TSTP Solution File: ANA034-2 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : ANA034-2 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n024.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Apr 30 10:31:19 EDT 2024
% Result : Unsatisfiable 0.22s 0.39s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 52
% Syntax : Number of formulae : 138 ( 22 unt; 0 def)
% Number of atoms : 427 ( 9 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 543 ( 254 ~; 252 |; 0 &)
% ( 37 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 46 ( 44 usr; 38 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 5 con; 0-3 aty)
% Number of variables : 116 ( 116 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f223,plain,
$false,
inference(avatar_sat_refutation,[],[f20,f25,f30,f35,f39,f43,f47,f51,f59,f64,f68,f72,f77,f82,f86,f92,f99,f104,f114,f118,f134,f138,f147,f153,f163,f166,f170,f177,f185,f191,f192,f196,f202,f209,f216,f221,f222]) ).
fof(f222,plain,
( ~ spl0_18
| ~ spl0_11
| spl0_36 ),
inference(avatar_split_clause,[],[f217,f213,f66,f101]) ).
fof(f101,plain,
( spl0_18
<=> class_OrderedGroup_Olordered__ab__group__abs(t_b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).
fof(f66,plain,
( spl0_11
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X0)
| c_lessequals(c_0,c_HOL_Oabs(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).
fof(f213,plain,
( spl0_36
<=> c_lessequals(c_0,c_HOL_Oabs(v_b(v_x),t_b),t_b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).
fof(f217,plain,
( ~ class_OrderedGroup_Olordered__ab__group__abs(t_b)
| ~ spl0_11
| spl0_36 ),
inference(resolution,[],[f215,f67]) ).
fof(f67,plain,
( ! [X0,X1] :
( c_lessequals(c_0,c_HOL_Oabs(X1,X0),X0)
| ~ class_OrderedGroup_Olordered__ab__group__abs(X0) )
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f66]) ).
fof(f215,plain,
( ~ c_lessequals(c_0,c_HOL_Oabs(v_b(v_x),t_b),t_b)
| spl0_36 ),
inference(avatar_component_clause,[],[f213]) ).
fof(f221,plain,
( spl0_37
| ~ spl0_21
| ~ spl0_31 ),
inference(avatar_split_clause,[],[f179,f175,f116,f219]) ).
fof(f219,plain,
( spl0_37
<=> ! [X0,X3,X2,X1] :
( c_lessequals(c_HOL_Oabs(c_times(X0,X1,t_b),t_b),c_HOL_Oabs(c_times(X2,X3,t_b),t_b),t_b)
| ~ c_lessequals(c_0,c_HOL_Oabs(X1,t_b),t_b)
| ~ c_lessequals(c_0,c_HOL_Oabs(X2,t_b),t_b)
| ~ c_lessequals(c_HOL_Oabs(X1,t_b),c_HOL_Oabs(X3,t_b),t_b)
| ~ c_lessequals(c_HOL_Oabs(X0,t_b),c_HOL_Oabs(X2,t_b),t_b) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).
fof(f116,plain,
( spl0_21
<=> ! [X0,X1] : c_HOL_Oabs(c_times(X0,X1,t_b),t_b) = c_times(c_HOL_Oabs(X0,t_b),c_HOL_Oabs(X1,t_b),t_b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).
fof(f175,plain,
( spl0_31
<=> ! [X0,X3,X2,X1] :
( c_lessequals(c_times(X2,X3,t_b),c_HOL_Oabs(c_times(X0,X1,t_b),t_b),t_b)
| ~ c_lessequals(c_0,X3,t_b)
| ~ c_lessequals(c_0,c_HOL_Oabs(X0,t_b),t_b)
| ~ c_lessequals(X3,c_HOL_Oabs(X1,t_b),t_b)
| ~ c_lessequals(X2,c_HOL_Oabs(X0,t_b),t_b) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).
fof(f179,plain,
( ! [X2,X3,X0,X1] :
( c_lessequals(c_HOL_Oabs(c_times(X0,X1,t_b),t_b),c_HOL_Oabs(c_times(X2,X3,t_b),t_b),t_b)
| ~ c_lessequals(c_0,c_HOL_Oabs(X1,t_b),t_b)
| ~ c_lessequals(c_0,c_HOL_Oabs(X2,t_b),t_b)
| ~ c_lessequals(c_HOL_Oabs(X1,t_b),c_HOL_Oabs(X3,t_b),t_b)
| ~ c_lessequals(c_HOL_Oabs(X0,t_b),c_HOL_Oabs(X2,t_b),t_b) )
| ~ spl0_21
| ~ spl0_31 ),
inference(superposition,[],[f176,f117]) ).
