%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP127-3.004 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 10:12:56 AM UTC 2026
% Result : Unsatisfiable 2.59s 1.22s
% Output : Refutation 3.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 110
% Syntax : Number of formulae : 538 ( 105 unt; 73 def)
% Number of atoms : 1430 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 1741 ( 849 ~; 819 |; 0 &)
% ( 73 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 80 ( 79 usr; 74 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 5 con; 0-0 aty)
% Number of variables : 191 ( 0 sgn 191 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
next(e_0,e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_0_then_e_1) ).
fof(f2,axiom,
next(e_1,e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_1_then_e_2) ).
fof(f3,axiom,
next(e_2,e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_2_then_e_3) ).
fof(f4,axiom,
next(e_3,e_4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_3_then_e_4) ).
fof(f5,axiom,
greater(e_1,e_0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_1_greater_e_0) ).
fof(f6,axiom,
greater(e_2,e_0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_2_greater_e_0) ).
fof(f7,axiom,
greater(e_3,e_0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_3_greater_e_0) ).
fof(f9,axiom,
greater(e_2,e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_2_greater_e_1) ).
fof(f10,axiom,
greater(e_3,e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_3_greater_e_1) ).
fof(f12,axiom,
greater(e_3,e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_3_greater_e_2) ).
fof(f13,axiom,
greater(e_4,e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_4_greater_e_2) ).
fof(f14,axiom,
greater(e_4,e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_4_greater_e_3) ).
fof(f16,axiom,
! [X0] :
( ~ group_element(X0)
| cycle(X0,e_0)
| cycle(X0,e_1)
| cycle(X0,e_2)
| cycle(X0,e_3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cycle2) ).
fof(f17,axiom,
cycle(e_4,e_0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cycle3) ).
fof(f18,axiom,
! [X2,X3,X0,X1,X4] :
( equalish(X1,X4)
| ~ cycle(X2,X3)
| ~ next(X0,X2)
| ~ greater(X1,e_0)
| ~ next(X3,X4)
| ~ cycle(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cycle4) ).
fof(f19,axiom,
! [X2,X3,X0,X1,X4] :
( ~ next(X2,X3)
| ~ cycle(X2,e_0)
| ~ cycle(X3,X4)
| ~ cycle(X0,X1)
| ~ greater(X2,X0)
| ~ greater(X1,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cycle5) ).
fof(f20,axiom,
! [X0,X1] :
( ~ cycle(X0,e_0)
| ~ product(X0,e_1,X1)
| ~ greater(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cycle6) ).
fof(f21,axiom,
! [X2,X3,X0,X1] :
( ~ next(X0,X3)
| ~ product(X0,e_1,X2)
| ~ greater(X1,e_0)
| ~ cycle(X0,X1)
| equalish(X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cycle7) ).
fof(f22,axiom,
group_element(e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_1) ).
fof(f23,axiom,
group_element(e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_2) ).
fof(f24,axiom,
group_element(e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_3) ).
fof(f25,axiom,
group_element(e_4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_4) ).
fof(f26,axiom,
~ equalish(e_1,e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_1_is_not_e_2) ).
fof(f27,axiom,
~ equalish(e_1,e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_1_is_not_e_3) ).
fof(f28,axiom,
~ equalish(e_1,e_4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_1_is_not_e_4) ).
fof(f29,axiom,
~ equalish(e_2,e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_2_is_not_e_1) ).
fof(f30,axiom,
~ equalish(e_2,e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_2_is_not_e_3) ).
fof(f31,axiom,
~ equalish(e_2,e_4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_2_is_not_e_4) ).
fof(f32,axiom,
~ equalish(e_3,e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_3_is_not_e_1) ).
fof(f33,axiom,
~ equalish(e_3,e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_3_is_not_e_2) ).
fof(f34,axiom,
~ equalish(e_3,e_4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_3_is_not_e_4) ).
fof(f37,axiom,
~ equalish(e_4,e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_4_is_not_e_3) ).
fof(f38,axiom,
! [X0,X1] :
( product(X0,X1,e_4)
| ~ group_element(X1)
| product(X0,X1,e_1)
| product(X0,X1,e_2)
| product(X0,X1,e_3)
| ~ group_element(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_total_function1) ).
fof(f39,axiom,
! [X2,X3,X0,X1] :
( equalish(X2,X3)
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_total_function2) ).
fof(f40,axiom,
! [X2,X3,X0,X1] :
( equalish(X1,X3)
| ~ product(X0,X3,X2)
| ~ product(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_right_cancellation) ).
fof(f42,axiom,
! [X0] : product(X0,X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_idempotence) ).
fof(f43,negated_conjecture,
! [X2,X3,X0,X1] :
( product(X3,X0,X1)
| ~ product(X2,X0,X3)
| ~ product(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qg3) ).
fof(f57,plain,
! [X0,X1] :
( ~ product(X0,X1,e_2)
| ~ product(X0,X1,e_1) ),
inference(resolution,[],[f39,f26]) ).
fof(f58,plain,
! [X0,X1] :
( ~ product(X0,X1,e_3)
| ~ product(X0,X1,e_1) ),
inference(resolution,[],[f39,f27]) ).
fof(f59,plain,
! [X0,X1] :
( ~ product(X0,X1,e_4)
| ~ product(X0,X1,e_1) ),
inference(resolution,[],[f39,f28]) ).
fof(f61,plain,
! [X0,X1] :
( ~ product(X0,X1,e_3)
| ~ product(X0,X1,e_2) ),
inference(resolution,[],[f39,f30]) ).
fof(f69,plain,
! [X0,X1] :
( ~ product(X0,e_2,X1)
| ~ product(X0,e_1,X1) ),
inference(resolution,[],[f40,f26]) ).
fof(f70,plain,
! [X0,X1] :
( ~ product(X0,e_3,X1)
| ~ product(X0,e_1,X1) ),
inference(resolution,[],[f40,f27]) ).
fof(f93,plain,
( cycle(e_1,e_0)
| cycle(e_1,e_1)
| cycle(e_1,e_2)
| cycle(e_1,e_3) ),
inference(resolution,[],[f16,f22]) ).
fof(f94,plain,
( cycle(e_2,e_0)
| cycle(e_2,e_1)
| cycle(e_2,e_2)
| cycle(e_2,e_3) ),
inference(resolution,[],[f16,f23]) ).
fof(f95,plain,
( cycle(e_3,e_0)
| cycle(e_3,e_1)
| cycle(e_3,e_2)
| cycle(e_3,e_3) ),
inference(resolution,[],[f16,f24]) ).
fof(f98,definition,
( spl0_1
<=> cycle(e_3,e_3) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f101,definition,
( spl0_2
<=> cycle(e_3,e_2) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f104,definition,
( spl0_3
<=> cycle(e_3,e_1) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f105,plain,
( cycle(e_3,e_1)
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f104]) ).
fof(f107,definition,
( spl0_4
<=> cycle(e_3,e_0) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f108,plain,
( cycle(e_3,e_0)
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f107]) ).
fof(f109,plain,
( spl0_1
| spl0_2
| spl0_3
| spl0_4 ),
inference(avatar_split_clause,[],[f95,f107,f104,f101,f98]) ).
fof(f111,definition,
( spl0_5
<=> cycle(e_2,e_3) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f114,definition,
( spl0_6
<=> cycle(e_2,e_2) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f115,plain,
( cycle(e_2,e_2)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f114]) ).
fof(f117,definition,
( spl0_7
<=> cycle(e_2,e_1) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f118,plain,
( cycle(e_2,e_1)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f117]) ).
fof(f120,definition,
( spl0_8
<=> cycle(e_2,e_0) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f121,plain,
( cycle(e_2,e_0)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f120]) ).
fof(f122,plain,
( spl0_5
| spl0_6
| spl0_7
| spl0_8 ),
inference(avatar_split_clause,[],[f94,f120,f117,f114,f111]) ).
fof(f124,definition,
( spl0_9
<=> cycle(e_1,e_3) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f125,plain,
( cycle(e_1,e_3)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f124]) ).
fof(f127,definition,
( spl0_10
<=> cycle(e_1,e_2) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f128,plain,
( cycle(e_1,e_2)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f127]) ).
fof(f130,definition,
( spl0_11
<=> cycle(e_1,e_1) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f131,plain,
( cycle(e_1,e_1)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f130]) ).
fof(f133,definition,
( spl0_12
<=> cycle(e_1,e_0) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f134,plain,
( cycle(e_1,e_0)
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f133]) ).
fof(f135,plain,
( spl0_9
| spl0_10
| spl0_11
| spl0_12 ),
inference(avatar_split_clause,[],[f93,f133,f130,f127,f124]) ).
fof(f142,plain,
! [X0,X1] :
( ~ product(e_1,e_1,X0)
| ~ greater(X1,e_0)
| ~ cycle(e_1,X1)
| equalish(X0,e_2) ),
inference(resolution,[],[f21,f2]) ).
fof(f143,plain,
! [X0,X1] :
( ~ product(e_2,e_1,X0)
| ~ greater(X1,e_0)
| ~ cycle(e_2,X1)
| equalish(X0,e_3) ),
inference(resolution,[],[f21,f3]) ).
fof(f144,plain,
! [X0,X1] :
( ~ product(e_3,e_1,X0)
| ~ greater(X1,e_0)
| ~ cycle(e_3,X1)
| equalish(X0,e_4) ),
inference(resolution,[],[f21,f4]) ).
fof(f146,definition,
( spl0_13
<=> ! [X1] :
( ~ greater(X1,e_0)
| ~ cycle(e_3,X1) ) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f147,plain,
( ! [X1] :
( ~ cycle(e_3,X1)
| ~ greater(X1,e_0) )
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f146]) ).
fof(f149,definition,
( spl0_14
<=> ! [X0] :
( ~ product(e_3,e_1,X0)
| equalish(X0,e_4) ) ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
fof(f150,plain,
( ! [X0] :
( ~ product(e_3,e_1,X0)
| equalish(X0,e_4) )
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f149]) ).
fof(f151,plain,
( spl0_13
| spl0_14 ),
inference(avatar_split_clause,[],[f144,f149,f146]) ).
fof(f153,definition,
( spl0_15
<=> ! [X1] :
( ~ greater(X1,e_0)
| ~ cycle(e_2,X1) ) ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
fof(f154,plain,
( ! [X1] :
( ~ cycle(e_2,X1)
| ~ greater(X1,e_0) )
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f153]) ).
fof(f156,definition,
( spl0_16
<=> ! [X0] :
( ~ product(e_2,e_1,X0)
| equalish(X0,e_3) ) ),
introduced(definition,[new_symbols(definition,[spl0_16])],[avatar_definition]) ).
fof(f157,plain,
( ! [X0] :
( ~ product(e_2,e_1,X0)
| equalish(X0,e_3) )
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f156]) ).
fof(f158,plain,
( spl0_15
| spl0_16 ),
inference(avatar_split_clause,[],[f143,f156,f153]) ).
fof(f160,definition,
( spl0_17
<=> ! [X1] :
( ~ greater(X1,e_0)
| ~ cycle(e_1,X1) ) ),
introduced(definition,[new_symbols(definition,[spl0_17])],[avatar_definition]) ).
fof(f161,plain,
( ! [X1] :
( ~ cycle(e_1,X1)
| ~ greater(X1,e_0) )
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f160]) ).
fof(f163,definition,
( spl0_18
<=> ! [X0] :
( ~ product(e_1,e_1,X0)
| equalish(X0,e_2) ) ),
introduced(definition,[new_symbols(definition,[spl0_18])],[avatar_definition]) ).
