,X1,X4,X5] :
( zero(X4) != apply(X1,X5)
| apply(X0,sK5(X0,X2,X5)) = X5
| ~ element(X5,X3)
| ~ morphism(X1,X3,X4)
| ~ morphism(X0,X2,X3)
| ~ exact(X0,X1) ),
inference(cnf_transformation,[],[f73]) ).
fof(f680,plain,
( ! [X21,X18,X19,X17,X20] :
( ~ element(X17,any1)
| apply(x,subtract(any1,sK7(X18,X19,any1,X20,X21),X17)) = subtract(any2,apply(x,sK7(X18,X19,any1,X20,X21)),apply(x,X17))
| element(sK6(X18,X19,any1,X20,X21),X20)
| exact(X18,X19)
| ~ morphism(X19,X20,X21)
| ~ morphism(X18,any1,X20) )
| ~ spl9_3 ),
inference(resolution,[],[f457,f108]) ).
fof(f679,plain,
( ! [X16,X14,X15,X12,X13] :
( ~ element(X12,any1)
| apply(x,subtract(any1,sK6(X13,X14,X15,any1,X16),X12)) = subtract(any2,apply(x,sK6(X13,X14,X15,any1,X16)),apply(x,X12))
| element(sK7(X13,X14,X15,any1,X16),X15)
| exact(X13,X14)
| ~ morphism(X14,any1,X16)
| ~ morphism(X13,X15,any1) )
| ~ spl9_3 ),
inference(resolution,[],[f457,f108]) ).
fof(f676,plain,
( ! [X8,X9,X7] :
( ~ element(X7,any1)
| apply(x,subtract(any1,sK2(X8,any1,X9),X7)) = subtract(any2,apply(x,sK2(X8,any1,X9)),apply(x,X7))
| injection_2(X8)
| ~ morphism(X8,any1,X9) )
| ~ spl9_3 ),
inference(resolution,[],[f457,f97]) ).
fof(f675,plain,
( ! [X6,X4,X5] :
( ~ element(X4,any1)
| apply(x,subtract(any1,sK1(X5,X6,any1),X4)) = subtract(any2,apply(x,sK1(X5,X6,any1)),apply(x,X4))
| surjection(X5)
| ~ morphism(X5,X6,any1) )
| ~ spl9_3 ),
inference(resolution,[],[f457,f95]) ).
fof(f674,plain,
( ! [X2,X3,X1] :
( ~ element(X1,any1)
| apply(x,subtract(any1,subtract(any1,X2,X3),X1)) = subtract(any2,apply(x,subtract(any1,X2,X3)),apply(x,X1))
| ~ element(X3,any1)
| ~ element(X2,any1) )
| ~ spl9_3 ),
inference(resolution,[],[f457,f93]) ).
fof(f457,plain,
( ! [X0,X1] :
( ~ element(X1,any1)
| ~ element(X0,any1)
| apply(x,subtract(any1,X1,X0)) = subtract(any2,apply(x,X1),apply(x,X0)) )
| ~ spl9_3 ),
inference(resolution,[],[f88,f128]) ).
fof(f638,plain,
( ! [X21,X24,X22,X25,X23] :
( element(sK7(X21,X22,X23,any1,X24),X23)
| exact(X21,X22)
| ~ morphism(X22,any1,X24)
| ~ morphism(X21,X23,any1)
| ~ element(X25,any2)
| apply(x,sK6(X21,X22,X23,any1,X24)) = subtract(any2,X25,subtract(any2,X25,apply(x,sK6(X21,X22,X23,any1,X24)))) )
| ~ spl9_3 ),
inference(resolution,[],[f108,f190]) ).
fof(f637,plain,
( ! [X18,X19,X17,X20] :
( element(sK7(X17,X18,X19,any1,X20),X19)
| exact(X17,X18)
| ~ morphism(X18,any1,X20)
| ~ morphism(X17,X19,any1)
| zero(any2) = subtract(any2,apply(x,sK6(X17,X18,X19,any1,X20)),apply(x,sK6(X17,X18,X19,any1,X20))) )
| ~ spl9_3 ),
inference(resolution,[],[f108,f165]) ).
fof(f634,plain,
! [X2,X3,X0,X1,X4,X5] :
( element(sK7(X0,X1,X2,X3,X4),X2)
| exact(X0,X1)
| ~ morphism(X1,X3,X4)
| ~ morphism(X0,X2,X3)
| ~ element(X5,X3)
| zero(X3) = subtract(X3,subtract(X3,sK6(X0,X1,X2,X3,X4),X5),subtract(X3,sK6(X0,X1,X2,X3,X4),X5)) ),
inference(resolution,[],[f108,f164]) ).
fof(f617,plain,
( ! [X21,X24,X22,X25,X23] :
( element(sK6(X21,X22,any1,X23,X24),X23)
| exact(X21,X22)
| ~ morphism(X22,X23,X24)
| ~ morphism(X21,any1,X23)
| ~ element(X25,any2)
| apply(x,sK7(X21,X22,any1,X23,X24)) = subtract(any2,X25,subtract(any2,X25,apply(x,sK7(X21,X22,any1,X23,X24)))) )
| ~ spl9_3 ),
inference(resolution,[],[f108,f190]) ).
fof(f616,plain,
( ! [X18,X19,X17,X20] :
( element(sK6(X17,X18,any1,X19,X20),X19)
| exact(X17,X18)
| ~ morphism(X18,X19,X20)
| ~ morphism(X17,any1,X19)
| zero(any2) = subtract(any2,apply(x,sK7(X17,X18,any1,X19,X20)),apply(x,sK7(X17,X18,any1,X19,X20))) )
| ~ spl9_3 ),
inference(resolution,[],[f108,f165]) ).
fof(f613,plain,
! [X2,X3,X0,X1,X4,X5] :
( element(sK6(X0,X1,X2,X3,X4),X3)
| exact(X0,X1)
| ~ morphism(X1,X3,X4)
| ~ morphism(X0,X2,X3)
| ~ element(X5,X2)
| zero(X2) = subtract(X2,subtract(X2,sK7(X0,X1,X2,X3,X4),X5),subtract(X2,sK7(X0,X1,X2,X3,X4),X5)) ),
inference(resolution,[],[f108,f164]) ).
fof(f108,plain,
! [X2,X3,X0,X1,X4] :
( element(sK7(X0,X1,X2,X3,X4),X2)
| element(sK6(X0,X1,X2,X3,X4),X3)
| exact(X0,X1)
| ~ morphism(X1,X3,X4)
| ~ morphism(X0,X2,X3) ),
inference(cnf_transformation,[],[f79]) ).
fof(f104,plain,
! [X2,X3,X0,X1,X4,X5] :
( zero(X4) != apply(X1,X5)
| element(sK5(X0,X2,X5),X2)
| ~ element(X5,X3)
| ~ morphism(X1,X3,X4)
| ~ morphism(X0,X2,X3)
| ~ exact(X0,X1) ),
inference(cnf_transformation,[],[f73]) ).
fof(f544,plain,
( ! [X8,X9,X7] :
( ~ element(X7,any2)
| apply(x,sK2(X8,any1,X9)) = subtract(any2,X7,subtract(any2,X7,apply(x,sK2(X8,any1,X9))))
| injection_2(X8)
| ~ morphism(X8,any1,X9) )
| ~ spl9_3 ),
inference(resolution,[],[f190,f97]) ).
fof(f543,plain,
( ! [X6,X4,X5] :
( ~ element(X4,any2)
| apply(x,sK1(X5,X6,any1)) = subtract(any2,X4,subtract(any2,X4,apply(x,sK1(X5,X6,any1))))
| surjection(X5)
| ~ morphism(X5,X6,any1) )
| ~ spl9_3 ),
inference(resolution,[],[f190,f95]) ).
fof(f542,plain,
( ! [X2,X3,X1] :
( ~ element(X1,any2)
| apply(x,subtract(any1,X2,X3)) = subtract(any2,X1,subtract(any2,X1,apply(x,subtract(any1,X2,X3))))
| ~ element(X3,any1)
| ~ element(X2,any1) )
| ~ spl9_3 ),
inference(resolution,[],[f190,f93]) ).
fof(f190,plain,
( ! [X0,X1] :
( ~ element(X1,any1)
| ~ element(X0,any2)
| apply(x,X1) = subtract(any2,X0,subtract(any2,X0,apply(x,X1))) )
| ~ spl9_3 ),
inference(resolution,[],[f94,f163]) ).
fof(f177,plain,
! [X2,X0,X1] :
( ~ morphism(X0,X1,X2)
| injection_2(X0)
| zero(X1) = subtract(X1,sK2(X0,X1,X2),sK2(X0,X1,X2)) ),
inference(resolution,[],[f97,f85]) ).
fof(f176,plain,
! [X2,X0,X1] :
( ~ morphism(X0,X1,X2)
| surjection(X0)
| zero(X2) = subtract(X2,sK1(X0,X1,X2),sK1(X0,X1,X2)) ),
inference(resolution,[],[f95,f85]) ).
fof(f107,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( apply(X0,X6) != X5
| zero(X4) = apply(X1,X5)
| ~ element(X6,X2)
| ~ morphism(X1,X3,X4)
| ~ morphism(X0,X2,X3)
| ~ exact(X0,X1) ),
inference(cnf_transformation,[],[f73]) ).
fof(f474,plain,
! [X16,X14,X15,X13] :
( ~ element(X13,X14)
| zero(X14) = subtract(X14,subtract(X14,sK2(X15,X14,X16),X13),subtract(X14,sK2(X15,X14,X16),X13))
| injection_2(X15)
| ~ morphism(X15,X14,X16) ),
inference(resolution,[],[f164,f97]) ).
fof(f473,plain,
! [X10,X11,X9,X12] :
( ~ element(X9,X10)
| zero(X10) = subtract(X10,subtract(X10,sK1(X11,X12,X10),X9),subtract(X10,sK1(X11,X12,X10),X9))
| surjection(X11)
| ~ morphism(X11,X12,X10) ),
inference(resolution,[],[f164,f95]) ).
fof(f472,plain,
! [X8,X6,X7,X5] :
( ~ element(X5,X6)
| zero(X6) = subtract(X6,subtract(X6,subtract(X6,X7,X8),X5),subtract(X6,subtract(X6,X7,X8),X5))
| ~ element(X8,X6)
| ~ element(X7,X6) ),
inference(resolution,[],[f164,f93]) ).
fof(f164,plain,
! [X2,X0,X1] :
( ~ element(X2,X1)
| ~ element(X0,X1)
| zero(X1) = subtract(X1,subtract(X1,X2,X0),subtract(X1,X2,X0)) ),
inference(resolution,[],[f93,f85]) ).
fof(f88,plain,
! [X2,X3,X0,X1,X4] :
( ~ morphism(X0,X1,X2)
| ~ element(X4,X1)
| ~ element(X3,X1)
| apply(X0,subtract(X1,X3,X4)) = subtract(X2,apply(X0,X3),apply(X0,X4)) ),
inference(cnf_transformation,[],[f35]) ).
fof(f35,plain,
! [X0,X1,X2] :
( ! [X3,X4] :
( apply(X0,subtract(X1,X3,X4)) = subtract(X2,apply(X0,X3),apply(X0,X4))
| ~ element(X4,X1)
| ~ element(X3,X1) )
| ~ morphism(X0,X1,X2) ),
inference(flattening,[],[f34]) ).
fof(f34,plain,
! [X0,X1,X2] :
( ! [X3,X4] :
( apply(X0,subtract(X1,X3,X4)) = subtract(X2,apply(X0,X3),apply(X0,X4))
| ~ element(X4,X1)
| ~ element(X3,X1) )
| ~ morphism(X0,X1,X2) ),
inference(ennf_transformation,[],[f20]) ).
fof(f20,plain,
! [X0,X1,X2] :
( morphism(X0,X1,X2)
=> ! [X3,X4] :
( ( element(X4,X1)
& element(X3,X1) )
=> apply(X0,subtract(X1,X3,X4)) = subtract(X2,apply(X0,X3),apply(X0,X4)) ) ),
inference(rectify,[],[f13]) ).
fof(f13,axiom,
! [X0,X1,X2] :
( morphism(X0,X1,X2)
=> ! [X4,X5] :
( ( element(X5,X1)
& element(X4,X1) )
=> apply(X0,subtract(X1,X4,X5)) = subtract(X2,apply(X0,X4),apply(X0,X5)) ) ),
file('/export/starexec/sandbox/tmp/tmp.YLPE9jctjB/Vampire---4.8_1232',subtract_distribution) ).
fof(f91,plain,
! [X2,X3,X0,X1] :
( apply(X0,X3) != zero(X2)
| zero(X1) = X3
| ~ element(X3,X1)
| ~ morphism(X0,X1,X2)
| ~ injection_2(X0) ),
inference(cnf_transformation,[],[f39]) ).
fof(f39,plain,
! [X0,X1,X2] :
( ! [X3] :
( zero(X1) = X3
| apply(X0,X3) != zero(X2)
| ~ element(X3,X1) )
| ~ morphism(X0,X1,X2)
| ~ injection_2(X0) ),
inference(flattening,[],[f38]) ).
fof(f38,plain,
! [X0,X1,X2] :
( ! [X3] :
( zero(X1) = X3
| apply(X0,X3) != zero(X2)
| ~ element(X3,X1) )
| ~ morphism(X0,X1,X2)
| ~ injection_2(X0) ),
inference(ennf_transformation,[],[f14]) ).
fof(f14,axiom,
! [X0,X1,X2] :
( ( morphism(X0,X1,X2)
& injection_2(X0) )
=> ! [X3] :
( ( apply(X0,X3) = zero(X2)
& element(X3,X1) )
=> zero(X1) = X3 ) ),
file('/export/starexec/sandbox/tmp/tmp.YLPE9jctjB/Vampire---4.8_1232',injection_properties_2) ).
fof(f102,plain,
! [X2,X0,X1] :
( ~ morphism(X0,X1,X2)
| apply(X0,sK3(X0,X1)) = apply(X0,sK4(X0,X1))
| injection(X0) ),
inference(cnf_transformation,[],[f68]) ).
fof(f68,plain,
! [X0,X1,X2] :
( injection(X0)
| ( sK3(X0,X1) != sK4(X0,X1)
& apply(X0,sK3(X0,X1)) = apply(X0,sK4(X0,X1))
& element(sK4(X0,X1),X1)
& element(sK3(X0,X1),X1) )
| ~ morphism(X0,X1,X2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4])],[f51,f67]) ).
fof(f67,plain,
! [X0,X1] :
( ? [X3,X4] :
( X3 != X4
& apply(X0,X3) = apply(X0,X4)
& element(X4,X1)
& element(X3,X1) )
=> ( sK3(X0,X1) != sK4(X0,X1)
& apply(X0,sK3(X0,X1)) = apply(X0,sK4(X0,X1))
& element(sK4(X0,X1),X1)
& element(sK3(X0,X1),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f51,plain,
! [X0,X1,X2] :
( injection(X0)
| ? [X3,X4] :
( X3 != X4
& apply(X0,X3) = apply(X0,X4)
& element(X4,X1)
& element(X3,X1) )
| ~ morphism(X0,X1,X2) ),
inference(flattening,[],[f50]) ).
fof(f50,plain,
! [X0,X1,X2] :
( injection(X0)
| ? [X3,X4] :
( X3 != X4
& apply(X0,X3) = apply(X0,X4)
& element(X4,X1)
& element(X3,X1) )
| ~ morphism(X0,X1,X2) ),
inference(ennf_transformation,[],[f26]) ).
fof(f26,plain,
! [X0,X1,X2] :
( ( ! [X3,X4] :
( ( apply(X0,X3) = apply(X0,X4)
& element(X4,X1)
& element(X3,X1) )
=> X3 = X4 )
& morphism(X0,X1,X2) )
=> injection(X0) ),
inference(rectify,[],[f3]) ).
fof(f3,axiom,
! [X0,X1,X2] :
( ( ! [X4,X5] :
( ( apply(X0,X4) = apply(X0,X5)
& element(X5,X1)
& element(X4,X1) )
=> X4 = X5 )
& morphism(X0,X1,X2) )
=> injection(X0) ),
file('/export/starexec/sandbox/tmp/tmp.YLPE9jctjB/Vampire---4.8_1232',properties_for_injection) ).
fof(f96,plain,
! [X2,X0,X1,X4] :
( apply(X0,X4) != sK1(X0,X1,X2)
| surjection(X0)
| ~ element(X4,X1)
| ~ morphism(X0,X1,X2) ),
inference(cnf_transformation,[],[f64]) ).
fof(f64,plain,
! [X0,X1,X2] :
( surjection(X0)
| ( ! [X4] :
( apply(X0,X4) != sK1(X0,X1,X2)
| ~ element(X4,X1) )
& element(sK1(X0,X1,X2),X2) )
| ~ morphism(X0,X1,X2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f47,f63]) ).
fof(f63,plain,
! [X0,X1,X2] :
( ? [X3] :
( ! [X4] :
( apply(X0,X4) != X3
| ~ element(X4,X1) )
& element(X3,X2) )
=> ( ! [X4] :
( apply(X0,X4) != sK1(X0,X1,X2)
| ~ element(X4,X1) )
& element(sK1(X0,X1,X2),X2) ) ),
introduced(choice_axiom,[]) ).
fof(f47,plain,
! [X0,X1,X2] :
( surjection(X0)
| ? [X3] :
( ! [X4] :
( apply(X0,X4) != X3
| ~ element(X4,X1) )
& element(X3,X2) )
| ~ morphism(X0,X1,X2) ),
inference(flattening,[],[f46]) ).
fof(f46,plain,
! [X0,X1,X2] :
( surjection(X0)
| ? [X3] :
( ! [X4] :
( apply(X0,X4) != X3
| ~ element(X4,X1) )
& element(X3,X2) )
| ~ morphism(X0,X1,X2) ),
inference(ennf_transformation,[],[f25]) ).
fof(f25,plain,
! [X0,X1,X2] :
( ( ! [X3] :
( element(X3,X2)
=> ? [X4] :
( apply(X0,X4) = X3
& element(X4,X1) ) )
& morphism(X0,X1,X2) )
=> surjection(X0) ),
inference(rectify,[],[f5]) ).
fof(f5,axiom,
! [X0,X1,X2] :
( ( ! [X6] :
( element(X6,X2)
=> ? [X7] :
( apply(X0,X7) = X6
& element(X7,X1) ) )
& morphism(X0,X1,X2) )
=> surjection(X0) ),
file('/export/starexec/sandbox/tmp/tmp.YLPE9jctjB/Vampire---4.8_1232',properties_for_surjection) ).
fof(f90,plain,
! [X2,X3,X0,X1] :
( ~ morphism(X0,X1,X2)
| ~ element(X3,X2)
| apply(X0,sK0(X0,X1,X3)) = X3
| ~ surjection(X0) ),
inference(cnf_transformation,[],[f62]) ).
fof(f62,plain,
! [X0,X1,X2] :
( ! [X3] :
( ( apply(X0,sK0(X0,X1,X3)) = X3
& element(sK0(X0,X1,X3),X1) )
| ~ element(X3,X2) )
| ~ morphism(X0,X1,X2)
| ~ surjection(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f37,f61]) ).
fof(f61,plain,
! [X0,X1,X3] :
( ? [X4] :
( apply(X0,X4) = X3
& element(X4,X1) )
=> ( apply(X0,sK0(X0,X1,X3)) = X3
& element(sK0(X0,X1,X3),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f37,plain,
! [X0,X1,X2] :
( ! [X3] :
( ? [X4] :
( apply(X0,X4) = X3
& element(X4,X1) )
| ~ element(X3,X2) )
| ~ morphism(X0,X1,X2)
| ~ surjection(X0) ),
inference(flattening,[],[f36]) ).
fof(f36,plain,
! [X0,X1,X2] :
( ! [X3] :
( ? [X4] :
( apply(X0,X4) = X3
& element(X4,X1) )
| ~ element(X3,X2) )
| ~ morphism(X0,X1,X2)
| ~ surjection(X0) ),
inference(ennf_transformation,[],[f21]) ).
fof(f21,plain,
! [X0,X1,X2] :
( ( morphism(X0,X1,X2)
& surjection(X0) )
=> ! [X3] :
( element(X3,X2)
=> ? [X4] :
( apply(X0,X4) = X3
& element(X4,X1) ) ) ),
inference(rectify,[],[f4]) ).
fof(f4,axiom,
! [X0,X1,X2] :
( ( morphism(X0,X1,X2)
& surjection(X0) )
=> ! [X6] :
( element(X6,X2)
=> ? [X7] :
( apply(X0,X7) = X6
& element(X7,X1) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.YLPE9jctjB/Vampire---4.8_1232',surjection_properties) ).
fof(f98,plain,
! [X2,X0,X1] :
( ~ morphism(X0,X1,X2)
| zero(X2) = apply(X0,sK2(X0,X1,X2))
| injection_2(X0) ),
inference(cnf_transformation,[],[f66]) ).
fof(f181,plain,
( ! [X0] :
( ~ element(X0,any2)
| element(sK0(x,any1,X0),any1)
| ~ surjection(x) )
| ~ spl9_3 ),
inference(resolution,[],[f89,f128]) ).
fof(f89,plain,
! [X2,X3,X0,X1] :
( ~ morphism(X0,X1,X2)
| ~ element(X3,X2)
| element(sK0(X0,X1,X3),X1)
| ~ surjection(X0) ),
inference(cnf_transformation,[],[f62]) ).
fof(f165,plain,
( ! [X0] :
( ~ element(X0,any1)
| zero(any2) = subtract(any2,apply(x,X0),apply(x,X0)) )
| ~ spl9_3 ),
inference(resolution,[],[f163,f85]) ).
fof(f103,plain,
! [X2,X0,X1] :
( sK3(X0,X1) != sK4(X0,X1)
| injection(X0)
| ~ morphism(X0,X1,X2) ),
inference(cnf_transformation,[],[f68]) ).
fof(f97,plain,
! [X2,X0,X1] :
( element(sK2(X0,X1,X2),X1)
| injection_2(X0)
| ~ morphism(X0,X1,X2) ),
inference(cnf_transformation,[],[f66]) ).
fof(f95,plain,
! [X2,X0,X1] :
( element(sK1(X0,X1,X2),X2)
| surjection(X0)
| ~ morphism(X0,X1,X2) ),
inference(cnf_transformation,[],[f64]) ).
fof(f163,plain,
( ! [X0] :
( element(apply(x,X0),any2)
| ~ element(X0,any1) )
| ~ spl9_3 ),
inference(resolution,[],[f86,f128]) ).
fof(f86,plain,
! [X2,X3,X0,X1] :
( ~ morphism(X0,X1,X2)
| ~ element(X3,X1)
| element(apply(X0,X3),X2) ),
inference(cnf_transformation,[],[f33]) ).
fof(f33,plain,
! [X0,X1,X2] :
( ( apply(X0,zero(X1)) = zero(X2)
& ! [X3] :
( element(apply(X0,X3),X2)
| ~ element(X3,X1) ) )
| ~ morphism(X0,X1,X2) ),
inference(ennf_transformation,[],[f1]) ).
fof(f1,axiom,
! [X0,X1,X2] :
( morphism(X0,X1,X2)
=> ( apply(X0,zero(X1)) = zero(X2)
& ! [X3] :
( element(X3,X1)
=> element(apply(X0,X3),X2) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.YLPE9jctjB/Vampire---4.8_1232',morphism) ).
fof(f101,plain,
! [X2,X0,X1] :
( ~ morphism(X0,X1,X2)
| element(sK4(X0,X1),X1)
| injection(X0) ),
inference(cnf_transformation,[],[f68]) ).
fof(f100,plain,
! [X2,X0,X1] :
( ~ morphism(X0,X1,X2)
| element(sK3(X0,X1),X1)
| injection(X0) ),
inference(cnf_transformation,[],[f68]) ).
fof(f130,plain,
( apply(x,zero(any1)) = zero(any2)
| ~ spl9_3 ),
inference(resolution,[],[f87,f128]) ).
fof(f87,plain,
! [X2,X0,X1] :
( ~ morphism(X0,X1,X2)
| apply(X0,zero(X1)) = zero(X2) ),
inference(cnf_transformation,[],[f33]) ).
fof(f85,plain,
! [X0,X1] :
( ~ element(X1,X0)
| zero(X0) = subtract(X0,X1,X1) ),
inference(cnf_transformation,[],[f32]) ).
fof(f32,plain,
! [X0,X1] :
( zero(X0) = subtract(X0,X1,X1)
| ~ element(X1,X0) ),
inference(ennf_transformation,[],[f19]) ).
fof(f19,plain,
! [X0,X1] :
( element(X1,X0)
=> zero(X0) = subtract(X0,X1,X1) ),
inference(rectify,[],[f11]) ).
fof(f11,axiom,
! [X1,X3] :
( element(X3,X1)
=> zero(X1) = subtract(X1,X3,X3) ),
file('/export/starexec/sandbox/tmp/tmp.YLPE9jctjB/Vampire---4.8_1232',subtract_to_0) ).
fof(f84,plain,
morphism(x,any1,any2),
inference(cnf_transformation,[],[f16]) ).
fof(f16,axiom,
morphism(x,any1,any2),
file('/export/starexec/sandbox/tmp/tmp.YLPE9jctjB/Vampire---4.8_1232',x_morphism) ).
fof(f82,plain,
( injection_2(x)
| injection(x) ),
inference(cnf_transformation,[],[f60]) ).
fof(f2690,plain,
( ~ spl9_99
| ~ spl9_3
| spl9_45
| ~ spl9_80 ),
inference(avatar_split_clause,[],[f2600,f1899,f798,f126,f2687]) ).
fof(f2687,plain,
( spl9_99
<=> element(subtract(any1,subtract(any1,sK4(x,any1),sK3(x,any1)),sK4(x,any1)),any1) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_99])]) ).
fof(f1899,plain,
( spl9_80
<=> subtract(any2,zero(any2),apply(x,sK3(x,any1))) = apply(x,subtract(any1,subtract(any1,sK4(x,any1),sK3(x,any1)),sK4(x,any1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_80])]) ).
fof(f2600,plain,
( ~ element(subtract(any1,subtract(any1,sK4(x,any1),sK3(x,any1)),sK4(x,any1)),any1)
| ~ spl9_3
| spl9_45
| ~ spl9_80 ),
inference(global_subsumption,[],[f82,f84,f128,f85,f87,f130,f100,f101,f86,f93,f163,f95,f97,f99,f103,f165,f89,f181,f94,f98,f90,f96,f102,f91,f92,f106,f88,f164,f472,f473,f474,f107,f176,f177,f190,f542,f543,f544,f104,f108,f613,f616,f617,f634,f637,f638,f457,f674,f675,f676,f679,f680,f105,f799,f113,f109,f875,f878,f879,f886,f110,f939,f942,f943,f950,f522,f1008,f115,f111,f114,f1113,f1114,f1116,f468,f1128,f1129,f1130,f1133,f1134,f1135,f1136,f178,f1142,f1143,f1144,f1147,f1148,f1149,f1150,f179,f112,f180,f191,f1279,f1283,f1287,f1288,f1291,f1292,f1293,f1294,f192,f193,f802,f1069,f615,f1719,f1720,f1721,f1722,f1723,f1724,f1725,f1732,f1733,f636,f1845,f1846,f1847,f1848,f1849,f1850,f1851,f1858,f1859,f1901,f1928,f1929,f1930,f1931,f877,f2017,f614,f2077,f1927,f240,f1315,f635,f2158,f941,f2191,f876,f2253,f940,f2302,f1926,f1925,f294,f1924,f1425,f1184,f540,f136,f162,f194,f83,f1923]) ).
fof(f1923,plain,
( element(subtract(any2,zero(any2),apply(x,sK3(x,any1))),any2)
| ~ element(subtract(any1,subtract(any1,sK4(x,any1),sK3(x,any1)),sK4(x,any1)),any1)
| ~ spl9_3
| ~ spl9_80 ),
inference(superposition,[],[f163,f1901]) ).
fof(f1924,plain,
( ! [X0,X1] :
( zero(X0) != subtract(any2,zero(any2),apply(x,sK3(x,any1)))
| zero(X1) = subtract(any1,subtract(any1,sK4(x,any1),sK3(x,any1)),sK4(x,any1))
| ~ element(subtract(any1,subtract(any1,sK4(x,any1),sK3(x,any1)),sK4(x,any1)),X1)
| ~ morphism(x,X1,X0)
| ~ injection_2(x) )
| ~ spl9_80 ),
inference(superposition,[],[f91,f1901]) ).
fof(f1925,plain,
( ! [X2,X3,X4] :
( subtract(any2,zero(any2),apply(x,sK3(x,any1))) != apply(x,X2)
| subtract(any1,subtract(any1,sK4(x,any1),sK3(x,any1)),sK4(x,any1)) = X2
| ~ element(X2,X3)
| ~ element(subtract(any1,subtract(any1,sK4(x,any1),sK3(x,any1)),sK4(x,any1)),X3)
| ~ morphism(x,X3,X4)
| ~ injection(x) )
| ~ spl9_80 ),
inference(superposition,[],[f92,f1901]) ).
fof(f1926,plain,
( ! [X6,X7,X5] :
( subtract(any2,zero(any2),apply(x,sK3(x,any1))) != apply(x,X5)
| subtract(any1,subtract(any1,sK4(x,any1),sK3(x,any1)),sK4(x,any1)) = X5
| ~ element(subtract(any1,subtract(any1,sK4(x,any1),sK3(x,any1)),sK4(x,any1)),X6)
| ~ element(X5,X6)
| ~ morphism(x,X6,X7)
| ~ injection(x) )
| ~ spl9_80 ),
inference(superposition,[],[f92,f1901]) ).
fof(f1927,plain,
( ! [X8,X9] :
( subtract(any2,zero(any2),apply(x,sK3(x,any1))) != sK1(x,X8,X9)
| surjection(x)
| ~ element(subtract(any1,subtract(any1,sK4(x,any1),sK3(x,any1)),sK4(x,any1)),X8)
| ~ morphism(x,X8,X9) )
| ~ spl9_80 ),
inference(superposition,[],[f96,f1901]) ).
fof(f1931,plain,
( ! [X26,X27,X24,X25,X23] :
( subtract(any2,zero(any2),apply(x,sK3(x,any1))) != X23
| zero(X24) = apply(X25,X23)
| ~ element(subtract(any1,subtract(any1,sK4(x,any1),sK3(x,any1)),sK4(x,any1)),X26)
| ~ morphism(X25,X27,X24)
| ~ morphism(x,X26,X27)
| ~ exact(x,X25) )
| ~ spl9_80 ),
inference(superposition,[],[f107,f1901]) ).
fof(f1930,plain,
( ! [X21,X18,X19,X22,X20] :
( subtract(any2,zero(any2),apply(x,sK3(x,any1))) != X18
| element(X18,X19)
| ~ element(subtract(any1,subtract(any1,sK4(x,any1),sK3(x,any1)),sK4(x,any1)),X20)
| ~ morphism(X21,X19,X22)
| ~ morphism(x,X20,X19)
| ~ exact(x,X21) )
| ~ spl9_80 ),
inference(superposition,[],[f106,f1901]) ).