fof(f117,plain,
( ! [X0,X1] : c_HOL_Oabs(c_times(X0,X1,t_b),t_b) = c_times(c_HOL_Oabs(X0,t_b),c_HOL_Oabs(X1,t_b),t_b)
| ~ spl0_21 ),
inference(avatar_component_clause,[],[f116]) ).
fof(f176,plain,
( ! [X2,X3,X0,X1] :
( c_lessequals(c_times(X2,X3,t_b),c_HOL_Oabs(c_times(X0,X1,t_b),t_b),t_b)
| ~ c_lessequals(c_0,X3,t_b)
| ~ c_lessequals(c_0,c_HOL_Oabs(X0,t_b),t_b)
| ~ c_lessequals(X3,c_HOL_Oabs(X1,t_b),t_b)
| ~ c_lessequals(X2,c_HOL_Oabs(X0,t_b),t_b) )
| ~ spl0_31 ),
inference(avatar_component_clause,[],[f175]) ).
fof(f216,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_36
| spl0_9
| ~ spl0_34 ),
inference(avatar_split_clause,[],[f203,f200,f56,f213,f32,f27]) ).
fof(f27,plain,
( spl0_3
<=> c_lessequals(c_HOL_Oabs(v_a(v_x),t_b),c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
fof(f32,plain,
( spl0_4
<=> c_lessequals(c_HOL_Oabs(v_b(v_x),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
fof(f56,plain,
( spl0_9
<=> c_lessequals(c_HOL_Oabs(c_times(v_a(v_x),v_b(v_x),t_b),t_b),c_times(c_times(v_c,v_ca,t_b),c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b),t_b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).
fof(f200,plain,
( spl0_34
<=> ! [X0,X1] :
( c_lessequals(c_HOL_Oabs(c_times(X0,X1,t_b),t_b),c_times(c_times(v_c,v_ca,t_b),c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b),t_b)
| ~ c_lessequals(c_0,c_HOL_Oabs(X1,t_b),t_b)
| ~ c_lessequals(c_HOL_Oabs(X1,t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b)
| ~ c_lessequals(c_HOL_Oabs(X0,t_b),c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).
fof(f203,plain,
( ~ c_lessequals(c_0,c_HOL_Oabs(v_b(v_x),t_b),t_b)
| ~ c_lessequals(c_HOL_Oabs(v_b(v_x),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b)
| ~ c_lessequals(c_HOL_Oabs(v_a(v_x),t_b),c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b)
| spl0_9
| ~ spl0_34 ),
inference(resolution,[],[f201,f58]) ).
fof(f58,plain,
( ~ c_lessequals(c_HOL_Oabs(c_times(v_a(v_x),v_b(v_x),t_b),t_b),c_times(c_times(v_c,v_ca,t_b),c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b),t_b)
| spl0_9 ),
inference(avatar_component_clause,[],[f56]) ).
fof(f201,plain,
( ! [X0,X1] :
( c_lessequals(c_HOL_Oabs(c_times(X0,X1,t_b),t_b),c_times(c_times(v_c,v_ca,t_b),c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b),t_b)
| ~ c_lessequals(c_0,c_HOL_Oabs(X1,t_b),t_b)
| ~ c_lessequals(c_HOL_Oabs(X1,t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b)
| ~ c_lessequals(c_HOL_Oabs(X0,t_b),c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b) )
| ~ spl0_34 ),
inference(avatar_component_clause,[],[f200]) ).
fof(f209,plain,
( spl0_35
| ~ spl0_21
| ~ spl0_30 ),
inference(avatar_split_clause,[],[f173,f168,f116,f207]) ).
fof(f207,plain,
( spl0_35
<=> ! [X0,X1] :
( c_lessequals(c_0,c_HOL_Oabs(c_HOL_Oabs(c_times(X0,X1,t_b),t_b),t_b),t_b)
| ~ c_lessequals(c_0,c_HOL_Oabs(c_HOL_Oabs(X1,t_b),t_b),t_b)
| ~ c_lessequals(c_0,c_HOL_Oabs(c_HOL_Oabs(X0,t_b),t_b),t_b) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).
