%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP338-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n009.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 10:13:41 AM UTC 2026
% Result : Unsatisfiable 2.75s 1.35s
% Output : Refutation 3.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 55
% Syntax : Number of formulae : 408 ( 25 unt; 25 def)
% Number of atoms : 1364 ( 393 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 1868 ( 912 ~; 931 |; 0 &)
% ( 25 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 27 ( 25 usr; 26 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 10 con; 0-2 aty)
% Number of variables : 74 ( 0 sgn 74 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_identity) ).
fof(f2,axiom,
! [X0] : multiply(inverse(X0),X0) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_inverse) ).
fof(f3,plain,
! [X0] : identity = multiply(inverse(X0),X0),
inference(reorient_equations,[],[f2]) ).
fof(f4,axiom,
! [X2,X0,X1] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity) ).
fof(f5,negated_conjecture,
( multiply(sk_c10,sk_c11) = sk_c9
| multiply(sk_c3,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,plain,
( multiply(sk_c10,sk_c11) = sk_c9
| sk_c10 = multiply(sk_c3,sk_c11) ),
inference(reorient_equations,[],[f5]) ).
fof(f7,negated_conjecture,
( multiply(sk_c10,sk_c11) = sk_c9
| inverse(sk_c3) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_2) ).
fof(f8,plain,
( multiply(sk_c10,sk_c11) = sk_c9
| sk_c11 = inverse(sk_c3) ),
inference(reorient_equations,[],[f7]) ).
fof(f9,negated_conjecture,
( multiply(sk_c10,sk_c11) = sk_c9
| multiply(sk_c4,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_3) ).
fof(f10,plain,
( multiply(sk_c10,sk_c11) = sk_c9
| sk_c9 = multiply(sk_c4,sk_c10) ),
inference(reorient_equations,[],[f9]) ).
fof(f11,negated_conjecture,
( multiply(sk_c10,sk_c11) = sk_c9
| inverse(sk_c4) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_4) ).
fof(f12,plain,
( multiply(sk_c10,sk_c11) = sk_c9
| sk_c10 = inverse(sk_c4) ),
inference(reorient_equations,[],[f11]) ).
fof(f13,negated_conjecture,
( multiply(sk_c10,sk_c11) = sk_c9
| multiply(sk_c5,sk_c8) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_5) ).
fof(f14,plain,
( multiply(sk_c10,sk_c11) = sk_c9
| sk_c11 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f13]) ).
fof(f15,negated_conjecture,
( multiply(sk_c10,sk_c11) = sk_c9
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_6) ).
fof(f16,plain,
( multiply(sk_c10,sk_c11) = sk_c9
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f15]) ).
fof(f24,negated_conjecture,
( inverse(sk_c1) = sk_c11
| multiply(sk_c3,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_11) ).
fof(f25,plain,
( sk_c11 = inverse(sk_c1)
| sk_c10 = multiply(sk_c3,sk_c11) ),
inference(reorient_equations,[],[f24]) ).
fof(f26,negated_conjecture,
( inverse(sk_c1) = sk_c11
| inverse(sk_c3) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_12) ).
fof(f27,plain,
( sk_c11 = inverse(sk_c1)
| sk_c11 = inverse(sk_c3) ),
inference(reorient_equations,[],[f26]) ).
fof(f28,negated_conjecture,
( inverse(sk_c1) = sk_c11
| multiply(sk_c4,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_13) ).
fof(f29,plain,
( sk_c11 = inverse(sk_c1)
| sk_c9 = multiply(sk_c4,sk_c10) ),
inference(reorient_equations,[],[f28]) ).
fof(f30,negated_conjecture,
( inverse(sk_c1) = sk_c11
| inverse(sk_c4) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_14) ).
fof(f31,plain,
( sk_c11 = inverse(sk_c1)
| sk_c10 = inverse(sk_c4) ),
inference(reorient_equations,[],[f30]) ).
fof(f32,negated_conjecture,
( inverse(sk_c1) = sk_c11
| multiply(sk_c5,sk_c8) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_15) ).
fof(f33,plain,
( sk_c11 = inverse(sk_c1)
| sk_c11 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f32]) ).
fof(f34,negated_conjecture,
( inverse(sk_c1) = sk_c11
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_16) ).
fof(f35,plain,
( sk_c11 = inverse(sk_c1)
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f34]) ).
fof(f48,negated_conjecture,
( multiply(sk_c1,sk_c10) = sk_c11
| multiply(sk_c4,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_23) ).
fof(f49,plain,
( sk_c11 = multiply(sk_c1,sk_c10)
| sk_c9 = multiply(sk_c4,sk_c10) ),
inference(reorient_equations,[],[f48]) ).
fof(f50,negated_conjecture,
( multiply(sk_c1,sk_c10) = sk_c11
| inverse(sk_c4) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_24) ).
fof(f51,plain,
( sk_c11 = multiply(sk_c1,sk_c10)
| sk_c10 = inverse(sk_c4) ),
inference(reorient_equations,[],[f50]) ).
fof(f64,negated_conjecture,
( multiply(sk_c2,sk_c10) = sk_c11
| multiply(sk_c3,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_31) ).
fof(f65,plain,
( sk_c11 = multiply(sk_c2,sk_c10)
| sk_c10 = multiply(sk_c3,sk_c11) ),
inference(reorient_equations,[],[f64]) ).
fof(f66,negated_conjecture,
( multiply(sk_c2,sk_c10) = sk_c11
| inverse(sk_c3) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_32) ).
fof(f67,plain,
( sk_c11 = multiply(sk_c2,sk_c10)
| sk_c11 = inverse(sk_c3) ),
inference(reorient_equations,[],[f66]) ).
fof(f68,negated_conjecture,
( multiply(sk_c2,sk_c10) = sk_c11
| multiply(sk_c4,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_33) ).
fof(f69,plain,
( sk_c11 = multiply(sk_c2,sk_c10)
| sk_c9 = multiply(sk_c4,sk_c10) ),
inference(reorient_equations,[],[f68]) ).
fof(f70,negated_conjecture,
( multiply(sk_c2,sk_c10) = sk_c11
| inverse(sk_c4) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_34) ).
fof(f71,plain,
( sk_c11 = multiply(sk_c2,sk_c10)
| sk_c10 = inverse(sk_c4) ),
inference(reorient_equations,[],[f70]) ).
fof(f72,negated_conjecture,
( multiply(sk_c2,sk_c10) = sk_c11
| multiply(sk_c5,sk_c8) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_35) ).
fof(f73,plain,
( sk_c11 = multiply(sk_c2,sk_c10)
| sk_c11 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f72]) ).
fof(f74,negated_conjecture,
( multiply(sk_c2,sk_c10) = sk_c11
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_36) ).
fof(f75,plain,
( sk_c11 = multiply(sk_c2,sk_c10)
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f74]) ).
fof(f84,negated_conjecture,
( inverse(sk_c2) = sk_c10
| multiply(sk_c3,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_41) ).
fof(f85,plain,
( sk_c10 = inverse(sk_c2)
| sk_c10 = multiply(sk_c3,sk_c11) ),
inference(reorient_equations,[],[f84]) ).
fof(f86,negated_conjecture,
( inverse(sk_c2) = sk_c10
| inverse(sk_c3) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_42) ).
fof(f87,plain,
( sk_c10 = inverse(sk_c2)
| sk_c11 = inverse(sk_c3) ),
inference(reorient_equations,[],[f86]) ).
fof(f88,negated_conjecture,
( inverse(sk_c2) = sk_c10
| multiply(sk_c4,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_43) ).
fof(f89,plain,
( sk_c10 = inverse(sk_c2)
| sk_c9 = multiply(sk_c4,sk_c10) ),
inference(reorient_equations,[],[f88]) ).
fof(f90,negated_conjecture,
( inverse(sk_c2) = sk_c10
| inverse(sk_c4) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_44) ).
fof(f91,plain,
( sk_c10 = inverse(sk_c2)
| sk_c10 = inverse(sk_c4) ),
inference(reorient_equations,[],[f90]) ).
fof(f92,negated_conjecture,
( inverse(sk_c2) = sk_c10
| multiply(sk_c5,sk_c8) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_45) ).
fof(f93,plain,
( sk_c10 = inverse(sk_c2)
| sk_c11 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f92]) ).
fof(f94,negated_conjecture,
( inverse(sk_c2) = sk_c10
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_46) ).
fof(f95,plain,
( sk_c10 = inverse(sk_c2)
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f94]) ).