fof(f1929,plain,
( ! [X16,X14,X17,X15] :
( subtract(any2,zero(any2),apply(x,sK3(x,any1))) != zero(X14)
| subtract(any1,subtract(any1,sK4(x,any1),sK3(x,any1)),sK4(x,any1)) = apply(X15,sK5(X15,X16,subtract(any1,subtract(any1,sK4(x,any1),sK3(x,any1)),sK4(x,any1))))
| ~ element(subtract(any1,subtract(any1,sK4(x,any1),sK3(x,any1)),sK4(x,any1)),X17)
| ~ morphism(x,X17,X14)
| ~ morphism(X15,X16,X17)
| ~ exact(X15,x) )
| ~ spl9_80 ),
inference(superposition,[],[f105,f1901]) ).
fof(f1928,plain,
( ! [X10,X11,X12,X13] :
( subtract(any2,zero(any2),apply(x,sK3(x,any1))) != zero(X10)
| element(sK5(X11,X12,subtract(any1,subtract(any1,sK4(x,any1),sK3(x,any1)),sK4(x,any1))),X12)
| ~ element(subtract(any1,subtract(any1,sK4(x,any1),sK3(x,any1)),sK4(x,any1)),X13)
| ~ morphism(x,X13,X10)
| ~ morphism(X11,X12,X13)
| ~ exact(X11,x) )
| ~ spl9_80 ),
inference(superposition,[],[f104,f1901]) ).
fof(f1901,plain,
( subtract(any2,zero(any2),apply(x,sK3(x,any1))) = apply(x,subtract(any1,subtract(any1,sK4(x,any1),sK3(x,any1)),sK4(x,any1)))
| ~ spl9_80 ),
inference(avatar_component_clause,[],[f1899]) ).
fof(f2685,plain,
( ~ spl9_98
| ~ spl9_3
| spl9_45
| ~ spl9_71 ),
inference(avatar_split_clause,[],[f2602,f1510,f798,f126,f2682]) ).
fof(f2682,plain,
( spl9_98
<=> element(sK0(x,any1,subtract(any2,zero(any2),apply(x,sK3(x,any1)))),any1) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_98])]) ).
fof(f1510,plain,
( spl9_71
<=> subtract(any2,zero(any2),apply(x,sK3(x,any1))) = apply(x,sK0(x,any1,subtract(any2,zero(any2),apply(x,sK3(x,any1))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_71])]) ).
fof(f2602,plain,
( ~ element(sK0(x,any1,subtract(any2,zero(any2),apply(x,sK3(x,any1)))),any1)
| ~ spl9_3
| spl9_45
| ~ spl9_71 ),
inference(global_subsumption,[],[f82,f84,f128,f85,f87,f130,f100,f101,f86,f93,f163,f95,f97,f99,f103,f165,f89,f181,f94,f98,f90,f96,f102,f91,f92,f106,f88,f164,f472,f473,f474,f107,f176,f177,f190,f542,f543,f544,f104,f108,f613,f616,f617,f634,f637,f638,f457,f674,f675,f676,f679,f680,f105,f799,f113,f109,f875,f878,f879,f886,f110,f939,f942,f943,f950,f522,f1008,f115,f111,f114,f1113,f1114,f1116,f468,f1128,f1129,f1130,f1133,f1134,f1135,f1136,f178,f1142,f1143,f1144,f1147,f1148,f1149,f1150,f179,f112,f180,f191,f1279,f1283,f1287,f1288,f1291,f1292,f1293,f1294,f192,f193,f802,f1512,f1520,f1521,f1522,f1523,f1069,f615,f1719,f1720,f1721,f1722,f1723,f1724,f1725,f1732,f1733,f636,f1845,f1846,f1847,f1848,f1849,f1850,f1851,f1858,f1859,f877,f2017,f614,f2077,f1519,f240,f1315,f635,f2158,f941,f2191,f876,f2253,f940,f2302,f1518,f1517,f294,f1516,f1425,f1184,f540,f136,f162,f194,f83,f1515]) ).
fof(f1515,plain,
( element(subtract(any2,zero(any2),apply(x,sK3(x,any1))),any2)
| ~ element(sK0(x,any1,subtract(any2,zero(any2),apply(x,sK3(x,any1)))),any1)
| ~ spl9_3
| ~ spl9_71 ),
inference(superposition,[],[f163,f1512]) ).
fof(f1516,plain,
( ! [X0,X1] :
( zero(X0) != subtract(any2,zero(any2),apply(x,sK3(x,any1)))
| zero(X1) = sK0(x,any1,subtract(any2,zero(any2),apply(x,sK3(x,any1))))
| ~ element(sK0(x,any1,subtract(any2,zero(any2),apply(x,sK3(x,any1)))),X1)
| ~ morphism(x,X1,X0)
| ~ injection_2(x) )
| ~ spl9_71 ),
inference(superposition,[],[f91,f1512]) ).
fof(f1517,plain,
( ! [X2,X3,X4] :
( subtract(any2,zero(any2),apply(x,sK3(x,any1))) != apply(x,X2)
| sK0(x,any1,subtract(any2,zero(any2),apply(x,sK3(x,any1)))) = X2
| ~ element(X2,X3)
| ~ element(sK0(x,any1,subtract(any2,zero(any2),apply(x,sK3(x,any1)))),X3)
| ~ morphism(x,X3,X4)
| ~ injection(x) )
| ~ spl9_71 ),
inference(superposition,[],[f92,f1512]) ).
fof(f1518,plain,
( ! [X6,X7,X5] :
( subtract(any2,zero(any2),apply(x,sK3(x,any1))) != apply(x,X5)
| sK0(x,any1,subtract(any2,zero(any2),apply(x,sK3(x,any1)))) = X5
| ~ element(sK0(x,any1,subtract(any2,zero(any2),apply(x,sK3(x,any1)))),X6)
| ~ element(X5,X6)
| ~ morphism(x,X6,X7)
| ~ injection(x) )
| ~ spl9_71 ),
inference(superposition,[],[f92,f1512]) ).
fof(f1519,plain,
( ! [X8,X9] :
( subtract(any2,zero(any2),apply(x,sK3(x,any1))) != sK1(x,X8,X9)
| surjection(x)
| ~ element(sK0(x,any1,subtract(any2,zero(any2),apply(x,sK3(x,any1)))),X8)
| ~ morphism(x,X8,X9) )
| ~ spl9_71 ),
inference(superposition,[],[f96,f1512]) ).
fof(f1523,plain,
( ! [X26,X27,X24,X25,X23] :
( subtract(any2,zero(any2),apply(x,sK3(x,any1))) != X23
| zero(X24) = apply(X25,X23)
| ~ element(sK0(x,any1,subtract(any2,zero(any2),apply(x,sK3(x,any1)))),X26)
| ~ morphism(X25,X27,X24)
| ~ morphism(x,X26,X27)
| ~ exact(x,X25) )
| ~ spl9_71 ),
inference(superposition,[],[f107,f1512]) ).
fof(f1522,plain,
( ! [X21,X18,X19,X22,X20] :
( subtract(any2,zero(any2),apply(x,sK3(x,any1))) != X18
| element(X18,X19)
| ~ element(sK0(x,any1,subtract(any2,zero(any2),apply(x,sK3(x,any1)))),X20)
| ~ morphism(X21,X19,X22)
| ~ morphism(x,X20,X19)
| ~ exact(x,X21) )
| ~ spl9_71 ),
inference(superposition,[],[f106,f1512]) ).
fof(f1521,plain,
( ! [X16,X14,X17,X15] :
( subtract(any2,zero(any2),apply(x,sK3(x,any1))) != zero(X14)
| sK0(x,any1,subtract(any2,zero(any2),apply(x,sK3(x,any1)))) = apply(X15,sK5(X15,X16,sK0(x,any1,subtract(any2,zero(any2),apply(x,sK3(x,any1))))))
| ~ element(sK0(x,any1,subtract(any2,zero(any2),apply(x,sK3(x,any1)))),X17)
| ~ morphism(x,X17,X14)
| ~ morphism(X15,X16,X17)
| ~ exact(X15,x) )
| ~ spl9_71 ),
inference(superposition,[],[f105,f1512]) ).
fof(f1520,plain,
( ! [X10,X11,X12,X13] :
( subtract(any2,zero(any2),apply(x,sK3(x,any1))) != zero(X10)
| element(sK5(X11,X12,sK0(x,any1,subtract(any2,zero(any2),apply(x,sK3(x,any1))))),X12)
| ~ element(sK0(x,any1,subtract(any2,zero(any2),apply(x,sK3(x,any1)))),X13)
| ~ morphism(x,X13,X10)
| ~ morphism(X11,X12,X13)
| ~ exact(X11,x) )
| ~ spl9_71 ),
inference(superposition,[],[f104,f1512]) ).
fof(f1512,plain,
( subtract(any2,zero(any2),apply(x,sK3(x,any1))) = apply(x,sK0(x,any1,subtract(any2,zero(any2),apply(x,sK3(x,any1)))))
| ~ spl9_71 ),
inference(avatar_component_clause,[],[f1510]) ).
fof(f2677,plain,
( spl9_17
| ~ spl9_66
| ~ spl9_70 ),
inference(avatar_split_clause,[],[f1505,f1499,f1463,f313]) ).
fof(f313,plain,
( spl9_17
<=> zero(any1) = subtract(any1,zero(any1),zero(any1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_17])]) ).
fof(f1463,plain,
( spl9_66
<=> zero(any1) = subtract(any1,sK0(x,any1,zero(any2)),sK0(x,any1,zero(any2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_66])]) ).
fof(f1505,plain,
( zero(any1) = subtract(any1,zero(any1),zero(any1))
| ~ spl9_66
| ~ spl9_70 ),
inference(superposition,[],[f1465,f1501]) ).
fof(f1465,plain,
( zero(any1) = subtract(any1,sK0(x,any1,zero(any2)),sK0(x,any1,zero(any2)))
| ~ spl9_66 ),
inference(avatar_component_clause,[],[f1463]) ).
fof(f2676,plain,
( spl9_17
| ~ spl9_66
| ~ spl9_70 ),
inference(avatar_split_clause,[],[f2648,f1499,f1463,f313]) ).
fof(f2648,plain,
( zero(any1) = subtract(any1,zero(any1),zero(any1))
| ~ spl9_66
| ~ spl9_70 ),
inference(forward_demodulation,[],[f1465,f1501]) ).
fof(f2653,plain,
( spl9_7
| ~ spl9_13
| ~ spl9_59
| ~ spl9_97 ),
inference(avatar_split_clause,[],[f2646,f2633,f1118,f219,f168]) ).
fof(f1118,plain,
( spl9_59
<=> zero(any1) = subtract(any1,subtract(any1,subtract(any1,zero(any1),sK3(x,any1)),sK4(x,any1)),subtract(any1,subtract(any1,zero(any1),sK3(x,any1)),sK4(x,any1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_59])]) ).
fof(f2646,plain,
( element(zero(any1),any1)
| ~ spl9_13
| ~ spl9_59
| ~ spl9_97 ),
inference(global_subsumption,[],[f1125,f82,f84,f85,f87,f100,f101,f86,f93,f95,f97,f99,f103,f89,f94,f98,f90,f244,f245,f96,f102,f91,f92,f106,f88,f164,f472,f473,f474,f107,f176,f177,f104,f108,f613,f634,f105,f113,f109,f875,f110,f939,f522,f115,f111,f114,f1113,f112,f191,f1283,f1287,f1288,f1291,f1292,f1293,f1294,f192,f193,f615,f1719,f1720,f1721,f1722,f636,f1845,f1846,f1847,f1848,f877,f614,f635,f941,f876,f940,f83,f220,f2611,f2612,f2613,f2614,f2635,f2642]) ).
fof(f2642,plain,
( element(zero(any1),any1)
| ~ spl9_13
| ~ spl9_97 ),
inference(subsumption_resolution,[],[f2638,f220]) ).
fof(f2638,plain,
( element(zero(any1),any1)
| ~ element(sK2(x,any1,any2),any1)
| ~ spl9_97 ),
inference(duplicate_literal_removal,[],[f2637]) ).
fof(f2637,plain,
( element(zero(any1),any1)
| ~ element(sK2(x,any1,any2),any1)
| ~ element(sK2(x,any1,any2),any1)
| ~ spl9_97 ),
inference(superposition,[],[f93,f2635]) ).
fof(f2614,plain,
( zero(any1) = subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2))
| ~ spl9_13 ),
inference(resolution,[],[f220,f85]) ).
fof(f2612,plain,
( ! [X6] :
( ~ element(X6,any1)
| zero(any1) = subtract(any1,subtract(any1,sK2(x,any1,any2),X6),subtract(any1,sK2(x,any1,any2),X6)) )
| ~ spl9_13 ),
inference(resolution,[],[f220,f164]) ).
fof(f2611,plain,
( ! [X4,X5] :
( ~ element(X4,any1)
| subtract(any1,X5,sK2(x,any1,any2)) = subtract(any1,X4,subtract(any1,X4,subtract(any1,X5,sK2(x,any1,any2))))
| ~ element(X5,any1) )
| ~ spl9_13 ),
inference(resolution,[],[f220,f191]) ).
fof(f245,plain,
( zero(any1) = subtract(any1,sK2(x,any1,any2),sK2(x,any1,any2))
| ~ spl9_13 ),
inference(resolution,[],[f220,f85]) ).
fof(f244,plain,
( ! [X0] :
( sK2(x,any1,any2) = subtract(any1,X0,subtract(any1,X0,sK2(x,any1,any2)))
| ~ element(X0,any1) )
| ~ spl9_13 ),
inference(resolution,[],[f220,f94]) ).
fof(f1125,plain,
( element(zero(any1),any1)
| ~ element(subtract(any1,subtract(any1,zero(any1),sK3(x,any1)),sK4(x,any1)),any1)
| ~ spl9_59 ),
inference(duplicate_literal_removal,[],[f1124]) ).
fof(f1124,plain,
( element(zero(any1),any1)
| ~ element(subtract(any1,subtract(any1,zero(any1),sK3(x,any1)),sK4(x,any1)),any1)
| ~ element(subtract(any1,subtract(any1,zero(any1),sK3(x,any1)),sK4(x,any1)),any1)
| ~ spl9_59 ),
inference(superposition,[],[f93,f1120]) ).
fof(f1120,plain,
( zero(any1) = subtract(any1,subtract(any1,subtract(any1,zero(any1),sK3(x,any1)),sK4(x,any1)),subtract(any1,subtract(any1,zero(any1),sK3(x,any1)),sK4(x,any1)))
| ~ spl9_59 ),
inference(avatar_component_clause,[],[f1118]) ).
fof(f2652,plain,
( spl9_7
| ~ spl9_13
| ~ spl9_58
| ~ spl9_97 ),
inference(avatar_split_clause,[],[f2645,f2633,f1109,f219,f168]) ).
fof(f1109,plain,
( spl9_58
<=> zero(any1) = subtract(any1,subtract(any1,subtract(any1,zero(any1),sK3(x,any1)),sK3(x,any1)),subtract(any1,subtract(any1,zero(any1),sK3(x,any1)),sK3(x,any1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_58])]) ).
fof(f2645,plain,
( element(zero(any1),any1)
| ~ spl9_13
| ~ spl9_58
| ~ spl9_97 ),
inference(global_subsumption,[],[f1123,f82,f84,f85,f87,f100,f101,f86,f93,f95,f97,f99,f103,f89,f94,f98,f90,f244,f245,f96,f102,f91,f92,f106,f88,f164,f472,f473,f474,f107,f176,f177,f104,f108,f613,f634,f105,f113,f109,f875,f110,f939,f522,f115,f111,f114,f1113,f112,f191,f1283,f1287,f1288,f1291,f1292,f1293,f1294,f192,f193,f615,f1719,f1720,f1721,f1722,f636,f1845,f1846,f1847,f1848,f877,f614,f635,f941,f876,f940,f83,f220,f2611,f2612,f2613,f2614,f2635,f2642]) ).
fof(f1123,plain,
( element(zero(any1),any1)
| ~ element(subtract(any1,subtract(any1,zero(any1),sK3(x,any1)),sK3(x,any1)),any1)
| ~ spl9_58 ),
inference(duplicate_literal_removal,[],[f1122]) ).
fof(f1122,plain,
( element(zero(any1),any1)
| ~ element(subtract(any1,subtract(any1,zero(any1),sK3(x,any1)),sK3(x,any1)),any1)
| ~ element(subtract(any1,subtract(any1,zero(any1),sK3(x,any1)),sK3(x,any1)),any1)
| ~ spl9_58 ),
inference(superposition,[],[f93,f1111]) ).
fof(f1111,plain,
( zero(any1) = subtract(any1,subtract(any1,subtract(any1,zero(any1),sK3(x,any1)),sK3(x,any1)),subtract(any1,subtract(any1,zero(any1),sK3(x,any1)),sK3(x,any1)))
| ~ spl9_58 ),
inference(avatar_component_clause,[],[f1109]) ).
fof(f2651,plain,
( spl9_7
| ~ spl9_13
| ~ spl9_57
| ~ spl9_97 ),
inference(avatar_split_clause,[],[f2644,f2633,f1099,f219,f168]) ).
fof(f1099,plain,
( spl9_57
<=> zero(any1) = subtract(any1,subtract(any1,sK4(x,any1),subtract(any1,zero(any1),sK3(x,any1))),subtract(any1,sK4(x,any1),subtract(any1,zero(any1),sK3(x,any1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_57])]) ).
fof(f2644,plain,
( element(zero(any1),any1)
| ~ spl9_13
| ~ spl9_57
| ~ spl9_97 ),
inference(global_subsumption,[],[f1107,f82,f84,f85,f87,f100,f101,f86,f93,f95,f97,f99,f103,f89,f94,f98,f90,f244,f245,f96,f102,f91,f92,f106,f88,f164,f472,f473,f474,f107,f176,f177,f104,f108,f613,f634,f105,f113,f109,f875,f110,f939,f522,f115,f111,f114,f1113,f112,f191,f1283,f1287,f1288,f1291,f1292,f1293,f1294,f192,f193,f615,f1719,f1720,f1721,f1722,f636,f1845,f1846,f1847,f1848,f877,f614,f635,f941,f876,f940,f83,f220,f2611,f2612,f2613,f2614,f2635,f2642]) ).
fof(f1107,plain,
( element(zero(any1),any1)
| ~ element(subtract(any1,sK4(x,any1),subtract(any1,zero(any1),sK3(x,any1))),any1)
| ~ spl9_57 ),
inference(duplicate_literal_removal,[],[f1106]) ).
fof(f1106,plain,
( element(zero(any1),any1)
| ~ element(subtract(any1,sK4(x,any1),subtract(any1,zero(any1),sK3(x,any1))),any1)
| ~ element(subtract(any1,sK4(x,any1),subtract(any1,zero(any1),sK3(x,any1))),any1)
| ~ spl9_57 ),
inference(superposition,[],[f93,f1101]) ).
fof(f1101,plain,
( zero(any1) = subtract(any1,subtract(any1,sK4(x,any1),subtract(any1,zero(any1),sK3(x,any1))),subtract(any1,sK4(x,any1),subtract(any1,zero(any1),sK3(x,any1))))
| ~ spl9_57 ),
inference(avatar_component_clause,[],[f1099]) ).
fof(f2650,plain,
( spl9_7
| ~ spl9_13
| ~ spl9_56
| ~ spl9_97 ),
inference(avatar_split_clause,[],[f2643,f2633,f1094,f219,f168]) ).
fof(f1094,plain,
( spl9_56
<=> zero(any1) = subtract(any1,subtract(any1,sK3(x,any1),subtract(any1,zero(any1),sK3(x,any1))),subtract(any1,sK3(x,any1),subtract(any1,zero(any1),sK3(x,any1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_56])]) ).
fof(f2643,plain,
( element(zero(any1),any1)
| ~ spl9_13
| ~ spl9_56
| ~ spl9_97 ),
inference(global_subsumption,[],[f1105,f82,f84,f85,f87,f100,f101,f86,f93,f95,f97,f99,f103,f89,f94,f98,f90,f244,f245,f96,f102,f91,f92,f106,f88,f164,f472,f473,f474,f107,f176,f177,f104,f108,f613,f634,f105,f113,f109,f875,f110,f939,f522,f115,f111,f114,f1113,f112,f191,f1283,f1287,f1288,f1291,f1292,f1293,f1294,f192,f193,f615,f1719,f1720,f1721,f1722,f636,f1845,f1846,f1847,f1848,f877,f614,f635,f941,f876,f940,f83,f220,f2611,f2612,f2613,f2614,f2635,f2642]) ).
fof(f1105,plain,
( element(zero(any1),any1)
| ~ element(subtract(any1,sK3(x,any1),subtract(any1,zero(any1),sK3(x,any1))),any1)
| ~ spl9_56 ),
inference(duplicate_literal_removal,[],[f1104]) ).
fof(f1104,plain,
( element(zero(any1),any1)
| ~ element(subtract(any1,sK3(x,any1),subtract(any1,zero(any1),sK3(x,any1))),any1)
| ~ element(subtract(any1,sK3(x,any1),subtract(any1,zero(any1),sK3(x,any1))),any1)
| ~ spl9_56 ),
inference(superposition,[],[f93,f1096]) ).
fof(f1096,plain,
( zero(any1) = subtract(any1,subtract(any1,sK3(x,any1),subtract(any1,zero(any1),sK3(x,any1))),subtract(any1,sK3(x,any1),subtract(any1,zero(any1),sK3(x,any1))))
| ~ spl9_56 ),
inference(avatar_component_clause,[],[f1094]) ).
fof(f2649,plain,
( spl9_7
| ~ spl9_13
| ~ spl9_97 ),
inference(avatar_split_clause,[],[f2642,f2633,f219,f168]) ).
fof(f2641,plain,
( spl9_7
| ~ spl9_13
| ~ spl9_97 ),
inference(avatar_contradiction_clause,[],[f2640]) ).
fof(f2640,plain,
( $false
| spl9_7
| ~ spl9_13
| ~ spl9_97 ),
inference(subsumption_resolution,[],[f2639,f220]) ).
fof(f2639,plain,
( ~ element(sK2(x,any1,any2),any1)
| spl9_7
| ~ spl9_97 ),
inference(subsumption_resolution,[],[f2638,f170]) ).
fof(f170,plain,
( ~ element(zero(any1),any1)
| spl9_7 ),
inference(avatar_component_clause,[],[f168]) ).
fof(f2636,plain,
( spl9_97
| ~ spl9_13 ),
inference(avatar_split_clause,[],[f2614,f219,f2633]) ).
fof(f2628,plain,
( ~ spl9_17
| spl9_66
| ~ spl9_70 ),
inference(avatar_split_clause,[],[f2553,f1499,f1463,f313]) ).
fof(f2553,plain,
( zero(any1) != subtract(any1,zero(any1),zero(any1))
| spl9_66
| ~ spl9_70 ),
inference(forward_demodulation,[],[f1464,f1501]) ).
fof(f1464,plain,
( zero(any1) != subtract(any1,sK0(x,any1,zero(any2)),sK0(x,any1,zero(any2)))
| spl9_66 ),
inference(avatar_component_clause,[],[f1463]) ).
fof(f2597,plain,
( ~ spl9_1
| ~ spl9_8
| spl9_23
| ~ spl9_25
| ~ spl9_26
| ~ spl9_45 ),
inference(avatar_contradiction_clause,[],[f2596]) ).
fof(f2596,plain,
( $false
| ~ spl9_1
| ~ spl9_8
| spl9_23
| ~ spl9_25
| ~ spl9_26
| ~ spl9_45 ),
inference(global_subsumption,[],[f119,f82,f84,f85,f87,f100,f101,f86,f93,f95,f97,f99,f103,f89,f94,f98,f90,f174,f242,f96,f102,f91,f241,f92,f409,f106,f419,f88,f164,f472,f473,f474,f470,f495,f496,f497,f107,f176,f177,f104,f108,f613,f631,f633,f634,f652,f654,f105,f113,f800,f842,f109,f875,f898,f900,f841,f110,f939,f963,f965,f522,f115,f111,f114,f1113,f112,f368,f1188,f1189,f1190,f1191,f1192,f1193,f1194,f1195,f1187,f1213,f1214,f1215,f1216,f1217,f1218,f1219,f369,f191,f1283,f1285,f1287,f1288,f1291,f1292,f1293,f1294,f192,f193,f615,f1719,f1720,f1721,f1722,f1754,f1756,f1759,f1763,f636,f1845,f1846,f1847,f1848,f1881,f1883,f1886,f1890,f877,f614,f635,f941,f876,f1281,f2288,f2290,f2291,f2292,f2293,f2294,f2295,f2296,f2297,f940,f370,f83,f2546,f845,f843,f2555]) ).
fof(f2555,plain,
( zero(any2) != subtract(any2,apply(x,sK3(x,any1)),apply(x,sK3(x,any1)))
| spl9_23
| ~ spl9_25 ),
inference(forward_demodulation,[],[f388,f409]) ).
fof(f388,plain,
( zero(any2) != subtract(any2,apply(x,sK3(x,any1)),subtract(any2,apply(x,sK3(x,any1)),zero(any2)))
| spl9_23 ),
inference(avatar_component_clause,[],[f387]) ).
fof(f387,plain,
( spl9_23
<=> zero(any2) = subtract(any2,apply(x,sK3(x,any1)),subtract(any2,apply(x,sK3(x,any1)),zero(any2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_23])]) ).
fof(f843,plain,
( ! [X1] :
( subtract(any2,zero(any2),apply(x,sK3(x,any1))) = subtract(any2,X1,subtract(any2,X1,subtract(any2,zero(any2),apply(x,sK3(x,any1)))))
| ~ element(X1,any2) )
| ~ spl9_45 ),
inference(resolution,[],[f800,f94]) ).
fof(f845,plain,
( zero(any2) = subtract(any2,apply(x,sK3(x,any1)),apply(x,sK3(x,any1)))
| ~ spl9_8
| ~ spl9_26
| ~ spl9_45 ),
inference(forward_demodulation,[],[f839,f419]) ).
fof(f839,plain,
( zero(any2) = subtract(any2,subtract(any2,zero(any2),subtract(any2,zero(any2),apply(x,sK3(x,any1)))),subtract(any2,zero(any2),subtract(any2,zero(any2),apply(x,sK3(x,any1)))))
| ~ spl9_8
| ~ spl9_45 ),
inference(resolution,[],[f800,f470]) ).
fof(f2546,plain,
( element(apply(x,sK3(x,any1)),any2)
| ~ spl9_8
| ~ spl9_26
| ~ spl9_45 ),
inference(subsumption_resolution,[],[f2545,f174]) ).
fof(f2545,plain,
( element(apply(x,sK3(x,any1)),any2)
| ~ element(zero(any2),any2)
| ~ spl9_26
| ~ spl9_45 ),
inference(subsumption_resolution,[],[f421,f800]) ).
fof(f421,plain,
( element(apply(x,sK3(x,any1)),any2)
| ~ element(subtract(any2,zero(any2),apply(x,sK3(x,any1))),any2)
| ~ element(zero(any2),any2)
| ~ spl9_26 ),
inference(superposition,[],[f93,f419]) ).
fof(f370,plain,
( ! [X6,X5] :
( ~ morphism(X5,any2,X6)
| injection_2(X5)
| zero(any2) = subtract(any2,sK2(X5,any2,X6),subtract(any2,sK2(X5,any2,X6),zero(any2))) )
| ~ spl9_8 ),
inference(resolution,[],[f241,f97]) ).
fof(f2297,plain,
( ! [X41,X44,X45,X42,X43] :
( subtract(any2,sK7(X41,X42,any2,X43,X44),zero(any2)) = subtract(any2,X45,subtract(any2,X45,subtract(any2,sK7(X41,X42,any2,X43,X44),zero(any2))))
| ~ element(X45,any2)
| element(sK6(X41,X42,any2,X43,X44),X43)
| exact(X41,X42)
| ~ morphism(X42,X43,X44)
| ~ morphism(X41,any2,X43) )
| ~ spl9_8 ),
inference(resolution,[],[f1281,f108]) ).
fof(f2296,plain,
( ! [X40,X38,X39,X36,X37] :
( subtract(any2,sK7(X36,X37,any2,X38,X39),zero(any2)) = subtract(any2,X40,subtract(any2,X40,subtract(any2,sK7(X36,X37,any2,X38,X39),zero(any2))))
| ~ element(X40,any2)
| exact(X36,X37)
| zero(X39) = apply(X37,sK6(X36,X37,any2,X38,X39))
| ~ morphism(X37,X38,X39)
| ~ morphism(X36,any2,X38) )
| ~ spl9_8 ),
inference(resolution,[],[f1281,f109]) ).
fof(f2295,plain,
( ! [X31,X34,X35,X32,X33] :
( subtract(any2,sK7(X31,X32,any2,X33,X34),zero(any2)) = subtract(any2,X35,subtract(any2,X35,subtract(any2,sK7(X31,X32,any2,X33,X34),zero(any2))))
| ~ element(X35,any2)
| exact(X31,X32)
| ~ morphism(X32,X33,X34)
| ~ morphism(X31,any2,X33)
| zero(X33) = subtract(X33,sK6(X31,X32,any2,X33,X34),sK6(X31,X32,any2,X33,X34)) )
| ~ spl9_8 ),
inference(resolution,[],[f1281,f636]) ).
fof(f2294,plain,
( ! [X28,X29,X26,X27,X30] :
( subtract(any2,sK6(X26,X27,X28,any2,X29),zero(any2)) = subtract(any2,X30,subtract(any2,X30,subtract(any2,sK6(X26,X27,X28,any2,X29),zero(any2))))
| ~ element(X30,any2)
| element(sK7(X26,X27,X28,any2,X29),X28)
| exact(X26,X27)
| ~ morphism(X27,any2,X29)
| ~ morphism(X26,X28,any2) )
| ~ spl9_8 ),
inference(resolution,[],[f1281,f108]) ).
fof(f2293,plain,
( ! [X21,X24,X22,X25,X23] :
( subtract(any2,sK6(X21,X22,X23,any2,X24),zero(any2)) = subtract(any2,X25,subtract(any2,X25,subtract(any2,sK6(X21,X22,X23,any2,X24),zero(any2))))
| ~ element(X25,any2)
| sK6(X21,X22,X23,any2,X24) = apply(X21,sK7(X21,X22,X23,any2,X24))
| exact(X21,X22)
| ~ morphism(X22,any2,X24)
| ~ morphism(X21,X23,any2) )
| ~ spl9_8 ),
inference(resolution,[],[f1281,f110]) ).
fof(f2292,plain,
( ! [X18,X19,X16,X17,X20] :
( subtract(any2,sK6(X16,X17,X18,any2,X19),zero(any2)) = subtract(any2,X20,subtract(any2,X20,subtract(any2,sK6(X16,X17,X18,any2,X19),zero(any2))))
| ~ element(X20,any2)
| exact(X16,X17)
| ~ morphism(X17,any2,X19)
| ~ morphism(X16,X18,any2)
| zero(X18) = subtract(X18,sK7(X16,X17,X18,any2,X19),sK7(X16,X17,X18,any2,X19)) )
| ~ spl9_8 ),
inference(resolution,[],[f1281,f615]) ).
fof(f2291,plain,
( ! [X14,X15,X13] :
( subtract(any2,sK2(X13,any2,X14),zero(any2)) = subtract(any2,X15,subtract(any2,X15,subtract(any2,sK2(X13,any2,X14),zero(any2))))
| ~ element(X15,any2)
| injection_2(X13)
| ~ morphism(X13,any2,X14) )
| ~ spl9_8 ),
inference(resolution,[],[f1281,f97]) ).