fof(f168,plain,
( spl0_30
<=> ! [X0,X1] :
( c_lessequals(c_0,c_HOL_Oabs(c_times(X0,X1,t_b),t_b),t_b)
| ~ c_lessequals(c_0,c_HOL_Oabs(X1,t_b),t_b)
| ~ c_lessequals(c_0,c_HOL_Oabs(X0,t_b),t_b) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).
fof(f173,plain,
( ! [X0,X1] :
( c_lessequals(c_0,c_HOL_Oabs(c_HOL_Oabs(c_times(X0,X1,t_b),t_b),t_b),t_b)
| ~ c_lessequals(c_0,c_HOL_Oabs(c_HOL_Oabs(X1,t_b),t_b),t_b)
| ~ c_lessequals(c_0,c_HOL_Oabs(c_HOL_Oabs(X0,t_b),t_b),t_b) )
| ~ spl0_21
| ~ spl0_30 ),
inference(superposition,[],[f169,f117]) ).
fof(f169,plain,
( ! [X0,X1] :
( c_lessequals(c_0,c_HOL_Oabs(c_times(X0,X1,t_b),t_b),t_b)
| ~ c_lessequals(c_0,c_HOL_Oabs(X1,t_b),t_b)
| ~ c_lessequals(c_0,c_HOL_Oabs(X0,t_b),t_b) )
| ~ spl0_30 ),
inference(avatar_component_clause,[],[f168]) ).
fof(f202,plain,
( spl0_34
| ~ spl0_21
| ~ spl0_33 ),
inference(avatar_split_clause,[],[f198,f194,f116,f200]) ).
fof(f194,plain,
( spl0_33
<=> ! [X0,X1] :
( c_lessequals(c_times(X0,X1,t_b),c_times(c_times(v_c,v_ca,t_b),c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b),t_b)
| ~ c_lessequals(c_0,X1,t_b)
| ~ c_lessequals(X1,c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b)
| ~ c_lessequals(X0,c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).
fof(f198,plain,
( ! [X0,X1] :
( c_lessequals(c_HOL_Oabs(c_times(X0,X1,t_b),t_b),c_times(c_times(v_c,v_ca,t_b),c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b),t_b)
| ~ c_lessequals(c_0,c_HOL_Oabs(X1,t_b),t_b)
| ~ c_lessequals(c_HOL_Oabs(X1,t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b)
| ~ c_lessequals(c_HOL_Oabs(X0,t_b),c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b) )
| ~ spl0_21
| ~ spl0_33 ),
inference(superposition,[],[f195,f117]) ).
fof(f195,plain,
( ! [X0,X1] :
( c_lessequals(c_times(X0,X1,t_b),c_times(c_times(v_c,v_ca,t_b),c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b),t_b)
| ~ c_lessequals(c_0,X1,t_b)
| ~ c_lessequals(X1,c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b)
| ~ c_lessequals(X0,c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b) )
| ~ spl0_33 ),
inference(avatar_component_clause,[],[f194]) ).
fof(f196,plain,
( ~ spl0_17
| ~ spl0_23
| spl0_33
| ~ spl0_10
| ~ spl0_16 ),
inference(avatar_split_clause,[],[f94,f90,f61,f194,f127,f96]) ).
fof(f96,plain,
( spl0_17
<=> class_Ring__and__Field_Opordered__semiring(t_b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).
fof(f127,plain,
( spl0_23
<=> c_lessequals(c_0,c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).
fof(f61,plain,
( spl0_10
<=> c_times(c_times(v_c,v_ca,t_b),c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b) = c_times(c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).
fof(f90,plain,
( spl0_16
<=> ! [X4,X0,X3,X2,X1] :
( ~ class_Ring__and__Field_Opordered__semiring(X0)
| ~ c_lessequals(X1,X2,X0)
| ~ c_lessequals(X3,X4,X0)
| ~ c_lessequals(c_0,X2,X0)
| ~ c_lessequals(c_0,X3,X0)
| c_lessequals(c_times(X1,X3,X0),c_times(X2,X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).