fof(f104,negated_conjecture,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( multiply(sk_c10,sk_c11) != sk_c9
| inverse(X0) != sk_c11
| multiply(X0,sk_c10) != sk_c11
| multiply(X1,sk_c10) != sk_c11
| inverse(X1) != sk_c10
| multiply(X2,sk_c11) != sk_c10
| inverse(X2) != sk_c11
| multiply(X3,sk_c10) != sk_c9
| inverse(X3) != sk_c10
| multiply(X4,X5) != sk_c11
| inverse(X4) != X5
| multiply(X5,sk_c10) != sk_c11
| inverse(X6) != X7
| inverse(X7) != X5
| multiply(X6,X5) != X7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_51) ).
fof(f105,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( multiply(sk_c10,sk_c11) != sk_c9
| inverse(X0) != sk_c11
| sk_c11 != multiply(X0,sk_c10)
| sk_c11 != multiply(X1,sk_c10)
| sk_c10 != inverse(X1)
| sk_c10 != multiply(X2,sk_c11)
| sk_c11 != inverse(X2)
| sk_c9 != multiply(X3,sk_c10)
| sk_c10 != inverse(X3)
| sk_c11 != multiply(X4,X5)
| inverse(X4) != X5
| sk_c11 != multiply(X5,sk_c10)
| inverse(X6) != X7
| inverse(X7) != X5
| multiply(X6,X5) != X7 ),
inference(reorient_equations,[],[f104]) ).
fof(f106,plain,
! [X2,X3,X0,X1,X6,X7,X4] :
( multiply(sk_c10,sk_c11) != sk_c9
| inverse(X0) != sk_c11
| sk_c11 != multiply(X0,sk_c10)
| sk_c11 != multiply(X1,sk_c10)
| sk_c10 != inverse(X1)
| sk_c10 != multiply(X2,sk_c11)
| sk_c11 != inverse(X2)
| sk_c9 != multiply(X3,sk_c10)
| sk_c10 != inverse(X3)
| sk_c11 != multiply(X4,inverse(X4))
| sk_c11 != multiply(inverse(X4),sk_c10)
| inverse(X6) != X7
| inverse(X4) != inverse(X7)
| multiply(X6,inverse(X4)) != X7 ),
inference(equality_resolution,[],[f105]) ).
fof(f107,plain,
! [X2,X3,X0,X1,X6,X4] :
( multiply(sk_c10,sk_c11) != sk_c9
| inverse(X0) != sk_c11
| sk_c11 != multiply(X0,sk_c10)
| sk_c11 != multiply(X1,sk_c10)
| sk_c10 != inverse(X1)
| sk_c10 != multiply(X2,sk_c11)
| sk_c11 != inverse(X2)
| sk_c9 != multiply(X3,sk_c10)
| sk_c10 != inverse(X3)
| sk_c11 != multiply(X4,inverse(X4))
| sk_c11 != multiply(inverse(X4),sk_c10)
| inverse(X4) != inverse(inverse(X6))
| inverse(X6) != multiply(X6,inverse(X4)) ),
inference(equality_resolution,[],[f106]) ).
fof(f109,definition,
( spl0_1
<=> ! [X6,X4] :
( sk_c11 != multiply(X4,inverse(X4))
| inverse(X6) != multiply(X6,inverse(X4))
| inverse(X4) != inverse(inverse(X6))
| sk_c11 != multiply(inverse(X4),sk_c10) ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f110,plain,
( ! [X6,X4] :
( sk_c11 != multiply(inverse(X4),sk_c10)
| inverse(X6) != multiply(X6,inverse(X4))
| inverse(X4) != inverse(inverse(X6))
| sk_c11 != multiply(X4,inverse(X4)) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f109]) ).
fof(f112,definition,
( spl0_2
<=> ! [X3] :
( sk_c9 != multiply(X3,sk_c10)
| sk_c10 != inverse(X3) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f113,plain,
( ! [X3] :
( sk_c9 != multiply(X3,sk_c10)
| sk_c10 != inverse(X3) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f112]) ).
fof(f115,definition,
( spl0_3
<=> ! [X2] :
( sk_c10 != multiply(X2,sk_c11)
| sk_c11 != inverse(X2) ) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f116,plain,
( ! [X2] :
( sk_c10 != multiply(X2,sk_c11)
| sk_c11 != inverse(X2) )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f115]) ).
fof(f118,definition,
( spl0_4
<=> ! [X1] :
( sk_c11 != multiply(X1,sk_c10)
| sk_c10 != inverse(X1) ) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f119,plain,
( ! [X1] :
( sk_c11 != multiply(X1,sk_c10)
| sk_c10 != inverse(X1) )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f118]) ).
fof(f121,definition,
( spl0_5
<=> ! [X0] :
( inverse(X0) != sk_c11
| sk_c11 != multiply(X0,sk_c10) ) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f122,plain,
( ! [X0] :
( sk_c11 != multiply(X0,sk_c10)
| inverse(X0) != sk_c11 )
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f121]) ).
fof(f124,definition,
( spl0_6
<=> multiply(sk_c10,sk_c11) = sk_c9 ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f125,plain,
( multiply(sk_c10,sk_c11) = sk_c9
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f124]) ).
fof(f126,plain,
( multiply(sk_c10,sk_c11) != sk_c9
| spl0_6 ),
inference(avatar_component_clause,[],[f124]) ).
fof(f127,plain,
( spl0_1
| spl0_2
| spl0_3
| spl0_4
| spl0_5
| ~ spl0_6 ),
inference(avatar_split_clause,[],[f107,f124,f121,f118,f115,f112,f109]) ).
fof(f133,definition,
( spl0_8
<=> sk_c10 = inverse(sk_c2) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f135,plain,
( sk_c10 = inverse(sk_c2)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f133]) ).
fof(f153,definition,
( spl0_12
<=> sk_c8 = inverse(sk_c5) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f155,plain,
( sk_c8 = inverse(sk_c5)
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f153]) ).
fof(f156,plain,
( spl0_12
| spl0_8 ),
inference(avatar_split_clause,[],[f95,f133,f153]) ).
fof(f158,definition,
( spl0_13
<=> sk_c11 = multiply(sk_c5,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f160,plain,
( sk_c11 = multiply(sk_c5,sk_c8)
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f158]) ).
fof(f161,plain,
( spl0_13
| spl0_8 ),
inference(avatar_split_clause,[],[f93,f133,f158]) ).
fof(f163,definition,
( spl0_14
<=> sk_c10 = inverse(sk_c4) ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
fof(f165,plain,
( sk_c10 = inverse(sk_c4)
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f163]) ).
fof(f166,plain,
( spl0_14
| spl0_8 ),
inference(avatar_split_clause,[],[f91,f133,f163]) ).
fof(f168,definition,
( spl0_15
<=> sk_c9 = multiply(sk_c4,sk_c10) ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
fof(f170,plain,
( sk_c9 = multiply(sk_c4,sk_c10)
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f168]) ).
fof(f171,plain,
( spl0_15
| spl0_8 ),
inference(avatar_split_clause,[],[f89,f133,f168]) ).
fof(f173,definition,
( spl0_16
<=> sk_c11 = inverse(sk_c3) ),
introduced(definition,[new_symbols(definition,[spl0_16])],[avatar_definition]) ).
fof(f175,plain,
( sk_c11 = inverse(sk_c3)
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f173]) ).
fof(f176,plain,
( spl0_16
| spl0_8 ),
inference(avatar_split_clause,[],[f87,f133,f173]) ).
fof(f178,definition,
( spl0_17
<=> sk_c10 = multiply(sk_c3,sk_c11) ),
introduced(definition,[new_symbols(definition,[spl0_17])],[avatar_definition]) ).
fof(f180,plain,
( sk_c10 = multiply(sk_c3,sk_c11)
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f178]) ).
fof(f181,plain,
( spl0_17
| spl0_8 ),
inference(avatar_split_clause,[],[f85,f133,f178]) ).
fof(f183,definition,
( spl0_18
<=> sk_c11 = multiply(sk_c2,sk_c10) ),
introduced(definition,[new_symbols(definition,[spl0_18])],[avatar_definition]) ).
fof(f185,plain,
( sk_c11 = multiply(sk_c2,sk_c10)
| ~ spl0_18 ),
inference(avatar_component_clause,[],[f183]) ).
fof(f190,plain,
( spl0_12
| spl0_18 ),
inference(avatar_split_clause,[],[f75,f183,f153]) ).
fof(f191,plain,
( spl0_13
| spl0_18 ),
inference(avatar_split_clause,[],[f73,f183,f158]) ).