fof(f2290,plain,
( ! [X10,X11,X12] :
( subtract(any2,sK1(X10,X11,any2),zero(any2)) = subtract(any2,X12,subtract(any2,X12,subtract(any2,sK1(X10,X11,any2),zero(any2))))
| ~ element(X12,any2)
| surjection(X10)
| ~ morphism(X10,X11,any2) )
| ~ spl9_8 ),
inference(resolution,[],[f1281,f95]) ).
fof(f2288,plain,
( ! [X8,X6,X7] :
( subtract(any2,subtract(any2,X6,X7),zero(any2)) = subtract(any2,X8,subtract(any2,X8,subtract(any2,subtract(any2,X6,X7),zero(any2))))
| ~ element(X8,any2)
| ~ element(X7,any2)
| ~ element(X6,any2) )
| ~ spl9_8 ),
inference(resolution,[],[f1281,f93]) ).
fof(f1281,plain,
( ! [X6,X5] :
( ~ element(X6,any2)
| subtract(any2,X6,zero(any2)) = subtract(any2,X5,subtract(any2,X5,subtract(any2,X6,zero(any2))))
| ~ element(X5,any2) )
| ~ spl9_8 ),
inference(resolution,[],[f191,f174]) ).
fof(f1890,plain,
( ! [X200,X198,X199,X197] :
( exact(X197,X198)
| ~ morphism(X198,X199,X200)
| ~ morphism(X197,any2,X199)
| zero(X199) = subtract(X199,sK6(X197,X198,any2,X199,X200),sK6(X197,X198,any2,X199,X200))
| zero(any2) = subtract(any2,subtract(any2,sK7(X197,X198,any2,X199,X200),zero(any2)),subtract(any2,subtract(any2,sK7(X197,X198,any2,X199,X200),zero(any2)),zero(any2))) )
| ~ spl9_8 ),
inference(resolution,[],[f636,f1187]) ).
fof(f1886,plain,
( ! [X181,X184,X182,X183] :
( exact(X181,X182)
| ~ morphism(X182,X183,X184)
| ~ morphism(X181,any2,X183)
| zero(X183) = subtract(X183,sK6(X181,X182,any2,X183,X184),sK6(X181,X182,any2,X183,X184))
| zero(any2) = subtract(any2,subtract(any2,zero(any2),sK7(X181,X182,any2,X183,X184)),subtract(any2,zero(any2),sK7(X181,X182,any2,X183,X184))) )
| ~ spl9_8 ),
inference(resolution,[],[f636,f470]) ).
fof(f1883,plain,
( ! [X170,X171,X168,X169,X167] :
( exact(X167,X168)
| ~ morphism(X168,X169,X170)
| ~ morphism(X167,any2,X169)
| zero(X169) = subtract(X169,sK6(X167,X168,any2,X169,X170),sK6(X167,X168,any2,X169,X170))
| zero(any2) = subtract(any2,subtract(any2,X171,sK7(X167,X168,any2,X169,X170)),subtract(any2,subtract(any2,X171,sK7(X167,X168,any2,X169,X170)),zero(any2)))
| ~ element(X171,any2) )
| ~ spl9_8 ),
inference(resolution,[],[f636,f368]) ).
fof(f1881,plain,
( ! [X162,X160,X161,X159] :
( exact(X159,X160)
| ~ morphism(X160,X161,X162)
| ~ morphism(X159,any2,X161)
| zero(X161) = subtract(X161,sK6(X159,X160,any2,X161,X162),sK6(X159,X160,any2,X161,X162))
| zero(any2) = subtract(any2,sK7(X159,X160,any2,X161,X162),subtract(any2,sK7(X159,X160,any2,X161,X162),zero(any2))) )
| ~ spl9_8 ),
inference(resolution,[],[f636,f241]) ).
fof(f1763,plain,
( ! [X194,X195,X193,X196] :
( exact(X193,X194)
| ~ morphism(X194,any2,X195)
| ~ morphism(X193,X196,any2)
| zero(X196) = subtract(X196,sK7(X193,X194,X196,any2,X195),sK7(X193,X194,X196,any2,X195))
| zero(any2) = subtract(any2,subtract(any2,sK6(X193,X194,X196,any2,X195),zero(any2)),subtract(any2,subtract(any2,sK6(X193,X194,X196,any2,X195),zero(any2)),zero(any2))) )
| ~ spl9_8 ),
inference(resolution,[],[f615,f1187]) ).
fof(f1759,plain,
( ! [X180,X178,X179,X177] :
( exact(X177,X178)
| ~ morphism(X178,any2,X179)
| ~ morphism(X177,X180,any2)
| zero(X180) = subtract(X180,sK7(X177,X178,X180,any2,X179),sK7(X177,X178,X180,any2,X179))
| zero(any2) = subtract(any2,subtract(any2,zero(any2),sK6(X177,X178,X180,any2,X179)),subtract(any2,zero(any2),sK6(X177,X178,X180,any2,X179))) )
| ~ spl9_8 ),
inference(resolution,[],[f615,f470]) ).
fof(f1756,plain,
( ! [X163,X166,X167,X164,X165] :
( exact(X163,X164)
| ~ morphism(X164,any2,X165)
| ~ morphism(X163,X166,any2)
| zero(X166) = subtract(X166,sK7(X163,X164,X166,any2,X165),sK7(X163,X164,X166,any2,X165))
| zero(any2) = subtract(any2,subtract(any2,X167,sK6(X163,X164,X166,any2,X165)),subtract(any2,subtract(any2,X167,sK6(X163,X164,X166,any2,X165)),zero(any2)))
| ~ element(X167,any2) )
| ~ spl9_8 ),
inference(resolution,[],[f615,f368]) ).
fof(f1754,plain,
( ! [X155,X158,X156,X157] :
( exact(X155,X156)
| ~ morphism(X156,any2,X157)
| ~ morphism(X155,X158,any2)
| zero(X158) = subtract(X158,sK7(X155,X156,X158,any2,X157),sK7(X155,X156,X158,any2,X157))
| zero(any2) = subtract(any2,sK6(X155,X156,X158,any2,X157),subtract(any2,sK6(X155,X156,X158,any2,X157),zero(any2))) )
| ~ spl9_8 ),
inference(resolution,[],[f615,f241]) ).
fof(f1285,plain,
( ! [X16,X17] :
( ~ element(X16,any2)
| subtract(any2,X17,subtract(any2,zero(any2),apply(x,sK3(x,any1)))) = subtract(any2,X16,subtract(any2,X16,subtract(any2,X17,subtract(any2,zero(any2),apply(x,sK3(x,any1))))))
| ~ element(X17,any2) )
| ~ spl9_45 ),
inference(resolution,[],[f191,f800]) ).
fof(f369,plain,
( ! [X3,X4] :
( ~ morphism(X3,X4,any2)
| surjection(X3)
| zero(any2) = subtract(any2,sK1(X3,X4,any2),subtract(any2,sK1(X3,X4,any2),zero(any2))) )
| ~ spl9_8 ),
inference(resolution,[],[f241,f95]) ).
fof(f1219,plain,
( ! [X21,X19,X22,X20] :
( zero(any2) = subtract(any2,subtract(any2,sK7(X19,X20,any2,X21,X22),zero(any2)),subtract(any2,subtract(any2,sK7(X19,X20,any2,X21,X22),zero(any2)),zero(any2)))
| element(sK6(X19,X20,any2,X21,X22),X21)
| exact(X19,X20)
| ~ morphism(X20,X21,X22)
| ~ morphism(X19,any2,X21) )
| ~ spl9_8 ),
inference(resolution,[],[f1187,f108]) ).
fof(f1218,plain,
( ! [X18,X16,X17,X15] :
( zero(any2) = subtract(any2,subtract(any2,sK7(X15,X16,any2,X17,X18),zero(any2)),subtract(any2,subtract(any2,sK7(X15,X16,any2,X17,X18),zero(any2)),zero(any2)))
| exact(X15,X16)
| zero(X18) = apply(X16,sK6(X15,X16,any2,X17,X18))
| ~ morphism(X16,X17,X18)
| ~ morphism(X15,any2,X17) )
| ~ spl9_8 ),
inference(resolution,[],[f1187,f109]) ).
fof(f1217,plain,
( ! [X11,X14,X12,X13] :
( zero(any2) = subtract(any2,subtract(any2,sK6(X11,X12,X13,any2,X14),zero(any2)),subtract(any2,subtract(any2,sK6(X11,X12,X13,any2,X14),zero(any2)),zero(any2)))
| element(sK7(X11,X12,X13,any2,X14),X13)
| exact(X11,X12)
| ~ morphism(X12,any2,X14)
| ~ morphism(X11,X13,any2) )
| ~ spl9_8 ),
inference(resolution,[],[f1187,f108]) ).
fof(f1216,plain,
( ! [X10,X8,X9,X7] :
( zero(any2) = subtract(any2,subtract(any2,sK6(X7,X8,X9,any2,X10),zero(any2)),subtract(any2,subtract(any2,sK6(X7,X8,X9,any2,X10),zero(any2)),zero(any2)))
| sK6(X7,X8,X9,any2,X10) = apply(X7,sK7(X7,X8,X9,any2,X10))
| exact(X7,X8)
| ~ morphism(X8,any2,X10)
| ~ morphism(X7,X9,any2) )
| ~ spl9_8 ),
inference(resolution,[],[f1187,f110]) ).
fof(f1215,plain,
( ! [X6,X5] :
( zero(any2) = subtract(any2,subtract(any2,sK2(X5,any2,X6),zero(any2)),subtract(any2,subtract(any2,sK2(X5,any2,X6),zero(any2)),zero(any2)))
| injection_2(X5)
| ~ morphism(X5,any2,X6) )
| ~ spl9_8 ),
inference(resolution,[],[f1187,f97]) ).
fof(f1214,plain,
( ! [X3,X4] :
( zero(any2) = subtract(any2,subtract(any2,sK1(X3,X4,any2),zero(any2)),subtract(any2,subtract(any2,sK1(X3,X4,any2),zero(any2)),zero(any2)))
| surjection(X3)
| ~ morphism(X3,X4,any2) )
| ~ spl9_8 ),
inference(resolution,[],[f1187,f95]) ).
fof(f1213,plain,
( ! [X2,X1] :
( zero(any2) = subtract(any2,subtract(any2,subtract(any2,X1,X2),zero(any2)),subtract(any2,subtract(any2,subtract(any2,X1,X2),zero(any2)),zero(any2)))
| ~ element(X2,any2)
| ~ element(X1,any2) )
| ~ spl9_8 ),
inference(resolution,[],[f1187,f93]) ).
fof(f1187,plain,
( ! [X3] :
( ~ element(X3,any2)
| zero(any2) = subtract(any2,subtract(any2,X3,zero(any2)),subtract(any2,subtract(any2,X3,zero(any2)),zero(any2))) )
| ~ spl9_8 ),
inference(resolution,[],[f368,f174]) ).
fof(f1195,plain,
( ! [X31,X29,X32,X30,X33] :
( zero(any2) = subtract(any2,subtract(any2,X29,sK7(X30,X31,any2,X32,X33)),subtract(any2,subtract(any2,X29,sK7(X30,X31,any2,X32,X33)),zero(any2)))
| ~ element(X29,any2)
| element(sK6(X30,X31,any2,X32,X33),X32)
| exact(X30,X31)
| ~ morphism(X31,X32,X33)
| ~ morphism(X30,any2,X32) )
| ~ spl9_8 ),
inference(resolution,[],[f368,f108]) ).
fof(f1194,plain,
( ! [X28,X26,X27,X24,X25] :
( zero(any2) = subtract(any2,subtract(any2,X24,sK7(X25,X26,any2,X27,X28)),subtract(any2,subtract(any2,X24,sK7(X25,X26,any2,X27,X28)),zero(any2)))
| ~ element(X24,any2)
| exact(X25,X26)
| zero(X28) = apply(X26,sK6(X25,X26,any2,X27,X28))
| ~ morphism(X26,X27,X28)
| ~ morphism(X25,any2,X27) )
| ~ spl9_8 ),
inference(resolution,[],[f368,f109]) ).
fof(f1193,plain,
( ! [X21,X19,X22,X23,X20] :
( zero(any2) = subtract(any2,subtract(any2,X19,sK6(X20,X21,X22,any2,X23)),subtract(any2,subtract(any2,X19,sK6(X20,X21,X22,any2,X23)),zero(any2)))
| ~ element(X19,any2)
| element(sK7(X20,X21,X22,any2,X23),X22)
| exact(X20,X21)
| ~ morphism(X21,any2,X23)
| ~ morphism(X20,X22,any2) )
| ~ spl9_8 ),
inference(resolution,[],[f368,f108]) ).
fof(f1192,plain,
( ! [X18,X16,X14,X17,X15] :
( zero(any2) = subtract(any2,subtract(any2,X14,sK6(X15,X16,X17,any2,X18)),subtract(any2,subtract(any2,X14,sK6(X15,X16,X17,any2,X18)),zero(any2)))
| ~ element(X14,any2)
| sK6(X15,X16,X17,any2,X18) = apply(X15,sK7(X15,X16,X17,any2,X18))
| exact(X15,X16)
| ~ morphism(X16,any2,X18)
| ~ morphism(X15,X17,any2) )
| ~ spl9_8 ),
inference(resolution,[],[f368,f110]) ).
fof(f1191,plain,
( ! [X11,X12,X13] :
( zero(any2) = subtract(any2,subtract(any2,X11,sK2(X12,any2,X13)),subtract(any2,subtract(any2,X11,sK2(X12,any2,X13)),zero(any2)))
| ~ element(X11,any2)
| injection_2(X12)
| ~ morphism(X12,any2,X13) )
| ~ spl9_8 ),
inference(resolution,[],[f368,f97]) ).
fof(f1190,plain,
( ! [X10,X8,X9] :
( zero(any2) = subtract(any2,subtract(any2,X8,sK1(X9,X10,any2)),subtract(any2,subtract(any2,X8,sK1(X9,X10,any2)),zero(any2)))
| ~ element(X8,any2)
| surjection(X9)
| ~ morphism(X9,X10,any2) )
| ~ spl9_8 ),
inference(resolution,[],[f368,f95]) ).
fof(f1189,plain,
( ! [X6,X7,X5] :
( zero(any2) = subtract(any2,subtract(any2,X5,subtract(any2,X6,X7)),subtract(any2,subtract(any2,X5,subtract(any2,X6,X7)),zero(any2)))
| ~ element(X5,any2)
| ~ element(X7,any2)
| ~ element(X6,any2) )
| ~ spl9_8 ),
inference(resolution,[],[f368,f93]) ).
fof(f1188,plain,
( ! [X4] :
( zero(any2) = subtract(any2,subtract(any2,X4,subtract(any2,zero(any2),apply(x,sK3(x,any1)))),subtract(any2,subtract(any2,X4,subtract(any2,zero(any2),apply(x,sK3(x,any1)))),zero(any2)))
| ~ element(X4,any2) )
| ~ spl9_8
| ~ spl9_45 ),
inference(resolution,[],[f368,f800]) ).
fof(f368,plain,
( ! [X2,X1] :
( ~ element(X2,any2)
| zero(any2) = subtract(any2,subtract(any2,X1,X2),subtract(any2,subtract(any2,X1,X2),zero(any2)))
| ~ element(X1,any2) )
| ~ spl9_8 ),
inference(resolution,[],[f241,f93]) ).
fof(f965,plain,
( ! [X113,X114,X115,X112] :
( sK6(X112,X113,X114,any2,X115) = apply(X112,sK7(X112,X113,X114,any2,X115))
| exact(X112,X113)
| ~ morphism(X113,any2,X115)
| ~ morphism(X112,X114,any2)
| zero(any2) = subtract(any2,sK6(X112,X113,X114,any2,X115),subtract(any2,sK6(X112,X113,X114,any2,X115),zero(any2))) )
| ~ spl9_8 ),
inference(resolution,[],[f110,f241]) ).
fof(f963,plain,
( ! [X106,X107,X104,X105] :
( sK6(X104,X105,X106,any2,X107) = apply(X104,sK7(X104,X105,X106,any2,X107))
| exact(X104,X105)
| ~ morphism(X105,any2,X107)
| ~ morphism(X104,X106,any2)
| zero(any2) = subtract(any2,subtract(any2,zero(any2),sK6(X104,X105,X106,any2,X107)),subtract(any2,zero(any2),sK6(X104,X105,X106,any2,X107))) )
| ~ spl9_8 ),
inference(resolution,[],[f110,f470]) ).
fof(f841,plain,
( zero(any2) = subtract(any2,subtract(any2,zero(any2),apply(x,sK3(x,any1))),subtract(any2,subtract(any2,zero(any2),apply(x,sK3(x,any1))),zero(any2)))
| ~ spl9_8
| ~ spl9_45 ),
inference(resolution,[],[f800,f241]) ).
fof(f900,plain,
( ! [X111,X108,X109,X110] :
( exact(X108,X109)
| zero(X110) = apply(X109,sK6(X108,X109,any2,X111,X110))
| ~ morphism(X109,X111,X110)
| ~ morphism(X108,any2,X111)
| zero(any2) = subtract(any2,sK7(X108,X109,any2,X111,X110),subtract(any2,sK7(X108,X109,any2,X111,X110),zero(any2))) )
| ~ spl9_8 ),
inference(resolution,[],[f109,f241]) ).
fof(f898,plain,
( ! [X101,X102,X103,X100] :
( exact(X100,X101)
| zero(X102) = apply(X101,sK6(X100,X101,any2,X103,X102))
| ~ morphism(X101,X103,X102)
| ~ morphism(X100,any2,X103)
| zero(any2) = subtract(any2,subtract(any2,zero(any2),sK7(X100,X101,any2,X103,X102)),subtract(any2,zero(any2),sK7(X100,X101,any2,X103,X102))) )
| ~ spl9_8 ),
inference(resolution,[],[f109,f470]) ).
fof(f842,plain,
( ! [X0] :
( ~ element(X0,any2)
| zero(any2) = subtract(any2,subtract(any2,subtract(any2,zero(any2),apply(x,sK3(x,any1))),X0),subtract(any2,subtract(any2,zero(any2),apply(x,sK3(x,any1))),X0)) )
| ~ spl9_45 ),
inference(resolution,[],[f800,f164]) ).
fof(f800,plain,
( element(subtract(any2,zero(any2),apply(x,sK3(x,any1))),any2)
| ~ spl9_45 ),
inference(avatar_component_clause,[],[f798]) ).
fof(f654,plain,
( ! [X90,X88,X89,X87] :
( element(sK7(X87,X88,X89,any2,X90),X89)
| exact(X87,X88)
| ~ morphism(X88,any2,X90)
| ~ morphism(X87,X89,any2)
| zero(any2) = subtract(any2,sK6(X87,X88,X89,any2,X90),subtract(any2,sK6(X87,X88,X89,any2,X90),zero(any2))) )
| ~ spl9_8 ),
inference(resolution,[],[f108,f241]) ).
fof(f652,plain,
( ! [X82,X80,X81,X79] :
( element(sK7(X79,X80,X81,any2,X82),X81)
| exact(X79,X80)
| ~ morphism(X80,any2,X82)
| ~ morphism(X79,X81,any2)
| zero(any2) = subtract(any2,subtract(any2,zero(any2),sK6(X79,X80,X81,any2,X82)),subtract(any2,zero(any2),sK6(X79,X80,X81,any2,X82))) )
| ~ spl9_8 ),
inference(resolution,[],[f108,f470]) ).
fof(f633,plain,
( ! [X90,X88,X89,X87] :
( element(sK6(X87,X88,any2,X89,X90),X89)
| exact(X87,X88)
| ~ morphism(X88,X89,X90)
| ~ morphism(X87,any2,X89)
| zero(any2) = subtract(any2,sK7(X87,X88,any2,X89,X90),subtract(any2,sK7(X87,X88,any2,X89,X90),zero(any2))) )
| ~ spl9_8 ),
inference(resolution,[],[f108,f241]) ).
fof(f631,plain,
( ! [X82,X80,X81,X79] :
( element(sK6(X79,X80,any2,X81,X82),X81)
| exact(X79,X80)
| ~ morphism(X80,X81,X82)
| ~ morphism(X79,any2,X81)
| zero(any2) = subtract(any2,subtract(any2,zero(any2),sK7(X79,X80,any2,X81,X82)),subtract(any2,zero(any2),sK7(X79,X80,any2,X81,X82))) )
| ~ spl9_8 ),
inference(resolution,[],[f108,f470]) ).
fof(f497,plain,
( ! [X6,X5] :
( zero(any2) = subtract(any2,subtract(any2,zero(any2),sK2(X5,any2,X6)),subtract(any2,zero(any2),sK2(X5,any2,X6)))
| injection_2(X5)
| ~ morphism(X5,any2,X6) )
| ~ spl9_8 ),
inference(resolution,[],[f470,f97]) ).
fof(f496,plain,
( ! [X3,X4] :
( zero(any2) = subtract(any2,subtract(any2,zero(any2),sK1(X3,X4,any2)),subtract(any2,zero(any2),sK1(X3,X4,any2)))
| surjection(X3)
| ~ morphism(X3,X4,any2) )
| ~ spl9_8 ),
inference(resolution,[],[f470,f95]) ).
fof(f495,plain,
( ! [X2,X1] :
( zero(any2) = subtract(any2,subtract(any2,zero(any2),subtract(any2,X1,X2)),subtract(any2,zero(any2),subtract(any2,X1,X2)))
| ~ element(X2,any2)
| ~ element(X1,any2) )
| ~ spl9_8 ),
inference(resolution,[],[f470,f93]) ).
fof(f470,plain,
( ! [X3] :
( ~ element(X3,any2)
| zero(any2) = subtract(any2,subtract(any2,zero(any2),X3),subtract(any2,zero(any2),X3)) )
| ~ spl9_8 ),
inference(resolution,[],[f164,f174]) ).
fof(f419,plain,
( apply(x,sK3(x,any1)) = subtract(any2,zero(any2),subtract(any2,zero(any2),apply(x,sK3(x,any1))))
| ~ spl9_26 ),
inference(avatar_component_clause,[],[f417]) ).
fof(f417,plain,
( spl9_26
<=> apply(x,sK3(x,any1)) = subtract(any2,zero(any2),subtract(any2,zero(any2),apply(x,sK3(x,any1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_26])]) ).
fof(f409,plain,
( apply(x,sK3(x,any1)) = subtract(any2,apply(x,sK3(x,any1)),zero(any2))
| ~ spl9_25 ),
inference(avatar_component_clause,[],[f407]) ).
fof(f407,plain,
( spl9_25
<=> apply(x,sK3(x,any1)) = subtract(any2,apply(x,sK3(x,any1)),zero(any2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_25])]) ).
fof(f241,plain,
( ! [X0] :
( ~ element(X0,any2)
| zero(any2) = subtract(any2,X0,subtract(any2,X0,zero(any2))) )
| ~ spl9_8 ),
inference(resolution,[],[f174,f94]) ).
fof(f242,plain,
( zero(any2) = subtract(any2,zero(any2),zero(any2))
| ~ spl9_8 ),
inference(resolution,[],[f174,f85]) ).
fof(f174,plain,
( element(zero(any2),any2)
| ~ spl9_8 ),
inference(avatar_component_clause,[],[f172]) ).
fof(f172,plain,
( spl9_8
<=> element(zero(any2),any2) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_8])]) ).
fof(f2595,plain,
( spl9_2
| ~ spl9_8
| spl9_23
| ~ spl9_25
| ~ spl9_26
| ~ spl9_45 ),
inference(avatar_contradiction_clause,[],[f2594]) ).
fof(f2594,plain,
( $false
| spl9_2
| ~ spl9_8
| spl9_23
| ~ spl9_25
| ~ spl9_26
| ~ spl9_45 ),
inference(global_subsumption,[],[f122,f82,f84,f85,f87,f100,f101,f86,f93,f95,f97,f99,f103,f89,f94,f98,f90,f174,f242,f96,f102,f91,f241,f92,f409,f106,f419,f88,f164,f472,f473,f474,f470,f495,f496,f497,f107,f176,f177,f104,f108,f613,f631,f633,f634,f652,f654,f105,f113,f800,f842,f109,f875,f898,f900,f841,f110,f939,f963,f965,f522,f115,f111,f114,f1113,f112,f368,f1188,f1189,f1190,f1191,f1192,f1193,f1194,f1195,f1187,f1213,f1214,f1215,f1216,f1217,f1218,f1219,f369,f191,f1283,f1285,f1287,f1288,f1291,f1292,f1293,f1294,f192,f193,f615,f1719,f1720,f1721,f1722,f1754,f1756,f1759,f1763,f636,f1845,f1846,f1847,f1848,f1881,f1883,f1886,f1890,f877,f614,f635,f941,f876,f1281,f2288,f2290,f2291,f2292,f2293,f2294,f2295,f2296,f2297,f940,f370,f83,f2546,f845,f843,f2555]) ).
fof(f2593,plain,
( spl9_2
| ~ spl9_3
| ~ spl9_8
| spl9_23
| ~ spl9_25
| ~ spl9_26
| ~ spl9_45 ),
inference(avatar_contradiction_clause,[],[f2592]) ).
fof(f2592,plain,
( $false
| spl9_2
| ~ spl9_3
| ~ spl9_8
| spl9_23
| ~ spl9_25
| ~ spl9_26
| ~ spl9_45 ),
inference(global_subsumption,[],[f215,f82,f84,f85,f87,f100,f101,f86,f93,f95,f97,f99,f103,f89,f94,f98,f90,f174,f242,f96,f102,f91,f241,f92,f409,f106,f419,f88,f164,f472,f473,f474,f470,f495,f496,f497,f107,f176,f177,f104,f108,f613,f631,f633,f634,f652,f654,f105,f113,f800,f842,f109,f875,f898,f900,f841,f110,f939,f963,f965,f522,f115,f111,f114,f1113,f112,f368,f1188,f1189,f1190,f1191,f1192,f1193,f1194,f1195,f1187,f1213,f1214,f1215,f1216,f1217,f1218,f1219,f369,f191,f1283,f1285,f1287,f1288,f1291,f1292,f1293,f1294,f192,f193,f615,f1719,f1720,f1721,f1722,f1754,f1756,f1759,f1763,f636,f1845,f1846,f1847,f1848,f1881,f1883,f1886,f1890,f877,f614,f635,f941,f876,f1281,f2288,f2290,f2291,f2292,f2293,f2294,f2295,f2296,f2297,f940,f370,f83,f2546,f845,f843,f2555]) ).
fof(f215,plain,
( injection(x)
| spl9_2
| ~ spl9_3 ),
inference(global_subsumption,[],[f162,f88,f90,f91,f92,f96,f102,f107,f106,f105,f104,f112,f111,f110,f109,f108,f114,f113,f115,f82,f84,f85,f87,f100,f122,f101,f86,f93,f164,f95,f176,f97,f177,f99,f103,f89,f94,f191,f192,f193,f98,f83,f213]) ).
fof(f213,plain,
( ~ injection_2(x)
| spl9_2 ),
inference(global_subsumption,[],[f88,f90,f91,f92,f96,f102,f107,f106,f105,f104,f112,f111,f110,f109,f108,f114,f113,f115,f82,f84,f85,f87,f100,f122,f101,f86,f93,f164,f95,f176,f97,f177,f99,f103,f89,f94,f191,f192,f193,f98,f83]) ).
fof(f2591,plain,
( spl9_5
| ~ spl9_8
| spl9_23
| ~ spl9_25
| ~ spl9_26
| ~ spl9_45 ),
inference(avatar_contradiction_clause,[],[f2590]) ).
fof(f2590,plain,
( $false
| spl9_5
| ~ spl9_8
| spl9_23
| ~ spl9_25
| ~ spl9_26
| ~ spl9_45 ),
inference(global_subsumption,[],[f140,f82,f84,f85,f87,f100,f101,f86,f93,f95,f97,f99,f103,f89,f94,f98,f90,f174,f242,f96,f102,f91,f241,f92,f409,f106,f419,f88,f164,f472,f473,f474,f470,f495,f496,f497,f107,f176,f177,f104,f108,f613,f631,f633,f634,f652,f654,f105,f113,f800,f842,f109,f875,f898,f900,f841,f110,f939,f963,f965,f522,f115,f111,f114,f1113,f112,f368,f1188,f1189,f1190,f1191,f1192,f1193,f1194,f1195,f1187,f1213,f1214,f1215,f1216,f1217,f1218,f1219,f369,f191,f1283,f1285,f1287,f1288,f1291,f1292,f1293,f1294,f192,f193,f615,f1719,f1720,f1721,f1722,f1754,f1756,f1759,f1763,f636,f1845,f1846,f1847,f1848,f1881,f1883,f1886,f1890,f877,f614,f635,f941,f876,f1281,f2288,f2290,f2291,f2292,f2293,f2294,f2295,f2296,f2297,f940,f370,f83,f2546,f845,f843,f2555]) ).
fof(f140,plain,
( ~ element(sK3(x,any1),any1)
| spl9_5 ),
inference(avatar_component_clause,[],[f139]) ).
fof(f139,plain,
( spl9_5
<=> element(sK3(x,any1),any1) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_5])]) ).
fof(f2589,plain,
( ~ spl9_3
| spl9_5
| ~ spl9_8
| spl9_23
| ~ spl9_25
| ~ spl9_26
| ~ spl9_45 ),
inference(avatar_contradiction_clause,[],[f2588]) ).
fof(f2588,plain,
( $false
| ~ spl9_3
| spl9_5
| ~ spl9_8
| spl9_23
| ~ spl9_25
| ~ spl9_26
| ~ spl9_45 ),
inference(global_subsumption,[],[f160,f82,f84,f85,f87,f100,f101,f86,f93,f95,f97,f99,f103,f89,f94,f98,f90,f174,f242,f96,f102,f91,f241,f92,f409,f106,f419,f88,f164,f472,f473,f474,f470,f495,f496,f497,f107,f176,f177,f104,f108,f613,f631,f633,f634,f652,f654,f105,f113,f800,f842,f109,f875,f898,f900,f841,f110,f939,f963,f965,f522,f115,f111,f114,f1113,f112,f368,f1188,f1189,f1190,f1191,f1192,f1193,f1194,f1195,f1187,f1213,f1214,f1215,f1216,f1217,f1218,f1219,f369,f191,f1283,f1285,f1287,f1288,f1291,f1292,f1293,f1294,f192,f193,f615,f1719,f1720,f1721,f1722,f1754,f1756,f1759,f1763,f636,f1845,f1846,f1847,f1848,f1881,f1883,f1886,f1890,f877,f614,f635,f941,f876,f1281,f2288,f2290,f2291,f2292,f2293,f2294,f2295,f2296,f2297,f940,f370,f83,f2546,f845,f843,f2555]) ).
fof(f160,plain,
( ~ injection_2(x)
| ~ spl9_3
| spl9_5 ),
inference(global_subsumption,[],[f86,f88,f90,f89,f91,f92,f93,f94,f96,f95,f99,f98,f97,f103,f102,f101,f107,f106,f105,f104,f112,f111,f110,f109,f108,f114,f113,f115,f82,f84,f128,f85,f87,f130,f100,f136,f140,f83]) ).
fof(f2587,plain,
( ~ spl9_3
| spl9_5
| ~ spl9_8
| spl9_23
| ~ spl9_25
| ~ spl9_26
| ~ spl9_45 ),
inference(avatar_contradiction_clause,[],[f2586]) ).