fof(f94,plain,
( ! [X0,X1] :
( c_lessequals(c_times(X0,X1,t_b),c_times(c_times(v_c,v_ca,t_b),c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b),t_b)
| ~ c_lessequals(X0,c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b)
| ~ c_lessequals(X1,c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b)
| ~ c_lessequals(c_0,c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b)
| ~ c_lessequals(c_0,X1,t_b)
| ~ class_Ring__and__Field_Opordered__semiring(t_b) )
| ~ spl0_10
| ~ spl0_16 ),
inference(superposition,[],[f91,f63]) ).
fof(f63,plain,
( c_times(c_times(v_c,v_ca,t_b),c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b) = c_times(c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f61]) ).
fof(f91,plain,
( ! [X2,X3,X0,X1,X4] :
( c_lessequals(c_times(X1,X3,X0),c_times(X2,X4,X0),X0)
| ~ c_lessequals(X1,X2,X0)
| ~ c_lessequals(X3,X4,X0)
| ~ c_lessequals(c_0,X2,X0)
| ~ c_lessequals(c_0,X3,X0)
| ~ class_Ring__and__Field_Opordered__semiring(X0) )
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f90]) ).
fof(f192,plain,
( ~ spl0_18
| ~ spl0_11
| spl0_27 ),
inference(avatar_split_clause,[],[f154,f150,f66,f101]) ).
fof(f150,plain,
( spl0_27
<=> c_lessequals(c_0,c_HOL_Oabs(v_f(v_x),t_b),t_b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).
fof(f154,plain,
( ~ class_OrderedGroup_Olordered__ab__group__abs(t_b)
| ~ spl0_11
| spl0_27 ),
inference(resolution,[],[f152,f67]) ).
fof(f152,plain,
( ~ c_lessequals(c_0,c_HOL_Oabs(v_f(v_x),t_b),t_b)
| spl0_27 ),
inference(avatar_component_clause,[],[f150]) ).
fof(f191,plain,
( ~ spl0_18
| ~ spl0_11
| spl0_28 ),
inference(avatar_split_clause,[],[f165,f156,f66,f101]) ).
fof(f156,plain,
( spl0_28
<=> c_lessequals(c_0,c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).
fof(f165,plain,
( ~ class_OrderedGroup_Olordered__ab__group__abs(t_b)
| ~ spl0_11
| spl0_28 ),
inference(resolution,[],[f158,f67]) ).
fof(f158,plain,
( ~ c_lessequals(c_0,c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b)
| spl0_28 ),
inference(avatar_component_clause,[],[f156]) ).
fof(f185,plain,
( ~ spl0_17
| spl0_32
| ~ spl0_16
| ~ spl0_21 ),
inference(avatar_split_clause,[],[f120,f116,f90,f183,f96]) ).
fof(f183,plain,
( spl0_32
<=> ! [X0,X3,X2,X1] :
( c_lessequals(c_HOL_Oabs(c_times(X0,X1,t_b),t_b),c_times(X2,X3,t_b),t_b)
| ~ c_lessequals(c_0,c_HOL_Oabs(X1,t_b),t_b)
| ~ c_lessequals(c_0,X2,t_b)
| ~ c_lessequals(c_HOL_Oabs(X1,t_b),X3,t_b)
| ~ c_lessequals(c_HOL_Oabs(X0,t_b),X2,t_b) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).
fof(f120,plain,
( ! [X2,X3,X0,X1] :
( c_lessequals(c_HOL_Oabs(c_times(X0,X1,t_b),t_b),c_times(X2,X3,t_b),t_b)
| ~ c_lessequals(c_HOL_Oabs(X0,t_b),X2,t_b)
| ~ c_lessequals(c_HOL_Oabs(X1,t_b),X3,t_b)
| ~ c_lessequals(c_0,X2,t_b)
| ~ c_lessequals(c_0,c_HOL_Oabs(X1,t_b),t_b)
| ~ class_Ring__and__Field_Opordered__semiring(t_b) )
| ~ spl0_16
| ~ spl0_21 ),
inference(superposition,[],[f91,f117]) ).
fof(f177,plain,
( ~ spl0_17
| spl0_31
| ~ spl0_16
| ~ spl0_21 ),
inference(avatar_split_clause,[],[f119,f116,f90,f175,f96]) ).