fof(f192,plain,
( spl0_14
| spl0_18 ),
inference(avatar_split_clause,[],[f71,f183,f163]) ).
fof(f193,plain,
( spl0_15
| spl0_18 ),
inference(avatar_split_clause,[],[f69,f183,f168]) ).
fof(f194,plain,
( spl0_16
| spl0_18 ),
inference(avatar_split_clause,[],[f67,f183,f173]) ).
fof(f195,plain,
( spl0_17
| spl0_18 ),
inference(avatar_split_clause,[],[f65,f183,f178]) ).
fof(f197,definition,
( spl0_19
<=> sk_c11 = multiply(sk_c1,sk_c10) ),
introduced(definition,[new_symbols(definition,[spl0_19])],[avatar_definition]) ).
fof(f199,plain,
( sk_c11 = multiply(sk_c1,sk_c10)
| ~ spl0_19 ),
inference(avatar_component_clause,[],[f197]) ).
fof(f206,plain,
( spl0_14
| spl0_19 ),
inference(avatar_split_clause,[],[f51,f197,f163]) ).
fof(f207,plain,
( spl0_15
| spl0_19 ),
inference(avatar_split_clause,[],[f49,f197,f168]) ).
fof(f211,definition,
( spl0_20
<=> sk_c11 = inverse(sk_c1) ),
introduced(definition,[new_symbols(definition,[spl0_20])],[avatar_definition]) ).
fof(f213,plain,
( sk_c11 = inverse(sk_c1)
| ~ spl0_20 ),
inference(avatar_component_clause,[],[f211]) ).
fof(f218,plain,
( spl0_12
| spl0_20 ),
inference(avatar_split_clause,[],[f35,f211,f153]) ).
fof(f219,plain,
( spl0_13
| spl0_20 ),
inference(avatar_split_clause,[],[f33,f211,f158]) ).
fof(f220,plain,
( spl0_14
| spl0_20 ),
inference(avatar_split_clause,[],[f31,f211,f163]) ).
fof(f221,plain,
( spl0_15
| spl0_20 ),
inference(avatar_split_clause,[],[f29,f211,f168]) ).
fof(f222,plain,
( spl0_16
| spl0_20 ),
inference(avatar_split_clause,[],[f27,f211,f173]) ).
fof(f223,plain,
( spl0_17
| spl0_20 ),
inference(avatar_split_clause,[],[f25,f211,f178]) ).
fof(f228,plain,
( spl0_12
| spl0_6 ),
inference(avatar_split_clause,[],[f16,f124,f153]) ).
fof(f229,plain,
( spl0_13
| spl0_6 ),
inference(avatar_split_clause,[],[f14,f124,f158]) ).
fof(f230,plain,
( spl0_14
| spl0_6 ),
inference(avatar_split_clause,[],[f12,f124,f163]) ).
fof(f231,plain,
( spl0_15
| spl0_6 ),
inference(avatar_split_clause,[],[f10,f124,f168]) ).
fof(f232,plain,
( spl0_16
| spl0_6 ),
inference(avatar_split_clause,[],[f8,f124,f173]) ).
fof(f233,plain,
( spl0_17
| spl0_6 ),
inference(avatar_split_clause,[],[f6,f124,f178]) ).
fof(f234,plain,
( identity = multiply(sk_c11,sk_c3)
| ~ spl0_16 ),
inference(superposition,[],[f3,f175]) ).
fof(f235,plain,
( identity = multiply(sk_c10,sk_c4)
| ~ spl0_14 ),
inference(superposition,[],[f3,f165]) ).
fof(f241,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[],[f4,f3]) ).
fof(f242,plain,
( ! [X0] : multiply(sk_c3,multiply(sk_c11,X0)) = multiply(sk_c10,X0)
| ~ spl0_17 ),
inference(superposition,[],[f4,f180]) ).
fof(f247,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f241,f1]) ).
fof(f250,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c11,multiply(sk_c3,X0))
| ~ spl0_16 ),
inference(superposition,[],[f4,f234]) ).
fof(f251,plain,
( ! [X0] : multiply(sk_c11,multiply(sk_c3,X0)) = X0
| ~ spl0_16 ),
inference(forward_demodulation,[],[f250,f1]) ).
fof(f264,plain,
( sk_c11 = multiply(sk_c11,sk_c10)
| ~ spl0_16
| ~ spl0_17 ),
inference(superposition,[],[f251,f180]) ).
fof(f273,plain,
( multiply(sk_c3,sk_c11) = multiply(sk_c10,sk_c10)
| ~ spl0_16
| ~ spl0_17 ),
inference(superposition,[],[f242,f264]) ).
fof(f275,plain,
( sk_c10 = multiply(sk_c10,sk_c10)
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f273,f180]) ).
fof(f311,plain,
( sk_c4 = multiply(inverse(sk_c10),identity)
| ~ spl0_14 ),
inference(superposition,[],[f247,f235]) ).
fof(f313,plain,
( sk_c3 = multiply(inverse(sk_c11),identity)
| ~ spl0_16 ),
inference(superposition,[],[f247,f234]) ).
fof(f315,plain,
( sk_c10 = multiply(inverse(sk_c11),sk_c11)
| ~ spl0_16
| ~ spl0_17 ),
inference(superposition,[],[f247,f264]) ).
fof(f319,plain,
( sk_c10 = multiply(inverse(sk_c4),sk_c9)
| ~ spl0_15 ),
inference(superposition,[],[f247,f170]) ).
fof(f321,plain,
( sk_c8 = multiply(inverse(sk_c5),sk_c11)
| ~ spl0_13 ),
inference(superposition,[],[f247,f160]) ).
fof(f338,plain,
( sk_c8 = multiply(sk_c8,sk_c11)
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f321,f155]) ).
fof(f340,plain,
( sk_c10 = multiply(sk_c10,sk_c9)
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f319,f165]) ).
fof(f344,plain,
( identity = sk_c10
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f315,f3]) ).
fof(f359,plain,
( sk_c11 = multiply(inverse(sk_c8),sk_c8)
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f247,f338]) ).
fof(f361,plain,
( identity = sk_c11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f359,f3]) ).
fof(f364,plain,
( sk_c10 = sk_c11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f361,f344]) ).
fof(f365,plain,
( sk_c9 != multiply(sk_c10,sk_c10)
| spl0_6
| ~ spl0_12
| ~ spl0_13
| ~ spl0_16
| ~ spl0_17 ),
inference(superposition,[],[f126,f364]) ).
fof(f375,plain,
( sk_c10 != sk_c9
| spl0_6
| ~ spl0_12
| ~ spl0_13
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f365,f275]) ).
fof(f379,plain,
( sk_c9 = multiply(inverse(sk_c10),sk_c10)
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f247,f340]) ).
fof(f381,plain,
( identity = sk_c9
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f379,f3]) ).
fof(f384,plain,
( sk_c10 = sk_c9
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f381,f344]) ).
fof(f388,plain,
( sk_c4 = multiply(inverse(sk_c10),sk_c10)
| ~ spl0_14
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f311,f344]) ).
fof(f389,plain,
( identity = sk_c4
| ~ spl0_14
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f388,f3]) ).
fof(f390,plain,
( sk_c10 = sk_c4
| ~ spl0_14
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f389,f344]) ).
fof(f394,plain,
( sk_c10 = inverse(sk_c10)
| ~ spl0_14
| ~ spl0_16
| ~ spl0_17 ),
inference(superposition,[],[f165,f390]) ).
fof(f398,plain,
( sk_c3 = multiply(inverse(sk_c11),sk_c10)
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f313,f344]) ).
fof(f399,plain,
( sk_c3 = multiply(inverse(sk_c10),sk_c10)
| ~ spl0_12
| ~ spl0_13
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f398,f364]) ).
fof(f400,plain,
( identity = sk_c3
| ~ spl0_12
| ~ spl0_13
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f399,f3]) ).
fof(f401,plain,
( sk_c10 = sk_c3
| ~ spl0_12
| ~ spl0_13
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f400,f344]) ).
fof(f414,plain,
( $false
| spl0_6
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f375,f384]) ).
fof(f415,plain,
( spl0_6
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(avatar_contradiction_clause,[],[f414]) ).
fof(f417,plain,
( sk_c10 = multiply(sk_c10,sk_c11)
| ~ spl0_6
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f125,f384]) ).
fof(f453,plain,
( identity = multiply(sk_c10,sk_c2)
| ~ spl0_8 ),
inference(superposition,[],[f3,f135]) ).