fof(f164,plain,
( ! [X0] :
( ~ product(e_1,e_1,X0)
| equalish(X0,e_2) )
| ~ spl0_18 ),
inference(avatar_component_clause,[],[f163]) ).
fof(f165,plain,
( spl0_17
| spl0_18 ),
inference(avatar_split_clause,[],[f142,f163,f160]) ).
fof(f177,plain,
( ~ greater(e_3,e_0)
| ~ spl0_9
| ~ spl0_17 ),
inference(resolution,[],[f161,f125]) ).
fof(f180,plain,
( ~ greater(e_2,e_0)
| ~ spl0_6
| ~ spl0_15 ),
inference(resolution,[],[f115,f154]) ).
fof(f182,plain,
( $false
| ~ spl0_9
| ~ spl0_17 ),
inference(resolution,[],[f177,f7]) ).
fof(f183,plain,
( ~ spl0_9
| ~ spl0_17 ),
inference(avatar_contradiction_clause,[],[f182]) ).
fof(f184,plain,
( ~ greater(e_2,e_0)
| ~ spl0_10
| ~ spl0_17 ),
inference(resolution,[],[f128,f161]) ).
fof(f186,plain,
( $false
| ~ spl0_6
| ~ spl0_15 ),
inference(resolution,[],[f180,f6]) ).
fof(f187,plain,
( ~ spl0_6
| ~ spl0_15 ),
inference(avatar_contradiction_clause,[],[f186]) ).
fof(f188,plain,
( ! [X0,X1] :
( equalish(X0,e_4)
| ~ product(X1,e_1,e_3)
| ~ product(e_1,X0,X1) )
| ~ spl0_14 ),
inference(resolution,[],[f150,f43]) ).
fof(f189,plain,
( ! [X0] :
( ~ product(X0,e_1,e_3)
| ~ product(e_1,e_1,X0) )
| ~ spl0_14 ),
inference(resolution,[],[f188,f28]) ).
fof(f190,plain,
( ! [X0] :
( ~ product(X0,e_1,e_3)
| ~ product(e_1,e_2,X0) )
| ~ spl0_14 ),
inference(resolution,[],[f188,f31]) ).
fof(f191,plain,
( ! [X0] :
( ~ product(X0,e_1,e_3)
| ~ product(e_1,e_3,X0) )
| ~ spl0_14 ),
inference(resolution,[],[f188,f34]) ).
fof(f193,plain,
( ! [X0,X1] :
( ~ product(e_1,e_1,X0)
| ~ product(X1,e_1,X0)
| ~ product(e_1,e_3,X1) )
| ~ spl0_14 ),
inference(resolution,[],[f189,f43]) ).
fof(f200,plain,
( $false
| ~ spl0_10
| ~ spl0_17 ),
inference(resolution,[],[f184,f6]) ).
fof(f201,plain,
( ~ spl0_10
| ~ spl0_17 ),
inference(avatar_contradiction_clause,[],[f200]) ).
fof(f204,plain,
( ~ greater(e_1,e_0)
| ~ spl0_11
| ~ spl0_17 ),
inference(resolution,[],[f131,f161]) ).
fof(f207,plain,
( $false
| ~ spl0_11
| ~ spl0_17 ),
inference(resolution,[],[f204,f5]) ).
fof(f208,plain,
( ~ spl0_11
| ~ spl0_17 ),
inference(avatar_contradiction_clause,[],[f207]) ).
fof(f212,plain,
( equalish(e_1,e_2)
| ~ spl0_18 ),
inference(resolution,[],[f164,f42]) ).
fof(f221,plain,
( $false
| ~ spl0_18 ),
inference(resolution,[],[f212,f26]) ).
fof(f222,plain,
~ spl0_18,
inference(avatar_contradiction_clause,[],[f221]) ).
fof(f226,plain,
( ! [X0] :
( ~ product(e_1,e_1,X0)
| ~ product(e_1,e_3,e_1) )
| ~ spl0_14 ),
inference(factoring,[],[f193]) ).
fof(f228,definition,
( spl0_21
<=> product(e_1,e_3,e_1) ),
introduced(definition,[new_symbols(definition,[spl0_21])],[avatar_definition]) ).
fof(f231,definition,
( spl0_22
<=> ! [X0] : ~ product(e_1,e_1,X0) ),
introduced(definition,[new_symbols(definition,[spl0_22])],[avatar_definition]) ).
fof(f232,plain,
( ! [X0] : ~ product(e_1,e_1,X0)
| ~ spl0_22 ),
inference(avatar_component_clause,[],[f231]) ).
fof(f233,plain,
( ~ spl0_21
| spl0_22
| ~ spl0_14 ),
inference(avatar_split_clause,[],[f226,f149,f231,f228]) ).
fof(f234,plain,
( ! [X0] :
( ~ greater(X0,e_1)
| ~ product(e_1,e_1,X0) )
| ~ spl0_12 ),
inference(resolution,[],[f134,f20]) ).
fof(f235,plain,
! [X2,X0,X1] :
( ~ cycle(X0,X1)
| ~ next(X2,X0)
| ~ greater(e_1,e_0)
| ~ next(X1,e_2)
| ~ cycle(X2,e_1) ),
inference(resolution,[],[f18,f26]) ).
fof(f238,plain,
! [X2,X0,X1] :
( ~ cycle(X0,X1)
| ~ next(X2,X0)
| ~ greater(e_2,e_0)
| ~ next(X1,e_1)
| ~ cycle(X2,e_2) ),
inference(resolution,[],[f18,f29]) ).
fof(f241,plain,
! [X2,X0,X1] :
( ~ cycle(X0,X1)
| ~ next(X2,X0)
| ~ greater(e_3,e_0)
| ~ next(X1,e_1)
| ~ cycle(X2,e_3) ),
inference(resolution,[],[f18,f32]) ).
fof(f242,plain,
! [X2,X0,X1] :
( ~ cycle(X0,X1)
| ~ next(X2,X0)
| ~ greater(e_3,e_0)
| ~ next(X1,e_2)
| ~ cycle(X2,e_3) ),
inference(resolution,[],[f18,f33]) ).
fof(f263,definition,
( spl0_27
<=> greater(e_3,e_0) ),
introduced(definition,[new_symbols(definition,[spl0_27])],[avatar_definition]) ).
fof(f264,plain,
( ~ greater(e_3,e_0)
| spl0_27 ),
inference(avatar_component_clause,[],[f263]) ).
fof(f270,definition,
( spl0_29
<=> ! [X2,X0,X1] :
( ~ cycle(X0,X1)
| ~ cycle(X2,e_3)
| ~ next(X1,e_2)
| ~ next(X2,X0) ) ),
introduced(definition,[new_symbols(definition,[spl0_29])],[avatar_definition]) ).
fof(f271,plain,
( ! [X2,X0,X1] :
( ~ next(X1,e_2)
| ~ next(X2,X0)
| ~ cycle(X0,X1)
| ~ cycle(X2,e_3) )
| ~ spl0_29 ),
inference(avatar_component_clause,[],[f270]) ).
fof(f272,plain,
( ~ spl0_27
| spl0_29 ),
inference(avatar_split_clause,[],[f242,f270,f263]) ).
fof(f274,definition,
( spl0_30
<=> ! [X2,X0,X1] :
( ~ cycle(X0,X1)
| ~ cycle(X2,e_3)
| ~ next(X1,e_1)
| ~ next(X2,X0) ) ),
introduced(definition,[new_symbols(definition,[spl0_30])],[avatar_definition]) ).
fof(f275,plain,
( ! [X2,X0,X1] :
( ~ next(X1,e_1)
| ~ next(X2,X0)
| ~ cycle(X0,X1)
| ~ cycle(X2,e_3) )
| ~ spl0_30 ),
inference(avatar_component_clause,[],[f274]) ).
fof(f276,plain,
( ~ spl0_27
| spl0_30 ),
inference(avatar_split_clause,[],[f241,f274,f263]) ).
fof(f278,definition,
( spl0_31
<=> greater(e_2,e_0) ),
introduced(definition,[new_symbols(definition,[spl0_31])],[avatar_definition]) ).
fof(f279,plain,
( ~ greater(e_2,e_0)
| spl0_31 ),
inference(avatar_component_clause,[],[f278]) ).
fof(f289,definition,
( spl0_34
<=> ! [X2,X0,X1] :
( ~ cycle(X0,X1)
| ~ cycle(X2,e_2)
| ~ next(X1,e_1)
| ~ next(X2,X0) ) ),
introduced(definition,[new_symbols(definition,[spl0_34])],[avatar_definition]) ).
fof(f290,plain,
( ! [X2,X0,X1] :
( ~ next(X1,e_1)
| ~ next(X2,X0)
| ~ cycle(X0,X1)
| ~ cycle(X2,e_2) )
| ~ spl0_34 ),
inference(avatar_component_clause,[],[f289]) ).
fof(f291,plain,
( ~ spl0_31
| spl0_34 ),
inference(avatar_split_clause,[],[f238,f289,f278]) ).
fof(f293,definition,
( spl0_35
<=> greater(e_1,e_0) ),
introduced(definition,[new_symbols(definition,[spl0_35])],[avatar_definition]) ).
fof(f294,plain,
( ~ greater(e_1,e_0)
| spl0_35 ),
inference(avatar_component_clause,[],[f293]) ).
fof(f304,definition,
( spl0_38
<=> ! [X2,X0,X1] :
( ~ cycle(X0,X1)
| ~ cycle(X2,e_1)
| ~ next(X1,e_2)
| ~ next(X2,X0) ) ),
introduced(definition,[new_symbols(definition,[spl0_38])],[avatar_definition]) ).
fof(f305,plain,
( ! [X2,X0,X1] :
( ~ next(X1,e_2)
| ~ next(X2,X0)
| ~ cycle(X0,X1)
| ~ cycle(X2,e_1) )
| ~ spl0_38 ),
inference(avatar_component_clause,[],[f304]) ).
fof(f306,plain,
( ~ spl0_35
| spl0_38 ),
inference(avatar_split_clause,[],[f235,f304,f293]) ).
fof(f312,plain,
( $false
| spl0_27 ),
inference(resolution,[],[f264,f7]) ).
fof(f313,plain,
spl0_27,
inference(avatar_contradiction_clause,[],[f312]) ).
fof(f318,plain,
( $false
| spl0_31 ),
inference(resolution,[],[f279,f6]) ).
fof(f319,plain,
spl0_31,
inference(avatar_contradiction_clause,[],[f318]) ).
fof(f322,plain,
( $false
| spl0_35 ),
inference(resolution,[],[f294,f5]) ).
fof(f323,plain,
spl0_35,
inference(avatar_contradiction_clause,[],[f322]) ).
fof(f333,definition,
( spl0_39
<=> product(e_2,e_2,e_1) ),
introduced(definition,[new_symbols(definition,[spl0_39])],[avatar_definition]) ).
fof(f334,plain,
( ~ product(e_2,e_2,e_1)
| spl0_39 ),
inference(avatar_component_clause,[],[f333]) ).
fof(f336,definition,
( spl0_40
<=> product(e_2,e_1,e_3) ),
introduced(definition,[new_symbols(definition,[spl0_40])],[avatar_definition]) ).
fof(f373,plain,
( ! [X0] :
( ~ product(X0,e_2,e_2)
| ~ product(e_2,e_1,X0) )
| spl0_39 ),
inference(resolution,[],[f334,f43]) ).
fof(f385,definition,
( spl0_50
<=> ! [X0] :
( ~ next(X0,e_2)
| ~ cycle(e_3,X0) ) ),
introduced(definition,[new_symbols(definition,[spl0_50])],[avatar_definition]) ).