fof(f119,plain,
( ! [X2,X3,X0,X1] :
( c_lessequals(c_times(X2,X3,t_b),c_HOL_Oabs(c_times(X0,X1,t_b),t_b),t_b)
| ~ c_lessequals(X2,c_HOL_Oabs(X0,t_b),t_b)
| ~ c_lessequals(X3,c_HOL_Oabs(X1,t_b),t_b)
| ~ c_lessequals(c_0,c_HOL_Oabs(X0,t_b),t_b)
| ~ c_lessequals(c_0,X3,t_b)
| ~ class_Ring__and__Field_Opordered__semiring(t_b) )
| ~ spl0_16
| ~ spl0_21 ),
inference(superposition,[],[f91,f117]) ).
fof(f170,plain,
( ~ spl0_13
| spl0_30
| ~ spl0_15
| ~ spl0_21 ),
inference(avatar_split_clause,[],[f121,f116,f84,f168,f74]) ).
fof(f74,plain,
( spl0_13
<=> class_Ring__and__Field_Opordered__cancel__semiring(t_b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).
fof(f84,plain,
( spl0_15
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X0)
| ~ c_lessequals(c_0,X1,X0)
| ~ c_lessequals(c_0,X2,X0)
| c_lessequals(c_0,c_times(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).
fof(f121,plain,
( ! [X0,X1] :
( c_lessequals(c_0,c_HOL_Oabs(c_times(X0,X1,t_b),t_b),t_b)
| ~ c_lessequals(c_0,c_HOL_Oabs(X0,t_b),t_b)
| ~ c_lessequals(c_0,c_HOL_Oabs(X1,t_b),t_b)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(t_b) )
| ~ spl0_15
| ~ spl0_21 ),
inference(superposition,[],[f85,f117]) ).
fof(f85,plain,
( ! [X2,X0,X1] :
( c_lessequals(c_0,c_times(X1,X2,X0),X0)
| ~ c_lessequals(c_0,X1,X0)
| ~ c_lessequals(c_0,X2,X0)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X0) )
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f84]) ).
fof(f166,plain,
( ~ spl0_18
| ~ spl0_11
| spl0_25 ),
inference(avatar_split_clause,[],[f148,f140,f66,f101]) ).
fof(f140,plain,
( spl0_25
<=> c_lessequals(c_0,c_HOL_Oabs(v_g(v_x),t_b),t_b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).
fof(f148,plain,
( ~ class_OrderedGroup_Olordered__ab__group__abs(t_b)
| ~ spl0_11
| spl0_25 ),
inference(resolution,[],[f142,f67]) ).
fof(f142,plain,
( ~ c_lessequals(c_0,c_HOL_Oabs(v_g(v_x),t_b),t_b)
| spl0_25 ),
inference(avatar_component_clause,[],[f140]) ).
fof(f163,plain,
( ~ spl0_13
| ~ spl0_28
| ~ spl0_29
| ~ spl0_15
| spl0_24 ),
inference(avatar_split_clause,[],[f137,f131,f84,f160,f156,f74]) ).
fof(f160,plain,
( spl0_29
<=> c_lessequals(c_0,c_times(v_c,v_ca,t_b),t_b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).
fof(f131,plain,
( spl0_24
<=> c_lessequals(c_0,c_times(c_times(v_c,v_ca,t_b),c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b),t_b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).
fof(f137,plain,
( ~ c_lessequals(c_0,c_times(v_c,v_ca,t_b),t_b)
| ~ c_lessequals(c_0,c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(t_b)
| ~ spl0_15
| spl0_24 ),
inference(resolution,[],[f132,f85]) ).
fof(f132,plain,
( ~ c_lessequals(c_0,c_times(c_times(v_c,v_ca,t_b),c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b),t_b)
| spl0_24 ),
inference(avatar_component_clause,[],[f131]) ).
fof(f153,plain,
( ~ spl0_13
| ~ spl0_27
| ~ spl0_19
| ~ spl0_15
| spl0_23 ),
inference(avatar_split_clause,[],[f136,f127,f84,f107,f150,f74]) ).
fof(f107,plain,
( spl0_19
<=> c_lessequals(c_0,v_c,t_b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).
fof(f136,plain,
( ~ c_lessequals(c_0,v_c,t_b)
| ~ c_lessequals(c_0,c_HOL_Oabs(v_f(v_x),t_b),t_b)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(t_b)
| ~ spl0_15
| spl0_23 ),
inference(resolution,[],[f129,f85]) ).
fof(f129,plain,
( ~ c_lessequals(c_0,c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b)
| spl0_23 ),
inference(avatar_component_clause,[],[f127]) ).