fof(f456,plain,
( identity = multiply(sk_c11,sk_c1)
| ~ spl0_20 ),
inference(superposition,[],[f3,f213]) ).
fof(f461,plain,
( sk_c10 = multiply(inverse(sk_c2),sk_c11)
| ~ spl0_18 ),
inference(superposition,[],[f247,f185]) ).
fof(f462,plain,
( ! [X0] : multiply(sk_c11,X0) = multiply(sk_c2,multiply(sk_c10,X0))
| ~ spl0_18 ),
inference(superposition,[],[f4,f185]) ).
fof(f463,plain,
( sk_c10 = multiply(sk_c10,sk_c11)
| ~ spl0_8
| ~ spl0_18 ),
inference(forward_demodulation,[],[f461,f135]) ).
fof(f467,plain,
( sk_c10 = multiply(inverse(sk_c1),sk_c11)
| ~ spl0_19 ),
inference(superposition,[],[f247,f199]) ).
fof(f469,plain,
( sk_c10 = multiply(sk_c11,sk_c11)
| ~ spl0_19
| ~ spl0_20 ),
inference(forward_demodulation,[],[f467,f213]) ).
fof(f472,plain,
( sk_c11 = multiply(inverse(sk_c10),sk_c10)
| ~ spl0_6
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(superposition,[],[f247,f417]) ).
fof(f474,plain,
( identity = sk_c11
| ~ spl0_6
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f472,f3]) ).
fof(f477,plain,
( sk_c10 = sk_c11
| ~ spl0_6
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f474,f344]) ).
fof(f481,plain,
( ! [X0,X1] :
( sk_c10 != multiply(X0,multiply(X1,sk_c11))
| sk_c11 != inverse(multiply(X0,X1)) )
| ~ spl0_3 ),
inference(superposition,[],[f116,f4]) ).
fof(f484,plain,
( sk_c10 != sk_c10
| sk_c11 != inverse(sk_c3)
| ~ spl0_3
| ~ spl0_17 ),
inference(superposition,[],[f116,f180]) ).
fof(f486,plain,
( sk_c11 != inverse(sk_c3)
| ~ spl0_3
| ~ spl0_17 ),
inference(trivial_inequality_removal,[],[f484]) ).
fof(f493,definition,
( spl0_25
<=> sk_c10 = sk_c11 ),
introduced(definition,[new_symbols(definition,[spl0_25])],[avatar_definition]) ).
fof(f494,plain,
( sk_c10 = sk_c11
| ~ spl0_25 ),
inference(avatar_component_clause,[],[f493]) ).
fof(f509,plain,
( ~ spl0_16
| ~ spl0_3
| ~ spl0_17 ),
inference(avatar_split_clause,[],[f486,f178,f115,f173]) ).
fof(f515,definition,
( spl0_27
<=> identity = sk_c10 ),
introduced(definition,[new_symbols(definition,[spl0_27])],[avatar_definition]) ).
fof(f516,plain,
( identity = sk_c10
| ~ spl0_27 ),
inference(avatar_component_clause,[],[f515]) ).
fof(f517,plain,
( identity != sk_c10
| spl0_27 ),
inference(avatar_component_clause,[],[f515]) ).
fof(f520,definition,
( spl0_28
<=> sk_c11 = inverse(identity) ),
introduced(definition,[new_symbols(definition,[spl0_28])],[avatar_definition]) ).
fof(f521,plain,
( sk_c11 = inverse(identity)
| ~ spl0_28 ),
inference(avatar_component_clause,[],[f520]) ).
fof(f522,plain,
( sk_c11 != inverse(identity)
| spl0_28 ),
inference(avatar_component_clause,[],[f520]) ).
fof(f529,plain,
( ! [X0] : multiply(sk_c9,X0) = multiply(sk_c10,multiply(sk_c11,X0))
| ~ spl0_6 ),
inference(superposition,[],[f4,f125]) ).
fof(f531,definition,
( spl0_29
<=> sk_c11 = inverse(sk_c10) ),
introduced(definition,[new_symbols(definition,[spl0_29])],[avatar_definition]) ).
fof(f532,plain,
( sk_c11 = inverse(sk_c10)
| ~ spl0_29 ),
inference(avatar_component_clause,[],[f531]) ).
fof(f535,definition,
( spl0_30
<=> sk_c10 = sk_c9 ),
introduced(definition,[new_symbols(definition,[spl0_30])],[avatar_definition]) ).
fof(f536,plain,
( sk_c10 = sk_c9
| ~ spl0_30 ),
inference(avatar_component_clause,[],[f535]) ).
fof(f540,plain,
( sk_c9 = multiply(sk_c11,sk_c1)
| ~ spl0_14
| ~ spl0_15
| ~ spl0_20 ),
inference(forward_demodulation,[],[f456,f381]) ).
fof(f561,plain,
( sk_c10 = sk_c9
| ~ spl0_6
| ~ spl0_8
| ~ spl0_18 ),
inference(superposition,[],[f125,f463]) ).
fof(f566,plain,
( sk_c11 = multiply(inverse(sk_c10),sk_c10)
| ~ spl0_8
| ~ spl0_18 ),
inference(superposition,[],[f247,f463]) ).
fof(f569,plain,
( identity = sk_c11
| ~ spl0_8
| ~ spl0_18 ),
inference(forward_demodulation,[],[f566,f3]) ).
fof(f573,plain,
( spl0_30
| ~ spl0_6
| ~ spl0_8
| ~ spl0_18 ),
inference(avatar_split_clause,[],[f561,f183,f133,f124,f535]) ).
fof(f574,plain,
( sk_c10 = multiply(sk_c10,sk_c10)
| ~ spl0_14
| ~ spl0_15
| ~ spl0_30 ),
inference(superposition,[],[f340,f536]) ).
fof(f576,plain,
( sk_c11 = sk_c9
| ~ spl0_8
| ~ spl0_14
| ~ spl0_15
| ~ spl0_18 ),
inference(superposition,[],[f381,f569]) ).
fof(f578,plain,
( sk_c10 = sk_c11
| ~ spl0_8
| ~ spl0_14
| ~ spl0_15
| ~ spl0_18
| ~ spl0_30 ),
inference(forward_demodulation,[],[f576,f536]) ).
fof(f585,plain,
( spl0_25
| ~ spl0_8
| ~ spl0_14
| ~ spl0_15
| ~ spl0_18
| ~ spl0_30 ),
inference(avatar_split_clause,[],[f578,f535,f183,f168,f163,f133,f493]) ).
fof(f616,plain,
( ! [X0] : multiply(sk_c9,X0) = multiply(sk_c10,multiply(sk_c10,X0))
| ~ spl0_6
| ~ spl0_25 ),
inference(forward_demodulation,[],[f529,f494]) ).
fof(f617,plain,
( ! [X0] : multiply(sk_c10,X0) = multiply(sk_c10,multiply(sk_c10,X0))
| ~ spl0_6
| ~ spl0_25
| ~ spl0_30 ),
inference(forward_demodulation,[],[f616,f536]) ).
fof(f629,plain,
( ! [X0] : multiply(sk_c10,X0) = multiply(inverse(sk_c10),multiply(sk_c10,X0))
| ~ spl0_6
| ~ spl0_25
| ~ spl0_30 ),
inference(superposition,[],[f247,f617]) ).
fof(f632,plain,
( ! [X0] : multiply(sk_c10,X0) = X0
| ~ spl0_6
| ~ spl0_25
| ~ spl0_30 ),
inference(forward_demodulation,[],[f629,f247]) ).
fof(f648,plain,
( ! [X0,X1] :
( sk_c10 != multiply(X0,multiply(X1,sk_c10))
| sk_c11 != inverse(multiply(X0,X1)) )
| ~ spl0_3
| ~ spl0_25 ),
inference(forward_demodulation,[],[f481,f494]) ).
fof(f649,plain,
( ! [X0,X1] :
( sk_c10 != multiply(X0,multiply(X1,sk_c10))
| sk_c10 != inverse(multiply(X0,X1)) )
| ~ spl0_3
| ~ spl0_25 ),
inference(forward_demodulation,[],[f648,f494]) ).
fof(f703,plain,
( sk_c10 != multiply(sk_c11,sk_c10)
| sk_c10 != inverse(multiply(sk_c2,sk_c10))
| ~ spl0_3
| ~ spl0_18
| ~ spl0_25 ),
inference(superposition,[],[f649,f462]) ).