fof(f386,plain,
( ! [X0] :
( ~ next(X0,e_2)
| ~ cycle(e_3,X0) )
| ~ spl0_50 ),
inference(avatar_component_clause,[],[f385]) ).
fof(f397,plain,
( ~ product(e_2,e_1,e_2)
| spl0_39 ),
inference(resolution,[],[f373,f42]) ).
fof(f406,definition,
( spl0_53
<=> ! [X0] :
( ~ next(X0,e_1)
| ~ cycle(e_4,X0) ) ),
introduced(definition,[new_symbols(definition,[spl0_53])],[avatar_definition]) ).
fof(f407,plain,
( ! [X0] :
( ~ next(X0,e_1)
| ~ cycle(e_4,X0) )
| ~ spl0_53 ),
inference(avatar_component_clause,[],[f406]) ).
fof(f410,definition,
( spl0_54
<=> ! [X0] :
( ~ next(X0,e_1)
| ~ cycle(e_3,X0) ) ),
introduced(definition,[new_symbols(definition,[spl0_54])],[avatar_definition]) ).
fof(f411,plain,
( ! [X0] :
( ~ next(X0,e_1)
| ~ cycle(e_3,X0) )
| ~ spl0_54 ),
inference(avatar_component_clause,[],[f410]) ).
fof(f457,plain,
( ! [X0] :
( ~ next(X0,e_2)
| ~ cycle(e_3,X0)
| ~ cycle(e_2,e_3) )
| ~ spl0_29 ),
inference(resolution,[],[f271,f3]) ).
fof(f461,plain,
( ~ spl0_5
| spl0_50
| ~ spl0_29 ),
inference(avatar_split_clause,[],[f457,f270,f385,f111]) ).
fof(f469,plain,
( ! [X0] :
( ~ next(X0,e_1)
| ~ cycle(e_3,X0)
| ~ cycle(e_2,e_3) )
| ~ spl0_30 ),
inference(resolution,[],[f275,f3]) ).
fof(f470,plain,
( ! [X0] :
( ~ next(X0,e_1)
| ~ cycle(e_4,X0)
| ~ cycle(e_3,e_3) )
| ~ spl0_30 ),
inference(resolution,[],[f275,f4]) ).
fof(f472,plain,
( ~ spl0_1
| spl0_53
| ~ spl0_30 ),
inference(avatar_split_clause,[],[f470,f274,f406,f98]) ).
fof(f473,plain,
( ~ spl0_5
| spl0_54
| ~ spl0_30 ),
inference(avatar_split_clause,[],[f469,f274,f410,f111]) ).
fof(f501,definition,
( spl0_63
<=> product(e_1,e_2,e_1) ),
introduced(definition,[new_symbols(definition,[spl0_63])],[avatar_definition]) ).
fof(f502,plain,
( ~ product(e_1,e_2,e_1)
| spl0_63 ),
inference(avatar_component_clause,[],[f501]) ).
fof(f517,plain,
( ! [X0,X1] :
( ~ next(X0,X1)
| ~ cycle(X1,e_0)
| ~ cycle(X0,e_2) )
| ~ spl0_34 ),
inference(resolution,[],[f290,f1]) ).
fof(f548,plain,
! [X2,X0,X1] :
( ~ cycle(e_3,e_0)
| ~ cycle(e_4,X0)
| ~ cycle(X1,X2)
| ~ greater(e_3,X1)
| ~ greater(X2,X0) ),
inference(resolution,[],[f19,f4]) ).
fof(f550,definition,
( spl0_65
<=> ! [X2,X0,X1] :
( ~ cycle(e_4,X0)
| ~ cycle(X1,X2)
| ~ greater(X2,X0)
| ~ greater(e_3,X1) ) ),
introduced(definition,[new_symbols(definition,[spl0_65])],[avatar_definition]) ).
fof(f551,plain,
( ! [X2,X0,X1] :
( ~ cycle(e_4,X0)
| ~ cycle(X1,X2)
| ~ greater(X2,X0)
| ~ greater(e_3,X1) )
| ~ spl0_65 ),
inference(avatar_component_clause,[],[f550]) ).
fof(f553,plain,
( spl0_65
| ~ spl0_4 ),
inference(avatar_split_clause,[],[f548,f107,f550]) ).
fof(f602,definition,
( spl0_70
<=> product(e_4,e_4,e_1) ),
introduced(definition,[new_symbols(definition,[spl0_70])],[avatar_definition]) ).
fof(f603,plain,
( ~ product(e_4,e_4,e_1)
| spl0_70 ),
inference(avatar_component_clause,[],[f602]) ).
fof(f605,definition,
( spl0_71
<=> product(e_4,e_1,e_2) ),
introduced(definition,[new_symbols(definition,[spl0_71])],[avatar_definition]) ).
fof(f611,plain,
( ! [X0] :
( ~ next(X0,e_2)
| ~ cycle(e_3,X0)
| ~ cycle(e_2,e_1) )
| ~ spl0_38 ),
inference(resolution,[],[f305,f3]) ).
fof(f617,plain,
( ! [X0] :
( ~ product(X0,e_4,e_4)
| ~ product(e_4,e_1,X0) )
| spl0_70 ),
inference(resolution,[],[f603,f43]) ).
fof(f646,plain,
( ~ product(e_4,e_1,e_4)
| spl0_70 ),
inference(resolution,[],[f617,f42]) ).
fof(f684,plain,
( ~ group_element(e_1)
| product(e_2,e_1,e_1)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_3)
| ~ group_element(e_2)
| equalish(e_4,e_3)
| ~ spl0_16 ),
inference(resolution,[],[f38,f157]) ).
fof(f704,definition,
( spl0_79
<=> group_element(e_4) ),
introduced(definition,[new_symbols(definition,[spl0_79])],[avatar_definition]) ).
fof(f705,plain,
( ~ group_element(e_4)
| spl0_79 ),
inference(avatar_component_clause,[],[f704]) ).
fof(f711,definition,
( spl0_81
<=> group_element(e_1) ),
introduced(definition,[new_symbols(definition,[spl0_81])],[avatar_definition]) ).
fof(f712,plain,
( ~ group_element(e_1)
| spl0_81 ),
inference(avatar_component_clause,[],[f711]) ).
fof(f714,definition,
( spl0_82
<=> product(e_1,e_4,e_3) ),
introduced(definition,[new_symbols(definition,[spl0_82])],[avatar_definition]) ).
fof(f717,definition,
( spl0_83
<=> product(e_1,e_4,e_2) ),
introduced(definition,[new_symbols(definition,[spl0_83])],[avatar_definition]) ).
fof(f720,definition,
( spl0_84
<=> product(e_1,e_4,e_1) ),
introduced(definition,[new_symbols(definition,[spl0_84])],[avatar_definition]) ).
fof(f727,definition,
( spl0_86
<=> product(e_1,e_3,e_3) ),
introduced(definition,[new_symbols(definition,[spl0_86])],[avatar_definition]) ).
fof(f730,definition,
( spl0_87
<=> product(e_1,e_3,e_2) ),
introduced(definition,[new_symbols(definition,[spl0_87])],[avatar_definition]) ).
fof(f734,definition,
( spl0_88
<=> group_element(e_3) ),
introduced(definition,[new_symbols(definition,[spl0_88])],[avatar_definition]) ).
fof(f735,plain,
( ~ group_element(e_3)
| spl0_88 ),
inference(avatar_component_clause,[],[f734]) ).
fof(f738,definition,
( spl0_89
<=> product(e_1,e_2,e_3) ),
introduced(definition,[new_symbols(definition,[spl0_89])],[avatar_definition]) ).
fof(f741,definition,
( spl0_90
<=> product(e_1,e_2,e_2) ),
introduced(definition,[new_symbols(definition,[spl0_90])],[avatar_definition]) ).
fof(f743,plain,
( product(e_1,e_2,e_1)
| ~ spl0_63 ),
inference(avatar_component_clause,[],[f501]) ).
fof(f745,definition,
( spl0_91
<=> group_element(e_2) ),
introduced(definition,[new_symbols(definition,[spl0_91])],[avatar_definition]) ).
fof(f746,plain,
( ~ group_element(e_2)
| spl0_91 ),
inference(avatar_component_clause,[],[f745]) ).
fof(f754,definition,
( spl0_93
<=> product(e_1,e_3,e_4) ),
introduced(definition,[new_symbols(definition,[spl0_93])],[avatar_definition]) ).
fof(f755,plain,
( ~ product(e_1,e_3,e_4)
| spl0_93 ),
inference(avatar_component_clause,[],[f754]) ).
fof(f765,definition,
( spl0_96
<=> product(e_1,e_4,e_4) ),
introduced(definition,[new_symbols(definition,[spl0_96])],[avatar_definition]) ).
fof(f766,plain,
( ~ product(e_1,e_4,e_4)
| spl0_96 ),
inference(avatar_component_clause,[],[f765]) ).
fof(f769,definition,
( spl0_97
<=> product(e_1,e_2,e_4) ),
introduced(definition,[new_symbols(definition,[spl0_97])],[avatar_definition]) ).
fof(f770,plain,
( ~ product(e_1,e_2,e_4)
| spl0_97 ),
inference(avatar_component_clause,[],[f769]) ).
fof(f783,definition,
( spl0_100
<=> product(e_3,e_1,e_3) ),
introduced(definition,[new_symbols(definition,[spl0_100])],[avatar_definition]) ).
fof(f786,definition,
( spl0_101
<=> product(e_3,e_1,e_2) ),
introduced(definition,[new_symbols(definition,[spl0_101])],[avatar_definition]) ).
fof(f787,plain,
( product(e_3,e_1,e_2)
| ~ spl0_101 ),
inference(avatar_component_clause,[],[f786]) ).
fof(f789,definition,
( spl0_102
<=> product(e_3,e_1,e_1) ),
introduced(definition,[new_symbols(definition,[spl0_102])],[avatar_definition]) ).
fof(f790,plain,
( product(e_3,e_1,e_1)
| ~ spl0_102 ),
inference(avatar_component_clause,[],[f789]) ).
fof(f793,definition,
( spl0_103
<=> equalish(e_4,e_3) ),
introduced(definition,[new_symbols(definition,[spl0_103])],[avatar_definition]) ).
fof(f794,plain,
( equalish(e_4,e_3)
| ~ spl0_103 ),
inference(avatar_component_clause,[],[f793]) ).
fof(f795,plain,
( product(e_2,e_1,e_3)
| ~ spl0_40 ),
inference(avatar_component_clause,[],[f336]) ).
fof(f797,definition,
( spl0_104
<=> product(e_2,e_1,e_2) ),
introduced(definition,[new_symbols(definition,[spl0_104])],[avatar_definition]) ).
fof(f798,plain,
( product(e_2,e_1,e_2)
| ~ spl0_104 ),
inference(avatar_component_clause,[],[f797]) ).
fof(f800,definition,
( spl0_105
<=> product(e_2,e_1,e_1) ),
introduced(definition,[new_symbols(definition,[spl0_105])],[avatar_definition]) ).
fof(f801,plain,
( product(e_2,e_1,e_1)
| ~ spl0_105 ),
inference(avatar_component_clause,[],[f800]) ).
fof(f802,plain,
( spl0_103
| ~ spl0_91
| spl0_40
| spl0_104
| spl0_105
| ~ spl0_81
| ~ spl0_16 ),
inference(avatar_split_clause,[],[f684,f156,f711,f800,f797,f336,f745,f793]) ).
fof(f804,definition,
( spl0_106
<=> product(e_4,e_1,e_3) ),
introduced(definition,[new_symbols(definition,[spl0_106])],[avatar_definition]) ).
fof(f805,plain,
( product(e_4,e_1,e_3)
| ~ spl0_106 ),
inference(avatar_component_clause,[],[f804]) ).