fof(f147,plain,
( ~ spl0_13
| ~ spl0_25
| ~ spl0_26
| ~ spl0_15
| spl0_22 ),
inference(avatar_split_clause,[],[f135,f123,f84,f144,f140,f74]) ).
fof(f144,plain,
( spl0_26
<=> c_lessequals(c_0,v_ca,t_b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).
fof(f123,plain,
( spl0_22
<=> c_lessequals(c_0,c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).
fof(f135,plain,
( ~ c_lessequals(c_0,v_ca,t_b)
| ~ c_lessequals(c_0,c_HOL_Oabs(v_g(v_x),t_b),t_b)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(t_b)
| ~ spl0_15
| spl0_22 ),
inference(resolution,[],[f125,f85]) ).
fof(f125,plain,
( ~ c_lessequals(c_0,c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b)
| spl0_22 ),
inference(avatar_component_clause,[],[f123]) ).
fof(f138,plain,
( spl0_20
| ~ spl0_5
| ~ spl0_18 ),
inference(avatar_split_clause,[],[f105,f101,f37,f111]) ).
fof(f111,plain,
( spl0_20
<=> class_Orderings_Oorder(t_b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).
fof(f37,plain,
( spl0_5
<=> ! [X7] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X7)
| class_Orderings_Oorder(X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
fof(f105,plain,
( class_Orderings_Oorder(t_b)
| ~ spl0_5
| ~ spl0_18 ),
inference(resolution,[],[f103,f38]) ).
fof(f38,plain,
( ! [X7] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X7)
| class_Orderings_Oorder(X7) )
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f37]) ).
fof(f103,plain,
( class_OrderedGroup_Olordered__ab__group__abs(t_b)
| ~ spl0_18 ),
inference(avatar_component_clause,[],[f101]) ).
fof(f134,plain,
( ~ spl0_13
| ~ spl0_22
| ~ spl0_23
| spl0_24
| ~ spl0_10
| ~ spl0_15 ),
inference(avatar_split_clause,[],[f88,f84,f61,f131,f127,f123,f74]) ).
fof(f88,plain,
( c_lessequals(c_0,c_times(c_times(v_c,v_ca,t_b),c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b),t_b)
| ~ c_lessequals(c_0,c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b)
| ~ c_lessequals(c_0,c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(t_b)
| ~ spl0_10
| ~ spl0_15 ),
inference(superposition,[],[f85,f63]) ).
fof(f118,plain,
( spl0_21
| ~ spl0_1
| ~ spl0_14 ),
inference(avatar_split_clause,[],[f87,f80,f17,f116]) ).
fof(f17,plain,
( spl0_1
<=> class_Ring__and__Field_Oordered__idom(t_b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
fof(f80,plain,
( spl0_14
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oabs(c_times(X1,X2,X0),X0) = c_times(c_HOL_Oabs(X1,X0),c_HOL_Oabs(X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).
fof(f87,plain,
( ! [X0,X1] : c_HOL_Oabs(c_times(X0,X1,t_b),t_b) = c_times(c_HOL_Oabs(X0,t_b),c_HOL_Oabs(X1,t_b),t_b)
| ~ spl0_1
| ~ spl0_14 ),
inference(resolution,[],[f81,f19]) ).
fof(f19,plain,
( class_Ring__and__Field_Oordered__idom(t_b)
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f17]) ).
fof(f81,plain,
( ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oabs(c_times(X1,X2,X0),X0) = c_times(c_HOL_Oabs(X1,X0),c_HOL_Oabs(X2,X0),X0) )
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f80]) ).
fof(f114,plain,
( spl0_19
| ~ spl0_20
| ~ spl0_2
| ~ spl0_12 ),
inference(avatar_split_clause,[],[f78,f70,f22,f111,f107]) ).
fof(f22,plain,
( spl0_2
<=> c_less(c_0,v_c,t_b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
fof(f70,plain,
( spl0_12
<=> ! [X6,X0,X5] :
( ~ class_Orderings_Oorder(X0)
| ~ c_less(X5,X6,X0)
| c_lessequals(X5,X6,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).
fof(f78,plain,
( ~ class_Orderings_Oorder(t_b)
| c_lessequals(c_0,v_c,t_b)
| ~ spl0_2
| ~ spl0_12 ),
inference(resolution,[],[f71,f24]) ).