fof(f705,plain,
( sk_c10 != multiply(sk_c10,sk_c10)
| sk_c10 != inverse(multiply(sk_c2,sk_c10))
| ~ spl0_3
| ~ spl0_18
| ~ spl0_25 ),
inference(forward_demodulation,[],[f703,f494]) ).
fof(f718,definition,
( spl0_32
<=> sk_c10 = multiply(sk_c10,sk_c10) ),
introduced(definition,[new_symbols(definition,[spl0_32])],[avatar_definition]) ).
fof(f719,plain,
( sk_c10 = multiply(sk_c10,sk_c10)
| ~ spl0_32 ),
inference(avatar_component_clause,[],[f718]) ).
fof(f732,plain,
( sk_c10 != inverse(sk_c11)
| sk_c10 != multiply(sk_c10,sk_c10)
| ~ spl0_3
| ~ spl0_18
| ~ spl0_25 ),
inference(forward_demodulation,[],[f705,f185]) ).
fof(f735,definition,
( spl0_33
<=> sk_c10 = inverse(sk_c10) ),
introduced(definition,[new_symbols(definition,[spl0_33])],[avatar_definition]) ).
fof(f736,plain,
( sk_c10 = inverse(sk_c10)
| ~ spl0_33 ),
inference(avatar_component_clause,[],[f735]) ).
fof(f748,plain,
( sk_c10 != inverse(sk_c10)
| sk_c10 != multiply(sk_c10,sk_c10)
| ~ spl0_3
| ~ spl0_18
| ~ spl0_25 ),
inference(forward_demodulation,[],[f732,f494]) ).
fof(f754,plain,
( ~ spl0_32
| ~ spl0_33
| ~ spl0_3
| ~ spl0_18
| ~ spl0_25 ),
inference(avatar_split_clause,[],[f748,f493,f183,f115,f735,f718]) ).
fof(f813,plain,
( identity = sk_c2
| ~ spl0_6
| ~ spl0_8
| ~ spl0_25
| ~ spl0_30 ),
inference(forward_demodulation,[],[f453,f632]) ).
fof(f816,plain,
( sk_c11 != inverse(sk_c11)
| ~ spl0_8
| ~ spl0_18
| spl0_28 ),
inference(forward_demodulation,[],[f522,f569]) ).
fof(f826,plain,
( sk_c11 = sk_c2
| ~ spl0_6
| ~ spl0_8
| ~ spl0_18
| ~ spl0_25
| ~ spl0_30 ),
inference(forward_demodulation,[],[f813,f569]) ).
fof(f839,plain,
( sk_c10 = sk_c2
| ~ spl0_6
| ~ spl0_8
| ~ spl0_18
| ~ spl0_25
| ~ spl0_30 ),
inference(forward_demodulation,[],[f826,f494]) ).
fof(f848,plain,
( sk_c10 = inverse(sk_c10)
| ~ spl0_6
| ~ spl0_8
| ~ spl0_18
| ~ spl0_25
| ~ spl0_30 ),
inference(superposition,[],[f135,f839]) ).
fof(f855,plain,
( ! [X0] : multiply(sk_c10,X0) = multiply(sk_c10,multiply(sk_c11,X0))
| ~ spl0_6
| ~ spl0_30 ),
inference(forward_demodulation,[],[f529,f536]) ).
fof(f857,plain,
( sk_c11 = multiply(sk_c11,sk_c1)
| ~ spl0_8
| ~ spl0_18
| ~ spl0_20 ),
inference(forward_demodulation,[],[f456,f569]) ).
fof(f865,plain,
( sk_c1 = multiply(inverse(sk_c11),sk_c11)
| ~ spl0_8
| ~ spl0_18
| ~ spl0_20 ),
inference(superposition,[],[f247,f857]) ).
fof(f867,plain,
( identity = sk_c1
| ~ spl0_8
| ~ spl0_18
| ~ spl0_20 ),
inference(forward_demodulation,[],[f865,f3]) ).
fof(f869,plain,
( sk_c11 = sk_c1
| ~ spl0_8
| ~ spl0_18
| ~ spl0_20 ),
inference(forward_demodulation,[],[f867,f569]) ).
fof(f888,plain,
( sk_c11 = inverse(sk_c11)
| ~ spl0_8
| ~ spl0_18
| ~ spl0_20 ),
inference(superposition,[],[f213,f869]) ).
fof(f889,plain,
( $false
| ~ spl0_8
| ~ spl0_18
| ~ spl0_20
| spl0_28 ),
inference(forward_subsumption_resolution,[],[f888,f816]) ).
fof(f890,plain,
( ~ spl0_8
| ~ spl0_18
| ~ spl0_20
| spl0_28 ),
inference(avatar_contradiction_clause,[],[f889]) ).
fof(f891,plain,
( sk_c11 = inverse(sk_c11)
| ~ spl0_8
| ~ spl0_18
| ~ spl0_28 ),
inference(forward_demodulation,[],[f521,f569]) ).
fof(f937,plain,
( multiply(sk_c10,sk_c11) = multiply(sk_c10,sk_c10)
| ~ spl0_6
| ~ spl0_19
| ~ spl0_20
| ~ spl0_30 ),
inference(superposition,[],[f855,f469]) ).
fof(f940,plain,
( sk_c10 != sk_c10
| sk_c11 != inverse(sk_c11)
| ~ spl0_3
| ~ spl0_19
| ~ spl0_20 ),
inference(superposition,[],[f116,f469]) ).
fof(f943,plain,
( sk_c11 != inverse(sk_c11)
| ~ spl0_3
| ~ spl0_19
| ~ spl0_20 ),
inference(trivial_inequality_removal,[],[f940]) ).
fof(f945,plain,
( $false
| ~ spl0_3
| ~ spl0_8
| ~ spl0_18
| ~ spl0_19
| ~ spl0_20
| ~ spl0_28 ),
inference(forward_subsumption_resolution,[],[f943,f891]) ).
fof(f946,plain,
( ~ spl0_3
| ~ spl0_8
| ~ spl0_18
| ~ spl0_19
| ~ spl0_20
| ~ spl0_28 ),
inference(avatar_contradiction_clause,[],[f945]) ).
fof(f948,plain,
( sk_c9 = multiply(sk_c10,sk_c10)
| ~ spl0_6
| ~ spl0_19
| ~ spl0_20
| ~ spl0_30 ),
inference(forward_demodulation,[],[f937,f125]) ).
fof(f950,plain,
( sk_c10 = multiply(sk_c10,sk_c10)
| ~ spl0_6
| ~ spl0_19
| ~ spl0_20
| ~ spl0_30 ),
inference(forward_demodulation,[],[f948,f536]) ).
fof(f951,plain,
( spl0_32
| ~ spl0_6
| ~ spl0_19
| ~ spl0_20
| ~ spl0_30 ),
inference(avatar_split_clause,[],[f950,f535,f211,f197,f124,f718]) ).
fof(f962,plain,
( sk_c10 = multiply(sk_c4,sk_c10)
| ~ spl0_15
| ~ spl0_30 ),
inference(forward_demodulation,[],[f170,f536]) ).
fof(f966,plain,
( spl0_32
| ~ spl0_14
| ~ spl0_15
| ~ spl0_30 ),
inference(avatar_split_clause,[],[f574,f535,f168,f163,f718]) ).
fof(f977,plain,
( spl0_25
| ~ spl0_6
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(avatar_split_clause,[],[f477,f178,f173,f168,f163,f124,f493]) ).
fof(f981,plain,
( sk_c11 = sk_c9
| ~ spl0_8
| ~ spl0_14
| ~ spl0_15
| ~ spl0_18
| ~ spl0_20 ),
inference(forward_demodulation,[],[f540,f857]) ).
fof(f983,plain,
( spl0_33
| ~ spl0_14
| ~ spl0_16
| ~ spl0_17 ),
inference(avatar_split_clause,[],[f394,f178,f173,f163,f735]) ).
fof(f984,plain,
( spl0_27
| ~ spl0_16
| ~ spl0_17 ),
inference(avatar_split_clause,[],[f344,f178,f173,f515]) ).
fof(f994,plain,
( spl0_33
| ~ spl0_6
| ~ spl0_8
| ~ spl0_18
| ~ spl0_25
| ~ spl0_30 ),
inference(avatar_split_clause,[],[f848,f535,f493,f183,f133,f124,f735]) ).
fof(f999,plain,
( sk_c10 = sk_c11
| ~ spl0_8
| ~ spl0_14
| ~ spl0_15
| ~ spl0_18
| ~ spl0_20
| ~ spl0_30 ),
inference(forward_demodulation,[],[f981,f536]) ).