fof(f806,plain,
( product(e_4,e_1,e_2)
| ~ spl0_71 ),
inference(avatar_component_clause,[],[f605]) ).
fof(f808,definition,
( spl0_107
<=> product(e_4,e_1,e_1) ),
introduced(definition,[new_symbols(definition,[spl0_107])],[avatar_definition]) ).
fof(f809,plain,
( product(e_4,e_1,e_1)
| ~ spl0_107 ),
inference(avatar_component_clause,[],[f808]) ).
fof(f830,definition,
( spl0_112
<=> product(e_4,e_2,e_1) ),
introduced(definition,[new_symbols(definition,[spl0_112])],[avatar_definition]) ).
fof(f831,plain,
( ~ product(e_4,e_2,e_1)
| spl0_112 ),
inference(avatar_component_clause,[],[f830]) ).
fof(f849,plain,
( $false
| spl0_81 ),
inference(resolution,[],[f712,f22]) ).
fof(f850,plain,
spl0_81,
inference(avatar_contradiction_clause,[],[f849]) ).
fof(f855,plain,
( $false
| spl0_88 ),
inference(resolution,[],[f735,f24]) ).
fof(f856,plain,
spl0_88,
inference(avatar_contradiction_clause,[],[f855]) ).
fof(f857,plain,
( $false
| spl0_91 ),
inference(resolution,[],[f746,f23]) ).
fof(f858,plain,
spl0_91,
inference(avatar_contradiction_clause,[],[f857]) ).
fof(f862,plain,
( ~ spl0_7
| spl0_50
| ~ spl0_38 ),
inference(avatar_split_clause,[],[f611,f304,f385,f117]) ).
fof(f869,plain,
( $false
| spl0_79 ),
inference(resolution,[],[f705,f25]) ).
fof(f870,plain,
spl0_79,
inference(avatar_contradiction_clause,[],[f869]) ).
fof(f875,plain,
( $false
| ~ spl0_22 ),
inference(resolution,[],[f232,f42]) ).
fof(f876,plain,
~ spl0_22,
inference(avatar_contradiction_clause,[],[f875]) ).
fof(f880,plain,
( ! [X0] :
( ~ greater(X0,e_2)
| ~ product(e_2,e_1,X0) )
| ~ spl0_8 ),
inference(resolution,[],[f121,f20]) ).
fof(f908,plain,
( ~ group_element(e_4)
| product(e_1,e_4,e_1)
| product(e_1,e_4,e_2)
| product(e_1,e_4,e_3)
| ~ group_element(e_1)
| spl0_96 ),
inference(resolution,[],[f766,f38]) ).
fof(f910,plain,
( ~ spl0_81
| spl0_82
| spl0_83
| spl0_84
| ~ spl0_79
| spl0_96 ),
inference(avatar_split_clause,[],[f908,f765,f704,f720,f717,f714,f711]) ).
fof(f911,plain,
( ~ group_element(e_2)
| product(e_1,e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_3)
| ~ group_element(e_1)
| spl0_97 ),
inference(resolution,[],[f770,f38]) ).
fof(f913,plain,
( ~ spl0_81
| spl0_89
| spl0_90
| spl0_63
| ~ spl0_91
| spl0_97 ),
inference(avatar_split_clause,[],[f911,f769,f745,f501,f741,f738,f711]) ).
fof(f919,plain,
( ! [X0] :
( ~ product(X0,e_2,e_4)
| ~ product(e_2,e_1,X0) )
| spl0_112 ),
inference(resolution,[],[f831,f43]) ).
fof(f932,definition,
( spl0_124
<=> product(e_1,e_1,e_2) ),
introduced(definition,[new_symbols(definition,[spl0_124])],[avatar_definition]) ).
fof(f933,plain,
( ~ product(e_1,e_1,e_2)
| spl0_124 ),
inference(avatar_component_clause,[],[f932]) ).
fof(f945,plain,
( ~ cycle(e_3,e_1)
| ~ spl0_50 ),
inference(resolution,[],[f386,f2]) ).
fof(f947,plain,
( ~ product(e_1,e_2,e_4)
| ~ spl0_14
| ~ spl0_106 ),
inference(resolution,[],[f805,f190]) ).
fof(f948,plain,
( ~ product(e_1,e_3,e_4)
| ~ spl0_14
| ~ spl0_106 ),
inference(resolution,[],[f805,f191]) ).
fof(f966,plain,
( ~ spl0_93
| ~ spl0_14
| ~ spl0_106 ),
inference(avatar_split_clause,[],[f948,f804,f149,f754]) ).
fof(f967,plain,
( ~ cycle(e_4,e_0)
| ~ spl0_53 ),
inference(resolution,[],[f407,f1]) ).
fof(f977,plain,
( ~ cycle(e_3,e_0)
| ~ spl0_54 ),
inference(resolution,[],[f411,f1]) ).
fof(f985,plain,
( ~ product(e_1,e_1,e_2)
| ~ spl0_12 ),
inference(resolution,[],[f234,f9]) ).
fof(f986,plain,
( ~ product(e_1,e_1,e_3)
| ~ spl0_12 ),
inference(resolution,[],[f234,f10]) ).
fof(f988,plain,
( ~ spl0_124
| ~ spl0_12 ),
inference(avatar_split_clause,[],[f985,f133,f932]) ).
fof(f989,plain,
( ! [X0] :
( ~ product(X0,e_1,e_1)
| ~ product(e_1,e_2,X0) )
| spl0_124 ),
inference(resolution,[],[f933,f43]) ).
fof(f990,plain,
( ~ product(e_2,e_1,e_3)
| ~ spl0_8 ),
inference(resolution,[],[f880,f12]) ).
fof(f991,plain,
( ~ product(e_2,e_1,e_4)
| ~ spl0_8 ),
inference(resolution,[],[f880,f13]) ).
fof(f992,plain,
( ~ spl0_40
| ~ spl0_8 ),
inference(avatar_split_clause,[],[f990,f120,f336]) ).
fof(f1014,plain,
( ~ group_element(e_1)
| product(e_4,e_1,e_1)
| product(e_4,e_1,e_2)
| product(e_4,e_1,e_3)
| ~ group_element(e_4)
| spl0_70 ),
inference(resolution,[],[f646,f38]) ).
fof(f1099,plain,
! [X2,X0,X1] :
( ~ product(X0,X1,e_1)
| ~ product(X2,X1,X0)
| ~ product(X1,e_2,X2) ),
inference(resolution,[],[f57,f43]) ).
fof(f1100,plain,
~ product(e_2,e_2,e_1),
inference(resolution,[],[f57,f42]) ).
fof(f1118,plain,
( ~ cycle(e_3,e_0)
| ~ cycle(e_2,e_2)
| ~ spl0_34 ),
inference(resolution,[],[f517,f3]) ).
fof(f1119,plain,
( ~ cycle(e_4,e_0)
| ~ cycle(e_3,e_2)
| ~ spl0_34 ),
inference(resolution,[],[f517,f4]) ).
fof(f1121,definition,
( spl0_136
<=> cycle(e_4,e_0) ),
introduced(definition,[new_symbols(definition,[spl0_136])],[avatar_definition]) ).
fof(f1122,plain,
( ~ cycle(e_4,e_0)
| spl0_136 ),
inference(avatar_component_clause,[],[f1121]) ).
fof(f1123,plain,
( ~ spl0_2
| ~ spl0_136
| ~ spl0_34 ),
inference(avatar_split_clause,[],[f1119,f289,f1121,f101]) ).
fof(f1141,plain,
! [X2,X0,X1] :
( ~ product(X0,X1,e_1)
| ~ product(X2,X1,X0)
| ~ product(X1,e_3,X2) ),
inference(resolution,[],[f58,f43]) ).
fof(f1176,plain,
( ~ product(e_1,e_1,e_1)
| ~ spl0_63
| spl0_124 ),
inference(resolution,[],[f989,f743]) ).
fof(f1180,plain,
( $false
| ~ spl0_63
| spl0_124 ),
inference(resolution,[],[f1176,f42]) ).
fof(f1181,plain,
( ~ spl0_63
| spl0_124 ),
inference(avatar_contradiction_clause,[],[f1180]) ).
fof(f1182,plain,
( ~ spl0_136
| ~ spl0_53 ),
inference(avatar_split_clause,[],[f967,f406,f1121]) ).
fof(f1183,plain,
( ! [X0] :
( ~ product(X0,e_2,e_1)
| ~ product(e_2,e_1,X0) )
| spl0_63 ),
inference(resolution,[],[f502,f43]) ).
fof(f1193,plain,
! [X0,X1] :
( ~ product(X1,X0,e_1)
| ~ product(e_4,X0,X1)
| ~ group_element(e_2)
| product(X0,e_2,e_1)
| product(X0,e_2,e_2)
| product(X0,e_2,e_3)
| ~ group_element(X0) ),
inference(resolution,[],[f1099,f38]) ).
fof(f1195,plain,
! [X0] :
( ~ product(e_1,X0,e_1)
| ~ product(X0,e_2,e_1) ),
inference(factoring,[],[f1099]) ).
fof(f1199,definition,
( spl0_140
<=> ! [X0,X1] :
( ~ product(X1,X0,e_1)
| ~ group_element(X0)
| product(X0,e_2,e_3)
| product(X0,e_2,e_2)
| product(X0,e_2,e_1)
| ~ product(e_4,X0,X1) ) ),
introduced(definition,[new_symbols(definition,[spl0_140])],[avatar_definition]) ).
fof(f1200,plain,
( ! [X0,X1] :
( ~ group_element(X0)
| ~ product(X1,X0,e_1)
| product(X0,e_2,e_3)
| product(X0,e_2,e_2)
| product(X0,e_2,e_1)
| ~ product(e_4,X0,X1) )
| ~ spl0_140 ),
inference(avatar_component_clause,[],[f1199]) ).
fof(f1201,plain,
( ~ spl0_91
| spl0_140 ),
inference(avatar_split_clause,[],[f1193,f1199,f745]) ).
fof(f1204,plain,
( ! [X0] :
( ~ product(X0,e_1,e_1)
| product(e_1,e_2,e_3)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1)
| ~ product(e_4,e_1,X0) )
| ~ spl0_140 ),
inference(resolution,[],[f1200,f22]) ).
fof(f1209,definition,
( spl0_141
<=> product(e_3,e_2,e_1) ),
introduced(definition,[new_symbols(definition,[spl0_141])],[avatar_definition]) ).
fof(f1210,plain,
( product(e_3,e_2,e_1)
| ~ spl0_141 ),
inference(avatar_component_clause,[],[f1209]) ).
fof(f1212,definition,
( spl0_142
<=> product(e_3,e_2,e_2) ),
introduced(definition,[new_symbols(definition,[spl0_142])],[avatar_definition]) ).
fof(f1213,plain,
( product(e_3,e_2,e_2)
| ~ spl0_142 ),
inference(avatar_component_clause,[],[f1212]) ).
fof(f1215,definition,
( spl0_143
<=> product(e_3,e_2,e_3) ),
introduced(definition,[new_symbols(definition,[spl0_143])],[avatar_definition]) ).
fof(f1216,plain,
( product(e_3,e_2,e_3)
| ~ spl0_143 ),
inference(avatar_component_clause,[],[f1215]) ).
fof(f1221,plain,
( ~ product(e_2,e_1,e_3)
| spl0_39
| ~ spl0_142 ),
inference(resolution,[],[f1213,f373]) ).
fof(f1228,plain,
( $false
| spl0_136 ),
inference(resolution,[],[f1122,f17]) ).