fof(f24,plain,
( c_less(c_0,v_c,t_b)
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f22]) ).
fof(f71,plain,
( ! [X0,X6,X5] :
( ~ c_less(X5,X6,X0)
| ~ class_Orderings_Oorder(X0)
| c_lessequals(X5,X6,X0) )
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f70]) ).
fof(f104,plain,
( spl0_18
| ~ spl0_1
| ~ spl0_8 ),
inference(avatar_split_clause,[],[f54,f49,f17,f101]) ).
fof(f49,plain,
( spl0_8
<=> ! [X7] :
( ~ class_Ring__and__Field_Oordered__idom(X7)
| class_OrderedGroup_Olordered__ab__group__abs(X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).
fof(f54,plain,
( class_OrderedGroup_Olordered__ab__group__abs(t_b)
| ~ spl0_1
| ~ spl0_8 ),
inference(resolution,[],[f50,f19]) ).
fof(f50,plain,
( ! [X7] :
( ~ class_Ring__and__Field_Oordered__idom(X7)
| class_OrderedGroup_Olordered__ab__group__abs(X7) )
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f49]) ).
fof(f99,plain,
( spl0_17
| ~ spl0_1
| ~ spl0_7 ),
inference(avatar_split_clause,[],[f53,f45,f17,f96]) ).
fof(f45,plain,
( spl0_7
<=> ! [X7] :
( ~ class_Ring__and__Field_Oordered__idom(X7)
| class_Ring__and__Field_Opordered__semiring(X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
fof(f53,plain,
( class_Ring__and__Field_Opordered__semiring(t_b)
| ~ spl0_1
| ~ spl0_7 ),
inference(resolution,[],[f46,f19]) ).
fof(f46,plain,
( ! [X7] :
( ~ class_Ring__and__Field_Oordered__idom(X7)
| class_Ring__and__Field_Opordered__semiring(X7) )
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f45]) ).
fof(f92,plain,
spl0_16,
inference(avatar_split_clause,[],[f2,f90]) ).
fof(f2,axiom,
! [X2,X3,X0,X1,X4] :
( ~ class_Ring__and__Field_Opordered__semiring(X0)
| ~ c_lessequals(X1,X2,X0)
| ~ c_lessequals(X3,X4,X0)
| ~ c_lessequals(c_0,X2,X0)
| ~ c_lessequals(c_0,X3,X0)
| c_lessequals(c_times(X1,X3,X0),c_times(X2,X4,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__mono_0) ).
fof(f86,plain,
spl0_15,
inference(avatar_split_clause,[],[f3,f84]) ).
fof(f3,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X0)
| ~ c_lessequals(c_0,X1,X0)
| ~ c_lessequals(c_0,X2,X0)
| c_lessequals(c_0,c_times(X1,X2,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__nonneg__nonneg_0) ).
fof(f82,plain,
spl0_14,
inference(avatar_split_clause,[],[f1,f80]) ).
fof(f1,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oabs(c_times(X1,X2,X0),X0) = c_times(c_HOL_Oabs(X1,X0),c_HOL_Oabs(X2,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Oabs__mult_0) ).
fof(f77,plain,
( spl0_13
| ~ spl0_1
| ~ spl0_6 ),
inference(avatar_split_clause,[],[f52,f41,f17,f74]) ).
fof(f41,plain,
( spl0_6
<=> ! [X7] :
( ~ class_Ring__and__Field_Oordered__idom(X7)
| class_Ring__and__Field_Opordered__cancel__semiring(X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
fof(f52,plain,
( class_Ring__and__Field_Opordered__cancel__semiring(t_b)
| ~ spl0_1
| ~ spl0_6 ),
inference(resolution,[],[f42,f19]) ).
fof(f42,plain,
( ! [X7] :
( ~ class_Ring__and__Field_Oordered__idom(X7)
| class_Ring__and__Field_Opordered__cancel__semiring(X7) )
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f41]) ).
fof(f72,plain,
spl0_12,
inference(avatar_split_clause,[],[f4,f70]) ).
fof(f4,axiom,
! [X0,X6,X5] :
( ~ class_Orderings_Oorder(X0)
| ~ c_less(X5,X6,X0)
| c_lessequals(X5,X6,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Oorder__less__imp__le_0) ).