fof(f1000,plain,
( spl0_25
| ~ spl0_8
| ~ spl0_14
| ~ spl0_15
| ~ spl0_18
| ~ spl0_20
| ~ spl0_30 ),
inference(avatar_split_clause,[],[f999,f535,f211,f183,f168,f163,f133,f493]) ).
fof(f1012,plain,
( sk_c10 = sk_c11
| ~ spl0_8
| ~ spl0_18
| ~ spl0_27 ),
inference(superposition,[],[f569,f516]) ).
fof(f1014,plain,
( spl0_25
| ~ spl0_8
| ~ spl0_18
| ~ spl0_27 ),
inference(avatar_split_clause,[],[f1012,f515,f183,f133,f493]) ).
fof(f1039,plain,
( sk_c10 != sk_c11
| sk_c10 != inverse(sk_c4)
| ~ spl0_4
| ~ spl0_15
| ~ spl0_30 ),
inference(superposition,[],[f119,f962]) ).
fof(f1042,plain,
( sk_c11 != sk_c11
| sk_c10 != inverse(sk_c2)
| ~ spl0_4
| ~ spl0_18 ),
inference(superposition,[],[f119,f185]) ).
fof(f1043,plain,
( sk_c10 != inverse(sk_c2)
| ~ spl0_4
| ~ spl0_18 ),
inference(trivial_inequality_removal,[],[f1042]) ).
fof(f1045,plain,
( $false
| ~ spl0_4
| ~ spl0_8
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[],[f1043,f135]) ).
fof(f1046,plain,
( ~ spl0_4
| ~ spl0_8
| ~ spl0_18 ),
inference(avatar_contradiction_clause,[],[f1045]) ).
fof(f1049,plain,
( sk_c10 != sk_c11
| ~ spl0_4
| ~ spl0_14
| ~ spl0_15
| ~ spl0_30 ),
inference(forward_subsumption_resolution,[],[f1039,f165]) ).
fof(f1054,plain,
( ~ spl0_25
| ~ spl0_4
| ~ spl0_14
| ~ spl0_15
| ~ spl0_30 ),
inference(avatar_split_clause,[],[f1049,f535,f168,f163,f118,f493]) ).
fof(f1086,definition,
( spl0_35
<=> ! [X0] :
( inverse(X0) != multiply(X0,sk_c10)
| sk_c10 != inverse(inverse(X0)) ) ),
introduced(definition,[new_symbols(definition,[spl0_35])],[avatar_definition]) ).
fof(f1087,plain,
( ! [X0] :
( sk_c10 != inverse(inverse(X0))
| inverse(X0) != multiply(X0,sk_c10) )
| ~ spl0_35 ),
inference(avatar_component_clause,[],[f1086]) ).
fof(f1089,definition,
( spl0_36
<=> sk_c11 = multiply(sk_c10,sk_c10) ),
introduced(definition,[new_symbols(definition,[spl0_36])],[avatar_definition]) ).
fof(f1090,plain,
( sk_c11 = multiply(sk_c10,sk_c10)
| ~ spl0_36 ),
inference(avatar_component_clause,[],[f1089]) ).
fof(f1091,plain,
( sk_c11 != multiply(sk_c10,sk_c10)
| spl0_36 ),
inference(avatar_component_clause,[],[f1089]) ).
fof(f1139,plain,
( sk_c10 != sk_c11
| sk_c11 != inverse(identity)
| ~ spl0_5 ),
inference(superposition,[],[f122,f1]) ).
fof(f1142,plain,
( sk_c10 != sk_c11
| sk_c11 != inverse(sk_c4)
| ~ spl0_5
| ~ spl0_15
| ~ spl0_30 ),
inference(superposition,[],[f122,f962]) ).
fof(f1151,plain,
( sk_c10 != sk_c11
| sk_c10 != sk_c11
| ~ spl0_5
| ~ spl0_14
| ~ spl0_15
| ~ spl0_30 ),
inference(forward_demodulation,[],[f1142,f165]) ).
fof(f1152,plain,
( sk_c10 != sk_c11
| ~ spl0_5
| ~ spl0_14
| ~ spl0_15
| ~ spl0_30 ),
inference(duplicate_literal_removal,[],[f1151]) ).
fof(f1154,plain,
( sk_c11 != inverse(sk_c11)
| sk_c10 != sk_c11
| ~ spl0_5
| ~ spl0_8
| ~ spl0_18 ),
inference(forward_demodulation,[],[f1139,f569]) ).
fof(f1159,plain,
( ~ spl0_25
| ~ spl0_5
| ~ spl0_14
| ~ spl0_15
| ~ spl0_30 ),
inference(avatar_split_clause,[],[f1152,f535,f168,f163,f121,f493]) ).
fof(f1160,plain,
( sk_c10 != sk_c11
| ~ spl0_5
| ~ spl0_8
| ~ spl0_18
| ~ spl0_28 ),
inference(forward_subsumption_resolution,[],[f1154,f891]) ).
fof(f1162,plain,
( ~ spl0_25
| ~ spl0_5
| ~ spl0_8
| ~ spl0_18
| ~ spl0_28 ),
inference(avatar_split_clause,[],[f1160,f520,f183,f133,f121,f493]) ).
fof(f1163,plain,
( ! [X3] :
( sk_c10 != multiply(X3,sk_c10)
| sk_c10 != inverse(X3) )
| ~ spl0_2
| ~ spl0_30 ),
inference(forward_demodulation,[],[f113,f536]) ).
fof(f1164,plain,
( sk_c11 = inverse(sk_c10)
| ~ spl0_12
| ~ spl0_13
| ~ spl0_16
| ~ spl0_17 ),
inference(superposition,[],[f175,f401]) ).
fof(f1167,plain,
( spl0_29
| ~ spl0_12
| ~ spl0_13
| ~ spl0_16
| ~ spl0_17 ),
inference(avatar_split_clause,[],[f1164,f178,f173,f158,f153,f531]) ).
fof(f1171,plain,
( sk_c10 != sk_c10
| sk_c10 != inverse(sk_c4)
| ~ spl0_2
| ~ spl0_15
| ~ spl0_30 ),
inference(superposition,[],[f1163,f962]) ).
fof(f1174,plain,
( sk_c10 != sk_c11
| sk_c10 != inverse(sk_c2)
| ~ spl0_2
| ~ spl0_18
| ~ spl0_30 ),
inference(superposition,[],[f1163,f185]) ).
fof(f1176,plain,
( sk_c10 != inverse(sk_c4)
| ~ spl0_2
| ~ spl0_15
| ~ spl0_30 ),
inference(trivial_inequality_removal,[],[f1171]) ).
fof(f1181,plain,
( $false
| ~ spl0_2
| ~ spl0_14
| ~ spl0_15
| ~ spl0_30 ),
inference(forward_subsumption_resolution,[],[f1176,f165]) ).
fof(f1182,plain,
( ~ spl0_2
| ~ spl0_14
| ~ spl0_15
| ~ spl0_30 ),
inference(avatar_contradiction_clause,[],[f1181]) ).
fof(f1230,plain,
( ! [X0] :
( sk_c11 != multiply(sk_c10,sk_c10)
| inverse(X0) != multiply(X0,sk_c10)
| sk_c10 != inverse(inverse(X0))
| sk_c11 != multiply(sk_c4,sk_c10) )
| ~ spl0_1
| ~ spl0_14 ),
inference(superposition,[],[f110,f165]) ).
fof(f1235,plain,
( ! [X0] :
( sk_c11 != multiply(sk_c10,sk_c10)
| inverse(X0) != multiply(X0,sk_c10)
| sk_c10 != inverse(inverse(X0))
| sk_c11 != multiply(sk_c2,sk_c10) )
| ~ spl0_1
| ~ spl0_8 ),
inference(superposition,[],[f110,f135]) ).
fof(f1238,plain,
( ! [X0] :
( sk_c11 != multiply(sk_c10,sk_c10)
| inverse(X0) != multiply(X0,sk_c10)
| sk_c10 != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_8
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[],[f1235,f185]) ).
fof(f1243,plain,
( ! [X0] :
( sk_c10 != sk_c11
| sk_c11 != multiply(sk_c10,sk_c10)
| inverse(X0) != multiply(X0,sk_c10)
| sk_c10 != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_14
| ~ spl0_15
| ~ spl0_30 ),
inference(forward_demodulation,[],[f1230,f962]) ).