fof(f1229,plain,
spl0_136,
inference(avatar_contradiction_clause,[],[f1228]) ).
fof(f1230,plain,
( ~ spl0_3
| ~ spl0_50 ),
inference(avatar_split_clause,[],[f945,f385,f104]) ).
fof(f1265,plain,
! [X2,X0,X1] :
( ~ product(X0,X1,e_1)
| ~ product(X2,X1,X0)
| ~ product(X1,e_4,X2) ),
inference(resolution,[],[f59,f43]) ).
fof(f1266,plain,
~ product(e_4,e_4,e_1),
inference(resolution,[],[f59,f42]) ).
fof(f1277,plain,
( ! [X0] :
( ~ product(X0,e_1,e_1)
| ~ product(e_1,e_3,X0) )
| ~ spl0_12 ),
inference(resolution,[],[f986,f43]) ).
fof(f1279,plain,
( ~ group_element(e_1)
| product(e_2,e_1,e_1)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_3)
| ~ group_element(e_2)
| ~ spl0_8 ),
inference(resolution,[],[f991,f38]) ).
fof(f1281,plain,
( ~ spl0_91
| spl0_40
| spl0_104
| spl0_105
| ~ spl0_81
| ~ spl0_8 ),
inference(avatar_split_clause,[],[f1279,f120,f711,f800,f797,f336,f745]) ).
fof(f1282,plain,
( ~ spl0_40
| spl0_39
| ~ spl0_142 ),
inference(avatar_split_clause,[],[f1221,f1212,f333,f336]) ).
fof(f1283,plain,
~ spl0_39,
inference(avatar_split_clause,[],[f1100,f333]) ).
fof(f1292,plain,
( ~ product(e_2,e_1,e_3)
| spl0_63
| ~ spl0_141 ),
inference(resolution,[],[f1210,f1183]) ).
fof(f1297,plain,
( ~ spl0_40
| spl0_63
| ~ spl0_141 ),
inference(avatar_split_clause,[],[f1292,f1209,f501,f336]) ).
fof(f1298,plain,
( ~ greater(e_1,e_0)
| ~ spl0_3
| ~ spl0_13 ),
inference(resolution,[],[f147,f105]) ).
fof(f1299,plain,
( ~ spl0_35
| ~ spl0_3
| ~ spl0_13 ),
inference(avatar_split_clause,[],[f1298,f146,f104,f293]) ).
fof(f1301,plain,
( ! [X0,X1] :
( equalish(X0,e_4)
| ~ product(X1,e_1,e_3)
| ~ product(e_1,X0,X1) )
| ~ spl0_14 ),
inference(resolution,[],[f150,f43]) ).
fof(f1308,plain,
( ! [X0,X1] :
( equalish(X0,e_3)
| ~ product(X1,e_1,e_2)
| ~ product(e_1,X0,X1) )
| ~ spl0_16 ),
inference(resolution,[],[f157,f43]) ).
fof(f1311,plain,
( ! [X0] :
( ~ product(X0,e_1,e_3)
| ~ product(e_1,e_2,X0) )
| ~ spl0_14 ),
inference(resolution,[],[f1301,f31]) ).
fof(f1312,plain,
( ! [X0] :
( ~ product(X0,e_1,e_3)
| ~ product(e_1,e_3,X0) )
| ~ spl0_14 ),
inference(resolution,[],[f1301,f34]) ).
fof(f1315,plain,
( ! [X0] :
( ~ product(X0,e_1,e_2)
| ~ product(e_1,e_2,X0) )
| ~ spl0_16 ),
inference(resolution,[],[f1308,f30]) ).
fof(f1331,plain,
( ~ product(e_1,e_2,e_2)
| ~ spl0_14
| ~ spl0_40 ),
inference(resolution,[],[f1311,f795]) ).
fof(f1333,plain,
( ~ spl0_90
| ~ spl0_14
| ~ spl0_40 ),
inference(avatar_split_clause,[],[f1331,f336,f149,f741]) ).
fof(f1334,plain,
( ! [X0,X1] :
( ~ product(e_1,e_3,X0)
| ~ product(X1,e_1,X0)
| ~ product(e_1,e_3,X1) )
| ~ spl0_14 ),
inference(resolution,[],[f1312,f43]) ).
fof(f1345,plain,
( ~ product(e_1,e_2,e_4)
| ~ spl0_16
| ~ spl0_71 ),
inference(resolution,[],[f1315,f806]) ).
fof(f1402,plain,
( ! [X0] :
( ~ product(e_1,e_3,X0)
| ~ product(X0,e_1,X0) )
| ~ spl0_14 ),
inference(factoring,[],[f1334]) ).
fof(f1406,plain,
( ~ product(e_1,e_3,e_4)
| ~ group_element(e_1)
| product(e_4,e_1,e_1)
| product(e_4,e_1,e_2)
| product(e_4,e_1,e_3)
| ~ group_element(e_4)
| ~ spl0_14 ),
inference(resolution,[],[f1402,f38]) ).
fof(f1464,plain,
! [X2,X0,X1] :
( ~ product(X0,X1,e_2)
| ~ product(X2,X1,X0)
| ~ product(X1,e_3,X2) ),
inference(resolution,[],[f61,f43]) ).
fof(f1478,definition,
( spl0_147
<=> product(e_3,e_1,e_4) ),
introduced(definition,[new_symbols(definition,[spl0_147])],[avatar_definition]) ).
fof(f1479,plain,
( ~ product(e_3,e_1,e_4)
| spl0_147 ),
inference(avatar_component_clause,[],[f1478]) ).
fof(f1637,definition,
( spl0_161
<=> product(e_1,e_1,e_1) ),
introduced(definition,[new_symbols(definition,[spl0_161])],[avatar_definition]) ).
fof(f1638,plain,
( ~ product(e_1,e_1,e_1)
| spl0_161 ),
inference(avatar_component_clause,[],[f1637]) ).
fof(f1644,plain,
( $false
| spl0_161 ),
inference(resolution,[],[f1638,f42]) ).
fof(f1645,plain,
spl0_161,
inference(avatar_contradiction_clause,[],[f1644]) ).
fof(f1706,plain,
( ~ product(e_1,e_2,e_3)
| ~ spl0_16
| ~ spl0_101 ),
inference(resolution,[],[f787,f1315]) ).
fof(f1734,plain,
( ~ spl0_89
| ~ spl0_16
| ~ spl0_101 ),
inference(avatar_split_clause,[],[f1706,f786,f156,f738]) ).
fof(f1740,plain,
( ~ product(e_1,e_2,e_3)
| ~ spl0_102
| spl0_124 ),
inference(resolution,[],[f790,f989]) ).
fof(f1777,plain,
( ~ spl0_89
| ~ spl0_102
| spl0_124 ),
inference(avatar_split_clause,[],[f1740,f932,f789,f738]) ).
fof(f1835,plain,
( ~ spl0_97
| ~ spl0_16
| ~ spl0_71 ),
inference(avatar_split_clause,[],[f1345,f605,f156,f769]) ).
fof(f1843,definition,
( spl0_170
<=> ! [X0] :
( ~ product(X0,e_1,e_1)
| ~ product(e_4,e_1,X0) ) ),
introduced(definition,[new_symbols(definition,[spl0_170])],[avatar_definition]) ).
fof(f1844,plain,
( ! [X0] :
( ~ product(X0,e_1,e_1)
| ~ product(e_4,e_1,X0) )
| ~ spl0_170 ),
inference(avatar_component_clause,[],[f1843]) ).
fof(f1845,plain,
( spl0_63
| spl0_90
| spl0_89
| spl0_170
| ~ spl0_140 ),
inference(avatar_split_clause,[],[f1204,f1199,f1843,f738,f741,f501]) ).
fof(f1858,plain,
( ~ spl0_79
| spl0_106
| spl0_71
| spl0_107
| ~ spl0_81
| spl0_70 ),
inference(avatar_split_clause,[],[f1014,f602,f711,f808,f605,f804,f704]) ).
fof(f1859,plain,
( ~ spl0_79
| spl0_106
| spl0_71
| spl0_107
| ~ spl0_81
| ~ spl0_93
| ~ spl0_14 ),
inference(avatar_split_clause,[],[f1406,f149,f754,f711,f808,f605,f804,f704]) ).
fof(f1895,plain,
( ~ spl0_4
| ~ spl0_54 ),
inference(avatar_split_clause,[],[f977,f410,f107]) ).
fof(f1896,plain,
( ~ spl0_6
| ~ spl0_4
| ~ spl0_34 ),
inference(avatar_split_clause,[],[f1118,f289,f107,f114]) ).
fof(f1908,plain,
( ~ product(e_1,e_2,e_4)
| ~ spl0_107
| spl0_124 ),
inference(resolution,[],[f809,f989]) ).
fof(f1909,plain,
( ~ product(e_1,e_3,e_4)
| ~ spl0_12
| ~ spl0_107 ),
inference(resolution,[],[f809,f1277]) ).
fof(f1924,plain,
( ~ spl0_93
| ~ spl0_12
| ~ spl0_107 ),
inference(avatar_split_clause,[],[f1909,f808,f133,f754]) ).
fof(f1925,plain,
( ~ spl0_97
| ~ spl0_107
| spl0_124 ),
inference(avatar_split_clause,[],[f1908,f932,f808,f769]) ).
fof(f1930,plain,
( ! [X0,X1] :
( ~ cycle(X0,X1)
| ~ greater(X1,e_0)
| ~ greater(e_3,X0) )
| ~ spl0_65 ),
inference(resolution,[],[f551,f17]) ).
fof(f1950,plain,
! [X0,X1] :
( ~ product(X1,X0,e_1)
| ~ product(e_4,X0,X1)
| ~ group_element(e_3)
| product(X0,e_3,e_1)
| product(X0,e_3,e_2)
| product(X0,e_3,e_3)
| ~ group_element(X0) ),
inference(resolution,[],[f1141,f38]) ).
fof(f1956,definition,
( spl0_176
<=> ! [X0,X1] :
( ~ product(X1,X0,e_1)
| ~ group_element(X0)
| product(X0,e_3,e_3)
| product(X0,e_3,e_2)
| product(X0,e_3,e_1)
| ~ product(e_4,X0,X1) ) ),
introduced(definition,[new_symbols(definition,[spl0_176])],[avatar_definition]) ).
fof(f1957,plain,
( ! [X0,X1] :
( ~ group_element(X0)
| ~ product(X1,X0,e_1)
| product(X0,e_3,e_3)
| product(X0,e_3,e_2)
| product(X0,e_3,e_1)
| ~ product(e_4,X0,X1) )
| ~ spl0_176 ),
inference(avatar_component_clause,[],[f1956]) ).
fof(f1958,plain,
( ~ spl0_88
| spl0_176 ),
inference(avatar_split_clause,[],[f1950,f1956,f734]) ).
fof(f1979,plain,
( ~ group_element(e_1)
| product(e_3,e_1,e_1)
| product(e_3,e_1,e_2)
| product(e_3,e_1,e_3)
| ~ group_element(e_3)
| spl0_147 ),
inference(resolution,[],[f1479,f38]) ).
fof(f1980,plain,
( ! [X0] :
( ~ product(X0,e_1,e_3)
| ~ product(e_1,e_4,X0) )
| spl0_147 ),
inference(resolution,[],[f1479,f43]) ).
fof(f1982,plain,
( ~ product(e_1,e_2,e_2)
| ~ spl0_105
| spl0_124 ),
inference(resolution,[],[f801,f989]) ).
fof(f1988,plain,
( ~ product(e_1,e_2,e_4)
| ~ spl0_105
| spl0_112 ),
inference(resolution,[],[f801,f919]) ).