fof(f68,plain,
spl0_11,
inference(avatar_split_clause,[],[f5,f66]) ).
fof(f5,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X0)
| c_lessequals(c_0,c_HOL_Oabs(X1,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__ge__zero_0) ).
fof(f64,plain,
spl0_10,
inference(avatar_split_clause,[],[f9,f61]) ).
fof(f9,axiom,
c_times(c_times(v_c,v_ca,t_b),c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b) = c_times(c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_4) ).
fof(f59,plain,
~ spl0_9,
inference(avatar_split_clause,[],[f10,f56]) ).
fof(f10,axiom,
~ c_lessequals(c_HOL_Oabs(c_times(v_a(v_x),v_b(v_x),t_b),t_b),c_times(c_times(v_c,v_ca,t_b),c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b),t_b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_5) ).
fof(f51,plain,
spl0_8,
inference(avatar_split_clause,[],[f15,f49]) ).
fof(f15,axiom,
! [X7] :
( ~ class_Ring__and__Field_Oordered__idom(X7)
| class_OrderedGroup_Olordered__ab__group__abs(X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_50) ).
fof(f47,plain,
spl0_7,
inference(avatar_split_clause,[],[f14,f45]) ).
fof(f14,axiom,
! [X7] :
( ~ class_Ring__and__Field_Oordered__idom(X7)
| class_Ring__and__Field_Opordered__semiring(X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_42) ).
fof(f43,plain,
spl0_6,
inference(avatar_split_clause,[],[f13,f41]) ).
fof(f13,axiom,
! [X7] :
( ~ class_Ring__and__Field_Oordered__idom(X7)
| class_Ring__and__Field_Opordered__cancel__semiring(X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_40) ).
fof(f39,plain,
spl0_5,
inference(avatar_split_clause,[],[f12,f37]) ).
fof(f12,axiom,
! [X7] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X7)
| class_Orderings_Oorder(X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_17) ).
fof(f35,plain,
spl0_4,
inference(avatar_split_clause,[],[f8,f32]) ).
fof(f8,axiom,
c_lessequals(c_HOL_Oabs(v_b(v_x),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).
fof(f30,plain,
spl0_3,
inference(avatar_split_clause,[],[f7,f27]) ).
fof(f7,axiom,
c_lessequals(c_HOL_Oabs(v_a(v_x),t_b),c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
fof(f25,plain,
spl0_2,
inference(avatar_split_clause,[],[f6,f22]) ).
fof(f6,axiom,
c_less(c_0,v_c,t_b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f20,plain,
spl0_1,
inference(avatar_split_clause,[],[f11,f17]) ).
fof(f11,axiom,
class_Ring__and__Field_Oordered__idom(t_b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tfree_tcs) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : ANA034-2 : TPTP v8.1.2. Released v3.2.0.
% 0.03/0.15 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.36 % Computer : n024.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Tue Apr 30 00:10:06 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.15/0.36 % (16426)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.38 % (16429)WARNING: value z3 for option sas not known
% 0.22/0.38 % (16430)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.22/0.38 % (16429)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.22/0.38 % (16428)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.22/0.38 % (16432)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.22/0.38 % (16431)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.22/0.38 % (16433)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.22/0.38 % (16427)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.22/0.38 TRYING [1]
% 0.22/0.38 TRYING [1]
% 0.22/0.38 TRYING [2]
% 0.22/0.38 TRYING [2]
% 0.22/0.38 TRYING [3]
% 0.22/0.38 TRYING [3]
% 0.22/0.39 % (16431)First to succeed.
% 0.22/0.39 TRYING [1]
% 0.22/0.39 TRYING [2]
% 0.22/0.39 % (16431)Refutation found. Thanks to Tanya!
% 0.22/0.39 % SZS status Unsatisfiable for theBenchmark
% 0.22/0.39 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.39 % (16431)------------------------------
% 0.22/0.39 % (16431)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.22/0.39 % (16431)Termination reason: Refutation
% 0.22/0.39
% 0.22/0.39 % (16431)Memory used [KB]: 901
% 0.22/0.39 % (16431)Time elapsed: 0.010 s
% 0.22/0.39 % (16431)Instructions burned: 13 (million)
% 0.22/0.39 % (16431)------------------------------
% 0.22/0.39 % (16431)------------------------------
% 0.22/0.39 % (16426)Success in time 0.026 s
%------------------------------------------------------------------------------