fof(f2586,plain,
( $false
| ~ spl9_3
| spl9_5
| ~ spl9_8
| spl9_23
| ~ spl9_25
| ~ spl9_26
| ~ spl9_45 ),
inference(global_subsumption,[],[f161,f82,f84,f85,f87,f100,f101,f86,f93,f95,f97,f99,f103,f89,f94,f98,f90,f174,f242,f96,f102,f91,f241,f92,f409,f106,f419,f88,f164,f472,f473,f474,f470,f495,f496,f497,f107,f176,f177,f104,f108,f613,f631,f633,f634,f652,f654,f105,f113,f800,f842,f109,f875,f898,f900,f841,f110,f939,f963,f965,f522,f115,f111,f114,f1113,f112,f368,f1188,f1189,f1190,f1191,f1192,f1193,f1194,f1195,f1187,f1213,f1214,f1215,f1216,f1217,f1218,f1219,f369,f191,f1283,f1285,f1287,f1288,f1291,f1292,f1293,f1294,f192,f193,f615,f1719,f1720,f1721,f1722,f1754,f1756,f1759,f1763,f636,f1845,f1846,f1847,f1848,f1881,f1883,f1886,f1890,f877,f614,f635,f941,f876,f1281,f2288,f2290,f2291,f2292,f2293,f2294,f2295,f2296,f2297,f940,f370,f83,f2546,f845,f843,f2555]) ).
fof(f161,plain,
( injection(x)
| ~ spl9_3
| spl9_5 ),
inference(global_subsumption,[],[f86,f88,f90,f89,f91,f92,f93,f94,f96,f95,f99,f98,f97,f103,f102,f101,f107,f106,f105,f104,f112,f111,f110,f109,f108,f114,f113,f115,f82,f84,f128,f85,f87,f130,f100,f140,f83,f160,f136]) ).
fof(f2585,plain,
( ~ spl9_3
| spl9_5
| ~ spl9_8
| spl9_23
| ~ spl9_25
| ~ spl9_26
| ~ spl9_45 ),
inference(avatar_contradiction_clause,[],[f2584]) ).
fof(f2584,plain,
( $false
| ~ spl9_3
| spl9_5
| ~ spl9_8
| spl9_23
| ~ spl9_25
| ~ spl9_26
| ~ spl9_45 ),
inference(global_subsumption,[],[f239,f82,f84,f85,f87,f100,f101,f86,f93,f95,f97,f99,f103,f89,f94,f98,f90,f174,f242,f96,f102,f91,f241,f92,f409,f106,f419,f88,f164,f472,f473,f474,f470,f495,f496,f497,f107,f176,f177,f104,f108,f613,f631,f633,f634,f652,f654,f105,f113,f800,f842,f109,f875,f898,f900,f841,f110,f939,f963,f965,f522,f115,f111,f114,f1113,f112,f368,f1188,f1189,f1190,f1191,f1192,f1193,f1194,f1195,f1187,f1213,f1214,f1215,f1216,f1217,f1218,f1219,f369,f191,f1283,f1285,f1287,f1288,f1291,f1292,f1293,f1294,f192,f193,f615,f1719,f1720,f1721,f1722,f1754,f1756,f1759,f1763,f636,f1845,f1846,f1847,f1848,f1881,f1883,f1886,f1890,f877,f614,f635,f941,f876,f1281,f2288,f2290,f2291,f2292,f2293,f2294,f2295,f2296,f2297,f940,f370,f83,f2546,f845,f843,f2555]) ).
fof(f239,plain,
( ~ injection_2(x)
| ~ spl9_3
| spl9_5 ),
inference(global_subsumption,[],[f88,f90,f91,f92,f96,f102,f107,f106,f105,f104,f112,f111,f110,f109,f108,f114,f113,f115,f82,f84,f128,f85,f87,f130,f100,f160,f161,f140,f101,f86,f93,f164,f163,f95,f176,f97,f177,f99,f103,f165,f178,f179,f180,f89,f181,f94,f190,f191,f192,f193,f98,f194,f162,f136,f83]) ).
fof(f2583,plain,
( spl9_6
| ~ spl9_8
| spl9_23
| ~ spl9_25
| ~ spl9_26
| ~ spl9_45 ),
inference(avatar_contradiction_clause,[],[f2582]) ).
fof(f2582,plain,
( $false
| spl9_6
| ~ spl9_8
| spl9_23
| ~ spl9_25
| ~ spl9_26
| ~ spl9_45 ),
inference(global_subsumption,[],[f146,f82,f84,f85,f87,f100,f101,f86,f93,f95,f97,f99,f103,f89,f94,f98,f90,f174,f242,f96,f102,f91,f241,f92,f409,f106,f419,f88,f164,f472,f473,f474,f470,f495,f496,f497,f107,f176,f177,f104,f108,f613,f631,f633,f634,f652,f654,f105,f113,f800,f842,f109,f875,f898,f900,f841,f110,f939,f963,f965,f522,f115,f111,f114,f1113,f112,f368,f1188,f1189,f1190,f1191,f1192,f1193,f1194,f1195,f1187,f1213,f1214,f1215,f1216,f1217,f1218,f1219,f369,f191,f1283,f1285,f1287,f1288,f1291,f1292,f1293,f1294,f192,f193,f615,f1719,f1720,f1721,f1722,f1754,f1756,f1759,f1763,f636,f1845,f1846,f1847,f1848,f1881,f1883,f1886,f1890,f877,f614,f635,f941,f876,f1281,f2288,f2290,f2291,f2292,f2293,f2294,f2295,f2296,f2297,f940,f370,f83,f2546,f845,f843,f2555]) ).
fof(f146,plain,
( zero(any1) != subtract(any1,sK3(x,any1),sK3(x,any1))
| spl9_6 ),
inference(avatar_component_clause,[],[f145]) ).
fof(f145,plain,
( spl9_6
<=> zero(any1) = subtract(any1,sK3(x,any1),sK3(x,any1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_6])]) ).
fof(f2581,plain,
( spl9_7
| ~ spl9_8
| spl9_23
| ~ spl9_25
| ~ spl9_26
| ~ spl9_45 ),
inference(avatar_contradiction_clause,[],[f2580]) ).
fof(f2580,plain,
( $false
| spl9_7
| ~ spl9_8
| spl9_23
| ~ spl9_25
| ~ spl9_26
| ~ spl9_45 ),
inference(global_subsumption,[],[f170,f82,f84,f85,f87,f100,f101,f86,f93,f95,f97,f99,f103,f89,f94,f98,f90,f174,f242,f96,f102,f91,f241,f92,f409,f106,f419,f88,f164,f472,f473,f474,f470,f495,f496,f497,f107,f176,f177,f104,f108,f613,f631,f633,f634,f652,f654,f105,f113,f800,f842,f109,f875,f898,f900,f841,f110,f939,f963,f965,f522,f115,f111,f114,f1113,f112,f368,f1188,f1189,f1190,f1191,f1192,f1193,f1194,f1195,f1187,f1213,f1214,f1215,f1216,f1217,f1218,f1219,f369,f191,f1283,f1285,f1287,f1288,f1291,f1292,f1293,f1294,f192,f193,f615,f1719,f1720,f1721,f1722,f1754,f1756,f1759,f1763,f636,f1845,f1846,f1847,f1848,f1881,f1883,f1886,f1890,f877,f614,f635,f941,f876,f1281,f2288,f2290,f2291,f2292,f2293,f2294,f2295,f2296,f2297,f940,f370,f83,f2546,f845,f843,f2555]) ).
fof(f2579,plain,
( ~ spl9_8
| ~ spl9_11
| spl9_23
| ~ spl9_25
| ~ spl9_26
| ~ spl9_45 ),
inference(avatar_contradiction_clause,[],[f2578]) ).
fof(f2578,plain,
( $false
| ~ spl9_8
| ~ spl9_11
| spl9_23
| ~ spl9_25
| ~ spl9_26
| ~ spl9_45 ),
inference(global_subsumption,[],[f199,f82,f84,f85,f87,f100,f101,f86,f93,f95,f97,f99,f103,f89,f94,f98,f90,f174,f242,f96,f102,f91,f241,f92,f409,f106,f419,f88,f164,f472,f473,f474,f470,f495,f496,f497,f107,f176,f177,f104,f108,f613,f631,f633,f634,f652,f654,f105,f113,f800,f842,f109,f875,f898,f900,f841,f110,f939,f963,f965,f522,f115,f111,f114,f1113,f112,f368,f1188,f1189,f1190,f1191,f1192,f1193,f1194,f1195,f1187,f1213,f1214,f1215,f1216,f1217,f1218,f1219,f369,f191,f1283,f1285,f1287,f1288,f1291,f1292,f1293,f1294,f192,f193,f615,f1719,f1720,f1721,f1722,f1754,f1756,f1759,f1763,f636,f1845,f1846,f1847,f1848,f1881,f1883,f1886,f1890,f877,f614,f635,f941,f876,f1281,f2288,f2290,f2291,f2292,f2293,f2294,f2295,f2296,f2297,f940,f370,f83,f2546,f845,f843,f2555]) ).
fof(f2577,plain,
( ~ spl9_8
| spl9_12
| spl9_23
| ~ spl9_25
| ~ spl9_26
| ~ spl9_45 ),
inference(avatar_contradiction_clause,[],[f2576]) ).
fof(f2576,plain,
( $false
| ~ spl9_8
| spl9_12
| spl9_23
| ~ spl9_25
| ~ spl9_26
| ~ spl9_45 ),
inference(global_subsumption,[],[f210,f82,f84,f85,f87,f100,f101,f86,f93,f95,f97,f99,f103,f89,f94,f98,f90,f174,f242,f96,f102,f91,f241,f92,f409,f106,f419,f88,f164,f472,f473,f474,f470,f495,f496,f497,f107,f176,f177,f104,f108,f613,f631,f633,f634,f652,f654,f105,f113,f800,f842,f109,f875,f898,f900,f841,f110,f939,f963,f965,f522,f115,f111,f114,f1113,f112,f368,f1188,f1189,f1190,f1191,f1192,f1193,f1194,f1195,f1187,f1213,f1214,f1215,f1216,f1217,f1218,f1219,f369,f191,f1283,f1285,f1287,f1288,f1291,f1292,f1293,f1294,f192,f193,f615,f1719,f1720,f1721,f1722,f1754,f1756,f1759,f1763,f636,f1845,f1846,f1847,f1848,f1881,f1883,f1886,f1890,f877,f614,f635,f941,f876,f1281,f2288,f2290,f2291,f2292,f2293,f2294,f2295,f2296,f2297,f940,f370,f83,f2546,f845,f843,f2555]) ).
fof(f210,plain,
( ~ element(sK4(x,any1),any1)
| spl9_12 ),
inference(avatar_component_clause,[],[f209]) ).
fof(f209,plain,
( spl9_12
<=> element(sK4(x,any1),any1) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_12])]) ).
fof(f2575,plain,
( ~ spl9_8
| ~ spl9_13
| spl9_23
| ~ spl9_25
| ~ spl9_26
| ~ spl9_45 ),
inference(avatar_contradiction_clause,[],[f2574]) ).
fof(f2574,plain,
( $false
| ~ spl9_8
| ~ spl9_13
| spl9_23
| ~ spl9_25
| ~ spl9_26
| ~ spl9_45 ),
inference(global_subsumption,[],[f220,f82,f84,f85,f87,f100,f101,f86,f93,f95,f97,f99,f103,f89,f94,f98,f90,f174,f242,f96,f102,f91,f241,f92,f409,f106,f419,f88,f164,f472,f473,f474,f470,f495,f496,f497,f107,f176,f177,f104,f108,f613,f631,f633,f634,f652,f654,f105,f113,f800,f842,f109,f875,f898,f900,f841,f110,f939,f963,f965,f522,f115,f111,f114,f1113,f112,f368,f1188,f1189,f1190,f1191,f1192,f1193,f1194,f1195,f1187,f1213,f1214,f1215,f1216,f1217,f1218,f1219,f369,f191,f1283,f1285,f1287,f1288,f1291,f1292,f1293,f1294,f192,f193,f615,f1719,f1720,f1721,f1722,f1754,f1756,f1759,f1763,f636,f1845,f1846,f1847,f1848,f1881,f1883,f1886,f1890,f877,f614,f635,f941,f876,f1281,f2288,f2290,f2291,f2292,f2293,f2294,f2295,f2296,f2297,f940,f370,f83,f2546,f845,f843,f2555]) ).
fof(f2573,plain,
( ~ spl9_8
| spl9_15
| spl9_23
| ~ spl9_25
| ~ spl9_26
| ~ spl9_45 ),
inference(avatar_contradiction_clause,[],[f2572]) ).
fof(f2572,plain,
( $false
| ~ spl9_8
| spl9_15
| spl9_23
| ~ spl9_25
| ~ spl9_26
| ~ spl9_45 ),
inference(global_subsumption,[],[f298,f82,f84,f85,f87,f100,f101,f86,f93,f95,f97,f99,f103,f89,f94,f98,f90,f174,f242,f96,f102,f91,f241,f92,f409,f106,f419,f88,f164,f472,f473,f474,f470,f495,f496,f497,f107,f176,f177,f104,f108,f613,f631,f633,f634,f652,f654,f105,f113,f800,f842,f109,f875,f898,f900,f841,f110,f939,f963,f965,f522,f115,f111,f114,f1113,f112,f368,f1188,f1189,f1190,f1191,f1192,f1193,f1194,f1195,f1187,f1213,f1214,f1215,f1216,f1217,f1218,f1219,f369,f191,f1283,f1285,f1287,f1288,f1291,f1292,f1293,f1294,f192,f193,f615,f1719,f1720,f1721,f1722,f1754,f1756,f1759,f1763,f636,f1845,f1846,f1847,f1848,f1881,f1883,f1886,f1890,f877,f614,f635,f941,f876,f1281,f2288,f2290,f2291,f2292,f2293,f2294,f2295,f2296,f2297,f940,f370,f83,f2546,f845,f843,f2555]) ).
fof(f298,plain,
( apply(x,sK3(x,any1)) != apply(x,sK4(x,any1))
| spl9_15 ),
inference(avatar_component_clause,[],[f297]) ).
fof(f297,plain,
( spl9_15
<=> apply(x,sK3(x,any1)) = apply(x,sK4(x,any1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_15])]) ).
fof(f2571,plain,
( ~ spl9_8
| spl9_16
| spl9_23
| ~ spl9_25
| ~ spl9_26
| ~ spl9_45 ),
inference(avatar_contradiction_clause,[],[f2570]) ).
fof(f2570,plain,
( $false
| ~ spl9_8
| spl9_16
| spl9_23
| ~ spl9_25
| ~ spl9_26
| ~ spl9_45 ),
inference(global_subsumption,[],[f307,f82,f84,f85,f87,f100,f101,f86,f93,f95,f97,f99,f103,f89,f94,f98,f90,f174,f242,f96,f102,f91,f241,f92,f409,f106,f419,f88,f164,f472,f473,f474,f470,f495,f496,f497,f107,f176,f177,f104,f108,f613,f631,f633,f634,f652,f654,f105,f113,f800,f842,f109,f875,f898,f900,f841,f110,f939,f963,f965,f522,f115,f111,f114,f1113,f112,f368,f1188,f1189,f1190,f1191,f1192,f1193,f1194,f1195,f1187,f1213,f1214,f1215,f1216,f1217,f1218,f1219,f369,f191,f1283,f1285,f1287,f1288,f1291,f1292,f1293,f1294,f192,f193,f615,f1719,f1720,f1721,f1722,f1754,f1756,f1759,f1763,f636,f1845,f1846,f1847,f1848,f1881,f1883,f1886,f1890,f877,f614,f635,f941,f876,f1281,f2288,f2290,f2291,f2292,f2293,f2294,f2295,f2296,f2297,f940,f370,f83,f2546,f845,f843,f2555]) ).
fof(f2569,plain,
( ~ spl9_8
| spl9_17
| spl9_23
| ~ spl9_25
| ~ spl9_26
| ~ spl9_45 ),
inference(avatar_contradiction_clause,[],[f2568]) ).
fof(f2568,plain,
( $false
| ~ spl9_8
| spl9_17
| spl9_23
| ~ spl9_25
| ~ spl9_26
| ~ spl9_45 ),
inference(global_subsumption,[],[f314,f82,f84,f85,f87,f100,f101,f86,f93,f95,f97,f99,f103,f89,f94,f98,f90,f174,f242,f96,f102,f91,f241,f92,f409,f106,f419,f88,f164,f472,f473,f474,f470,f495,f496,f497,f107,f176,f177,f104,f108,f613,f631,f633,f634,f652,f654,f105,f113,f800,f842,f109,f875,f898,f900,f841,f110,f939,f963,f965,f522,f115,f111,f114,f1113,f112,f368,f1188,f1189,f1190,f1191,f1192,f1193,f1194,f1195,f1187,f1213,f1214,f1215,f1216,f1217,f1218,f1219,f369,f191,f1283,f1285,f1287,f1288,f1291,f1292,f1293,f1294,f192,f193,f615,f1719,f1720,f1721,f1722,f1754,f1756,f1759,f1763,f636,f1845,f1846,f1847,f1848,f1881,f1883,f1886,f1890,f877,f614,f635,f941,f876,f1281,f2288,f2290,f2291,f2292,f2293,f2294,f2295,f2296,f2297,f940,f370,f83,f2546,f845,f843,f2555]) ).
fof(f314,plain,
( zero(any1) != subtract(any1,zero(any1),zero(any1))
| spl9_17 ),
inference(avatar_component_clause,[],[f313]) ).
fof(f2567,plain,
( ~ spl9_8
| spl9_18
| spl9_23
| ~ spl9_25
| ~ spl9_26
| ~ spl9_45 ),
inference(avatar_contradiction_clause,[],[f2566]) ).
fof(f2566,plain,
( $false
| ~ spl9_8
| spl9_18
| spl9_23
| ~ spl9_25
| ~ spl9_26
| ~ spl9_45 ),
inference(global_subsumption,[],[f321,f82,f84,f85,f87,f100,f101,f86,f93,f95,f97,f99,f103,f89,f94,f98,f90,f174,f242,f96,f102,f91,f241,f92,f409,f106,f419,f88,f164,f472,f473,f474,f470,f495,f496,f497,f107,f176,f177,f104,f108,f613,f631,f633,f634,f652,f654,f105,f113,f800,f842,f109,f875,f898,f900,f841,f110,f939,f963,f965,f522,f115,f111,f114,f1113,f112,f368,f1188,f1189,f1190,f1191,f1192,f1193,f1194,f1195,f1187,f1213,f1214,f1215,f1216,f1217,f1218,f1219,f369,f191,f1283,f1285,f1287,f1288,f1291,f1292,f1293,f1294,f192,f193,f615,f1719,f1720,f1721,f1722,f1754,f1756,f1759,f1763,f636,f1845,f1846,f1847,f1848,f1881,f1883,f1886,f1890,f877,f614,f635,f941,f876,f1281,f2288,f2290,f2291,f2292,f2293,f2294,f2295,f2296,f2297,f940,f370,f83,f2546,f845,f843,f2555]) ).
fof(f321,plain,
( zero(any1) != subtract(any1,sK4(x,any1),sK4(x,any1))
| spl9_18 ),
inference(avatar_component_clause,[],[f320]) ).
fof(f320,plain,
( spl9_18
<=> zero(any1) = subtract(any1,sK4(x,any1),sK4(x,any1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_18])]) ).
fof(f2565,plain,
( ~ spl9_8
| spl9_19
| spl9_23
| ~ spl9_25
| ~ spl9_26
| ~ spl9_45 ),
inference(avatar_contradiction_clause,[],[f2564]) ).
fof(f2564,plain,
( $false
| ~ spl9_8
| spl9_19
| spl9_23
| ~ spl9_25
| ~ spl9_26
| ~ spl9_45 ),
inference(global_subsumption,[],[f328,f82,f84,f85,f87,f100,f101,f86,f93,f95,f97,f99,f103,f89,f94,f98,f90,f174,f242,f96,f102,f91,f241,f92,f409,f106,f419,f88,f164,f472,f473,f474,f470,f495,f496,f497,f107,f176,f177,f104,f108,f613,f631,f633,f634,f652,f654,f105,f113,f800,f842,f109,f875,f898,f900,f841,f110,f939,f963,f965,f522,f115,f111,f114,f1113,f112,f368,f1188,f1189,f1190,f1191,f1192,f1193,f1194,f1195,f1187,f1213,f1214,f1215,f1216,f1217,f1218,f1219,f369,f191,f1283,f1285,f1287,f1288,f1291,f1292,f1293,f1294,f192,f193,f615,f1719,f1720,f1721,f1722,f1754,f1756,f1759,f1763,f636,f1845,f1846,f1847,f1848,f1881,f1883,f1886,f1890,f877,f614,f635,f941,f876,f1281,f2288,f2290,f2291,f2292,f2293,f2294,f2295,f2296,f2297,f940,f370,f83,f2546,f845,f843,f2555]) ).
fof(f328,plain,
( zero(any2) != subtract(any2,apply(x,sK3(x,any1)),apply(x,sK3(x,any1)))
| spl9_19 ),
inference(avatar_component_clause,[],[f327]) ).
fof(f327,plain,
( spl9_19
<=> zero(any2) = subtract(any2,apply(x,sK3(x,any1)),apply(x,sK3(x,any1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_19])]) ).
fof(f2563,plain,
( ~ spl9_8
| spl9_20
| spl9_23
| ~ spl9_25
| ~ spl9_26
| ~ spl9_45 ),
inference(avatar_contradiction_clause,[],[f2562]) ).
fof(f2562,plain,
( $false
| ~ spl9_8
| spl9_20
| spl9_23
| ~ spl9_25
| ~ spl9_26
| ~ spl9_45 ),
inference(global_subsumption,[],[f347,f82,f84,f85,f87,f100,f101,f86,f93,f95,f97,f99,f103,f89,f94,f98,f90,f174,f242,f96,f102,f91,f241,f92,f409,f106,f419,f88,f164,f472,f473,f474,f470,f495,f496,f497,f107,f176,f177,f104,f108,f613,f631,f633,f634,f652,f654,f105,f113,f800,f842,f109,f875,f898,f900,f841,f110,f939,f963,f965,f522,f115,f111,f114,f1113,f112,f368,f1188,f1189,f1190,f1191,f1192,f1193,f1194,f1195,f1187,f1213,f1214,f1215,f1216,f1217,f1218,f1219,f369,f191,f1283,f1285,f1287,f1288,f1291,f1292,f1293,f1294,f192,f193,f615,f1719,f1720,f1721,f1722,f1754,f1756,f1759,f1763,f636,f1845,f1846,f1847,f1848,f1881,f1883,f1886,f1890,f877,f614,f635,f941,f876,f1281,f2288,f2290,f2291,f2292,f2293,f2294,f2295,f2296,f2297,f940,f370,f83,f2546,f845,f843,f2555]) ).
fof(f347,plain,
( sK3(x,any1) != subtract(any1,sK3(x,any1),zero(any1))
| spl9_20 ),
inference(avatar_component_clause,[],[f346]) ).
fof(f346,plain,
( spl9_20
<=> sK3(x,any1) = subtract(any1,sK3(x,any1),zero(any1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_20])]) ).
fof(f2561,plain,
( ~ spl9_8
| spl9_21
| spl9_23
| ~ spl9_25
| ~ spl9_26
| ~ spl9_45 ),
inference(avatar_contradiction_clause,[],[f2560]) ).
fof(f2560,plain,
( $false
| ~ spl9_8
| spl9_21
| spl9_23
| ~ spl9_25
| ~ spl9_26
| ~ spl9_45 ),
inference(global_subsumption,[],[f353,f82,f84,f85,f87,f100,f101,f86,f93,f95,f97,f99,f103,f89,f94,f98,f90,f174,f242,f96,f102,f91,f241,f92,f409,f106,f419,f88,f164,f472,f473,f474,f470,f495,f496,f497,f107,f176,f177,f104,f108,f613,f631,f633,f634,f652,f654,f105,f113,f800,f842,f109,f875,f898,f900,f841,f110,f939,f963,f965,f522,f115,f111,f114,f1113,f112,f368,f1188,f1189,f1190,f1191,f1192,f1193,f1194,f1195,f1187,f1213,f1214,f1215,f1216,f1217,f1218,f1219,f369,f191,f1283,f1285,f1287,f1288,f1291,f1292,f1293,f1294,f192,f193,f615,f1719,f1720,f1721,f1722,f1754,f1756,f1759,f1763,f636,f1845,f1846,f1847,f1848,f1881,f1883,f1886,f1890,f877,f614,f635,f941,f876,f1281,f2288,f2290,f2291,f2292,f2293,f2294,f2295,f2296,f2297,f940,f370,f83,f2546,f845,f843,f2555]) ).
fof(f353,plain,
( sK3(x,any1) != subtract(any1,zero(any1),subtract(any1,zero(any1),sK3(x,any1)))
| spl9_21 ),
inference(avatar_component_clause,[],[f352]) ).
fof(f352,plain,
( spl9_21
<=> sK3(x,any1) = subtract(any1,zero(any1),subtract(any1,zero(any1),sK3(x,any1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_21])]) ).
fof(f2559,plain,
( ~ spl9_8
| spl9_22
| spl9_23
| ~ spl9_25
| ~ spl9_26
| ~ spl9_45 ),
inference(avatar_contradiction_clause,[],[f2558]) ).
fof(f2558,plain,
( $false
| ~ spl9_8
| spl9_22
| spl9_23
| ~ spl9_25
| ~ spl9_26
| ~ spl9_45 ),
inference(global_subsumption,[],[f359,f82,f84,f85,f87,f100,f101,f86,f93,f95,f97,f99,f103,f89,f94,f98,f90,f174,f242,f96,f102,f91,f241,f92,f409,f106,f419,f88,f164,f472,f473,f474,f470,f495,f496,f497,f107,f176,f177,f104,f108,f613,f631,f633,f634,f652,f654,f105,f113,f800,f842,f109,f875,f898,f900,f841,f110,f939,f963,f965,f522,f115,f111,f114,f1113,f112,f368,f1188,f1189,f1190,f1191,f1192,f1193,f1194,f1195,f1187,f1213,f1214,f1215,f1216,f1217,f1218,f1219,f369,f191,f1283,f1285,f1287,f1288,f1291,f1292,f1293,f1294,f192,f193,f615,f1719,f1720,f1721,f1722,f1754,f1756,f1759,f1763,f636,f1845,f1846,f1847,f1848,f1881,f1883,f1886,f1890,f877,f614,f635,f941,f876,f1281,f2288,f2290,f2291,f2292,f2293,f2294,f2295,f2296,f2297,f940,f370,f83,f2546,f845,f843,f2555]) ).
fof(f359,plain,
( sK3(x,any1) != subtract(any1,sK4(x,any1),subtract(any1,sK4(x,any1),sK3(x,any1)))
| spl9_22 ),
inference(avatar_component_clause,[],[f358]) ).
fof(f358,plain,
( spl9_22
<=> sK3(x,any1) = subtract(any1,sK4(x,any1),subtract(any1,sK4(x,any1),sK3(x,any1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_22])]) ).
fof(f2557,plain,
( ~ spl9_8
| spl9_23
| ~ spl9_25
| ~ spl9_26
| ~ spl9_45 ),
inference(avatar_contradiction_clause,[],[f2556]) ).
fof(f2556,plain,
( $false
| ~ spl9_8
| spl9_23
| ~ spl9_25
| ~ spl9_26
| ~ spl9_45 ),
inference(global_subsumption,[],[f82,f84,f85,f87,f100,f101,f86,f93,f95,f97,f99,f103,f89,f94,f98,f90,f174,f242,f96,f102,f91,f241,f92,f409,f106,f419,f88,f164,f472,f473,f474,f470,f495,f496,f497,f107,f176,f177,f104,f108,f613,f631,f633,f634,f652,f654,f105,f113,f800,f842,f109,f875,f898,f900,f841,f110,f939,f963,f965,f522,f115,f111,f114,f1113,f112,f368,f1188,f1189,f1190,f1191,f1192,f1193,f1194,f1195,f1187,f1213,f1214,f1215,f1216,f1217,f1218,f1219,f369,f191,f1283,f1285,f1287,f1288,f1291,f1292,f1293,f1294,f192,f193,f615,f1719,f1720,f1721,f1722,f1754,f1756,f1759,f1763,f636,f1845,f1846,f1847,f1848,f1881,f1883,f1886,f1890,f877,f614,f635,f941,f876,f1281,f2288,f2290,f2291,f2292,f2293,f2294,f2295,f2296,f2297,f940,f370,f83,f2546,f845,f843,f2555]) ).
fof(f2492,plain,
( ~ spl9_3
| ~ spl9_69 ),
inference(avatar_contradiction_clause,[],[f2491]) ).
fof(f2491,plain,
( $false
| ~ spl9_3
| ~ spl9_69 ),
inference(subsumption_resolution,[],[f2490,f128]) ).
fof(f2490,plain,
( ~ morphism(x,any1,any2)
| ~ spl9_69 ),
inference(equality_resolution,[],[f1497]) ).
fof(f1497,plain,
( ! [X0] :
( zero(X0) != zero(any2)
| ~ morphism(x,any1,X0) )
| ~ spl9_69 ),
inference(avatar_component_clause,[],[f1496]) ).
fof(f1496,plain,
( spl9_69
<=> ! [X0] :
( zero(X0) != zero(any2)
| ~ morphism(x,any1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_69])]) ).
fof(f2489,plain,
( spl9_1
| ~ spl9_3
| ~ spl9_96 ),
inference(avatar_contradiction_clause,[],[f2488]) ).
fof(f2488,plain,
( $false
| spl9_1
| ~ spl9_3
| ~ spl9_96 ),
inference(resolution,[],[f2487,f128]) ).
fof(f2487,plain,
( ! [X28] : ~ morphism(x,any1,X28)
| spl9_1
| ~ spl9_96 ),
inference(subsumption_resolution,[],[f2447,f118]) ).
fof(f118,plain,
( ~ injection(x)
| spl9_1 ),
inference(avatar_component_clause,[],[f117]) ).
fof(f2447,plain,
( ! [X28] :
( injection(x)
| ~ morphism(x,any1,X28) )
| ~ spl9_96 ),
inference(trivial_inequality_removal,[],[f2446]) ).
fof(f2446,plain,
( ! [X28] :
( sK3(x,any1) != sK3(x,any1)
| injection(x)
| ~ morphism(x,any1,X28) )
| ~ spl9_96 ),
inference(superposition,[],[f103,f2401]) ).
fof(f2401,plain,
( sK3(x,any1) = sK4(x,any1)
| ~ spl9_96 ),
inference(avatar_component_clause,[],[f2399]) ).
fof(f2399,plain,
( spl9_96
<=> sK3(x,any1) = sK4(x,any1) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_96])]) ).
fof(f2402,plain,
( spl9_96
| ~ spl9_20
| ~ spl9_28
| ~ spl9_95 ),
inference(avatar_split_clause,[],[f2396,f2384,f437,f346,f2399]) ).
fof(f437,plain,
( spl9_28
<=> sK4(x,any1) = subtract(any1,sK3(x,any1),subtract(any1,sK3(x,any1),sK4(x,any1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_28])]) ).
fof(f2384,plain,
( spl9_95
<=> zero(any1) = subtract(any1,sK3(x,any1),sK4(x,any1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_95])]) ).
fof(f2396,plain,
( sK3(x,any1) = sK4(x,any1)
| ~ spl9_20
| ~ spl9_28
| ~ spl9_95 ),
inference(forward_demodulation,[],[f2388,f348]) ).
fof(f348,plain,
( sK3(x,any1) = subtract(any1,sK3(x,any1),zero(any1))
| ~ spl9_20 ),
inference(avatar_component_clause,[],[f346]) ).