fof(f1998,plain,
( ~ spl0_97
| ~ spl0_105
| spl0_112 ),
inference(avatar_split_clause,[],[f1988,f830,f800,f769]) ).
fof(f2002,plain,
( ~ spl0_90
| ~ spl0_105
| spl0_124 ),
inference(avatar_split_clause,[],[f1982,f932,f800,f741]) ).
fof(f2024,plain,
( product(e_4,e_2,e_1)
| ~ spl0_112 ),
inference(avatar_component_clause,[],[f830]) ).
fof(f2042,plain,
( ~ product(e_1,e_4,e_1)
| ~ spl0_112 ),
inference(resolution,[],[f2024,f1195]) ).
fof(f2055,plain,
( ! [X0] :
( ~ product(X0,e_1,e_1)
| product(e_1,e_3,e_3)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1)
| ~ product(e_4,e_1,X0) )
| ~ spl0_176 ),
inference(resolution,[],[f1957,f22]) ).
fof(f2067,definition,
( spl0_182
<=> product(e_2,e_3,e_3) ),
introduced(definition,[new_symbols(definition,[spl0_182])],[avatar_definition]) ).
fof(f2073,plain,
( spl0_21
| spl0_87
| spl0_86
| spl0_170
| ~ spl0_176 ),
inference(avatar_split_clause,[],[f2055,f1956,f1843,f727,f730,f228]) ).
fof(f2082,plain,
( ~ greater(e_1,e_0)
| ~ greater(e_3,e_2)
| ~ spl0_7
| ~ spl0_65 ),
inference(resolution,[],[f118,f1930]) ).
fof(f2086,definition,
( spl0_184
<=> greater(e_3,e_2) ),
introduced(definition,[new_symbols(definition,[spl0_184])],[avatar_definition]) ).
fof(f2087,plain,
( ~ greater(e_3,e_2)
| spl0_184 ),
inference(avatar_component_clause,[],[f2086]) ).
fof(f2088,plain,
( ~ spl0_184
| ~ spl0_35
| ~ spl0_7
| ~ spl0_65 ),
inference(avatar_split_clause,[],[f2082,f550,f117,f293,f2086]) ).
fof(f2091,plain,
( $false
| ~ spl0_103 ),
inference(resolution,[],[f794,f37]) ).
fof(f2092,plain,
~ spl0_103,
inference(avatar_contradiction_clause,[],[f2091]) ).
fof(f2120,plain,
( $false
| spl0_184 ),
inference(resolution,[],[f2087,f12]) ).
fof(f2121,plain,
spl0_184,
inference(avatar_contradiction_clause,[],[f2120]) ).
fof(f2134,plain,
( $false
| spl0_39
| ~ spl0_104 ),
inference(resolution,[],[f798,f397]) ).
fof(f2150,plain,
( spl0_39
| ~ spl0_104 ),
inference(avatar_contradiction_clause,[],[f2134]) ).
fof(f2151,plain,
( ~ spl0_97
| ~ spl0_14
| ~ spl0_106 ),
inference(avatar_split_clause,[],[f947,f804,f149,f769]) ).
fof(f2153,plain,
( ~ spl0_88
| spl0_100
| spl0_101
| spl0_102
| ~ spl0_81
| spl0_147 ),
inference(avatar_split_clause,[],[f1979,f1478,f711,f789,f786,f783,f734]) ).
fof(f2176,plain,
( ~ group_element(e_3)
| product(e_1,e_3,e_1)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_3)
| ~ group_element(e_1)
| spl0_93 ),
inference(resolution,[],[f755,f38]) ).
fof(f2195,plain,
( ~ product(e_2,e_1,e_1)
| ~ product(e_1,e_2,e_3)
| ~ spl0_101 ),
inference(resolution,[],[f787,f1099]) ).
fof(f2197,plain,
( ~ spl0_89
| ~ spl0_105
| ~ spl0_101 ),
inference(avatar_split_clause,[],[f2195,f786,f800,f738]) ).
fof(f2200,plain,
( ~ spl0_81
| spl0_86
| spl0_87
| spl0_21
| ~ spl0_88
| spl0_93 ),
inference(avatar_split_clause,[],[f2176,f754,f734,f228,f730,f727,f711]) ).
fof(f2201,plain,
~ spl0_70,
inference(avatar_split_clause,[],[f1266,f602]) ).
fof(f2222,plain,
( ~ product(e_1,e_1,e_1)
| ~ product(e_1,e_3,e_2)
| ~ spl0_105 ),
inference(resolution,[],[f801,f1141]) ).
fof(f2224,plain,
( ~ spl0_87
| ~ spl0_161
| ~ spl0_105 ),
inference(avatar_split_clause,[],[f2222,f800,f1637,f730]) ).
fof(f2236,plain,
( ~ product(e_2,e_1,e_1)
| ~ spl0_71
| ~ spl0_170 ),
inference(resolution,[],[f806,f1844]) ).
fof(f2244,plain,
( ~ spl0_105
| ~ spl0_71
| ~ spl0_170 ),
inference(avatar_split_clause,[],[f2236,f1843,f605,f800]) ).
fof(f2247,plain,
( ! [X0] :
( ~ greater(X0,e_3)
| ~ product(e_3,e_1,X0) )
| ~ spl0_4 ),
inference(resolution,[],[f108,f20]) ).
fof(f2263,plain,
( ~ group_element(e_1)
| product(e_4,e_1,e_1)
| product(e_4,e_1,e_2)
| product(e_4,e_1,e_3)
| ~ group_element(e_4)
| spl0_70 ),
inference(resolution,[],[f646,f38]) ).
fof(f2265,plain,
( ~ product(e_3,e_1,e_4)
| ~ spl0_4 ),
inference(resolution,[],[f2247,f14]) ).
fof(f2534,plain,
( ! [X0] :
( ~ product(X0,e_1,e_2)
| ~ product(e_1,e_4,X0) )
| ~ spl0_105 ),
inference(resolution,[],[f1265,f801]) ).
fof(f2539,plain,
( ~ product(e_1,e_1,e_1)
| ~ product(e_1,e_4,e_2)
| ~ spl0_105 ),
inference(resolution,[],[f1265,f801]) ).
fof(f2555,plain,
( ! [X0,X1] :
( ~ product(e_1,e_4,X0)
| ~ product(X1,e_1,X0)
| ~ product(e_1,e_2,X1) )
| ~ spl0_105 ),
inference(resolution,[],[f2534,f43]) ).
fof(f2575,plain,
( ~ product(e_1,e_4,e_3)
| ~ product(e_1,e_2,e_4)
| ~ spl0_105
| ~ spl0_106 ),
inference(resolution,[],[f2555,f805]) ).
fof(f2717,plain,
( ~ product(e_1,e_4,e_4)
| ~ spl0_106
| spl0_147 ),
inference(resolution,[],[f1980,f805]) ).
fof(f2719,plain,
( ~ spl0_96
| ~ spl0_106
| spl0_147 ),
inference(avatar_split_clause,[],[f2717,f1478,f804,f765]) ).
fof(f2722,plain,
( ~ spl0_97
| ~ spl0_82
| ~ spl0_105
| ~ spl0_106 ),
inference(avatar_split_clause,[],[f2575,f804,f800,f714,f769]) ).
fof(f2723,plain,
( ~ spl0_84
| ~ spl0_112 ),
inference(avatar_split_clause,[],[f2042,f830,f720]) ).
fof(f2731,plain,
( ~ spl0_83
| ~ spl0_161
| ~ spl0_105 ),
inference(avatar_split_clause,[],[f2539,f800,f1637,f717]) ).
fof(f2762,plain,
( ~ spl0_147
| ~ spl0_4 ),
inference(avatar_split_clause,[],[f2265,f107,f1478]) ).
fof(f3048,plain,
! [X0] :
( ~ product(X0,e_1,e_4)
| ~ group_element(e_2)
| product(X0,e_2,e_1)
| product(X0,e_2,e_2)
| product(X0,e_2,e_3)
| ~ group_element(X0) ),
inference(resolution,[],[f69,f38]) ).
fof(f3054,definition,
( spl0_224
<=> ! [X0] :
( ~ product(X0,e_1,e_4)
| ~ group_element(X0)
| product(X0,e_2,e_3)
| product(X0,e_2,e_2)
| product(X0,e_2,e_1) ) ),
introduced(definition,[new_symbols(definition,[spl0_224])],[avatar_definition]) ).
fof(f3055,plain,
( ! [X0] :
( ~ group_element(X0)
| ~ product(X0,e_1,e_4)
| product(X0,e_2,e_3)
| product(X0,e_2,e_2)
| product(X0,e_2,e_1) )
| ~ spl0_224 ),
inference(avatar_component_clause,[],[f3054]) ).
fof(f3056,plain,
( ~ spl0_91
| spl0_224 ),
inference(avatar_split_clause,[],[f3048,f3054,f745]) ).
fof(f3062,plain,
( ~ product(e_3,e_1,e_4)
| product(e_3,e_2,e_3)
| product(e_3,e_2,e_2)
| product(e_3,e_2,e_1)
| ~ spl0_224 ),
inference(resolution,[],[f3055,f24]) ).
fof(f3155,plain,
( ~ product(e_3,e_3,e_2)
| ~ product(e_2,e_3,e_3) ),
inference(factoring,[],[f1464]) ).
fof(f3157,plain,
( ~ product(e_2,e_3,e_3)
| spl0_182 ),
inference(avatar_component_clause,[],[f2067]) ).
fof(f3159,definition,
( spl0_225
<=> product(e_3,e_3,e_2) ),
introduced(definition,[new_symbols(definition,[spl0_225])],[avatar_definition]) ).
fof(f3160,plain,
( ~ product(e_3,e_3,e_2)
| spl0_225 ),
inference(avatar_component_clause,[],[f3159]) ).
fof(f3161,plain,
( ~ spl0_182
| ~ spl0_225 ),
inference(avatar_split_clause,[],[f3155,f3159,f2067]) ).
fof(f3166,plain,
( ! [X0] :
( ~ product(X0,e_3,e_3)
| ~ product(e_3,e_2,X0) )
| spl0_225 ),
inference(resolution,[],[f3160,f43]) ).
fof(f3177,plain,
( ~ product(e_3,e_2,e_3)
| spl0_225 ),
inference(resolution,[],[f3166,f42]) ).
fof(f3186,plain,
( ! [X0] :
( ~ product(X0,e_3,e_2)
| ~ product(e_3,e_3,X0) )
| spl0_182 ),
inference(resolution,[],[f3157,f43]) ).
fof(f3243,plain,
( ~ product(e_3,e_3,e_2)
| spl0_182 ),
inference(resolution,[],[f3186,f42]) ).
fof(f3244,plain,
( ~ spl0_225
| spl0_182 ),
inference(avatar_split_clause,[],[f3243,f2067,f3159]) ).
fof(f3246,plain,
( spl0_141
| spl0_142
| spl0_143
| ~ spl0_147
| ~ spl0_224 ),
inference(avatar_split_clause,[],[f3062,f3054,f1478,f1215,f1212,f1209]) ).
fof(f3247,plain,
( ! [X0] :
( ~ product(X0,e_3,e_3)
| ~ product(e_3,e_2,X0) )
| spl0_225 ),
inference(resolution,[],[f3160,f43]) ).
fof(f3261,plain,
( $false
| ~ spl0_143
| spl0_225 ),
inference(resolution,[],[f3177,f1216]) ).
fof(f3263,plain,
( ~ spl0_143
| spl0_225 ),
inference(avatar_contradiction_clause,[],[f3261]) ).
fof(f3287,plain,
~ product(e_3,e_1,e_3),
inference(resolution,[],[f70,f42]) ).