fof(f1247,plain,
( spl0_35
| ~ spl0_36
| ~ spl0_1
| ~ spl0_8
| ~ spl0_18 ),
inference(avatar_split_clause,[],[f1238,f183,f133,f109,f1089,f1086]) ).
fof(f1251,plain,
( spl0_35
| ~ spl0_36
| ~ spl0_25
| ~ spl0_1
| ~ spl0_14
| ~ spl0_15
| ~ spl0_30 ),
inference(avatar_split_clause,[],[f1243,f535,f168,f163,f109,f493,f1089,f1086]) ).
fof(f1307,plain,
( sk_c10 != inverse(sk_c11)
| sk_c11 != multiply(sk_c11,sk_c10)
| ~ spl0_8
| ~ spl0_18
| ~ spl0_28
| ~ spl0_35 ),
inference(superposition,[],[f1087,f891]) ).
fof(f1309,plain,
( sk_c10 != inverse(sk_c10)
| sk_c10 != multiply(sk_c4,sk_c10)
| ~ spl0_14
| ~ spl0_35 ),
inference(superposition,[],[f1087,f165]) ).
fof(f1314,plain,
( sk_c10 != inverse(sk_c10)
| sk_c10 != multiply(sk_c2,sk_c10)
| ~ spl0_8
| ~ spl0_35 ),
inference(superposition,[],[f1087,f135]) ).
fof(f1315,plain,
( sk_c10 != sk_c11
| sk_c10 != multiply(sk_c2,sk_c10)
| ~ spl0_8
| ~ spl0_29
| ~ spl0_35 ),
inference(forward_demodulation,[],[f1314,f532]) ).
fof(f1320,plain,
( sk_c10 != inverse(sk_c10)
| ~ spl0_14
| ~ spl0_15
| ~ spl0_30
| ~ spl0_35 ),
inference(forward_subsumption_resolution,[],[f1309,f962]) ).
fof(f1322,plain,
( sk_c10 != sk_c11
| sk_c11 != multiply(sk_c11,sk_c10)
| ~ spl0_8
| ~ spl0_18
| ~ spl0_28
| ~ spl0_35 ),
inference(forward_demodulation,[],[f1307,f891]) ).
fof(f1324,plain,
( sk_c10 != multiply(sk_c2,sk_c10)
| ~ spl0_8
| ~ spl0_25
| ~ spl0_29
| ~ spl0_35 ),
inference(forward_subsumption_resolution,[],[f1315,f494]) ).
fof(f1329,plain,
( sk_c10 != sk_c11
| ~ spl0_14
| ~ spl0_15
| ~ spl0_29
| ~ spl0_30
| ~ spl0_35 ),
inference(forward_demodulation,[],[f1320,f532]) ).
fof(f1331,plain,
( sk_c11 != multiply(sk_c11,sk_c10)
| ~ spl0_8
| ~ spl0_18
| ~ spl0_25
| ~ spl0_28
| ~ spl0_35 ),
inference(forward_subsumption_resolution,[],[f1322,f494]) ).
fof(f1333,plain,
( sk_c10 != sk_c11
| ~ spl0_8
| ~ spl0_18
| ~ spl0_25
| ~ spl0_29
| ~ spl0_35 ),
inference(forward_demodulation,[],[f1324,f185]) ).
fof(f1339,plain,
( $false
| ~ spl0_14
| ~ spl0_15
| ~ spl0_25
| ~ spl0_29
| ~ spl0_30
| ~ spl0_35 ),
inference(forward_subsumption_resolution,[],[f1329,f494]) ).
fof(f1340,plain,
( ~ spl0_14
| ~ spl0_15
| ~ spl0_25
| ~ spl0_29
| ~ spl0_30
| ~ spl0_35 ),
inference(avatar_contradiction_clause,[],[f1339]) ).
fof(f1342,plain,
( sk_c10 != multiply(sk_c10,sk_c10)
| ~ spl0_8
| ~ spl0_18
| ~ spl0_25
| ~ spl0_28
| ~ spl0_35 ),
inference(forward_demodulation,[],[f1331,f494]) ).
fof(f1345,plain,
( $false
| ~ spl0_8
| ~ spl0_18
| ~ spl0_25
| ~ spl0_29
| ~ spl0_35 ),
inference(forward_subsumption_resolution,[],[f1333,f494]) ).
fof(f1346,plain,
( ~ spl0_8
| ~ spl0_18
| ~ spl0_25
| ~ spl0_29
| ~ spl0_35 ),
inference(avatar_contradiction_clause,[],[f1345]) ).
fof(f1352,plain,
( sk_c10 != sk_c11
| ~ spl0_8
| ~ spl0_18
| ~ spl0_25
| ~ spl0_28
| ~ spl0_35
| ~ spl0_36 ),
inference(forward_demodulation,[],[f1342,f1090]) ).
fof(f1357,plain,
( $false
| ~ spl0_8
| ~ spl0_18
| ~ spl0_25
| ~ spl0_28
| ~ spl0_35
| ~ spl0_36 ),
inference(forward_subsumption_resolution,[],[f1352,f494]) ).
fof(f1358,plain,
( ~ spl0_8
| ~ spl0_18
| ~ spl0_25
| ~ spl0_28
| ~ spl0_35
| ~ spl0_36 ),
inference(avatar_contradiction_clause,[],[f1357]) ).
fof(f1377,plain,
( sk_c10 != multiply(sk_c10,sk_c10)
| ~ spl0_25
| spl0_36 ),
inference(forward_demodulation,[],[f1091,f494]) ).
fof(f1396,plain,
( ~ spl0_32
| ~ spl0_25
| spl0_36 ),
inference(avatar_split_clause,[],[f1377,f1089,f493,f718]) ).
fof(f1430,plain,
( spl0_30
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(avatar_split_clause,[],[f384,f178,f173,f168,f163,f535]) ).
fof(f1455,plain,
( sk_c10 = sk_c9
| ~ spl0_14
| ~ spl0_15
| ~ spl0_27 ),
inference(forward_demodulation,[],[f381,f516]) ).
fof(f1486,plain,
( spl0_30
| ~ spl0_14
| ~ spl0_15
| ~ spl0_27 ),
inference(avatar_split_clause,[],[f1455,f515,f168,f163,f535]) ).
fof(f1522,plain,
( ~ spl0_8
| ~ spl0_25
| ~ spl0_2
| ~ spl0_18
| ~ spl0_30 ),
inference(avatar_split_clause,[],[f1174,f535,f183,f112,f493,f133]) ).
fof(f1573,plain,
( identity = multiply(sk_c10,sk_c10)
| ~ spl0_33 ),
inference(superposition,[],[f3,f736]) ).
fof(f1574,plain,
( sk_c11 = multiply(sk_c10,sk_c10)
| ~ spl0_12
| ~ spl0_13
| ~ spl0_33 ),
inference(forward_demodulation,[],[f1573,f361]) ).
fof(f1579,plain,
( spl0_36
| ~ spl0_12
| ~ spl0_13
| ~ spl0_33 ),
inference(avatar_split_clause,[],[f1574,f735,f158,f153,f1089]) ).
fof(f1715,plain,
( sk_c10 = multiply(inverse(sk_c10),sk_c10)
| ~ spl0_32 ),
inference(superposition,[],[f247,f719]) ).
fof(f1718,plain,
( identity = sk_c10
| ~ spl0_32 ),
inference(forward_demodulation,[],[f1715,f3]) ).
fof(f1728,plain,
( $false
| spl0_27
| ~ spl0_32 ),
inference(forward_subsumption_resolution,[],[f1718,f517]) ).
fof(f1729,plain,
( spl0_27
| ~ spl0_32 ),
inference(avatar_contradiction_clause,[],[f1728]) ).
cnf(s1,plain,
( spl0_1
| spl0_2
| spl0_3
| spl0_4
| spl0_5
| ~ spl0_6 ),
inference(sat_conversion,[],[f127]) ).
cnf(s6,plain,
( spl0_8
| spl0_12 ),
inference(sat_conversion,[],[f156]) ).
cnf(s7,plain,
( spl0_8
| spl0_13 ),
inference(sat_conversion,[],[f161]) ).
cnf(s8,plain,
( spl0_8
| spl0_14 ),
inference(sat_conversion,[],[f166]) ).
cnf(s9,plain,
( spl0_8
| spl0_15 ),
inference(sat_conversion,[],[f171]) ).
cnf(s10,plain,
( spl0_8
| spl0_16 ),
inference(sat_conversion,[],[f176]) ).