fof(f2388,plain,
( sK4(x,any1) = subtract(any1,sK3(x,any1),zero(any1))
| ~ spl9_28
| ~ spl9_95 ),
inference(superposition,[],[f439,f2386]) ).
fof(f2386,plain,
( zero(any1) = subtract(any1,sK3(x,any1),sK4(x,any1))
| ~ spl9_95 ),
inference(avatar_component_clause,[],[f2384]) ).
fof(f439,plain,
( sK4(x,any1) = subtract(any1,sK3(x,any1),subtract(any1,sK3(x,any1),sK4(x,any1)))
| ~ spl9_28 ),
inference(avatar_component_clause,[],[f437]) ).
fof(f2387,plain,
( spl9_69
| spl9_95
| ~ spl9_2
| ~ spl9_5
| ~ spl9_12
| ~ spl9_40 ),
inference(avatar_split_clause,[],[f2382,f698,f209,f139,f121,f2384,f1496]) ).
fof(f698,plain,
( spl9_40
<=> zero(any2) = apply(x,subtract(any1,sK3(x,any1),sK4(x,any1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_40])]) ).
fof(f2382,plain,
( ! [X0] :
( zero(any1) = subtract(any1,sK3(x,any1),sK4(x,any1))
| zero(X0) != zero(any2)
| ~ morphism(x,any1,X0) )
| ~ spl9_2
| ~ spl9_5
| ~ spl9_12
| ~ spl9_40 ),
inference(subsumption_resolution,[],[f2381,f141]) ).
fof(f141,plain,
( element(sK3(x,any1),any1)
| ~ spl9_5 ),
inference(avatar_component_clause,[],[f139]) ).
fof(f2381,plain,
( ! [X0] :
( zero(any1) = subtract(any1,sK3(x,any1),sK4(x,any1))
| zero(X0) != zero(any2)
| ~ morphism(x,any1,X0)
| ~ element(sK3(x,any1),any1) )
| ~ spl9_2
| ~ spl9_12
| ~ spl9_40 ),
inference(subsumption_resolution,[],[f2380,f211]) ).
fof(f211,plain,
( element(sK4(x,any1),any1)
| ~ spl9_12 ),
inference(avatar_component_clause,[],[f209]) ).
fof(f2380,plain,
( ! [X0] :
( zero(any1) = subtract(any1,sK3(x,any1),sK4(x,any1))
| zero(X0) != zero(any2)
| ~ morphism(x,any1,X0)
| ~ element(sK4(x,any1),any1)
| ~ element(sK3(x,any1),any1) )
| ~ spl9_2
| ~ spl9_40 ),
inference(resolution,[],[f710,f93]) ).
fof(f710,plain,
( ! [X0,X1] :
( ~ element(subtract(any1,sK3(x,any1),sK4(x,any1)),X1)
| zero(X1) = subtract(any1,sK3(x,any1),sK4(x,any1))
| zero(X0) != zero(any2)
| ~ morphism(x,X1,X0) )
| ~ spl9_2
| ~ spl9_40 ),
inference(subsumption_resolution,[],[f703,f123]) ).
fof(f123,plain,
( injection_2(x)
| ~ spl9_2 ),
inference(avatar_component_clause,[],[f121]) ).
fof(f703,plain,
( ! [X0,X1] :
( zero(X0) != zero(any2)
| zero(X1) = subtract(any1,sK3(x,any1),sK4(x,any1))
| ~ element(subtract(any1,sK3(x,any1),sK4(x,any1)),X1)
| ~ morphism(x,X1,X0)
| ~ injection_2(x) )
| ~ spl9_40 ),
inference(superposition,[],[f91,f700]) ).
fof(f700,plain,
( zero(any2) = apply(x,subtract(any1,sK3(x,any1),sK4(x,any1)))
| ~ spl9_40 ),
inference(avatar_component_clause,[],[f698]) ).
fof(f2277,plain,
( spl9_94
| ~ spl9_73 ),
inference(avatar_split_clause,[],[f1715,f1609,f2273]) ).
fof(f2273,plain,
( spl9_94
<=> zero(any1) = subtract(any1,subtract(any1,zero(any1),subtract(any1,sK4(x,any1),sK3(x,any1))),subtract(any1,zero(any1),subtract(any1,sK4(x,any1),sK3(x,any1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_94])]) ).
fof(f1609,plain,
( spl9_73
<=> element(subtract(any1,zero(any1),subtract(any1,sK4(x,any1),sK3(x,any1))),any1) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_73])]) ).
fof(f1715,plain,
( zero(any1) = subtract(any1,subtract(any1,zero(any1),subtract(any1,sK4(x,any1),sK3(x,any1))),subtract(any1,zero(any1),subtract(any1,sK4(x,any1),sK3(x,any1))))
| ~ spl9_73 ),
inference(resolution,[],[f1610,f85]) ).
fof(f1610,plain,
( element(subtract(any1,zero(any1),subtract(any1,sK4(x,any1),sK3(x,any1))),any1)
| ~ spl9_73 ),
inference(avatar_component_clause,[],[f1609]) ).
fof(f2276,plain,
( spl9_94
| ~ spl9_7
| ~ spl9_74 ),
inference(avatar_split_clause,[],[f1633,f1613,f168,f2273]) ).
fof(f1613,plain,
( spl9_74
<=> element(subtract(any1,sK4(x,any1),sK3(x,any1)),any1) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_74])]) ).
fof(f1633,plain,
( zero(any1) = subtract(any1,subtract(any1,zero(any1),subtract(any1,sK4(x,any1),sK3(x,any1))),subtract(any1,zero(any1),subtract(any1,sK4(x,any1),sK3(x,any1))))
| ~ spl9_7
| ~ spl9_74 ),
inference(resolution,[],[f1615,f471]) ).
fof(f471,plain,
( ! [X4] :
( ~ element(X4,any1)
| zero(any1) = subtract(any1,subtract(any1,zero(any1),X4),subtract(any1,zero(any1),X4)) )
| ~ spl9_7 ),
inference(resolution,[],[f164,f169]) ).
fof(f1615,plain,
( element(subtract(any1,sK4(x,any1),sK3(x,any1)),any1)
| ~ spl9_74 ),
inference(avatar_component_clause,[],[f1613]) ).
fof(f2250,plain,
( spl9_93
| ~ spl9_16
| ~ spl9_65 ),
inference(avatar_split_clause,[],[f2230,f1344,f306,f2247]) ).
fof(f2247,plain,
( spl9_93
<=> zero(any2) = subtract(any2,subtract(any2,sK1(x,any1,any2),apply(x,sK3(x,any1))),subtract(any2,sK1(x,any1,any2),apply(x,sK3(x,any1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_93])]) ).
fof(f2230,plain,
( zero(any2) = subtract(any2,subtract(any2,sK1(x,any1,any2),apply(x,sK3(x,any1))),subtract(any2,sK1(x,any1,any2),apply(x,sK3(x,any1))))
| ~ spl9_16
| ~ spl9_65 ),
inference(resolution,[],[f2139,f308]) ).
fof(f308,plain,
( element(apply(x,sK3(x,any1)),any2)
| ~ spl9_16 ),
inference(avatar_component_clause,[],[f306]) ).
fof(f2139,plain,
( ! [X4] :
( ~ element(X4,any2)
| zero(any2) = subtract(any2,subtract(any2,sK1(x,any1,any2),X4),subtract(any2,sK1(x,any1,any2),X4)) )
| ~ spl9_65 ),
inference(resolution,[],[f1346,f164]) ).
fof(f2206,plain,
( spl9_92
| ~ spl9_64 ),
inference(avatar_split_clause,[],[f2155,f1340,f2202]) ).
fof(f2202,plain,
( spl9_92
<=> zero(any2) = subtract(any2,subtract(any2,zero(any2),sK1(x,any1,any2)),subtract(any2,zero(any2),sK1(x,any1,any2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_92])]) ).
fof(f1340,plain,
( spl9_64
<=> element(subtract(any2,zero(any2),sK1(x,any1,any2)),any2) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_64])]) ).
fof(f2155,plain,
( zero(any2) = subtract(any2,subtract(any2,zero(any2),sK1(x,any1,any2)),subtract(any2,zero(any2),sK1(x,any1,any2)))
| ~ spl9_64 ),
inference(resolution,[],[f1341,f85]) ).
fof(f1341,plain,
( element(subtract(any2,zero(any2),sK1(x,any1,any2)),any2)
| ~ spl9_64 ),
inference(avatar_component_clause,[],[f1340]) ).
fof(f2205,plain,
( spl9_92
| ~ spl9_8
| ~ spl9_65 ),
inference(avatar_split_clause,[],[f2133,f1344,f172,f2202]) ).
fof(f2133,plain,
( zero(any2) = subtract(any2,subtract(any2,zero(any2),sK1(x,any1,any2)),subtract(any2,zero(any2),sK1(x,any1,any2)))
| ~ spl9_8
| ~ spl9_65 ),
inference(resolution,[],[f1346,f470]) ).
fof(f2198,plain,
( spl9_91
| ~ spl9_16
| ~ spl9_65 ),
inference(avatar_split_clause,[],[f2132,f1344,f306,f2195]) ).
fof(f2195,plain,
( spl9_91
<=> zero(any2) = subtract(any2,subtract(any2,apply(x,sK3(x,any1)),sK1(x,any1,any2)),subtract(any2,apply(x,sK3(x,any1)),sK1(x,any1,any2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_91])]) ).
fof(f2132,plain,
( zero(any2) = subtract(any2,subtract(any2,apply(x,sK3(x,any1)),sK1(x,any1,any2)),subtract(any2,apply(x,sK3(x,any1)),sK1(x,any1,any2)))
| ~ spl9_16
| ~ spl9_65 ),
inference(resolution,[],[f1346,f469]) ).
fof(f469,plain,
( ! [X2] :
( ~ element(X2,any2)
| zero(any2) = subtract(any2,subtract(any2,apply(x,sK3(x,any1)),X2),subtract(any2,apply(x,sK3(x,any1)),X2)) )
| ~ spl9_16 ),
inference(resolution,[],[f164,f308]) ).
fof(f2189,plain,
( spl9_90
| ~ spl9_3
| spl9_9
| ~ spl9_16 ),
inference(avatar_split_clause,[],[f2170,f306,f183,f126,f2186]) ).
fof(f2186,plain,
( spl9_90
<=> sK1(x,any1,any2) = subtract(any2,apply(x,sK3(x,any1)),subtract(any2,apply(x,sK3(x,any1)),sK1(x,any1,any2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_90])]) ).
fof(f183,plain,
( spl9_9
<=> surjection(x) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_9])]) ).
fof(f2170,plain,
( sK1(x,any1,any2) = subtract(any2,apply(x,sK3(x,any1)),subtract(any2,apply(x,sK3(x,any1)),sK1(x,any1,any2)))
| ~ spl9_3
| spl9_9
| ~ spl9_16 ),
inference(resolution,[],[f2125,f308]) ).
fof(f2125,plain,
( ! [X0] :
( ~ element(X0,any2)
| sK1(x,any1,any2) = subtract(any2,X0,subtract(any2,X0,sK1(x,any1,any2))) )
| ~ spl9_3
| spl9_9 ),
inference(global_subsumption,[],[f82,f84,f128,f85,f87,f130,f100,f101,f86,f93,f163,f95,f97,f99,f103,f165,f89,f181,f94,f98,f162,f90,f83,f136,f194,f96,f102,f91,f92,f106,f88,f164,f472,f473,f474,f107,f176,f532,f177,f190,f542,f543,f544,f104,f108,f613,f616,f617,f634,f635,f637,f638,f457,f674,f675,f676,f679,f680,f105,f113,f109,f875,f876,f878,f879,f886,f110,f939,f940,f941,f942,f943,f950,f522,f1008,f115,f111,f114,f1113,f1114,f1116,f468,f1128,f1129,f1130,f1133,f1134,f1135,f1136,f178,f1142,f1143,f1144,f1147,f1148,f1149,f1150,f179,f112,f180,f191,f1279,f1283,f1287,f1288,f1291,f1292,f1293,f1294,f1311,f185,f192,f1316,f1321,f1325,f1326,f1327,f1328,f1329,f1330,f1331,f193,f802,f1069,f615,f1719,f1720,f1721,f1722,f1723,f1724,f1725,f1732,f1733,f636,f1845,f1846,f1847,f1848,f1849,f1850,f1851,f1858,f1859,f877,f2017,f614,f2077,f240,f2122,f1315]) ).
fof(f2122,plain,
( ~ surjection(x)
| ~ spl9_3
| spl9_9 ),
inference(global_subsumption,[],[f240,f82,f84,f85,f87,f100,f101,f86,f93,f95,f97,f99,f103,f89,f94,f98,f90,f83,f96,f102,f91,f92,f106,f88,f164,f472,f473,f474,f107,f176,f177,f104,f108,f613,f634,f635,f105,f113,f109,f875,f876,f110,f939,f940,f941,f522,f115,f111,f114,f1113,f112,f191,f1283,f1287,f1288,f1291,f1292,f1293,f1294,f185,f192,f193,f615,f1719,f1720,f1721,f1722,f636,f1845,f1846,f1847,f1848,f877,f614]) ).
fof(f1331,plain,
( ! [X21,X19,X22,X20] :
( sK1(x,any1,any2) = subtract(any2,sK7(X19,X20,any2,X21,X22),subtract(any2,sK7(X19,X20,any2,X21,X22),sK1(x,any1,any2)))
| element(sK6(X19,X20,any2,X21,X22),X21)
| exact(X19,X20)
| ~ morphism(X20,X21,X22)
| ~ morphism(X19,any2,X21) )
| ~ spl9_3
| spl9_9 ),
inference(resolution,[],[f1316,f108]) ).
fof(f1330,plain,
( ! [X18,X16,X17,X15] :
( sK1(x,any1,any2) = subtract(any2,sK7(X15,X16,any2,X17,X18),subtract(any2,sK7(X15,X16,any2,X17,X18),sK1(x,any1,any2)))
| exact(X15,X16)
| zero(X18) = apply(X16,sK6(X15,X16,any2,X17,X18))
| ~ morphism(X16,X17,X18)
| ~ morphism(X15,any2,X17) )
| ~ spl9_3
| spl9_9 ),
inference(resolution,[],[f1316,f109]) ).
fof(f1329,plain,
( ! [X11,X14,X12,X13] :
( sK1(x,any1,any2) = subtract(any2,sK6(X11,X12,X13,any2,X14),subtract(any2,sK6(X11,X12,X13,any2,X14),sK1(x,any1,any2)))
| element(sK7(X11,X12,X13,any2,X14),X13)
| exact(X11,X12)
| ~ morphism(X12,any2,X14)
| ~ morphism(X11,X13,any2) )
| ~ spl9_3
| spl9_9 ),
inference(resolution,[],[f1316,f108]) ).
fof(f1328,plain,
( ! [X10,X8,X9,X7] :
( sK1(x,any1,any2) = subtract(any2,sK6(X7,X8,X9,any2,X10),subtract(any2,sK6(X7,X8,X9,any2,X10),sK1(x,any1,any2)))
| sK6(X7,X8,X9,any2,X10) = apply(X7,sK7(X7,X8,X9,any2,X10))
| exact(X7,X8)
| ~ morphism(X8,any2,X10)
| ~ morphism(X7,X9,any2) )
| ~ spl9_3
| spl9_9 ),
inference(resolution,[],[f1316,f110]) ).
fof(f1327,plain,
( ! [X6,X5] :
( sK1(x,any1,any2) = subtract(any2,sK2(X5,any2,X6),subtract(any2,sK2(X5,any2,X6),sK1(x,any1,any2)))
| injection_2(X5)
| ~ morphism(X5,any2,X6) )
| ~ spl9_3
| spl9_9 ),
inference(resolution,[],[f1316,f97]) ).
fof(f1326,plain,
( ! [X3,X4] :
( sK1(x,any1,any2) = subtract(any2,sK1(X3,X4,any2),subtract(any2,sK1(X3,X4,any2),sK1(x,any1,any2)))
| surjection(X3)
| ~ morphism(X3,X4,any2) )
| ~ spl9_3
| spl9_9 ),
inference(resolution,[],[f1316,f95]) ).
fof(f1325,plain,
( ! [X2,X1] :
( sK1(x,any1,any2) = subtract(any2,subtract(any2,X1,X2),subtract(any2,subtract(any2,X1,X2),sK1(x,any1,any2)))
| ~ element(X2,any2)
| ~ element(X1,any2) )
| ~ spl9_3
| spl9_9 ),
inference(resolution,[],[f1316,f93]) ).
fof(f1321,plain,
( ! [X0] :
( sK1(x,any1,any2) = subtract(any2,apply(x,X0),subtract(any2,apply(x,X0),sK1(x,any1,any2)))
| ~ element(X0,any1) )
| ~ spl9_3
| spl9_9 ),
inference(resolution,[],[f1316,f163]) ).
fof(f1316,plain,
( ! [X0] :
( ~ element(X0,any2)
| sK1(x,any1,any2) = subtract(any2,X0,subtract(any2,X0,sK1(x,any1,any2))) )
| ~ spl9_3
| spl9_9 ),
inference(subsumption_resolution,[],[f1315,f185]) ).
fof(f185,plain,
( ~ surjection(x)
| spl9_9 ),
inference(avatar_component_clause,[],[f183]) ).
fof(f1311,plain,
( ~ surjection(x)
| ~ spl9_3
| spl9_9 ),
inference(global_subsumption,[],[f240,f82,f84,f85,f87,f100,f101,f86,f93,f95,f97,f99,f103,f89,f94,f192,f193,f185,f98,f90,f83,f96,f102,f91,f92,f106,f88,f164,f472,f473,f474,f107,f176,f177,f104,f108,f613,f614,f615,f634,f635,f636,f105,f113,f109,f875,f876,f877,f110,f939,f940,f941,f522,f115,f111,f114,f1113,f112,f191,f1283,f1287,f1288,f1291,f1292,f1293,f1294]) ).
fof(f532,plain,
( zero(any2) = subtract(any2,sK1(x,any1,any2),sK1(x,any1,any2))
| ~ spl9_3
| spl9_9 ),
inference(subsumption_resolution,[],[f531,f185]) ).
fof(f531,plain,
( surjection(x)
| zero(any2) = subtract(any2,sK1(x,any1,any2),sK1(x,any1,any2))
| ~ spl9_3 ),
inference(resolution,[],[f176,f128]) ).
fof(f2163,plain,
( spl9_89
| ~ spl9_3
| spl9_9
| ~ spl9_33
| ~ spl9_65 ),
inference(avatar_split_clause,[],[f1367,f1344,f534,f183,f126,f2160]) ).
fof(f2160,plain,
( spl9_89
<=> sK1(x,any1,any2) = subtract(any2,sK1(x,any1,any2),zero(any2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_89])]) ).
fof(f534,plain,
( spl9_33
<=> zero(any2) = subtract(any2,sK1(x,any1,any2),sK1(x,any1,any2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_33])]) ).
fof(f1367,plain,
( sK1(x,any1,any2) = subtract(any2,sK1(x,any1,any2),zero(any2))
| ~ spl9_3
| spl9_9
| ~ spl9_33
| ~ spl9_65 ),
inference(forward_demodulation,[],[f1362,f536]) ).
fof(f536,plain,
( zero(any2) = subtract(any2,sK1(x,any1,any2),sK1(x,any1,any2))
| ~ spl9_33 ),
inference(avatar_component_clause,[],[f534]) ).
fof(f1362,plain,
( sK1(x,any1,any2) = subtract(any2,sK1(x,any1,any2),subtract(any2,sK1(x,any1,any2),sK1(x,any1,any2)))
| ~ spl9_3
| spl9_9
| ~ spl9_65 ),
inference(resolution,[],[f1346,f1316]) ).
fof(f2111,plain,
( ~ spl9_10
| ~ spl9_16
| spl9_88 ),
inference(avatar_contradiction_clause,[],[f2110]) ).
fof(f2110,plain,
( $false
| ~ spl9_10
| ~ spl9_16
| spl9_88 ),
inference(subsumption_resolution,[],[f2109,f308]) ).
fof(f2109,plain,
( ~ element(apply(x,sK3(x,any1)),any2)
| ~ spl9_10
| spl9_88 ),
inference(resolution,[],[f2106,f188]) ).
fof(f188,plain,
( ! [X0] :
( element(sK0(x,any1,X0),any1)
| ~ element(X0,any2) )
| ~ spl9_10 ),
inference(avatar_component_clause,[],[f187]) ).
fof(f187,plain,
( spl9_10
<=> ! [X0] :
( ~ element(X0,any2)
| element(sK0(x,any1,X0),any1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_10])]) ).
fof(f2106,plain,
( ~ element(sK0(x,any1,apply(x,sK3(x,any1))),any1)
| spl9_88 ),
inference(avatar_component_clause,[],[f2105]) ).
fof(f2105,plain,
( spl9_88
<=> element(sK0(x,any1,apply(x,sK3(x,any1))),any1) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_88])]) ).
fof(f2108,plain,
( ~ spl9_87
| spl9_88
| ~ spl9_7
| ~ spl9_86 ),
inference(avatar_split_clause,[],[f2099,f2094,f168,f2105,f2101]) ).
fof(f2101,plain,
( spl9_87
<=> element(subtract(any1,zero(any1),sK0(x,any1,apply(x,sK3(x,any1)))),any1) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_87])]) ).
fof(f2094,plain,
( spl9_86
<=> sK0(x,any1,apply(x,sK3(x,any1))) = subtract(any1,zero(any1),subtract(any1,zero(any1),sK0(x,any1,apply(x,sK3(x,any1))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_86])]) ).
fof(f2099,plain,
( element(sK0(x,any1,apply(x,sK3(x,any1))),any1)
| ~ element(subtract(any1,zero(any1),sK0(x,any1,apply(x,sK3(x,any1)))),any1)
| ~ spl9_7
| ~ spl9_86 ),
inference(subsumption_resolution,[],[f2098,f169]) ).
fof(f2098,plain,
( element(sK0(x,any1,apply(x,sK3(x,any1))),any1)
| ~ element(subtract(any1,zero(any1),sK0(x,any1,apply(x,sK3(x,any1)))),any1)
| ~ element(zero(any1),any1)
| ~ spl9_86 ),
inference(superposition,[],[f93,f2096]) ).
fof(f2096,plain,
( sK0(x,any1,apply(x,sK3(x,any1))) = subtract(any1,zero(any1),subtract(any1,zero(any1),sK0(x,any1,apply(x,sK3(x,any1)))))
| ~ spl9_86 ),
inference(avatar_component_clause,[],[f2094]) ).
fof(f2097,plain,
( spl9_86
| ~ spl9_7
| ~ spl9_10
| ~ spl9_16 ),
inference(avatar_split_clause,[],[f2079,f306,f187,f168,f2094]) ).
fof(f2079,plain,
( sK0(x,any1,apply(x,sK3(x,any1))) = subtract(any1,zero(any1),subtract(any1,zero(any1),sK0(x,any1,apply(x,sK3(x,any1)))))
| ~ spl9_7
| ~ spl9_10
| ~ spl9_16 ),
inference(resolution,[],[f2046,f308]) ).
fof(f2046,plain,
( ! [X0] :
( ~ element(X0,any2)
| sK0(x,any1,X0) = subtract(any1,zero(any1),subtract(any1,zero(any1),sK0(x,any1,X0))) )
| ~ spl9_7
| ~ spl9_10 ),
inference(resolution,[],[f1412,f169]) ).
fof(f1412,plain,
( ! [X40,X39] :
( ~ element(X40,any1)
| sK0(x,any1,X39) = subtract(any1,X40,subtract(any1,X40,sK0(x,any1,X39)))
| ~ element(X39,any2) )
| ~ spl9_10 ),
inference(resolution,[],[f188,f94]) ).
fof(f2035,plain,
( spl9_85
| ~ spl9_3
| ~ spl9_14
| ~ spl9_41
| ~ spl9_73
| ~ spl9_74
| ~ spl9_75 ),
inference(avatar_split_clause,[],[f1832,f1772,f1613,f1609,f734,f248,f126,f2032]) ).
fof(f2032,plain,
( spl9_85
<=> zero(any2) = apply(x,subtract(any1,subtract(any1,sK4(x,any1),sK3(x,any1)),subtract(any1,zero(any1),subtract(any1,sK4(x,any1),sK3(x,any1))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_85])]) ).
fof(f248,plain,
( spl9_14
<=> zero(any2) = subtract(any2,zero(any2),zero(any2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_14])]) ).
fof(f734,plain,
( spl9_41
<=> zero(any2) = apply(x,subtract(any1,sK4(x,any1),sK3(x,any1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_41])]) ).
fof(f1772,plain,
( spl9_75
<=> zero(any2) = apply(x,subtract(any1,zero(any1),subtract(any1,sK4(x,any1),sK3(x,any1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_75])]) ).
fof(f1832,plain,
( zero(any2) = apply(x,subtract(any1,subtract(any1,sK4(x,any1),sK3(x,any1)),subtract(any1,zero(any1),subtract(any1,sK4(x,any1),sK3(x,any1)))))
| ~ spl9_3
| ~ spl9_14
| ~ spl9_41
| ~ spl9_73
| ~ spl9_74
| ~ spl9_75 ),
inference(forward_demodulation,[],[f1831,f250]) ).
fof(f250,plain,
( zero(any2) = subtract(any2,zero(any2),zero(any2))
| ~ spl9_14 ),
inference(avatar_component_clause,[],[f248]) ).
fof(f1831,plain,
( subtract(any2,zero(any2),zero(any2)) = apply(x,subtract(any1,subtract(any1,sK4(x,any1),sK3(x,any1)),subtract(any1,zero(any1),subtract(any1,sK4(x,any1),sK3(x,any1)))))
| ~ spl9_3
| ~ spl9_41
| ~ spl9_73
| ~ spl9_74
| ~ spl9_75 ),
inference(forward_demodulation,[],[f1811,f1774]) ).
fof(f1774,plain,
( zero(any2) = apply(x,subtract(any1,zero(any1),subtract(any1,sK4(x,any1),sK3(x,any1))))
| ~ spl9_75 ),
inference(avatar_component_clause,[],[f1772]) ).
fof(f1811,plain,
( subtract(any2,zero(any2),apply(x,subtract(any1,zero(any1),subtract(any1,sK4(x,any1),sK3(x,any1))))) = apply(x,subtract(any1,subtract(any1,sK4(x,any1),sK3(x,any1)),subtract(any1,zero(any1),subtract(any1,sK4(x,any1),sK3(x,any1)))))
| ~ spl9_3
| ~ spl9_41
| ~ spl9_73
| ~ spl9_74 ),
inference(resolution,[],[f1662,f1610]) ).
fof(f1662,plain,
( ! [X7] :
( ~ element(X7,any1)
| apply(x,subtract(any1,subtract(any1,sK4(x,any1),sK3(x,any1)),X7)) = subtract(any2,zero(any2),apply(x,X7)) )
| ~ spl9_3
| ~ spl9_41
| ~ spl9_74 ),
inference(forward_demodulation,[],[f1631,f736]) ).
fof(f736,plain,
( zero(any2) = apply(x,subtract(any1,sK4(x,any1),sK3(x,any1)))
| ~ spl9_41 ),
inference(avatar_component_clause,[],[f734]) ).
fof(f1631,plain,
( ! [X7] :
( ~ element(X7,any1)
| apply(x,subtract(any1,subtract(any1,sK4(x,any1),sK3(x,any1)),X7)) = subtract(any2,apply(x,subtract(any1,sK4(x,any1),sK3(x,any1))),apply(x,X7)) )
| ~ spl9_3
| ~ spl9_74 ),
inference(resolution,[],[f1615,f457]) ).
fof(f2029,plain,
( spl9_84
| ~ spl9_12
| ~ spl9_74 ),
inference(avatar_split_clause,[],[f1625,f1613,f209,f2026]) ).
fof(f2026,plain,
( spl9_84
<=> sK4(x,any1) = subtract(any1,subtract(any1,sK4(x,any1),sK3(x,any1)),subtract(any1,subtract(any1,sK4(x,any1),sK3(x,any1)),sK4(x,any1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_84])]) ).
fof(f1625,plain,
( sK4(x,any1) = subtract(any1,subtract(any1,sK4(x,any1),sK3(x,any1)),subtract(any1,subtract(any1,sK4(x,any1),sK3(x,any1)),sK4(x,any1)))
| ~ spl9_12
| ~ spl9_74 ),
inference(resolution,[],[f1615,f231]) ).
fof(f231,plain,
( ! [X0] :
( ~ element(X0,any1)
| sK4(x,any1) = subtract(any1,X0,subtract(any1,X0,sK4(x,any1))) )
| ~ spl9_12 ),
inference(resolution,[],[f211,f94]) ).
fof(f2022,plain,
( spl9_83
| ~ spl9_5
| ~ spl9_12 ),
inference(avatar_split_clause,[],[f1595,f209,f139,f2019]) ).
fof(f2019,plain,
( spl9_83
<=> subtract(any1,sK4(x,any1),sK3(x,any1)) = subtract(any1,sK3(x,any1),subtract(any1,sK3(x,any1),subtract(any1,sK4(x,any1),sK3(x,any1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_83])]) ).
fof(f1595,plain,
( subtract(any1,sK4(x,any1),sK3(x,any1)) = subtract(any1,sK3(x,any1),subtract(any1,sK3(x,any1),subtract(any1,sK4(x,any1),sK3(x,any1))))
| ~ spl9_5
| ~ spl9_12 ),
inference(resolution,[],[f1532,f141]) ).
fof(f1532,plain,
( ! [X14] :
( ~ element(X14,any1)
| subtract(any1,sK4(x,any1),sK3(x,any1)) = subtract(any1,X14,subtract(any1,X14,subtract(any1,sK4(x,any1),sK3(x,any1)))) )
| ~ spl9_5
| ~ spl9_12 ),
inference(resolution,[],[f1289,f211]) ).
fof(f1289,plain,
( ! [X31,X32] :
( ~ element(X32,any1)
| subtract(any1,X32,sK3(x,any1)) = subtract(any1,X31,subtract(any1,X31,subtract(any1,X32,sK3(x,any1))))
| ~ element(X31,any1) )
| ~ spl9_5 ),
inference(resolution,[],[f191,f141]) ).
fof(f2016,plain,
( spl9_82
| ~ spl9_5
| ~ spl9_10
| ~ spl9_16 ),
inference(avatar_split_clause,[],[f1477,f306,f187,f139,f2013]) ).
fof(f2013,plain,
( spl9_82
<=> sK3(x,any1) = subtract(any1,sK0(x,any1,apply(x,sK3(x,any1))),subtract(any1,sK0(x,any1,apply(x,sK3(x,any1))),sK3(x,any1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_82])]) ).
fof(f1477,plain,
( sK3(x,any1) = subtract(any1,sK0(x,any1,apply(x,sK3(x,any1))),subtract(any1,sK0(x,any1,apply(x,sK3(x,any1))),sK3(x,any1)))
| ~ spl9_5
| ~ spl9_10
| ~ spl9_16 ),
inference(resolution,[],[f1386,f308]) ).
fof(f1386,plain,
( ! [X6] :
( ~ element(X6,any2)
| sK3(x,any1) = subtract(any1,sK0(x,any1,X6),subtract(any1,sK0(x,any1,X6),sK3(x,any1))) )
| ~ spl9_5
| ~ spl9_10 ),
inference(resolution,[],[f188,f285]) ).