fof(f3289,plain,
~ spl0_100,
inference(avatar_split_clause,[],[f3287,f783]) ).
fof(f3309,plain,
( ! [X0,X1] :
( ~ product(X0,e_3,e_3)
| ~ product(X1,e_2,e_3)
| ~ product(e_2,X0,X1) )
| spl0_225 ),
inference(resolution,[],[f3247,f43]) ).
fof(f3505,plain,
( ~ spl0_79
| spl0_106
| spl0_71
| spl0_107
| ~ spl0_81
| spl0_70 ),
inference(avatar_split_clause,[],[f2263,f602,f711,f808,f605,f804,f704]) ).
fof(f3616,plain,
( ~ product(e_1,e_3,e_3)
| ~ product(e_1,e_2,e_3)
| ~ spl0_105
| spl0_225 ),
inference(resolution,[],[f3309,f801]) ).
fof(f3624,plain,
( ~ spl0_89
| ~ spl0_86
| ~ spl0_105
| spl0_225 ),
inference(avatar_split_clause,[],[f3616,f3159,f800,f727,f738]) ).
cnf(s1,plain,
( spl0_1
| spl0_2
| spl0_3
| spl0_4 ),
inference(sat_conversion,[],[f109]) ).
cnf(s2,plain,
( spl0_5
| spl0_6
| spl0_7
| spl0_8 ),
inference(sat_conversion,[],[f122]) ).
cnf(s3,plain,
( spl0_9
| spl0_10
| spl0_11
| spl0_12 ),
inference(sat_conversion,[],[f135]) ).
cnf(s4,plain,
( spl0_13
| spl0_14 ),
inference(sat_conversion,[],[f151]) ).
cnf(s5,plain,
( spl0_15
| spl0_16 ),
inference(sat_conversion,[],[f158]) ).
cnf(s6,plain,
( spl0_17
| spl0_18 ),
inference(sat_conversion,[],[f165]) ).
cnf(s10,plain,
( ~ spl0_9
| ~ spl0_17 ),
inference(sat_conversion,[],[f183]) ).
cnf(s11,plain,
( ~ spl0_6
| ~ spl0_15 ),
inference(sat_conversion,[],[f187]) ).
cnf(s12,plain,
( ~ spl0_10
| ~ spl0_17 ),
inference(sat_conversion,[],[f201]) ).
cnf(s13,plain,
( ~ spl0_11
| ~ spl0_17 ),
inference(sat_conversion,[],[f208]) ).
cnf(s14,plain,
~ spl0_18,
inference(sat_conversion,[],[f222]) ).
cnf(s15,plain,
( ~ spl0_14
| ~ spl0_21
| spl0_22 ),
inference(sat_conversion,[],[f233]) ).
cnf(s20,plain,
( ~ spl0_27
| spl0_29 ),
inference(sat_conversion,[],[f272]) ).
cnf(s21,plain,
( ~ spl0_27
| spl0_30 ),
inference(sat_conversion,[],[f276]) ).
cnf(s24,plain,
( ~ spl0_31
| spl0_34 ),
inference(sat_conversion,[],[f291]) ).
cnf(s27,plain,
( ~ spl0_35
| spl0_38 ),
inference(sat_conversion,[],[f306]) ).
cnf(s29,plain,
spl0_27,
inference(sat_conversion,[],[f313]) ).
cnf(s30,plain,
spl0_31,
inference(sat_conversion,[],[f319]) ).
cnf(s31,plain,
spl0_35,
inference(sat_conversion,[],[f323]) ).
cnf(s50,plain,
( ~ spl0_5
| ~ spl0_29
| spl0_50 ),
inference(sat_conversion,[],[f461]) ).
cnf(s53,plain,
( ~ spl0_1
| ~ spl0_30
| spl0_53 ),
inference(sat_conversion,[],[f472]) ).
cnf(s54,plain,
( ~ spl0_5
| ~ spl0_30
| spl0_54 ),
inference(sat_conversion,[],[f473]) ).
cnf(s73,plain,
( ~ spl0_4
| spl0_65 ),
inference(sat_conversion,[],[f553]) ).
cnf(s104,plain,
( ~ spl0_16
| spl0_40
| ~ spl0_81
| ~ spl0_91
| spl0_103
| spl0_104
| spl0_105 ),
inference(sat_conversion,[],[f802]) ).
cnf(s116,plain,
spl0_81,
inference(sat_conversion,[],[f850]) ).
cnf(s118,plain,
spl0_88,
inference(sat_conversion,[],[f856]) ).
cnf(s119,plain,
spl0_91,
inference(sat_conversion,[],[f858]) ).
cnf(s122,plain,
( ~ spl0_7
| ~ spl0_38
| spl0_50 ),
inference(sat_conversion,[],[f862]) ).
cnf(s124,plain,
spl0_79,
inference(sat_conversion,[],[f870]) ).
cnf(s126,plain,
~ spl0_22,
inference(sat_conversion,[],[f876]) ).
cnf(s131,plain,
( ~ spl0_79
| ~ spl0_81
| spl0_82
| spl0_83
| spl0_84
| spl0_96 ),
inference(sat_conversion,[],[f910]) ).
cnf(s132,plain,
( spl0_63
| ~ spl0_81
| spl0_89
| spl0_90
| ~ spl0_91
| spl0_97 ),
inference(sat_conversion,[],[f913]) ).
cnf(s144,plain,
( ~ spl0_14
| ~ spl0_93
| ~ spl0_106 ),
inference(sat_conversion,[],[f966]) ).
cnf(s150,plain,
( ~ spl0_12
| ~ spl0_124 ),
inference(sat_conversion,[],[f988]) ).
cnf(s151,plain,
( ~ spl0_8
| ~ spl0_40 ),
inference(sat_conversion,[],[f992]) ).
cnf(s161,plain,
( ~ spl0_2
| ~ spl0_34
| ~ spl0_136 ),
inference(sat_conversion,[],[f1123]) ).
cnf(s165,plain,
( ~ spl0_63
| spl0_124 ),
inference(sat_conversion,[],[f1181]) ).
cnf(s166,plain,
( ~ spl0_53
| ~ spl0_136 ),
inference(sat_conversion,[],[f1182]) ).
cnf(s168,plain,
( ~ spl0_91
| spl0_140 ),
inference(sat_conversion,[],[f1201]) ).
cnf(s170,plain,
spl0_136,
inference(sat_conversion,[],[f1229]) ).
cnf(s171,plain,
( ~ spl0_3
| ~ spl0_50 ),
inference(sat_conversion,[],[f1230]) ).
cnf(s177,plain,
( ~ spl0_8
| spl0_40
| ~ spl0_81
| ~ spl0_91
| spl0_104
| spl0_105 ),
inference(sat_conversion,[],[f1281]) ).
cnf(s178,plain,
( spl0_39
| ~ spl0_40
| ~ spl0_142 ),
inference(sat_conversion,[],[f1282]) ).
cnf(s179,plain,
~ spl0_39,
inference(sat_conversion,[],[f1283]) ).
cnf(s182,plain,
( ~ spl0_40
| spl0_63
| ~ spl0_141 ),
inference(sat_conversion,[],[f1297]) ).
cnf(s183,plain,
( ~ spl0_3
| ~ spl0_13
| ~ spl0_35 ),
inference(sat_conversion,[],[f1299]) ).
cnf(s185,plain,
( ~ spl0_14
| ~ spl0_40
| ~ spl0_90 ),
inference(sat_conversion,[],[f1333]) ).
cnf(s205,plain,
spl0_161,
inference(sat_conversion,[],[f1645]) ).
cnf(s222,plain,
( ~ spl0_16
| ~ spl0_89
| ~ spl0_101 ),
inference(sat_conversion,[],[f1734]) ).
cnf(s229,plain,
( ~ spl0_89
| ~ spl0_102
| spl0_124 ),
inference(sat_conversion,[],[f1777]) ).
cnf(s250,plain,
( ~ spl0_16
| ~ spl0_71
| ~ spl0_97 ),
inference(sat_conversion,[],[f1835]) ).
cnf(s254,plain,
( spl0_63
| spl0_89
| spl0_90
| ~ spl0_140
| spl0_170 ),
inference(sat_conversion,[],[f1845]) ).
cnf(s261,plain,
( spl0_70
| spl0_71
| ~ spl0_79
| ~ spl0_81
| spl0_106
| spl0_107 ),
inference(sat_conversion,[],[f1858]) ).
cnf(s262,plain,
( ~ spl0_14
| spl0_71
| ~ spl0_79
| ~ spl0_81
| ~ spl0_93
| spl0_106
| spl0_107 ),
inference(sat_conversion,[],[f1859]) ).
cnf(s277,plain,
( ~ spl0_4
| ~ spl0_54 ),
inference(sat_conversion,[],[f1895]) ).
cnf(s278,plain,
( ~ spl0_4
| ~ spl0_6
| ~ spl0_34 ),
inference(sat_conversion,[],[f1896]) ).
cnf(s283,plain,
( ~ spl0_12
| ~ spl0_93
| ~ spl0_107 ),
inference(sat_conversion,[],[f1924]) ).
cnf(s284,plain,
( ~ spl0_97
| ~ spl0_107
| spl0_124 ),
inference(sat_conversion,[],[f1925]) ).
cnf(s289,plain,
( ~ spl0_88
| spl0_176 ),
inference(sat_conversion,[],[f1958]) ).
cnf(s295,plain,
( ~ spl0_97
| ~ spl0_105
| spl0_112 ),
inference(sat_conversion,[],[f1998]) ).
cnf(s299,plain,
( ~ spl0_90
| ~ spl0_105
| spl0_124 ),
inference(sat_conversion,[],[f2002]) ).
cnf(s307,plain,
( spl0_21
| spl0_86
| spl0_87
| spl0_170
| ~ spl0_176 ),
inference(sat_conversion,[],[f2073]) ).
cnf(s310,plain,
( ~ spl0_7
| ~ spl0_35
| ~ spl0_65
| ~ spl0_184 ),
inference(sat_conversion,[],[f2088]) ).
cnf(s311,plain,
~ spl0_103,
inference(sat_conversion,[],[f2092]) ).
cnf(s313,plain,
spl0_184,
inference(sat_conversion,[],[f2121]) ).
cnf(s315,plain,
( spl0_39
| ~ spl0_104 ),
inference(sat_conversion,[],[f2150]) ).
cnf(s316,plain,
( ~ spl0_14
| ~ spl0_97
| ~ spl0_106 ),
inference(sat_conversion,[],[f2151]) ).
cnf(s320,plain,
( ~ spl0_81
| ~ spl0_88
| spl0_100
| spl0_101
| spl0_102
| spl0_147 ),
inference(sat_conversion,[],[f2153]) ).
cnf(s324,plain,
( ~ spl0_89
| ~ spl0_101
| ~ spl0_105 ),
inference(sat_conversion,[],[f2197]) ).
cnf(s328,plain,
( spl0_21
| ~ spl0_81
| spl0_86
| spl0_87
| ~ spl0_88
| spl0_93 ),
inference(sat_conversion,[],[f2200]) ).
cnf(s329,plain,
~ spl0_70,
inference(sat_conversion,[],[f2201]) ).
cnf(s331,plain,
( ~ spl0_87
| ~ spl0_105
| ~ spl0_161 ),
inference(sat_conversion,[],[f2224]) ).
cnf(s335,plain,
( ~ spl0_71
| ~ spl0_105
| ~ spl0_170 ),
inference(sat_conversion,[],[f2244]) ).
cnf(s387,plain,
( ~ spl0_96
| ~ spl0_106
| spl0_147 ),
inference(sat_conversion,[],[f2719]) ).