fof(f285,plain,
( ! [X0] :
( ~ element(X0,any1)
| sK3(x,any1) = subtract(any1,X0,subtract(any1,X0,sK3(x,any1))) )
| ~ spl9_5 ),
inference(resolution,[],[f141,f94]) ).
fof(f2010,plain,
( spl9_81
| ~ spl9_7
| ~ spl9_10
| ~ spl9_16 ),
inference(avatar_split_clause,[],[f1992,f306,f187,f168,f2007]) ).
fof(f2007,plain,
( spl9_81
<=> zero(any1) = subtract(any1,sK0(x,any1,apply(x,sK3(x,any1))),subtract(any1,sK0(x,any1,apply(x,sK3(x,any1))),zero(any1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_81])]) ).
fof(f1992,plain,
( zero(any1) = subtract(any1,sK0(x,any1,apply(x,sK3(x,any1))),subtract(any1,sK0(x,any1,apply(x,sK3(x,any1))),zero(any1)))
| ~ spl9_7
| ~ spl9_10
| ~ spl9_16 ),
inference(resolution,[],[f1387,f308]) ).
fof(f1387,plain,
( ! [X7] :
( ~ element(X7,any2)
| zero(any1) = subtract(any1,sK0(x,any1,X7),subtract(any1,sK0(x,any1,X7),zero(any1))) )
| ~ spl9_7
| ~ spl9_10 ),
inference(resolution,[],[f188,f288]) ).
fof(f288,plain,
( ! [X0] :
( ~ element(X0,any1)
| zero(any1) = subtract(any1,X0,subtract(any1,X0,zero(any1))) )
| ~ spl9_7 ),
inference(resolution,[],[f169,f94]) ).
fof(f1902,plain,
( spl9_80
| ~ spl9_3
| ~ spl9_12
| ~ spl9_15
| ~ spl9_41
| ~ spl9_74 ),
inference(avatar_split_clause,[],[f1833,f1613,f734,f297,f209,f126,f1899]) ).
fof(f1833,plain,
( subtract(any2,zero(any2),apply(x,sK3(x,any1))) = apply(x,subtract(any1,subtract(any1,sK4(x,any1),sK3(x,any1)),sK4(x,any1)))
| ~ spl9_3
| ~ spl9_12
| ~ spl9_15
| ~ spl9_41
| ~ spl9_74 ),
inference(forward_demodulation,[],[f1817,f299]) ).
fof(f299,plain,
( apply(x,sK3(x,any1)) = apply(x,sK4(x,any1))
| ~ spl9_15 ),
inference(avatar_component_clause,[],[f297]) ).
fof(f1817,plain,
( subtract(any2,zero(any2),apply(x,sK4(x,any1))) = apply(x,subtract(any1,subtract(any1,sK4(x,any1),sK3(x,any1)),sK4(x,any1)))
| ~ spl9_3
| ~ spl9_12
| ~ spl9_41
| ~ spl9_74 ),
inference(resolution,[],[f1662,f211]) ).
fof(f1844,plain,
( spl9_79
| ~ spl9_3
| ~ spl9_26
| ~ spl9_41
| ~ spl9_42
| ~ spl9_44
| ~ spl9_74 ),
inference(avatar_split_clause,[],[f1827,f1613,f794,f762,f734,f417,f126,f1841]) ).
fof(f1841,plain,
( spl9_79
<=> apply(x,sK3(x,any1)) = apply(x,subtract(any1,subtract(any1,sK4(x,any1),sK3(x,any1)),subtract(any1,zero(any1),sK3(x,any1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_79])]) ).
fof(f762,plain,
( spl9_42
<=> subtract(any2,zero(any2),apply(x,sK3(x,any1))) = apply(x,subtract(any1,zero(any1),sK3(x,any1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_42])]) ).
fof(f794,plain,
( spl9_44
<=> element(subtract(any1,zero(any1),sK3(x,any1)),any1) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_44])]) ).
fof(f1827,plain,
( apply(x,sK3(x,any1)) = apply(x,subtract(any1,subtract(any1,sK4(x,any1),sK3(x,any1)),subtract(any1,zero(any1),sK3(x,any1))))
| ~ spl9_3
| ~ spl9_26
| ~ spl9_41
| ~ spl9_42
| ~ spl9_44
| ~ spl9_74 ),
inference(forward_demodulation,[],[f1826,f419]) ).
fof(f1826,plain,
( subtract(any2,zero(any2),subtract(any2,zero(any2),apply(x,sK3(x,any1)))) = apply(x,subtract(any1,subtract(any1,sK4(x,any1),sK3(x,any1)),subtract(any1,zero(any1),sK3(x,any1))))
| ~ spl9_3
| ~ spl9_41
| ~ spl9_42
| ~ spl9_44
| ~ spl9_74 ),
inference(forward_demodulation,[],[f1809,f764]) ).
fof(f764,plain,
( subtract(any2,zero(any2),apply(x,sK3(x,any1))) = apply(x,subtract(any1,zero(any1),sK3(x,any1)))
| ~ spl9_42 ),
inference(avatar_component_clause,[],[f762]) ).
fof(f1809,plain,
( subtract(any2,zero(any2),apply(x,subtract(any1,zero(any1),sK3(x,any1)))) = apply(x,subtract(any1,subtract(any1,sK4(x,any1),sK3(x,any1)),subtract(any1,zero(any1),sK3(x,any1))))
| ~ spl9_3
| ~ spl9_41
| ~ spl9_44
| ~ spl9_74 ),
inference(resolution,[],[f1662,f795]) ).
fof(f795,plain,
( element(subtract(any1,zero(any1),sK3(x,any1)),any1)
| ~ spl9_44 ),
inference(avatar_component_clause,[],[f794]) ).
fof(f1839,plain,
( spl9_78
| ~ spl9_3
| ~ spl9_5
| ~ spl9_41
| ~ spl9_74 ),
inference(avatar_split_clause,[],[f1816,f1613,f734,f139,f126,f1836]) ).
fof(f1816,plain,
( subtract(any2,zero(any2),apply(x,sK3(x,any1))) = apply(x,subtract(any1,subtract(any1,sK4(x,any1),sK3(x,any1)),sK3(x,any1)))
| ~ spl9_3
| ~ spl9_5
| ~ spl9_41
| ~ spl9_74 ),
inference(resolution,[],[f1662,f141]) ).
fof(f1795,plain,
( spl9_77
| ~ spl9_5
| ~ spl9_12
| ~ spl9_35
| ~ spl9_74 ),
inference(avatar_split_clause,[],[f1676,f1613,f587,f209,f139,f1792]) ).
fof(f1792,plain,
( spl9_77
<=> subtract(any1,sK4(x,any1),sK3(x,any1)) = subtract(any1,subtract(any1,sK4(x,any1),sK3(x,any1)),zero(any1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_77])]) ).
fof(f587,plain,
( spl9_35
<=> zero(any1) = subtract(any1,subtract(any1,sK4(x,any1),sK3(x,any1)),subtract(any1,sK4(x,any1),sK3(x,any1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_35])]) ).
fof(f1676,plain,
( subtract(any1,sK4(x,any1),sK3(x,any1)) = subtract(any1,subtract(any1,sK4(x,any1),sK3(x,any1)),zero(any1))
| ~ spl9_5
| ~ spl9_12
| ~ spl9_35
| ~ spl9_74 ),
inference(forward_demodulation,[],[f1652,f589]) ).
fof(f589,plain,
( zero(any1) = subtract(any1,subtract(any1,sK4(x,any1),sK3(x,any1)),subtract(any1,sK4(x,any1),sK3(x,any1)))
| ~ spl9_35 ),
inference(avatar_component_clause,[],[f587]) ).
fof(f1652,plain,
( subtract(any1,sK4(x,any1),sK3(x,any1)) = subtract(any1,subtract(any1,sK4(x,any1),sK3(x,any1)),subtract(any1,subtract(any1,sK4(x,any1),sK3(x,any1)),subtract(any1,sK4(x,any1),sK3(x,any1))))
| ~ spl9_5
| ~ spl9_12
| ~ spl9_74 ),
inference(resolution,[],[f1615,f1532]) ).
fof(f1790,plain,
( spl9_76
| ~ spl9_3
| ~ spl9_5
| ~ spl9_25
| ~ spl9_41
| ~ spl9_74 ),
inference(avatar_split_clause,[],[f1670,f1613,f734,f407,f139,f126,f1787]) ).
fof(f1787,plain,
( spl9_76
<=> apply(x,sK3(x,any1)) = apply(x,subtract(any1,sK3(x,any1),subtract(any1,sK4(x,any1),sK3(x,any1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_76])]) ).
fof(f1670,plain,
( apply(x,sK3(x,any1)) = apply(x,subtract(any1,sK3(x,any1),subtract(any1,sK4(x,any1),sK3(x,any1))))
| ~ spl9_3
| ~ spl9_5
| ~ spl9_25
| ~ spl9_41
| ~ spl9_74 ),
inference(forward_demodulation,[],[f1669,f409]) ).
fof(f1669,plain,
( subtract(any2,apply(x,sK3(x,any1)),zero(any2)) = apply(x,subtract(any1,sK3(x,any1),subtract(any1,sK4(x,any1),sK3(x,any1))))
| ~ spl9_3
| ~ spl9_5
| ~ spl9_41
| ~ spl9_74 ),
inference(forward_demodulation,[],[f1642,f736]) ).
fof(f1642,plain,
( subtract(any2,apply(x,sK3(x,any1)),apply(x,subtract(any1,sK4(x,any1),sK3(x,any1)))) = apply(x,subtract(any1,sK3(x,any1),subtract(any1,sK4(x,any1),sK3(x,any1))))
| ~ spl9_3
| ~ spl9_5
| ~ spl9_74 ),
inference(resolution,[],[f1615,f677]) ).
fof(f677,plain,
( ! [X10] :
( ~ element(X10,any1)
| apply(x,subtract(any1,sK3(x,any1),X10)) = subtract(any2,apply(x,sK3(x,any1)),apply(x,X10)) )
| ~ spl9_3
| ~ spl9_5 ),
inference(resolution,[],[f457,f141]) ).
fof(f1775,plain,
( spl9_75
| ~ spl9_3
| ~ spl9_4
| ~ spl9_7
| ~ spl9_14
| ~ spl9_41
| ~ spl9_74 ),
inference(avatar_split_clause,[],[f1672,f1613,f734,f248,f168,f132,f126,f1772]) ).
fof(f1672,plain,
( zero(any2) = apply(x,subtract(any1,zero(any1),subtract(any1,sK4(x,any1),sK3(x,any1))))
| ~ spl9_3
| ~ spl9_4
| ~ spl9_7
| ~ spl9_14
| ~ spl9_41
| ~ spl9_74 ),
inference(forward_demodulation,[],[f1671,f250]) ).
fof(f1671,plain,
( subtract(any2,zero(any2),zero(any2)) = apply(x,subtract(any1,zero(any1),subtract(any1,sK4(x,any1),sK3(x,any1))))
| ~ spl9_3
| ~ spl9_4
| ~ spl9_7
| ~ spl9_41
| ~ spl9_74 ),
inference(forward_demodulation,[],[f1643,f736]) ).
fof(f1643,plain,
( subtract(any2,zero(any2),apply(x,subtract(any1,sK4(x,any1),sK3(x,any1)))) = apply(x,subtract(any1,zero(any1),subtract(any1,sK4(x,any1),sK3(x,any1))))
| ~ spl9_3
| ~ spl9_4
| ~ spl9_7
| ~ spl9_74 ),
inference(resolution,[],[f1615,f681]) ).
fof(f681,plain,
( ! [X0] :
( ~ element(X0,any1)
| subtract(any2,zero(any2),apply(x,X0)) = apply(x,subtract(any1,zero(any1),X0)) )
| ~ spl9_3
| ~ spl9_4
| ~ spl9_7 ),
inference(forward_demodulation,[],[f673,f134]) ).
fof(f673,plain,
( ! [X0] :
( ~ element(X0,any1)
| apply(x,subtract(any1,zero(any1),X0)) = subtract(any2,apply(x,zero(any1)),apply(x,X0)) )
| ~ spl9_3
| ~ spl9_7 ),
inference(resolution,[],[f457,f169]) ).
fof(f1680,plain,
( ~ spl9_7
| spl9_73
| ~ spl9_74 ),
inference(avatar_contradiction_clause,[],[f1679]) ).
fof(f1679,plain,
( $false
| ~ spl9_7
| spl9_73
| ~ spl9_74 ),
inference(subsumption_resolution,[],[f1678,f169]) ).
fof(f1678,plain,
( ~ element(zero(any1),any1)
| spl9_73
| ~ spl9_74 ),
inference(subsumption_resolution,[],[f1677,f1615]) ).
fof(f1677,plain,
( ~ element(subtract(any1,sK4(x,any1),sK3(x,any1)),any1)
| ~ element(zero(any1),any1)
| spl9_73 ),
inference(resolution,[],[f1611,f93]) ).
fof(f1611,plain,
( ~ element(subtract(any1,zero(any1),subtract(any1,sK4(x,any1),sK3(x,any1))),any1)
| spl9_73 ),
inference(avatar_component_clause,[],[f1609]) ).
fof(f1620,plain,
( ~ spl9_5
| ~ spl9_12
| spl9_74 ),
inference(avatar_contradiction_clause,[],[f1619]) ).
fof(f1619,plain,
( $false
| ~ spl9_5
| ~ spl9_12
| spl9_74 ),
inference(subsumption_resolution,[],[f1618,f211]) ).
fof(f1618,plain,
( ~ element(sK4(x,any1),any1)
| ~ spl9_5
| spl9_74 ),
inference(subsumption_resolution,[],[f1617,f141]) ).
fof(f1617,plain,
( ~ element(sK3(x,any1),any1)
| ~ element(sK4(x,any1),any1)
| spl9_74 ),
inference(resolution,[],[f1614,f93]) ).
fof(f1614,plain,
( ~ element(subtract(any1,sK4(x,any1),sK3(x,any1)),any1)
| spl9_74 ),
inference(avatar_component_clause,[],[f1613]) ).
fof(f1616,plain,
( ~ spl9_73
| spl9_74
| ~ spl9_7
| ~ spl9_72 ),
inference(avatar_split_clause,[],[f1607,f1602,f168,f1613,f1609]) ).
fof(f1602,plain,
( spl9_72
<=> subtract(any1,sK4(x,any1),sK3(x,any1)) = subtract(any1,zero(any1),subtract(any1,zero(any1),subtract(any1,sK4(x,any1),sK3(x,any1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_72])]) ).
fof(f1607,plain,
( element(subtract(any1,sK4(x,any1),sK3(x,any1)),any1)
| ~ element(subtract(any1,zero(any1),subtract(any1,sK4(x,any1),sK3(x,any1))),any1)
| ~ spl9_7
| ~ spl9_72 ),
inference(subsumption_resolution,[],[f1606,f169]) ).
fof(f1606,plain,
( element(subtract(any1,sK4(x,any1),sK3(x,any1)),any1)
| ~ element(subtract(any1,zero(any1),subtract(any1,sK4(x,any1),sK3(x,any1))),any1)
| ~ element(zero(any1),any1)
| ~ spl9_72 ),
inference(superposition,[],[f93,f1604]) ).
fof(f1604,plain,
( subtract(any1,sK4(x,any1),sK3(x,any1)) = subtract(any1,zero(any1),subtract(any1,zero(any1),subtract(any1,sK4(x,any1),sK3(x,any1))))
| ~ spl9_72 ),
inference(avatar_component_clause,[],[f1602]) ).
fof(f1605,plain,
( spl9_72
| ~ spl9_5
| ~ spl9_7
| ~ spl9_12 ),
inference(avatar_split_clause,[],[f1589,f209,f168,f139,f1602]) ).
fof(f1589,plain,
( subtract(any1,sK4(x,any1),sK3(x,any1)) = subtract(any1,zero(any1),subtract(any1,zero(any1),subtract(any1,sK4(x,any1),sK3(x,any1))))
| ~ spl9_5
| ~ spl9_7
| ~ spl9_12 ),
inference(resolution,[],[f1532,f169]) ).
fof(f1514,plain,
( spl9_71
| ~ spl9_3
| ~ spl9_9
| ~ spl9_42
| ~ spl9_44 ),
inference(avatar_split_clause,[],[f1449,f794,f762,f183,f126,f1510]) ).
fof(f1449,plain,
( subtract(any2,zero(any2),apply(x,sK3(x,any1))) = apply(x,sK0(x,any1,subtract(any2,zero(any2),apply(x,sK3(x,any1)))))
| ~ spl9_3
| ~ spl9_9
| ~ spl9_42
| ~ spl9_44 ),
inference(forward_demodulation,[],[f1437,f764]) ).
fof(f1437,plain,
( apply(x,subtract(any1,zero(any1),sK3(x,any1))) = apply(x,sK0(x,any1,apply(x,subtract(any1,zero(any1),sK3(x,any1)))))
| ~ spl9_3
| ~ spl9_9
| ~ spl9_44 ),
inference(resolution,[],[f1414,f795]) ).
fof(f1414,plain,
( ! [X0] :
( ~ element(X0,any1)
| apply(x,X0) = apply(x,sK0(x,any1,apply(x,X0))) )
| ~ spl9_3
| ~ spl9_9 ),
inference(resolution,[],[f1377,f163]) ).
fof(f1377,plain,
( ! [X0] :
( ~ element(X0,any2)
| apply(x,sK0(x,any1,X0)) = X0 )
| ~ spl9_3
| ~ spl9_9 ),
inference(global_subsumption,[],[f82,f84,f128,f85,f87,f130,f100,f101,f86,f93,f163,f95,f97,f99,f103,f165,f89,f181,f94,f193,f98,f162,f90,f83,f136,f194,f96,f102,f91,f92,f106,f88,f164,f472,f473,f474,f107,f176,f177,f190,f542,f543,f544,f104,f108,f613,f614,f615,f616,f617,f634,f635,f636,f637,f638,f457,f674,f675,f676,f679,f680,f105,f113,f802,f109,f875,f876,f877,f878,f879,f886,f110,f939,f940,f941,f942,f943,f950,f522,f1008,f115,f111,f1069,f114,f1113,f1114,f1116,f468,f1128,f1129,f1130,f1133,f1134,f1135,f1136,f178,f1142,f1143,f1144,f1147,f1148,f1149,f1150,f179,f112,f180,f184,f1262,f1263,f1267,f1268,f1269,f1270,f1271,f1272,f1273,f191,f1279,f1283,f1287,f1288,f1291,f1292,f1293,f1294,f192,f1315,f1374,f240]) ).
fof(f1374,plain,
( surjection(x)
| ~ spl9_3
| ~ spl9_9 ),
inference(global_subsumption,[],[f1315,f82,f84,f85,f87,f100,f101,f86,f93,f95,f97,f99,f103,f89,f94,f193,f98,f90,f83,f96,f102,f91,f92,f106,f88,f164,f472,f473,f474,f107,f176,f177,f104,f108,f613,f614,f615,f634,f635,f636,f105,f113,f109,f875,f876,f877,f110,f939,f940,f941,f522,f115,f111,f114,f1113,f112,f184,f191,f1283,f1287,f1288,f1291,f1292,f1293,f1294,f192]) ).
fof(f1273,plain,
( ! [X21,X19,X22,X20] :
( sK7(X19,X20,any2,X21,X22) = apply(x,sK0(x,any1,sK7(X19,X20,any2,X21,X22)))
| element(sK6(X19,X20,any2,X21,X22),X21)
| exact(X19,X20)
| ~ morphism(X20,X21,X22)
| ~ morphism(X19,any2,X21) )
| ~ spl9_3
| ~ spl9_9 ),
inference(resolution,[],[f1262,f108]) ).
fof(f1272,plain,
( ! [X18,X16,X17,X15] :
( sK7(X15,X16,any2,X17,X18) = apply(x,sK0(x,any1,sK7(X15,X16,any2,X17,X18)))
| exact(X15,X16)
| zero(X18) = apply(X16,sK6(X15,X16,any2,X17,X18))
| ~ morphism(X16,X17,X18)
| ~ morphism(X15,any2,X17) )
| ~ spl9_3
| ~ spl9_9 ),
inference(resolution,[],[f1262,f109]) ).
fof(f1271,plain,
( ! [X11,X14,X12,X13] :
( sK6(X11,X12,X13,any2,X14) = apply(x,sK0(x,any1,sK6(X11,X12,X13,any2,X14)))
| element(sK7(X11,X12,X13,any2,X14),X13)
| exact(X11,X12)
| ~ morphism(X12,any2,X14)
| ~ morphism(X11,X13,any2) )
| ~ spl9_3
| ~ spl9_9 ),
inference(resolution,[],[f1262,f108]) ).
fof(f1270,plain,
( ! [X10,X8,X9,X7] :
( sK6(X7,X8,X9,any2,X10) = apply(x,sK0(x,any1,sK6(X7,X8,X9,any2,X10)))
| sK6(X7,X8,X9,any2,X10) = apply(X7,sK7(X7,X8,X9,any2,X10))
| exact(X7,X8)
| ~ morphism(X8,any2,X10)
| ~ morphism(X7,X9,any2) )
| ~ spl9_3
| ~ spl9_9 ),
inference(resolution,[],[f1262,f110]) ).
fof(f1269,plain,
( ! [X6,X5] :
( sK2(X5,any2,X6) = apply(x,sK0(x,any1,sK2(X5,any2,X6)))
| injection_2(X5)
| ~ morphism(X5,any2,X6) )
| ~ spl9_3
| ~ spl9_9 ),
inference(resolution,[],[f1262,f97]) ).
fof(f1268,plain,
( ! [X3,X4] :
( sK1(X3,X4,any2) = apply(x,sK0(x,any1,sK1(X3,X4,any2)))
| surjection(X3)
| ~ morphism(X3,X4,any2) )
| ~ spl9_3
| ~ spl9_9 ),
inference(resolution,[],[f1262,f95]) ).
fof(f1267,plain,
( ! [X2,X1] :
( subtract(any2,X1,X2) = apply(x,sK0(x,any1,subtract(any2,X1,X2)))
| ~ element(X2,any2)
| ~ element(X1,any2) )
| ~ spl9_3
| ~ spl9_9 ),
inference(resolution,[],[f1262,f93]) ).
fof(f1263,plain,
( ! [X0] :
( apply(x,X0) = apply(x,sK0(x,any1,apply(x,X0)))
| ~ element(X0,any1) )
| ~ spl9_3
| ~ spl9_9 ),
inference(resolution,[],[f1262,f163]) ).
fof(f1262,plain,
( ! [X0] :
( ~ element(X0,any2)
| apply(x,sK0(x,any1,X0)) = X0 )
| ~ spl9_3
| ~ spl9_9 ),
inference(subsumption_resolution,[],[f240,f184]) ).
fof(f184,plain,
( surjection(x)
| ~ spl9_9 ),
inference(avatar_component_clause,[],[f183]) ).
fof(f1513,plain,
( spl9_71
| ~ spl9_3
| ~ spl9_9
| ~ spl9_45 ),
inference(avatar_split_clause,[],[f1417,f798,f183,f126,f1510]) ).
fof(f1417,plain,
( subtract(any2,zero(any2),apply(x,sK3(x,any1))) = apply(x,sK0(x,any1,subtract(any2,zero(any2),apply(x,sK3(x,any1)))))
| ~ spl9_3
| ~ spl9_9
| ~ spl9_45 ),
inference(resolution,[],[f1377,f800]) ).
fof(f1502,plain,
( spl9_69
| spl9_70
| ~ spl9_2
| ~ spl9_8
| ~ spl9_10
| ~ spl9_61 ),
inference(avatar_split_clause,[],[f1494,f1275,f187,f172,f121,f1499,f1496]) ).
fof(f1494,plain,
( ! [X0] :
( zero(any1) = sK0(x,any1,zero(any2))
| zero(X0) != zero(any2)
| ~ morphism(x,any1,X0) )
| ~ spl9_2
| ~ spl9_8
| ~ spl9_10
| ~ spl9_61 ),
inference(subsumption_resolution,[],[f1493,f174]) ).
fof(f1493,plain,
( ! [X0] :
( zero(any1) = sK0(x,any1,zero(any2))
| zero(X0) != zero(any2)
| ~ morphism(x,any1,X0)
| ~ element(zero(any2),any2) )
| ~ spl9_2
| ~ spl9_10
| ~ spl9_61 ),
inference(resolution,[],[f1304,f188]) ).
fof(f1304,plain,
( ! [X0,X1] :
( ~ element(sK0(x,any1,zero(any2)),X1)
| zero(X1) = sK0(x,any1,zero(any2))
| zero(X0) != zero(any2)
| ~ morphism(x,X1,X0) )
| ~ spl9_2
| ~ spl9_61 ),
inference(subsumption_resolution,[],[f1296,f123]) ).
fof(f1296,plain,
( ! [X0,X1] :
( zero(X0) != zero(any2)
| zero(X1) = sK0(x,any1,zero(any2))
| ~ element(sK0(x,any1,zero(any2)),X1)
| ~ morphism(x,X1,X0)
| ~ injection_2(x) )
| ~ spl9_61 ),
inference(superposition,[],[f91,f1277]) ).
fof(f1491,plain,
( spl9_68
| ~ spl9_5
| ~ spl9_8
| ~ spl9_10 ),
inference(avatar_split_clause,[],[f1478,f187,f172,f139,f1488]) ).
fof(f1488,plain,
( spl9_68
<=> sK3(x,any1) = subtract(any1,sK0(x,any1,zero(any2)),subtract(any1,sK0(x,any1,zero(any2)),sK3(x,any1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_68])]) ).
fof(f1478,plain,
( sK3(x,any1) = subtract(any1,sK0(x,any1,zero(any2)),subtract(any1,sK0(x,any1,zero(any2)),sK3(x,any1)))
| ~ spl9_5
| ~ spl9_8
| ~ spl9_10 ),
inference(resolution,[],[f1386,f174]) ).
fof(f1473,plain,
( spl9_67
| ~ spl9_10
| ~ spl9_16 ),
inference(avatar_split_clause,[],[f1452,f306,f187,f1470]) ).
fof(f1470,plain,
( spl9_67
<=> zero(any1) = subtract(any1,sK0(x,any1,apply(x,sK3(x,any1))),sK0(x,any1,apply(x,sK3(x,any1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_67])]) ).
fof(f1452,plain,
( zero(any1) = subtract(any1,sK0(x,any1,apply(x,sK3(x,any1))),sK0(x,any1,apply(x,sK3(x,any1))))
| ~ spl9_10
| ~ spl9_16 ),
inference(resolution,[],[f1413,f308]) ).
fof(f1413,plain,
( ! [X41] :
( ~ element(X41,any2)
| zero(any1) = subtract(any1,sK0(x,any1,X41),sK0(x,any1,X41)) )
| ~ spl9_10 ),
inference(resolution,[],[f188,f85]) ).
fof(f1466,plain,
( spl9_66
| ~ spl9_8
| ~ spl9_10 ),
inference(avatar_split_clause,[],[f1453,f187,f172,f1463]) ).
fof(f1453,plain,
( zero(any1) = subtract(any1,sK0(x,any1,zero(any2)),sK0(x,any1,zero(any2)))
| ~ spl9_8
| ~ spl9_10 ),
inference(resolution,[],[f1413,f174]) ).
fof(f1371,plain,
( ~ spl9_8
| spl9_64
| ~ spl9_65 ),
inference(avatar_contradiction_clause,[],[f1370]) ).
fof(f1370,plain,
( $false
| ~ spl9_8
| spl9_64
| ~ spl9_65 ),
inference(subsumption_resolution,[],[f1369,f174]) ).
fof(f1369,plain,
( ~ element(zero(any2),any2)
| spl9_64
| ~ spl9_65 ),
inference(subsumption_resolution,[],[f1368,f1346]) ).
fof(f1368,plain,
( ~ element(sK1(x,any1,any2),any2)
| ~ element(zero(any2),any2)
| spl9_64 ),
inference(resolution,[],[f1342,f93]) ).
fof(f1342,plain,
( ~ element(subtract(any2,zero(any2),sK1(x,any1,any2)),any2)
| spl9_64 ),
inference(avatar_component_clause,[],[f1340]) ).
fof(f1351,plain,
( ~ spl9_3
| spl9_9
| spl9_65 ),
inference(avatar_contradiction_clause,[],[f1350]) ).
fof(f1350,plain,
( $false
| ~ spl9_3
| spl9_9
| spl9_65 ),
inference(subsumption_resolution,[],[f1349,f128]) ).
fof(f1349,plain,
( ~ morphism(x,any1,any2)
| spl9_9
| spl9_65 ),
inference(subsumption_resolution,[],[f1348,f185]) ).
fof(f1348,plain,
( surjection(x)
| ~ morphism(x,any1,any2)
| spl9_65 ),
inference(resolution,[],[f1345,f95]) ).
fof(f1345,plain,
( ~ element(sK1(x,any1,any2),any2)
| spl9_65 ),
inference(avatar_component_clause,[],[f1344]) ).
fof(f1347,plain,
( ~ spl9_64
| spl9_65
| ~ spl9_8
| ~ spl9_63 ),
inference(avatar_split_clause,[],[f1338,f1333,f172,f1344,f1340]) ).
fof(f1333,plain,
( spl9_63
<=> sK1(x,any1,any2) = subtract(any2,zero(any2),subtract(any2,zero(any2),sK1(x,any1,any2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_63])]) ).
fof(f1338,plain,
( element(sK1(x,any1,any2),any2)
| ~ element(subtract(any2,zero(any2),sK1(x,any1,any2)),any2)
| ~ spl9_8
| ~ spl9_63 ),
inference(subsumption_resolution,[],[f1337,f174]) ).
fof(f1337,plain,
( element(sK1(x,any1,any2),any2)
| ~ element(subtract(any2,zero(any2),sK1(x,any1,any2)),any2)
| ~ element(zero(any2),any2)
| ~ spl9_63 ),
inference(superposition,[],[f93,f1335]) ).
fof(f1335,plain,
( sK1(x,any1,any2) = subtract(any2,zero(any2),subtract(any2,zero(any2),sK1(x,any1,any2)))
| ~ spl9_63 ),
inference(avatar_component_clause,[],[f1333]) ).
fof(f1336,plain,
( spl9_63
| ~ spl9_3
| ~ spl9_8
| spl9_9 ),
inference(avatar_split_clause,[],[f1323,f183,f172,f126,f1333]) ).
fof(f1323,plain,
( sK1(x,any1,any2) = subtract(any2,zero(any2),subtract(any2,zero(any2),sK1(x,any1,any2)))
| ~ spl9_3
| ~ spl9_8
| spl9_9 ),
inference(resolution,[],[f1316,f174]) ).
fof(f1309,plain,
( spl9_62
| ~ spl9_3
| ~ spl9_9
| ~ spl9_16 ),
inference(avatar_split_clause,[],[f1264,f306,f183,f126,f1306]) ).
fof(f1306,plain,
( spl9_62
<=> apply(x,sK3(x,any1)) = apply(x,sK0(x,any1,apply(x,sK3(x,any1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_62])]) ).
fof(f1264,plain,
( apply(x,sK3(x,any1)) = apply(x,sK0(x,any1,apply(x,sK3(x,any1))))
| ~ spl9_3
| ~ spl9_9
| ~ spl9_16 ),
inference(resolution,[],[f1262,f308]) ).
fof(f1278,plain,
( spl9_61
| ~ spl9_3
| ~ spl9_8
| ~ spl9_9 ),
inference(avatar_split_clause,[],[f1265,f183,f172,f126,f1275]) ).
fof(f1265,plain,
( zero(any2) = apply(x,sK0(x,any1,zero(any2)))
| ~ spl9_3
| ~ spl9_8
| ~ spl9_9 ),
inference(resolution,[],[f1262,f174]) ).
fof(f1230,plain,
( spl9_60
| ~ spl9_3
| ~ spl9_8
| spl9_9 ),
inference(avatar_split_clause,[],[f1225,f183,f172,f126,f1227]) ).
fof(f1227,plain,
( spl9_60
<=> zero(any2) = subtract(any2,sK1(x,any1,any2),subtract(any2,sK1(x,any1,any2),zero(any2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_60])]) ).
fof(f1225,plain,
( zero(any2) = subtract(any2,sK1(x,any1,any2),subtract(any2,sK1(x,any1,any2),zero(any2)))
| ~ spl9_3
| ~ spl9_8
| spl9_9 ),
inference(subsumption_resolution,[],[f1224,f185]) ).
fof(f1224,plain,
( surjection(x)
| zero(any2) = subtract(any2,sK1(x,any1,any2),subtract(any2,sK1(x,any1,any2),zero(any2)))
| ~ spl9_3
| ~ spl9_8 ),
inference(resolution,[],[f369,f128]) ).
fof(f1121,plain,
( spl9_59
| ~ spl9_12
| ~ spl9_44 ),
inference(avatar_split_clause,[],[f982,f794,f209,f1118]) ).
fof(f982,plain,
( zero(any1) = subtract(any1,subtract(any1,subtract(any1,zero(any1),sK3(x,any1)),sK4(x,any1)),subtract(any1,subtract(any1,zero(any1),sK3(x,any1)),sK4(x,any1)))
| ~ spl9_12
| ~ spl9_44 ),
inference(resolution,[],[f825,f211]) ).
fof(f825,plain,
( ! [X3] :
( ~ element(X3,any1)
| zero(any1) = subtract(any1,subtract(any1,subtract(any1,zero(any1),sK3(x,any1)),X3),subtract(any1,subtract(any1,zero(any1),sK3(x,any1)),X3)) )
| ~ spl9_44 ),
inference(resolution,[],[f795,f164]) ).
fof(f1112,plain,
( spl9_58
| ~ spl9_5
| ~ spl9_44 ),
inference(avatar_split_clause,[],[f981,f794,f139,f1109]) ).
fof(f981,plain,
( zero(any1) = subtract(any1,subtract(any1,subtract(any1,zero(any1),sK3(x,any1)),sK3(x,any1)),subtract(any1,subtract(any1,zero(any1),sK3(x,any1)),sK3(x,any1)))
| ~ spl9_5
| ~ spl9_44 ),
inference(resolution,[],[f825,f141]) ).
fof(f1103,plain,
( spl9_56
| ~ spl9_5
| ~ spl9_7
| ~ spl9_44
| ~ spl9_47 ),
inference(avatar_split_clause,[],[f1053,f863,f794,f168,f139,f1094]) ).
fof(f863,plain,
( spl9_47
<=> subtract(any1,zero(any1),sK3(x,any1)) = subtract(any1,subtract(any1,zero(any1),sK3(x,any1)),zero(any1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_47])]) ).
fof(f1053,plain,
( zero(any1) = subtract(any1,subtract(any1,sK3(x,any1),subtract(any1,zero(any1),sK3(x,any1))),subtract(any1,sK3(x,any1),subtract(any1,zero(any1),sK3(x,any1))))
| ~ spl9_5
| ~ spl9_7
| ~ spl9_44
| ~ spl9_47 ),
inference(forward_demodulation,[],[f1041,f865]) ).
fof(f865,plain,
( subtract(any1,zero(any1),sK3(x,any1)) = subtract(any1,subtract(any1,zero(any1),sK3(x,any1)),zero(any1))
| ~ spl9_47 ),
inference(avatar_component_clause,[],[f863]) ).
fof(f1041,plain,
( zero(any1) = subtract(any1,subtract(any1,sK3(x,any1),subtract(any1,subtract(any1,zero(any1),sK3(x,any1)),zero(any1))),subtract(any1,sK3(x,any1),subtract(any1,subtract(any1,zero(any1),sK3(x,any1)),zero(any1))))
| ~ spl9_5
| ~ spl9_7
| ~ spl9_44 ),
inference(resolution,[],[f1029,f795]) ).
fof(f1029,plain,
( ! [X0] :
( ~ element(X0,any1)
| zero(any1) = subtract(any1,subtract(any1,sK3(x,any1),subtract(any1,X0,zero(any1))),subtract(any1,sK3(x,any1),subtract(any1,X0,zero(any1)))) )
| ~ spl9_5
| ~ spl9_7 ),
inference(resolution,[],[f478,f169]) ).
fof(f478,plain,
( ! [X0,X1] :
( ~ element(X1,any1)
| zero(any1) = subtract(any1,subtract(any1,sK3(x,any1),subtract(any1,X0,X1)),subtract(any1,sK3(x,any1),subtract(any1,X0,X1)))
| ~ element(X0,any1) )
| ~ spl9_5 ),
inference(resolution,[],[f475,f93]) ).
fof(f475,plain,
( ! [X17] :
( ~ element(X17,any1)
| zero(any1) = subtract(any1,subtract(any1,sK3(x,any1),X17),subtract(any1,sK3(x,any1),X17)) )
| ~ spl9_5 ),
inference(resolution,[],[f164,f141]) ).
fof(f1102,plain,
( spl9_57
| ~ spl9_12
| ~ spl9_44 ),
inference(avatar_split_clause,[],[f818,f794,f209,f1099]) ).
fof(f818,plain,
( zero(any1) = subtract(any1,subtract(any1,sK4(x,any1),subtract(any1,zero(any1),sK3(x,any1))),subtract(any1,sK4(x,any1),subtract(any1,zero(any1),sK3(x,any1))))
| ~ spl9_12
| ~ spl9_44 ),
inference(resolution,[],[f795,f476]) ).
fof(f476,plain,
( ! [X18] :
( ~ element(X18,any1)
| zero(any1) = subtract(any1,subtract(any1,sK4(x,any1),X18),subtract(any1,sK4(x,any1),X18)) )
| ~ spl9_12 ),
inference(resolution,[],[f164,f211]) ).
fof(f1097,plain,
( spl9_56
| ~ spl9_5
| ~ spl9_44 ),
inference(avatar_split_clause,[],[f817,f794,f139,f1094]) ).
fof(f817,plain,
( zero(any1) = subtract(any1,subtract(any1,sK3(x,any1),subtract(any1,zero(any1),sK3(x,any1))),subtract(any1,sK3(x,any1),subtract(any1,zero(any1),sK3(x,any1))))
| ~ spl9_5
| ~ spl9_44 ),
inference(resolution,[],[f795,f475]) ).
fof(f1091,plain,
( spl9_55
| ~ spl9_3
| spl9_9
| ~ spl9_16 ),
inference(avatar_split_clause,[],[f1086,f306,f183,f126,f1088]) ).
fof(f1086,plain,
( apply(x,sK3(x,any1)) = subtract(any2,sK1(x,any1,any2),subtract(any2,sK1(x,any1,any2),apply(x,sK3(x,any1))))
| ~ spl9_3
| spl9_9
| ~ spl9_16 ),
inference(subsumption_resolution,[],[f1085,f185]) ).
fof(f1085,plain,
( surjection(x)
| apply(x,sK3(x,any1)) = subtract(any2,sK1(x,any1,any2),subtract(any2,sK1(x,any1,any2),apply(x,sK3(x,any1))))
| ~ spl9_3
| ~ spl9_16 ),
inference(resolution,[],[f403,f128]) ).
fof(f403,plain,
( ! [X3,X4] :
( ~ morphism(X3,X4,any2)
| surjection(X3)
| apply(x,sK3(x,any1)) = subtract(any2,sK1(X3,X4,any2),subtract(any2,sK1(X3,X4,any2),apply(x,sK3(x,any1)))) )
| ~ spl9_16 ),
inference(resolution,[],[f310,f95]) ).
fof(f310,plain,
( ! [X0] :
( ~ element(X0,any2)
| apply(x,sK3(x,any1)) = subtract(any2,X0,subtract(any2,X0,apply(x,sK3(x,any1)))) )
| ~ spl9_16 ),
inference(resolution,[],[f308,f94]) ).
fof(f1005,plain,
( spl9_54
| ~ spl9_3
| ~ spl9_31
| ~ spl9_42
| ~ spl9_44
| ~ spl9_45 ),
inference(avatar_split_clause,[],[f1000,f798,f794,f762,f500,f126,f1002]) ).
fof(f1002,plain,
( spl9_54
<=> subtract(any2,zero(any2),apply(x,sK3(x,any1))) = subtract(any2,subtract(any2,zero(any2),apply(x,sK3(x,any1))),zero(any2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_54])]) ).
fof(f500,plain,
( spl9_31
<=> zero(any2) = subtract(any2,subtract(any2,zero(any2),apply(x,sK3(x,any1))),subtract(any2,zero(any2),apply(x,sK3(x,any1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_31])]) ).
fof(f1000,plain,
( subtract(any2,zero(any2),apply(x,sK3(x,any1))) = subtract(any2,subtract(any2,zero(any2),apply(x,sK3(x,any1))),zero(any2))
| ~ spl9_3
| ~ spl9_31
| ~ spl9_42
| ~ spl9_44
| ~ spl9_45 ),
inference(forward_demodulation,[],[f992,f502]) ).
fof(f502,plain,
( zero(any2) = subtract(any2,subtract(any2,zero(any2),apply(x,sK3(x,any1))),subtract(any2,zero(any2),apply(x,sK3(x,any1))))
| ~ spl9_31 ),
inference(avatar_component_clause,[],[f500]) ).
fof(f992,plain,
( subtract(any2,zero(any2),apply(x,sK3(x,any1))) = subtract(any2,subtract(any2,zero(any2),apply(x,sK3(x,any1))),subtract(any2,subtract(any2,zero(any2),apply(x,sK3(x,any1))),subtract(any2,zero(any2),apply(x,sK3(x,any1)))))
| ~ spl9_3
| ~ spl9_42
| ~ spl9_44
| ~ spl9_45 ),
inference(resolution,[],[f829,f800]) ).
fof(f829,plain,
( ! [X0] :
( ~ element(X0,any2)
| subtract(any2,zero(any2),apply(x,sK3(x,any1))) = subtract(any2,X0,subtract(any2,X0,subtract(any2,zero(any2),apply(x,sK3(x,any1))))) )
| ~ spl9_3
| ~ spl9_42
| ~ spl9_44 ),
inference(forward_demodulation,[],[f808,f764]) ).
fof(f808,plain,
( ! [X0] :
( ~ element(X0,any2)
| apply(x,subtract(any1,zero(any1),sK3(x,any1))) = subtract(any2,X0,subtract(any2,X0,apply(x,subtract(any1,zero(any1),sK3(x,any1))))) )
| ~ spl9_3
| ~ spl9_44 ),
inference(resolution,[],[f795,f190]) ).
fof(f973,plain,
( spl9_52
| spl9_53
| ~ spl9_3
| ~ spl9_5
| ~ spl9_12
| ~ spl9_40 ),
inference(avatar_split_clause,[],[f966,f698,f209,f139,f126,f971,f968]) ).
fof(f966,plain,
( ! [X2,X0,X1] :
( zero(any2) != X0
| ~ morphism(X1,any2,X2)
| element(X0,any2)
| ~ exact(x,X1) )
| ~ spl9_3
| ~ spl9_5
| ~ spl9_12
| ~ spl9_40 ),
inference(resolution,[],[f938,f128]) ).
fof(f938,plain,
( ! [X2,X3,X0,X1] :
( ~ morphism(x,any1,X1)
| zero(any2) != X0
| ~ morphism(X2,X1,X3)
| element(X0,X1)
| ~ exact(x,X2) )
| ~ spl9_5
| ~ spl9_12
| ~ spl9_40 ),
inference(subsumption_resolution,[],[f937,f141]) ).
fof(f937,plain,
( ! [X2,X3,X0,X1] :
( element(X0,X1)
| zero(any2) != X0
| ~ morphism(X2,X1,X3)
| ~ morphism(x,any1,X1)
| ~ exact(x,X2)
| ~ element(sK3(x,any1),any1) )
| ~ spl9_12
| ~ spl9_40 ),
inference(subsumption_resolution,[],[f936,f211]) ).
fof(f936,plain,
( ! [X2,X3,X0,X1] :
( element(X0,X1)
| zero(any2) != X0
| ~ morphism(X2,X1,X3)
| ~ morphism(x,any1,X1)
| ~ exact(x,X2)
| ~ element(sK4(x,any1),any1)
| ~ element(sK3(x,any1),any1) )
| ~ spl9_40 ),
inference(resolution,[],[f708,f93]) ).
fof(f708,plain,
( ! [X18,X16,X14,X17,X15] :
( ~ element(subtract(any1,sK3(x,any1),sK4(x,any1)),X16)
| element(X14,X15)
| zero(any2) != X14
| ~ morphism(X17,X15,X18)
| ~ morphism(x,X16,X15)
| ~ exact(x,X17) )
| ~ spl9_40 ),
inference(superposition,[],[f106,f700]) ).
fof(f918,plain,
( spl9_51
| ~ spl9_8
| ~ spl9_45 ),
inference(avatar_split_clause,[],[f841,f798,f172,f914]) ).
fof(f914,plain,
( spl9_51
<=> zero(any2) = subtract(any2,subtract(any2,zero(any2),apply(x,sK3(x,any1))),subtract(any2,subtract(any2,zero(any2),apply(x,sK3(x,any1))),zero(any2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_51])]) ).
fof(f917,plain,
( spl9_51
| ~ spl9_3
| ~ spl9_8
| ~ spl9_42
| ~ spl9_44 ),
inference(avatar_split_clause,[],[f830,f794,f762,f172,f126,f914]) ).
fof(f830,plain,
( zero(any2) = subtract(any2,subtract(any2,zero(any2),apply(x,sK3(x,any1))),subtract(any2,subtract(any2,zero(any2),apply(x,sK3(x,any1))),zero(any2)))
| ~ spl9_3
| ~ spl9_8
| ~ spl9_42
| ~ spl9_44 ),
inference(forward_demodulation,[],[f813,f764]) ).
fof(f813,plain,
( zero(any2) = subtract(any2,apply(x,subtract(any1,zero(any1),sK3(x,any1))),subtract(any2,apply(x,subtract(any1,zero(any1),sK3(x,any1))),zero(any2)))
| ~ spl9_3
| ~ spl9_8
| ~ spl9_44 ),
inference(resolution,[],[f795,f365]) ).
fof(f365,plain,
( ! [X0] :
( ~ element(X0,any1)
| zero(any2) = subtract(any2,apply(x,X0),subtract(any2,apply(x,X0),zero(any2))) )
| ~ spl9_3
| ~ spl9_8 ),
inference(resolution,[],[f241,f163]) ).
fof(f910,plain,
( spl9_50
| ~ spl9_12
| ~ spl9_44 ),
inference(avatar_split_clause,[],[f858,f794,f209,f907]) ).
fof(f907,plain,
( spl9_50
<=> subtract(any1,zero(any1),sK3(x,any1)) = subtract(any1,sK4(x,any1),subtract(any1,sK4(x,any1),subtract(any1,zero(any1),sK3(x,any1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_50])]) ).
fof(f858,plain,
( subtract(any1,zero(any1),sK3(x,any1)) = subtract(any1,sK4(x,any1),subtract(any1,sK4(x,any1),subtract(any1,zero(any1),sK3(x,any1))))
| ~ spl9_12
| ~ spl9_44 ),
inference(resolution,[],[f826,f211]) ).
fof(f826,plain,
( ! [X4] :
( ~ element(X4,any1)
| subtract(any1,zero(any1),sK3(x,any1)) = subtract(any1,X4,subtract(any1,X4,subtract(any1,zero(any1),sK3(x,any1)))) )
| ~ spl9_44 ),
inference(resolution,[],[f795,f94]) ).
fof(f905,plain,
( spl9_49
| ~ spl9_5
| ~ spl9_44 ),
inference(avatar_split_clause,[],[f857,f794,f139,f902]) ).
fof(f902,plain,
( spl9_49
<=> subtract(any1,zero(any1),sK3(x,any1)) = subtract(any1,sK3(x,any1),subtract(any1,sK3(x,any1),subtract(any1,zero(any1),sK3(x,any1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_49])]) ).
fof(f857,plain,
( subtract(any1,zero(any1),sK3(x,any1)) = subtract(any1,sK3(x,any1),subtract(any1,sK3(x,any1),subtract(any1,zero(any1),sK3(x,any1))))
| ~ spl9_5
| ~ spl9_44 ),
inference(resolution,[],[f826,f141]) ).
fof(f873,plain,
( spl9_48
| ~ spl9_12
| ~ spl9_44 ),
inference(avatar_split_clause,[],[f809,f794,f209,f870]) ).
fof(f870,plain,
( spl9_48
<=> sK4(x,any1) = subtract(any1,subtract(any1,zero(any1),sK3(x,any1)),subtract(any1,subtract(any1,zero(any1),sK3(x,any1)),sK4(x,any1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_48])]) ).
fof(f809,plain,
( sK4(x,any1) = subtract(any1,subtract(any1,zero(any1),sK3(x,any1)),subtract(any1,subtract(any1,zero(any1),sK3(x,any1)),sK4(x,any1)))
| ~ spl9_12
| ~ spl9_44 ),
inference(resolution,[],[f795,f231]) ).
fof(f866,plain,
( spl9_47
| ~ spl9_32
| ~ spl9_44 ),
inference(avatar_split_clause,[],[f861,f794,f514,f863]) ).
fof(f514,plain,
( spl9_32
<=> zero(any1) = subtract(any1,subtract(any1,zero(any1),sK3(x,any1)),subtract(any1,zero(any1),sK3(x,any1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_32])]) ).
fof(f861,plain,
( subtract(any1,zero(any1),sK3(x,any1)) = subtract(any1,subtract(any1,zero(any1),sK3(x,any1)),zero(any1))
| ~ spl9_32
| ~ spl9_44 ),
inference(forward_demodulation,[],[f853,f516]) ).
fof(f516,plain,
( zero(any1) = subtract(any1,subtract(any1,zero(any1),sK3(x,any1)),subtract(any1,zero(any1),sK3(x,any1)))
| ~ spl9_32 ),
inference(avatar_component_clause,[],[f514]) ).
fof(f853,plain,
( subtract(any1,zero(any1),sK3(x,any1)) = subtract(any1,subtract(any1,zero(any1),sK3(x,any1)),subtract(any1,subtract(any1,zero(any1),sK3(x,any1)),subtract(any1,zero(any1),sK3(x,any1))))
| ~ spl9_44 ),
inference(resolution,[],[f826,f795]) ).
fof(f850,plain,
( spl9_46
| ~ spl9_7
| ~ spl9_44 ),
inference(avatar_split_clause,[],[f811,f794,f168,f847]) ).
fof(f847,plain,
( spl9_46
<=> zero(any1) = subtract(any1,subtract(any1,zero(any1),sK3(x,any1)),subtract(any1,subtract(any1,zero(any1),sK3(x,any1)),zero(any1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_46])]) ).
fof(f811,plain,
( zero(any1) = subtract(any1,subtract(any1,zero(any1),sK3(x,any1)),subtract(any1,subtract(any1,zero(any1),sK3(x,any1)),zero(any1)))
| ~ spl9_7
| ~ spl9_44 ),
inference(resolution,[],[f795,f288]) ).
fof(f806,plain,
( ~ spl9_5
| ~ spl9_7
| spl9_44 ),
inference(avatar_contradiction_clause,[],[f805]) ).
fof(f805,plain,
( $false
| ~ spl9_5
| ~ spl9_7
| spl9_44 ),
inference(subsumption_resolution,[],[f804,f169]) ).
fof(f804,plain,
( ~ element(zero(any1),any1)
| ~ spl9_5
| spl9_44 ),
inference(subsumption_resolution,[],[f803,f141]) ).
fof(f803,plain,
( ~ element(sK3(x,any1),any1)
| ~ element(zero(any1),any1)
| spl9_44 ),
inference(resolution,[],[f796,f93]) ).
fof(f796,plain,
( ~ element(subtract(any1,zero(any1),sK3(x,any1)),any1)
| spl9_44 ),
inference(avatar_component_clause,[],[f794]) ).
fof(f801,plain,
( ~ spl9_44
| spl9_45
| ~ spl9_3
| ~ spl9_42 ),
inference(avatar_split_clause,[],[f771,f762,f126,f798,f794]) ).
fof(f771,plain,
( element(subtract(any2,zero(any2),apply(x,sK3(x,any1))),any2)
| ~ element(subtract(any1,zero(any1),sK3(x,any1)),any1)
| ~ spl9_3
| ~ spl9_42 ),
inference(superposition,[],[f163,f764]) ).
fof(f770,plain,
( spl9_43
| ~ spl9_3
| ~ spl9_4
| ~ spl9_7
| ~ spl9_12
| ~ spl9_15 ),
inference(avatar_split_clause,[],[f760,f297,f209,f168,f132,f126,f767]) ).
fof(f767,plain,
( spl9_43
<=> subtract(any2,zero(any2),apply(x,sK3(x,any1))) = apply(x,subtract(any1,zero(any1),sK4(x,any1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_43])]) ).
fof(f760,plain,
( subtract(any2,zero(any2),apply(x,sK3(x,any1))) = apply(x,subtract(any1,zero(any1),sK4(x,any1)))
| ~ spl9_3
| ~ spl9_4
| ~ spl9_7
| ~ spl9_12
| ~ spl9_15 ),
inference(forward_demodulation,[],[f755,f299]) ).
fof(f755,plain,
( subtract(any2,zero(any2),apply(x,sK4(x,any1))) = apply(x,subtract(any1,zero(any1),sK4(x,any1)))
| ~ spl9_3
| ~ spl9_4
| ~ spl9_7
| ~ spl9_12 ),
inference(resolution,[],[f681,f211]) ).
fof(f765,plain,
( spl9_42
| ~ spl9_3
| ~ spl9_4
| ~ spl9_5
| ~ spl9_7 ),
inference(avatar_split_clause,[],[f754,f168,f139,f132,f126,f762]) ).
fof(f754,plain,
( subtract(any2,zero(any2),apply(x,sK3(x,any1))) = apply(x,subtract(any1,zero(any1),sK3(x,any1)))
| ~ spl9_3
| ~ spl9_4
| ~ spl9_5
| ~ spl9_7 ),
inference(resolution,[],[f681,f141]) ).
fof(f737,plain,
( spl9_41
| ~ spl9_3
| ~ spl9_5
| ~ spl9_12
| ~ spl9_15
| ~ spl9_19 ),
inference(avatar_split_clause,[],[f729,f327,f297,f209,f139,f126,f734]) ).
fof(f729,plain,
( zero(any2) = apply(x,subtract(any1,sK4(x,any1),sK3(x,any1)))
| ~ spl9_3
| ~ spl9_5
| ~ spl9_12
| ~ spl9_15
| ~ spl9_19 ),
inference(forward_demodulation,[],[f722,f329]) ).
fof(f329,plain,
( zero(any2) = subtract(any2,apply(x,sK3(x,any1)),apply(x,sK3(x,any1)))
| ~ spl9_19 ),
inference(avatar_component_clause,[],[f327]) ).
fof(f722,plain,
( subtract(any2,apply(x,sK3(x,any1)),apply(x,sK3(x,any1))) = apply(x,subtract(any1,sK4(x,any1),sK3(x,any1)))
| ~ spl9_3
| ~ spl9_5
| ~ spl9_12
| ~ spl9_15 ),
inference(resolution,[],[f682,f141]) ).
fof(f682,plain,
( ! [X11] :
( ~ element(X11,any1)
| apply(x,subtract(any1,sK4(x,any1),X11)) = subtract(any2,apply(x,sK3(x,any1)),apply(x,X11)) )
| ~ spl9_3
| ~ spl9_12
| ~ spl9_15 ),
inference(forward_demodulation,[],[f678,f299]) ).
fof(f678,plain,
( ! [X11] :
( ~ element(X11,any1)
| apply(x,subtract(any1,sK4(x,any1),X11)) = subtract(any2,apply(x,sK4(x,any1)),apply(x,X11)) )
| ~ spl9_3
| ~ spl9_12 ),
inference(resolution,[],[f457,f211]) ).
fof(f701,plain,
( spl9_40
| ~ spl9_3
| ~ spl9_5
| ~ spl9_12
| ~ spl9_15
| ~ spl9_19 ),
inference(avatar_split_clause,[],[f696,f327,f297,f209,f139,f126,f698]) ).
fof(f696,plain,
( zero(any2) = apply(x,subtract(any1,sK3(x,any1),sK4(x,any1)))
| ~ spl9_3
| ~ spl9_5
| ~ spl9_12
| ~ spl9_15
| ~ spl9_19 ),
inference(forward_demodulation,[],[f695,f329]) ).
fof(f695,plain,
( subtract(any2,apply(x,sK3(x,any1)),apply(x,sK3(x,any1))) = apply(x,subtract(any1,sK3(x,any1),sK4(x,any1)))
| ~ spl9_3
| ~ spl9_5
| ~ spl9_12
| ~ spl9_15 ),
inference(forward_demodulation,[],[f688,f299]) ).
fof(f688,plain,
( apply(x,subtract(any1,sK3(x,any1),sK4(x,any1))) = subtract(any2,apply(x,sK3(x,any1)),apply(x,sK4(x,any1)))
| ~ spl9_3
| ~ spl9_5
| ~ spl9_12 ),
inference(resolution,[],[f677,f211]) ).
fof(f670,plain,
( spl9_39
| ~ spl9_5
| ~ spl9_12 ),
inference(avatar_split_clause,[],[f610,f209,f139,f667]) ).
fof(f667,plain,
( spl9_39
<=> sK3(x,any1) = subtract(any1,subtract(any1,sK3(x,any1),sK4(x,any1)),subtract(any1,subtract(any1,sK3(x,any1),sK4(x,any1)),sK3(x,any1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_39])]) ).
fof(f610,plain,
( sK3(x,any1) = subtract(any1,subtract(any1,sK3(x,any1),sK4(x,any1)),subtract(any1,subtract(any1,sK3(x,any1),sK4(x,any1)),sK3(x,any1)))
| ~ spl9_5
| ~ spl9_12 ),
inference(resolution,[],[f561,f141]) ).
fof(f561,plain,
( ! [X11] :
( ~ element(X11,any1)
| sK3(x,any1) = subtract(any1,subtract(any1,X11,sK4(x,any1)),subtract(any1,subtract(any1,X11,sK4(x,any1)),sK3(x,any1))) )
| ~ spl9_5
| ~ spl9_12 ),
inference(resolution,[],[f339,f211]) ).
fof(f339,plain,
( ! [X0,X1] :
( ~ element(X1,any1)
| sK3(x,any1) = subtract(any1,subtract(any1,X0,X1),subtract(any1,subtract(any1,X0,X1),sK3(x,any1)))
| ~ element(X0,any1) )
| ~ spl9_5 ),
inference(resolution,[],[f285,f93]) ).
fof(f665,plain,
( spl9_38
| ~ spl9_5
| ~ spl9_12 ),
inference(avatar_split_clause,[],[f598,f209,f139,f662]) ).
fof(f662,plain,
( spl9_38
<=> sK3(x,any1) = subtract(any1,subtract(any1,sK4(x,any1),sK3(x,any1)),subtract(any1,subtract(any1,sK4(x,any1),sK3(x,any1)),sK3(x,any1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_38])]) ).
fof(f598,plain,
( sK3(x,any1) = subtract(any1,subtract(any1,sK4(x,any1),sK3(x,any1)),subtract(any1,subtract(any1,sK4(x,any1),sK3(x,any1)),sK3(x,any1)))
| ~ spl9_5
| ~ spl9_12 ),
inference(resolution,[],[f560,f211]) ).
fof(f560,plain,
( ! [X10] :
( ~ element(X10,any1)
| sK3(x,any1) = subtract(any1,subtract(any1,X10,sK3(x,any1)),subtract(any1,subtract(any1,X10,sK3(x,any1)),sK3(x,any1))) )
| ~ spl9_5 ),
inference(resolution,[],[f339,f141]) ).
fof(f659,plain,
( spl9_37
| ~ spl9_5
| ~ spl9_7
| ~ spl9_12 ),
inference(avatar_split_clause,[],[f606,f209,f168,f139,f656]) ).
fof(f656,plain,
( spl9_37
<=> sK3(x,any1) = subtract(any1,subtract(any1,zero(any1),sK4(x,any1)),subtract(any1,subtract(any1,zero(any1),sK4(x,any1)),sK3(x,any1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_37])]) ).
fof(f606,plain,
( sK3(x,any1) = subtract(any1,subtract(any1,zero(any1),sK4(x,any1)),subtract(any1,subtract(any1,zero(any1),sK4(x,any1)),sK3(x,any1)))
| ~ spl9_5
| ~ spl9_7
| ~ spl9_12 ),
inference(resolution,[],[f561,f169]) ).
fof(f604,plain,
( spl9_36
| ~ spl9_5
| ~ spl9_7 ),
inference(avatar_split_clause,[],[f593,f168,f139,f601]) ).
fof(f601,plain,
( spl9_36
<=> sK3(x,any1) = subtract(any1,subtract(any1,zero(any1),sK3(x,any1)),subtract(any1,subtract(any1,zero(any1),sK3(x,any1)),sK3(x,any1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_36])]) ).
fof(f593,plain,
( sK3(x,any1) = subtract(any1,subtract(any1,zero(any1),sK3(x,any1)),subtract(any1,subtract(any1,zero(any1),sK3(x,any1)),sK3(x,any1)))
| ~ spl9_5
| ~ spl9_7 ),
inference(resolution,[],[f560,f169]) ).
fof(f590,plain,
( spl9_35
| ~ spl9_5
| ~ spl9_12 ),
inference(avatar_split_clause,[],[f582,f209,f139,f587]) ).
fof(f582,plain,
( zero(any1) = subtract(any1,subtract(any1,sK4(x,any1),sK3(x,any1)),subtract(any1,sK4(x,any1),sK3(x,any1)))
| ~ spl9_5
| ~ spl9_12 ),
inference(resolution,[],[f476,f141]) ).
fof(f553,plain,
( spl9_34
| ~ spl9_7
| ~ spl9_12 ),
inference(avatar_split_clause,[],[f511,f209,f168,f550]) ).
fof(f550,plain,
( spl9_34
<=> zero(any1) = subtract(any1,subtract(any1,zero(any1),sK4(x,any1)),subtract(any1,zero(any1),sK4(x,any1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_34])]) ).
fof(f511,plain,
( zero(any1) = subtract(any1,subtract(any1,zero(any1),sK4(x,any1)),subtract(any1,zero(any1),sK4(x,any1)))
| ~ spl9_7
| ~ spl9_12 ),
inference(resolution,[],[f471,f211]) ).
fof(f537,plain,
( spl9_33
| ~ spl9_3
| spl9_9 ),
inference(avatar_split_clause,[],[f532,f183,f126,f534]) ).
fof(f517,plain,
( spl9_32
| ~ spl9_5
| ~ spl9_7 ),
inference(avatar_split_clause,[],[f510,f168,f139,f514]) ).
fof(f510,plain,
( zero(any1) = subtract(any1,subtract(any1,zero(any1),sK3(x,any1)),subtract(any1,zero(any1),sK3(x,any1)))
| ~ spl9_5
| ~ spl9_7 ),
inference(resolution,[],[f471,f141]) ).