cnf(s390,plain,
( ~ spl0_82
| ~ spl0_97
| ~ spl0_105
| ~ spl0_106 ),
inference(sat_conversion,[],[f2722]) ).
cnf(s391,plain,
( ~ spl0_84
| ~ spl0_112 ),
inference(sat_conversion,[],[f2723]) ).
cnf(s397,plain,
( ~ spl0_83
| ~ spl0_105
| ~ spl0_161 ),
inference(sat_conversion,[],[f2731]) ).
cnf(s421,plain,
( ~ spl0_4
| ~ spl0_147 ),
inference(sat_conversion,[],[f2762]) ).
cnf(s456,plain,
( ~ spl0_91
| spl0_224 ),
inference(sat_conversion,[],[f3056]) ).
cnf(s465,plain,
( ~ spl0_182
| ~ spl0_225 ),
inference(sat_conversion,[],[f3161]) ).
cnf(s480,plain,
( spl0_182
| ~ spl0_225 ),
inference(sat_conversion,[],[f3244]) ).
cnf(s482,plain,
( spl0_141
| spl0_142
| spl0_143
| ~ spl0_147
| ~ spl0_224 ),
inference(sat_conversion,[],[f3246]) ).
cnf(s485,plain,
( ~ spl0_143
| spl0_225 ),
inference(sat_conversion,[],[f3263]) ).
cnf(s489,plain,
~ spl0_100,
inference(sat_conversion,[],[f3289]) ).
cnf(s518,plain,
( spl0_70
| spl0_71
| ~ spl0_79
| ~ spl0_81
| spl0_106
| spl0_107 ),
inference(sat_conversion,[],[f3505]) ).
cnf(s532,plain,
( ~ spl0_86
| ~ spl0_89
| ~ spl0_105
| spl0_225 ),
inference(sat_conversion,[],[f3624]) ).
cnf(s542,plain,
( ~ spl0_81
| ~ spl0_88
| spl0_101
| spl0_102
| spl0_147 ),
inference(rat,[],[s320,s489]) ).
cnf(s543,plain,
( ~ spl0_7
| ~ spl0_35
| ~ spl0_65 ),
inference(rat,[],[s310,s313]) ).
cnf(s546,plain,
( spl0_71
| ~ spl0_79
| ~ spl0_81
| spl0_106
| spl0_107 ),
inference(rat,[],[s261,s329]) ).
cnf(s550,plain,
~ spl0_104,
inference(rat,[],[s315,s179]) ).
cnf(s551,plain,
( ~ spl0_40
| ~ spl0_142 ),
inference(rat,[],[s178,s179]) ).
cnf(s552,plain,
( ~ spl0_8
| spl0_40
| ~ spl0_81
| ~ spl0_91
| spl0_105 ),
inference(rat,[],[s177,s550]) ).
cnf(s554,plain,
~ spl0_53,
inference(rat,[],[s166,s170]) ).
cnf(s555,plain,
( ~ spl0_2
| ~ spl0_34 ),
inference(rat,[],[s161,s170]) ).
cnf(s562,plain,
spl0_224,
inference(rat,[],[s456,s119]) ).
cnf(s563,plain,
spl0_140,
inference(rat,[],[s168,s119]) ).
cnf(s566,plain,
spl0_176,
inference(rat,[],[s289,s118]) ).
cnf(s578,plain,
( ~ spl0_16
| spl0_40
| spl0_105 ),
inference(rat,[],[s104,s550,s311,s119,s116]) ).
cnf(s593,plain,
( ~ spl0_1
| ~ spl0_30 ),
inference(rat,[],[s53,s554]) ).
cnf(s595,plain,
spl0_38,
inference(rat,[],[s27,s31]) ).
cnf(s598,plain,
spl0_34,
inference(rat,[],[s24,s30]) ).
cnf(s599,plain,
~ spl0_2,
inference(rat,[],[s555,s598]) ).
cnf(s602,plain,
spl0_30,
inference(rat,[],[s21,s29]) ).
cnf(s603,plain,
~ spl0_1,
inference(rat,[],[s593,s602]) ).
cnf(s604,plain,
spl0_29,
inference(rat,[],[s20,s29]) ).
cnf(s610,plain,
( ~ spl0_14
| ~ spl0_21 ),
inference(rat,[],[s15,s126]) ).
cnf(s611,plain,
spl0_17,
inference(rat,[],[s6,s14]) ).
cnf(s612,plain,
~ spl0_11,
inference(rat,[],[s13,s611]) ).
cnf(s613,plain,
~ spl0_10,
inference(rat,[],[s12,s611]) ).
cnf(s614,plain,
~ spl0_9,
inference(rat,[],[s10,s611]) ).
cnf(s615,plain,
spl0_12,
inference(rat,[],[s3,s612,s613,s614]) ).
cnf(s617,plain,
~ spl0_124,
inference(rat,[],[s150,s615]) ).
cnf(s619,plain,
~ spl0_63,
inference(rat,[],[s165,s617]) ).
cnf(s620,plain,
( spl0_3
| spl0_4 ),
inference(rat,[],[s1,s599,s603]) ).
cnf(s621,plain,
( ~ spl0_89
| ~ spl0_4 ),
inference(rat,[],[s542,s229,s324,s421,s552,s151,s2,s54,s277,s543,s73,s278,s118,s116,s617,s598,s31,s602,s119]) ).
cnf(s622,plain,
~ spl0_4,
inference(rat,[],[s131,s390,s387,s546,s391,s335,s284,s295,s132,s254,s621,s299,s397,s552,s151,s2,s543,s54,s73,s277,s278,s421,s124,s116,s617,s619,s119,s563,s205,s31,s602,s598]) ).
cnf(s623,plain,
spl0_3,
inference(rat,[],[s620,s622]) ).
cnf(s624,plain,
~ spl0_13,
inference(rat,[],[s183,s31,s623]) ).
cnf(s626,plain,
~ spl0_50,
inference(rat,[],[s171,s623]) ).
cnf(s630,plain,
spl0_14,
inference(rat,[],[s4,s624]) ).
cnf(s631,plain,
~ spl0_7,
inference(rat,[],[s122,s595,s626]) ).
cnf(s632,plain,
~ spl0_5,
inference(rat,[],[s50,s604,s626]) ).
cnf(s638,plain,
~ spl0_21,
inference(rat,[],[s610,s630]) ).
cnf(s639,plain,
~ spl0_225,
inference(rat,[],[s465,s480]) ).
cnf(s640,plain,
~ spl0_143,
inference(rat,[],[s485,s639]) ).
cnf(s641,plain,
( ~ spl0_105
| ~ spl0_89 ),
inference(rat,[],[s262,s144,s283,s335,s328,s307,s532,s331,s124,s116,s630,s615,s638,s118,s566,s639,s205]) ).
cnf(s642,plain,
( spl0_40
| spl0_105 ),
inference(rat,[],[s11,s5,s2,s578,s552,s119,s116,s632,s631]) ).
cnf(s643,plain,
~ spl0_89,
inference(rat,[],[s5,s222,s11,s542,s2,s482,s151,s551,s182,s642,s641,s229,s118,s116,s631,s632,s640,s562,s619,s617]) ).
cnf(s645,plain,
~ spl0_105,
inference(rat,[],[s518,s316,s284,s335,s132,s254,s299,s329,s124,s116,s630,s617,s619,s119,s643,s563]) ).
cnf(s646,plain,
spl0_40,
inference(rat,[],[s642,s645]) ).
cnf(s648,plain,
~ spl0_90,
inference(rat,[],[s185,s630,s646]) ).
cnf(s651,plain,
~ spl0_8,
inference(rat,[],[s151,s646]) ).
cnf(s653,plain,
spl0_97,
inference(rat,[],[s132,s643,s119,s619,s116,s648]) ).
cnf(s656,plain,
spl0_6,
inference(rat,[],[s2,s632,s631,s651]) ).
cnf(s659,plain,
~ spl0_107,
inference(rat,[],[s284,s617,s653]) ).
cnf(s660,plain,
~ spl0_106,
inference(rat,[],[s316,s630,s653]) ).
cnf(s666,plain,
~ spl0_15,
inference(rat,[],[s11,s656]) ).
cnf(s668,plain,
spl0_71,
inference(rat,[],[s546,s659,s116,s124,s660]) ).
cnf(s669,plain,
spl0_16,
inference(rat,[],[s5,s666]) ).
cnf(s671,plain,
$false,
inference(rat,[],[s250,s653,s668,s669]) ).
fof(f3625,plain,
$false,
inference(avatar_sat_refutation,[],[s671]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP127-3.004 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n013.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Sun Sep 27 09:24:51 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.59/1.22 % (4153967)Input is clausal, will run a generic CNF schedule.
% 2.59/1.22 % (4154064)dis-21_1_sil=8000:lcm=predicate:random_seed=3309265151:st=5:avsq=on:i=117:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/117Mi)
% 2.59/1.22 % (4154059)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=4047542935:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.59/1.22 % (4154063)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=462204755:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.59/1.22 % (4154061)lrs+10_1_sil=8000:sp=occurrence:random_seed=2336117326:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.59/1.22 % (4154058)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=1162673619:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.59/1.22 % (4154062)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=944087538:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.59/1.22 % (4154060)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=137252649:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.59/1.22 % (4154064)First to succeed.
% 2.59/1.22 % (4154064)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-4153967"
% 2.59/1.22 % (4154063)Also succeeded, but the first one will report.
% 2.59/1.22 % (4154062)Instruction limit reached!
% 2.59/1.22 % (4154062)------------------------------
% 2.59/1.22 % (4154062)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.59/1.22 % (4154062)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.59/1.22 % (4154062)CaDiCaL version: 2.1.3
% 2.59/1.22 % (4154062)Termination reason: Instruction limit
% 2.59/1.22 % (4154062)Termination phase: Saturation
% 2.59/1.22 % (4154062)Time elapsed: 0.063 s
% 2.59/1.22 % (4154062)Peak memory usage: 88 MB
% 2.59/1.22 % (4154062)Instructions burned: 116 (million)
% 2.59/1.22 % (4154061)Instruction limit reached!
% 2.59/1.22 % (4154061)------------------------------
% 2.59/1.22 % (4154061)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.59/1.22 % (4154061)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.59/1.22 % (4154061)CaDiCaL version: 2.1.3
% 2.59/1.22 % (4154061)Termination reason: Instruction limit
% 2.59/1.22 % (4154061)Termination phase: Saturation
% 2.59/1.22 % (4154061)Time elapsed: 0.066 s
% 2.59/1.22 % (4154061)Peak memory usage: 88 MB
% 2.59/1.22 % (4154061)Instructions burned: 108 (million)
% 2.59/1.22 % (4154064)Refutation found. Thanks to Tanya!
% 2.59/1.22 % SZS status Unsatisfiable for theBenchmark
% 2.59/1.22 % SZS output start Proof for theBenchmark
% See solution above
% 3.02/1.32 % (4154064)------------------------------
% 3.02/1.32 % (4154064)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.02/1.32 % (4154064)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.02/1.32 % (4154064)CaDiCaL version: 2.1.3
% 3.02/1.32 % (4154064)Termination reason: Refutation
% 3.02/1.32 % (4154064)Time elapsed: 0.045 s
% 3.02/1.32 % (4154064)Peak memory usage: 90 MB
% 3.02/1.32 % (4154064)Instructions burned: 123 (million)
% 3.02/1.32 % (4154064)------------------------------
% 3.02/1.32 % (4154064)------------------------------
% 3.02/1.32 % (4153967)Success in time 0.351 s
% 3.02/1.32 % Vampire exiting
%------------------------------------------------------------------------------