fof(f503,plain,
( spl9_31
| ~ spl9_8
| ~ spl9_16 ),
inference(avatar_split_clause,[],[f493,f306,f172,f500]) ).
fof(f493,plain,
( zero(any2) = subtract(any2,subtract(any2,zero(any2),apply(x,sK3(x,any1))),subtract(any2,zero(any2),apply(x,sK3(x,any1))))
| ~ spl9_8
| ~ spl9_16 ),
inference(resolution,[],[f470,f308]) ).
fof(f489,plain,
( spl9_30
| ~ spl9_5
| ~ spl9_12 ),
inference(avatar_split_clause,[],[f482,f209,f139,f486]) ).
fof(f486,plain,
( spl9_30
<=> zero(any1) = subtract(any1,subtract(any1,sK3(x,any1),sK4(x,any1)),subtract(any1,sK3(x,any1),sK4(x,any1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_30])]) ).
fof(f482,plain,
( zero(any1) = subtract(any1,subtract(any1,sK3(x,any1),sK4(x,any1)),subtract(any1,sK3(x,any1),sK4(x,any1)))
| ~ spl9_5
| ~ spl9_12 ),
inference(resolution,[],[f475,f211]) ).
fof(f446,plain,
( spl9_29
| ~ spl9_7
| ~ spl9_12 ),
inference(avatar_split_clause,[],[f422,f209,f168,f443]) ).
fof(f443,plain,
( spl9_29
<=> sK4(x,any1) = subtract(any1,zero(any1),subtract(any1,zero(any1),sK4(x,any1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_29])]) ).
fof(f422,plain,
( sK4(x,any1) = subtract(any1,zero(any1),subtract(any1,zero(any1),sK4(x,any1)))
| ~ spl9_7
| ~ spl9_12 ),
inference(resolution,[],[f231,f169]) ).
fof(f440,plain,
( spl9_28
| ~ spl9_5
| ~ spl9_12 ),
inference(avatar_split_clause,[],[f426,f209,f139,f437]) ).
fof(f426,plain,
( sK4(x,any1) = subtract(any1,sK3(x,any1),subtract(any1,sK3(x,any1),sK4(x,any1)))
| ~ spl9_5
| ~ spl9_12 ),
inference(resolution,[],[f231,f141]) ).
fof(f433,plain,
( spl9_27
| ~ spl9_12
| ~ spl9_18 ),
inference(avatar_split_clause,[],[f428,f320,f209,f430]) ).
fof(f430,plain,
( spl9_27
<=> sK4(x,any1) = subtract(any1,sK4(x,any1),zero(any1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_27])]) ).
fof(f428,plain,
( sK4(x,any1) = subtract(any1,sK4(x,any1),zero(any1))
| ~ spl9_12
| ~ spl9_18 ),
inference(forward_demodulation,[],[f427,f322]) ).
fof(f322,plain,
( zero(any1) = subtract(any1,sK4(x,any1),sK4(x,any1))
| ~ spl9_18 ),
inference(avatar_component_clause,[],[f320]) ).
fof(f427,plain,
( sK4(x,any1) = subtract(any1,sK4(x,any1),subtract(any1,sK4(x,any1),sK4(x,any1)))
| ~ spl9_12 ),
inference(resolution,[],[f231,f211]) ).
fof(f420,plain,
( spl9_26
| ~ spl9_8
| ~ spl9_16 ),
inference(avatar_split_clause,[],[f401,f306,f172,f417]) ).
fof(f401,plain,
( apply(x,sK3(x,any1)) = subtract(any2,zero(any2),subtract(any2,zero(any2),apply(x,sK3(x,any1))))
| ~ spl9_8
| ~ spl9_16 ),
inference(resolution,[],[f310,f174]) ).
fof(f410,plain,
( spl9_25
| ~ spl9_16
| ~ spl9_19 ),
inference(avatar_split_clause,[],[f405,f327,f306,f407]) ).
fof(f405,plain,
( apply(x,sK3(x,any1)) = subtract(any2,apply(x,sK3(x,any1)),zero(any2))
| ~ spl9_16
| ~ spl9_19 ),
inference(forward_demodulation,[],[f400,f329]) ).
fof(f400,plain,
( apply(x,sK3(x,any1)) = subtract(any2,apply(x,sK3(x,any1)),subtract(any2,apply(x,sK3(x,any1)),apply(x,sK3(x,any1))))
| ~ spl9_16 ),
inference(resolution,[],[f310,f308]) ).
fof(f397,plain,
( spl9_24
| ~ spl9_7
| ~ spl9_12 ),
inference(avatar_split_clause,[],[f383,f209,f168,f394]) ).
fof(f394,plain,
( spl9_24
<=> zero(any1) = subtract(any1,sK4(x,any1),subtract(any1,sK4(x,any1),zero(any1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_24])]) ).
fof(f383,plain,
( zero(any1) = subtract(any1,sK4(x,any1),subtract(any1,sK4(x,any1),zero(any1)))
| ~ spl9_7
| ~ spl9_12 ),
inference(resolution,[],[f288,f211]) ).
fof(f390,plain,
( spl9_23
| ~ spl9_8
| ~ spl9_16 ),
inference(avatar_split_clause,[],[f366,f306,f172,f387]) ).
fof(f366,plain,
( zero(any2) = subtract(any2,apply(x,sK3(x,any1)),subtract(any2,apply(x,sK3(x,any1)),zero(any2)))
| ~ spl9_8
| ~ spl9_16 ),
inference(resolution,[],[f241,f308]) ).
fof(f361,plain,
( spl9_22
| ~ spl9_5
| ~ spl9_12 ),
inference(avatar_split_clause,[],[f343,f209,f139,f358]) ).
fof(f343,plain,
( sK3(x,any1) = subtract(any1,sK4(x,any1),subtract(any1,sK4(x,any1),sK3(x,any1)))
| ~ spl9_5
| ~ spl9_12 ),
inference(resolution,[],[f285,f211]) ).
fof(f355,plain,
( spl9_21
| ~ spl9_5
| ~ spl9_7 ),
inference(avatar_split_clause,[],[f338,f168,f139,f352]) ).
fof(f338,plain,
( sK3(x,any1) = subtract(any1,zero(any1),subtract(any1,zero(any1),sK3(x,any1)))
| ~ spl9_5
| ~ spl9_7 ),
inference(resolution,[],[f285,f169]) ).
fof(f349,plain,
( spl9_20
| ~ spl9_5
| ~ spl9_6 ),
inference(avatar_split_clause,[],[f344,f145,f139,f346]) ).
fof(f344,plain,
( sK3(x,any1) = subtract(any1,sK3(x,any1),zero(any1))
| ~ spl9_5
| ~ spl9_6 ),
inference(forward_demodulation,[],[f342,f147]) ).
fof(f147,plain,
( zero(any1) = subtract(any1,sK3(x,any1),sK3(x,any1))
| ~ spl9_6 ),
inference(avatar_component_clause,[],[f145]) ).
fof(f342,plain,
( sK3(x,any1) = subtract(any1,sK3(x,any1),subtract(any1,sK3(x,any1),sK3(x,any1)))
| ~ spl9_5 ),
inference(resolution,[],[f285,f141]) ).
fof(f331,plain,
( spl9_19
| ~ spl9_16 ),
inference(avatar_split_clause,[],[f311,f306,f327]) ).
fof(f311,plain,
( zero(any2) = subtract(any2,apply(x,sK3(x,any1)),apply(x,sK3(x,any1)))
| ~ spl9_16 ),
inference(resolution,[],[f308,f85]) ).
fof(f330,plain,
( spl9_19
| ~ spl9_3
| ~ spl9_5 ),
inference(avatar_split_clause,[],[f284,f139,f126,f327]) ).
fof(f284,plain,
( zero(any2) = subtract(any2,apply(x,sK3(x,any1)),apply(x,sK3(x,any1)))
| ~ spl9_3
| ~ spl9_5 ),
inference(resolution,[],[f141,f165]) ).
fof(f323,plain,
( spl9_18
| ~ spl9_12 ),
inference(avatar_split_clause,[],[f232,f209,f320]) ).
fof(f232,plain,
( zero(any1) = subtract(any1,sK4(x,any1),sK4(x,any1))
| ~ spl9_12 ),
inference(resolution,[],[f211,f85]) ).
fof(f316,plain,
( spl9_17
| ~ spl9_7 ),
inference(avatar_split_clause,[],[f289,f168,f313]) ).
fof(f289,plain,
( zero(any1) = subtract(any1,zero(any1),zero(any1))
| ~ spl9_7 ),
inference(resolution,[],[f169,f85]) ).
fof(f309,plain,
( spl9_16
| ~ spl9_3
| ~ spl9_12
| ~ spl9_15 ),
inference(avatar_split_clause,[],[f303,f297,f209,f126,f306]) ).
fof(f303,plain,
( element(apply(x,sK3(x,any1)),any2)
| ~ spl9_3
| ~ spl9_12
| ~ spl9_15 ),
inference(subsumption_resolution,[],[f301,f211]) ).
fof(f301,plain,
( element(apply(x,sK3(x,any1)),any2)
| ~ element(sK4(x,any1),any1)
| ~ spl9_3
| ~ spl9_15 ),
inference(superposition,[],[f163,f299]) ).
fof(f300,plain,
( spl9_15
| spl9_1
| ~ spl9_3 ),
inference(avatar_split_clause,[],[f295,f126,f117,f297]) ).
fof(f295,plain,
( apply(x,sK3(x,any1)) = apply(x,sK4(x,any1))
| spl9_1
| ~ spl9_3 ),
inference(subsumption_resolution,[],[f294,f118]) ).
fof(f283,plain,
( spl9_7
| ~ spl9_5
| ~ spl9_6 ),
inference(avatar_split_clause,[],[f254,f145,f139,f168]) ).
fof(f254,plain,
( element(zero(any1),any1)
| ~ spl9_5
| ~ spl9_6 ),
inference(global_subsumption,[],[f88,f91,f92,f96,f102,f107,f106,f105,f104,f112,f111,f110,f109,f108,f114,f113,f115,f82,f84,f85,f87,f100,f143,f101,f86,f93,f164,f95,f176,f97,f177,f99,f103,f89,f94,f191,f192,f193,f98,f141,f206,f207,f147,f90,f83,f234]) ).
fof(f234,plain,
( element(zero(any1),any1)
| ~ element(sK3(x,any1),any1)
| ~ spl9_6 ),
inference(duplicate_literal_removal,[],[f233]) ).
fof(f233,plain,
( element(zero(any1),any1)
| ~ element(sK3(x,any1),any1)
| ~ element(sK3(x,any1),any1)
| ~ spl9_6 ),
inference(superposition,[],[f93,f147]) ).
fof(f207,plain,
( zero(any1) = subtract(any1,sK3(x,any1),sK3(x,any1))
| ~ spl9_5 ),
inference(resolution,[],[f141,f85]) ).
fof(f206,plain,
( ! [X0] :
( sK3(x,any1) = subtract(any1,X0,subtract(any1,X0,sK3(x,any1)))
| ~ element(X0,any1) )
| ~ spl9_5 ),
inference(resolution,[],[f141,f94]) ).
fof(f143,plain,
( zero(any1) = subtract(any1,sK3(x,any1),sK3(x,any1))
| ~ spl9_5 ),
inference(resolution,[],[f141,f85]) ).
fof(f280,plain,
( spl9_1
| ~ spl9_8
| spl9_14 ),
inference(avatar_contradiction_clause,[],[f279]) ).
fof(f279,plain,
( $false
| spl9_1
| ~ spl9_8
| spl9_14 ),
inference(global_subsumption,[],[f118,f88,f91,f92,f96,f102,f107,f106,f105,f104,f112,f111,f110,f109,f108,f114,f113,f115,f82,f84,f85,f87,f100,f101,f86,f93,f164,f95,f176,f97,f177,f99,f103,f89,f94,f191,f192,f193,f98,f90,f174,f241,f242,f83,f249]) ).
fof(f249,plain,
( zero(any2) != subtract(any2,zero(any2),zero(any2))
| spl9_14 ),
inference(avatar_component_clause,[],[f248]) ).
fof(f278,plain,
( ~ spl9_2
| ~ spl9_8
| spl9_14 ),
inference(avatar_contradiction_clause,[],[f277]) ).
fof(f277,plain,
( $false
| ~ spl9_2
| ~ spl9_8
| spl9_14 ),
inference(global_subsumption,[],[f123,f88,f91,f92,f96,f102,f107,f106,f105,f104,f112,f111,f110,f109,f108,f114,f113,f115,f82,f84,f85,f87,f100,f101,f86,f93,f164,f95,f176,f97,f177,f99,f103,f89,f94,f191,f192,f193,f98,f90,f174,f241,f242,f83,f249]) ).
fof(f276,plain,
( ~ spl9_2
| ~ spl9_8
| spl9_14 ),
inference(avatar_contradiction_clause,[],[f275]) ).
fof(f275,plain,
( $false
| ~ spl9_2
| ~ spl9_8
| spl9_14 ),
inference(global_subsumption,[],[f151,f88,f91,f92,f96,f102,f107,f106,f105,f104,f112,f111,f110,f109,f108,f114,f113,f115,f82,f84,f85,f87,f100,f101,f86,f93,f164,f95,f176,f97,f177,f99,f103,f89,f94,f191,f192,f193,f98,f90,f174,f241,f242,f83,f249]) ).
fof(f151,plain,
( ~ injection(x)
| ~ spl9_2 ),
inference(subsumption_resolution,[],[f83,f123]) ).
fof(f274,plain,
( ~ spl9_2
| ~ spl9_8
| spl9_14 ),
inference(avatar_contradiction_clause,[],[f273]) ).
fof(f273,plain,
( $false
| ~ spl9_2
| ~ spl9_8
| spl9_14 ),
inference(global_subsumption,[],[f204,f88,f91,f92,f96,f102,f107,f106,f105,f104,f112,f111,f110,f109,f108,f114,f113,f115,f82,f84,f85,f87,f100,f101,f86,f93,f164,f95,f176,f97,f177,f99,f103,f89,f94,f191,f192,f193,f98,f90,f174,f241,f242,f83,f249]) ).
fof(f204,plain,
( ~ injection(x)
| ~ spl9_2 ),
inference(global_subsumption,[],[f88,f90,f91,f92,f96,f102,f107,f106,f105,f104,f112,f111,f110,f109,f108,f114,f113,f115,f82,f84,f123,f85,f87,f100,f151,f101,f86,f93,f164,f95,f176,f97,f177,f99,f103,f89,f94,f191,f192,f193,f98,f83]) ).
fof(f272,plain,
( ~ spl9_5
| ~ spl9_8
| spl9_14 ),
inference(avatar_contradiction_clause,[],[f271]) ).
fof(f271,plain,
( $false
| ~ spl9_5
| ~ spl9_8
| spl9_14 ),
inference(global_subsumption,[],[f141,f88,f91,f92,f96,f102,f107,f106,f105,f104,f112,f111,f110,f109,f108,f114,f113,f115,f82,f84,f85,f87,f100,f101,f86,f93,f164,f95,f176,f97,f177,f99,f103,f89,f94,f191,f192,f193,f98,f90,f174,f241,f242,f83,f249]) ).
fof(f270,plain,
( ~ spl9_7
| ~ spl9_8
| spl9_14 ),
inference(avatar_contradiction_clause,[],[f269]) ).
fof(f269,plain,
( $false
| ~ spl9_7
| ~ spl9_8
| spl9_14 ),
inference(global_subsumption,[],[f169,f88,f91,f92,f96,f102,f107,f106,f105,f104,f112,f111,f110,f109,f108,f114,f113,f115,f82,f84,f85,f87,f100,f101,f86,f93,f164,f95,f176,f97,f177,f99,f103,f89,f94,f191,f192,f193,f98,f90,f174,f241,f242,f83,f249]) ).
fof(f268,plain,
( ~ spl9_8
| spl9_11
| spl9_14 ),
inference(avatar_contradiction_clause,[],[f267]) ).
fof(f267,plain,
( $false
| ~ spl9_8
| spl9_11
| spl9_14 ),
inference(global_subsumption,[],[f198,f88,f91,f92,f96,f102,f107,f106,f105,f104,f112,f111,f110,f109,f108,f114,f113,f115,f82,f84,f85,f87,f100,f101,f86,f93,f164,f95,f176,f97,f177,f99,f103,f89,f94,f191,f192,f193,f98,f90,f174,f241,f242,f83,f249]) ).
fof(f198,plain,
( zero(any2) != apply(x,sK2(x,any1,any2))
| spl9_11 ),
inference(avatar_component_clause,[],[f197]) ).
fof(f266,plain,
( ~ spl9_8
| spl9_13
| spl9_14 ),
inference(avatar_contradiction_clause,[],[f265]) ).
fof(f265,plain,
( $false
| ~ spl9_8
| spl9_13
| spl9_14 ),
inference(global_subsumption,[],[f221,f88,f91,f92,f96,f102,f107,f106,f105,f104,f112,f111,f110,f109,f108,f114,f113,f115,f82,f84,f85,f87,f100,f101,f86,f93,f164,f95,f176,f97,f177,f99,f103,f89,f94,f191,f192,f193,f98,f90,f174,f241,f242,f83,f249]) ).
fof(f221,plain,
( ~ element(sK2(x,any1,any2),any1)
| spl9_13 ),
inference(avatar_component_clause,[],[f219]) ).
fof(f264,plain,
( ~ spl9_3
| ~ spl9_8
| spl9_13
| spl9_14 ),
inference(avatar_contradiction_clause,[],[f263]) ).
fof(f263,plain,
( $false
| ~ spl9_3
| ~ spl9_8
| spl9_13
| spl9_14 ),
inference(global_subsumption,[],[f262,f88,f91,f92,f96,f102,f107,f106,f105,f104,f112,f111,f110,f109,f108,f114,f113,f115,f82,f84,f85,f87,f100,f101,f86,f93,f164,f95,f176,f97,f177,f99,f103,f89,f94,f191,f192,f193,f98,f90,f174,f241,f242,f83,f249]) ).
fof(f262,plain,
( injection_2(x)
| ~ spl9_3
| spl9_13 ),
inference(subsumption_resolution,[],[f223,f128]) ).
fof(f223,plain,
( injection_2(x)
| ~ morphism(x,any1,any2)
| spl9_13 ),
inference(resolution,[],[f221,f97]) ).
fof(f261,plain,
( ~ spl9_3
| ~ spl9_8
| spl9_13
| spl9_14 ),
inference(avatar_contradiction_clause,[],[f260]) ).
fof(f260,plain,
( $false
| ~ spl9_3
| ~ spl9_8
| spl9_13
| spl9_14 ),
inference(global_subsumption,[],[f227,f88,f91,f92,f96,f102,f107,f106,f105,f104,f112,f111,f110,f109,f108,f114,f113,f115,f82,f84,f85,f87,f100,f101,f86,f93,f164,f95,f176,f97,f177,f99,f103,f89,f94,f191,f192,f193,f98,f90,f174,f241,f242,f83,f249]) ).
fof(f227,plain,
( injection_2(x)
| ~ spl9_3
| spl9_13 ),
inference(subsumption_resolution,[],[f223,f128]) ).
fof(f259,plain,
( ~ spl9_3
| ~ spl9_8
| spl9_13
| spl9_14 ),
inference(avatar_contradiction_clause,[],[f258]) ).
fof(f258,plain,
( $false
| ~ spl9_3
| ~ spl9_8
| spl9_13
| spl9_14 ),
inference(global_subsumption,[],[f229,f88,f91,f92,f96,f102,f107,f106,f105,f104,f112,f111,f110,f109,f108,f114,f113,f115,f82,f84,f85,f87,f100,f101,f86,f93,f164,f95,f176,f97,f177,f99,f103,f89,f94,f191,f192,f193,f98,f90,f174,f241,f242,f83,f249]) ).
fof(f229,plain,
( ~ injection(x)
| ~ spl9_3
| spl9_13 ),
inference(global_subsumption,[],[f88,f90,f91,f92,f96,f102,f107,f106,f105,f104,f112,f111,f110,f109,f108,f114,f113,f115,f82,f84,f128,f85,f87,f130,f100,f101,f86,f93,f164,f163,f95,f176,f97,f177,f99,f103,f165,f178,f179,f180,f89,f181,f94,f190,f191,f192,f193,f98,f136,f194,f221,f227,f162,f228,f83]) ).
fof(f228,plain,
( element(sK4(x,any1),any1)
| ~ spl9_3
| spl9_13 ),
inference(global_subsumption,[],[f88,f90,f91,f92,f96,f102,f107,f106,f105,f104,f112,f111,f110,f109,f108,f114,f113,f115,f82,f84,f128,f85,f87,f130,f100,f101,f86,f93,f164,f163,f95,f176,f97,f177,f99,f103,f165,f178,f179,f180,f89,f181,f94,f190,f191,f192,f193,f98,f136,f83,f194,f221,f227,f162]) ).
fof(f257,plain,
( ~ spl9_8
| spl9_14 ),
inference(avatar_contradiction_clause,[],[f256]) ).
fof(f256,plain,
( $false
| ~ spl9_8
| spl9_14 ),
inference(global_subsumption,[],[f88,f91,f92,f96,f102,f107,f106,f105,f104,f112,f111,f110,f109,f108,f114,f113,f115,f82,f84,f85,f87,f100,f101,f86,f93,f164,f95,f176,f97,f177,f99,f103,f89,f94,f191,f192,f193,f98,f90,f174,f241,f242,f83,f249]) ).
fof(f251,plain,
( spl9_14
| ~ spl9_3
| ~ spl9_11
| ~ spl9_13 ),
inference(avatar_split_clause,[],[f246,f219,f197,f126,f248]) ).
fof(f246,plain,
( zero(any2) = subtract(any2,zero(any2),zero(any2))
| ~ spl9_3
| ~ spl9_11
| ~ spl9_13 ),
inference(forward_demodulation,[],[f243,f199]) ).
fof(f243,plain,
( zero(any2) = subtract(any2,apply(x,sK2(x,any1,any2)),apply(x,sK2(x,any1,any2)))
| ~ spl9_3
| ~ spl9_13 ),
inference(resolution,[],[f220,f165]) ).
fof(f237,plain,
( ~ spl9_5
| ~ spl9_6
| spl9_7 ),
inference(avatar_contradiction_clause,[],[f236]) ).
fof(f236,plain,
( $false
| ~ spl9_5
| ~ spl9_6
| spl9_7 ),
inference(subsumption_resolution,[],[f235,f141]) ).
fof(f235,plain,
( ~ element(sK3(x,any1),any1)
| ~ spl9_6
| spl9_7 ),
inference(subsumption_resolution,[],[f234,f170]) ).
fof(f226,plain,
( spl9_2
| ~ spl9_3
| spl9_13 ),
inference(avatar_contradiction_clause,[],[f225]) ).
fof(f225,plain,
( $false
| spl9_2
| ~ spl9_3
| spl9_13 ),
inference(subsumption_resolution,[],[f224,f128]) ).
fof(f224,plain,
( ~ morphism(x,any1,any2)
| spl9_2
| spl9_13 ),
inference(subsumption_resolution,[],[f223,f122]) ).
fof(f222,plain,
( ~ spl9_13
| ~ spl9_3
| spl9_8
| ~ spl9_11 ),
inference(avatar_split_clause,[],[f217,f197,f172,f126,f219]) ).
fof(f217,plain,
( ~ element(sK2(x,any1,any2),any1)
| ~ spl9_3
| spl9_8
| ~ spl9_11 ),
inference(subsumption_resolution,[],[f216,f173]) ).
fof(f173,plain,
( ~ element(zero(any2),any2)
| spl9_8 ),
inference(avatar_component_clause,[],[f172]) ).
fof(f216,plain,
( element(zero(any2),any2)
| ~ element(sK2(x,any1,any2),any1)
| ~ spl9_3
| ~ spl9_11 ),
inference(superposition,[],[f163,f199]) ).
fof(f212,plain,
( spl9_12
| ~ spl9_2
| ~ spl9_3 ),
inference(avatar_split_clause,[],[f201,f126,f121,f209]) ).
fof(f201,plain,
( element(sK4(x,any1),any1)
| ~ spl9_2
| ~ spl9_3 ),
inference(global_subsumption,[],[f88,f90,f91,f92,f96,f102,f107,f106,f105,f104,f112,f111,f110,f109,f108,f114,f113,f115,f82,f84,f123,f128,f85,f87,f130,f100,f151,f83,f136,f101,f86,f93,f164,f163,f95,f176,f97,f177,f99,f103,f165,f178,f179,f180,f89,f181,f94,f190,f191,f192,f193,f98,f162]) ).
fof(f200,plain,
( spl9_11
| spl9_2
| ~ spl9_3 ),
inference(avatar_split_clause,[],[f195,f126,f121,f197]) ).
fof(f195,plain,
( zero(any2) = apply(x,sK2(x,any1,any2))
| spl9_2
| ~ spl9_3 ),
inference(subsumption_resolution,[],[f194,f122]) ).
fof(f189,plain,
( ~ spl9_9
| spl9_10
| ~ spl9_3 ),
inference(avatar_split_clause,[],[f181,f126,f187,f183]) ).
fof(f175,plain,
( ~ spl9_7
| spl9_8
| ~ spl9_3
| ~ spl9_4 ),
inference(avatar_split_clause,[],[f166,f132,f126,f172,f168]) ).
fof(f166,plain,
( element(zero(any2),any2)
| ~ element(zero(any1),any1)
| ~ spl9_3
| ~ spl9_4 ),
inference(superposition,[],[f163,f134]) ).
fof(f159,plain,
( ~ spl9_1
| ~ spl9_2
| ~ spl9_3
| spl9_5 ),
inference(avatar_contradiction_clause,[],[f158]) ).
fof(f158,plain,
( $false
| ~ spl9_1
| ~ spl9_2
| ~ spl9_3
| spl9_5 ),
inference(global_subsumption,[],[f119,f86,f88,f90,f89,f91,f92,f93,f94,f96,f95,f99,f98,f97,f103,f102,f101,f107,f106,f105,f104,f112,f111,f110,f109,f108,f114,f113,f115,f82,f84,f83,f123,f128,f85,f87,f130,f100,f136,f151,f140]) ).
fof(f157,plain,
( ~ spl9_2
| ~ spl9_3
| spl9_5 ),
inference(avatar_contradiction_clause,[],[f156]) ).
fof(f156,plain,
( $false
| ~ spl9_2
| ~ spl9_3
| spl9_5 ),
inference(global_subsumption,[],[f86,f88,f90,f89,f91,f92,f93,f94,f96,f95,f99,f98,f97,f103,f102,f101,f107,f106,f105,f104,f112,f111,f110,f109,f108,f114,f113,f115,f82,f84,f83,f123,f128,f85,f87,f130,f100,f136,f151,f140]) ).
fof(f155,plain,
( ~ spl9_1
| ~ spl9_2
| spl9_6 ),
inference(avatar_contradiction_clause,[],[f154]) ).
fof(f154,plain,
( $false
| ~ spl9_1
| ~ spl9_2
| spl9_6 ),
inference(global_subsumption,[],[f146,f86,f88,f90,f89,f91,f92,f93,f94,f96,f95,f99,f98,f97,f103,f102,f101,f107,f106,f105,f104,f112,f111,f110,f109,f108,f114,f113,f115,f82,f119,f84,f83,f123,f85,f87,f100,f151]) ).
fof(f153,plain,
( ~ spl9_1
| ~ spl9_2 ),
inference(avatar_contradiction_clause,[],[f152]) ).
fof(f152,plain,
( $false
| ~ spl9_1
| ~ spl9_2 ),
inference(global_subsumption,[],[f86,f88,f90,f89,f91,f92,f93,f94,f96,f95,f99,f98,f97,f103,f102,f101,f107,f106,f105,f104,f112,f111,f110,f109,f108,f114,f113,f115,f82,f119,f84,f83,f123,f85,f87,f100,f151]) ).
fof(f150,plain,
( ~ spl9_1
| ~ spl9_2
| ~ spl9_3 ),
inference(avatar_contradiction_clause,[],[f149]) ).
fof(f149,plain,
( $false
| ~ spl9_1
| ~ spl9_2
| ~ spl9_3 ),
inference(global_subsumption,[],[f136,f86,f88,f90,f89,f91,f92,f93,f94,f96,f95,f99,f98,f97,f103,f102,f101,f107,f106,f105,f104,f112,f111,f110,f109,f108,f114,f113,f115,f82,f119,f84,f83,f123,f85,f87,f100]) ).
fof(f148,plain,
( spl9_6
| ~ spl9_5 ),
inference(avatar_split_clause,[],[f143,f139,f145]) ).
fof(f142,plain,
( spl9_5
| spl9_1
| ~ spl9_3 ),
inference(avatar_split_clause,[],[f137,f126,f117,f139]) ).
fof(f137,plain,
( element(sK3(x,any1),any1)
| spl9_1
| ~ spl9_3 ),
inference(subsumption_resolution,[],[f136,f118]) ).
fof(f135,plain,
( spl9_4
| ~ spl9_3 ),
inference(avatar_split_clause,[],[f130,f126,f132]) ).
fof(f129,plain,
spl9_3,
inference(avatar_split_clause,[],[f84,f126]) ).
fof(f124,plain,
( spl9_1
| spl9_2 ),
inference(avatar_split_clause,[],[f82,f121,f117]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : HAL002+1 : TPTP v8.1.2. Released v2.6.0.
% 0.00/0.14 % Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.14/0.35 % Computer : n008.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Wed Aug 30 16:59:02 EDT 2023
% 0.21/0.35 % CPUTime :
% 0.21/0.41 % (1440)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.41 % (1442)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on Vampire---4 for (793ds/0Mi)
% 0.21/0.41 % (1441)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on Vampire---4 for (846ds/0Mi)
% 0.21/0.41 % (1444)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on Vampire---4 for (533ds/0Mi)
% 0.21/0.41 % (1443)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)
% 0.21/0.41 % (1446)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)
% 0.21/0.41 % (1445)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)
% 0.21/0.41 % (1447)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)
% 0.21/0.42 TRYING [1]
% 0.21/0.42 TRYING [1]
% 0.21/0.42 TRYING [2]
% 0.21/0.42 TRYING [2]
% 0.21/0.43 TRYING [3]
% 0.21/0.43 TRYING [3]
% 0.21/0.45 TRYING [4]
% 0.21/0.45 TRYING [4]
% 0.21/0.53 TRYING [5]
% 0.21/0.53 TRYING [5]
% 0.21/0.69 TRYING [6]
% 0.21/0.69 TRYING [6]
% 0.21/0.70 % (1443)First to succeed.
% 0.21/0.71 % (1443)Refutation found. Thanks to Tanya!
% 0.21/0.71 % SZS status Theorem for Vampire---4
% 0.21/0.71 % SZS output start Proof for Vampire---4
% See solution above
% 0.21/0.73 % (1443)------------------------------
% 0.21/0.73 % (1443)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.21/0.73 % (1443)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.21/0.73 % (1443)Termination reason: Refutation
% 0.21/0.73
% 0.21/0.73 % (1443)Memory used [KB]: 8443
% 0.21/0.73 % (1443)Time elapsed: 0.302 s
% 0.21/0.73 % (1443)------------------------------
% 0.21/0.73 % (1443)------------------------------
% 0.21/0.73 % (1440)Success in time 0.353 s
% 0.21/0.73 % Vampire---4.8 exiting
%------------------------------------------------------------------------------