cnf(s11,plain,
( spl0_8
| spl0_17 ),
inference(sat_conversion,[],[f181]) ).
cnf(s16,plain,
( spl0_12
| spl0_18 ),
inference(sat_conversion,[],[f190]) ).
cnf(s17,plain,
( spl0_13
| spl0_18 ),
inference(sat_conversion,[],[f191]) ).
cnf(s18,plain,
( spl0_14
| spl0_18 ),
inference(sat_conversion,[],[f192]) ).
cnf(s19,plain,
( spl0_15
| spl0_18 ),
inference(sat_conversion,[],[f193]) ).
cnf(s20,plain,
( spl0_16
| spl0_18 ),
inference(sat_conversion,[],[f194]) ).
cnf(s21,plain,
( spl0_17
| spl0_18 ),
inference(sat_conversion,[],[f195]) ).
cnf(s28,plain,
( spl0_14
| spl0_19 ),
inference(sat_conversion,[],[f206]) ).
cnf(s29,plain,
( spl0_15
| spl0_19 ),
inference(sat_conversion,[],[f207]) ).
cnf(s36,plain,
( spl0_12
| spl0_20 ),
inference(sat_conversion,[],[f218]) ).
cnf(s37,plain,
( spl0_13
| spl0_20 ),
inference(sat_conversion,[],[f219]) ).
cnf(s38,plain,
( spl0_14
| spl0_20 ),
inference(sat_conversion,[],[f220]) ).
cnf(s39,plain,
( spl0_15
| spl0_20 ),
inference(sat_conversion,[],[f221]) ).
cnf(s40,plain,
( spl0_16
| spl0_20 ),
inference(sat_conversion,[],[f222]) ).
cnf(s41,plain,
( spl0_17
| spl0_20 ),
inference(sat_conversion,[],[f223]) ).
cnf(s46,plain,
( spl0_6
| spl0_12 ),
inference(sat_conversion,[],[f228]) ).
cnf(s47,plain,
( spl0_6
| spl0_13 ),
inference(sat_conversion,[],[f229]) ).
cnf(s48,plain,
( spl0_6
| spl0_14 ),
inference(sat_conversion,[],[f230]) ).
cnf(s49,plain,
( spl0_6
| spl0_15 ),
inference(sat_conversion,[],[f231]) ).
cnf(s50,plain,
( spl0_6
| spl0_16 ),
inference(sat_conversion,[],[f232]) ).
cnf(s51,plain,
( spl0_6
| spl0_17 ),
inference(sat_conversion,[],[f233]) ).
cnf(s52,plain,
( spl0_6
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(sat_conversion,[],[f415]) ).
cnf(s61,plain,
( ~ spl0_3
| ~ spl0_16
| ~ spl0_17 ),
inference(sat_conversion,[],[f509]) ).
cnf(s65,plain,
( ~ spl0_6
| ~ spl0_8
| ~ spl0_18
| spl0_30 ),
inference(sat_conversion,[],[f573]) ).
cnf(s69,plain,
( ~ spl0_8
| ~ spl0_14
| ~ spl0_15
| ~ spl0_18
| spl0_25
| ~ spl0_30 ),
inference(sat_conversion,[],[f585]) ).
cnf(s76,plain,
( ~ spl0_3
| ~ spl0_18
| ~ spl0_25
| ~ spl0_32
| ~ spl0_33 ),
inference(sat_conversion,[],[f754]) ).
cnf(s85,plain,
( ~ spl0_8
| ~ spl0_18
| ~ spl0_20
| spl0_28 ),
inference(sat_conversion,[],[f890]) ).
cnf(s87,plain,
( ~ spl0_3
| ~ spl0_8
| ~ spl0_18
| ~ spl0_19
| ~ spl0_20
| ~ spl0_28 ),
inference(sat_conversion,[],[f946]) ).
cnf(s88,plain,
( ~ spl0_6
| ~ spl0_19
| ~ spl0_20
| ~ spl0_30
| spl0_32 ),
inference(sat_conversion,[],[f951]) ).
cnf(s94,plain,
( ~ spl0_14
| ~ spl0_15
| ~ spl0_30
| spl0_32 ),
inference(sat_conversion,[],[f966]) ).
cnf(s98,plain,
( ~ spl0_6
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17
| spl0_25 ),
inference(sat_conversion,[],[f977]) ).
cnf(s100,plain,
( ~ spl0_14
| ~ spl0_16
| ~ spl0_17
| spl0_33 ),
inference(sat_conversion,[],[f983]) ).
cnf(s101,plain,
( ~ spl0_16
| ~ spl0_17
| spl0_27 ),
inference(sat_conversion,[],[f984]) ).
cnf(s105,plain,
( ~ spl0_6
| ~ spl0_8
| ~ spl0_18
| ~ spl0_25
| ~ spl0_30
| spl0_33 ),
inference(sat_conversion,[],[f994]) ).
cnf(s115,plain,
( ~ spl0_8
| ~ spl0_14
| ~ spl0_15
| ~ spl0_18
| ~ spl0_20
| spl0_25
| ~ spl0_30 ),
inference(sat_conversion,[],[f1000]) ).
cnf(s116,plain,
( ~ spl0_8
| ~ spl0_18
| spl0_25
| ~ spl0_27 ),
inference(sat_conversion,[],[f1014]) ).
cnf(s122,plain,
( ~ spl0_4
| ~ spl0_8
| ~ spl0_18 ),
inference(sat_conversion,[],[f1046]) ).
cnf(s124,plain,
( ~ spl0_4
| ~ spl0_14
| ~ spl0_15
| ~ spl0_25
| ~ spl0_30 ),
inference(sat_conversion,[],[f1054]) ).
cnf(s141,plain,
( ~ spl0_5
| ~ spl0_14
| ~ spl0_15
| ~ spl0_25
| ~ spl0_30 ),
inference(sat_conversion,[],[f1159]) ).
cnf(s143,plain,
( ~ spl0_5
| ~ spl0_8
| ~ spl0_18
| ~ spl0_25
| ~ spl0_28 ),
inference(sat_conversion,[],[f1162]) ).
cnf(s144,plain,
( ~ spl0_12
| ~ spl0_13
| ~ spl0_16
| ~ spl0_17
| spl0_29 ),
inference(sat_conversion,[],[f1167]) ).
cnf(s145,plain,
( ~ spl0_2
| ~ spl0_14
| ~ spl0_15
| ~ spl0_30 ),
inference(sat_conversion,[],[f1182]) ).
cnf(s172,plain,
( ~ spl0_1
| ~ spl0_8
| ~ spl0_18
| spl0_35
| ~ spl0_36 ),
inference(sat_conversion,[],[f1247]) ).
cnf(s174,plain,
( ~ spl0_1
| ~ spl0_14
| ~ spl0_15
| ~ spl0_25
| ~ spl0_30
| spl0_35
| ~ spl0_36 ),
inference(sat_conversion,[],[f1251]) ).
cnf(s185,plain,
( ~ spl0_14
| ~ spl0_15
| ~ spl0_25
| ~ spl0_29
| ~ spl0_30
| ~ spl0_35 ),
inference(sat_conversion,[],[f1340]) ).
cnf(s187,plain,
( ~ spl0_8
| ~ spl0_18
| ~ spl0_25
| ~ spl0_29
| ~ spl0_35 ),
inference(sat_conversion,[],[f1346]) ).
cnf(s190,plain,
( ~ spl0_8
| ~ spl0_18
| ~ spl0_25
| ~ spl0_28
| ~ spl0_35
| ~ spl0_36 ),
inference(sat_conversion,[],[f1358]) ).
cnf(s203,plain,
( ~ spl0_25
| ~ spl0_32
| spl0_36 ),
inference(sat_conversion,[],[f1396]) ).
cnf(s217,plain,
( ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17
| spl0_30 ),
inference(sat_conversion,[],[f1430]) ).
cnf(s232,plain,
( ~ spl0_14
| ~ spl0_15
| ~ spl0_27
| spl0_30 ),
inference(sat_conversion,[],[f1486]) ).
cnf(s254,plain,
( ~ spl0_2
| ~ spl0_8
| ~ spl0_18
| ~ spl0_25
| ~ spl0_30 ),
inference(sat_conversion,[],[f1522]) ).
cnf(s268,plain,
( ~ spl0_12
| ~ spl0_13
| ~ spl0_33
| spl0_36 ),
inference(sat_conversion,[],[f1579]) ).
cnf(s281,plain,
( spl0_27
| ~ spl0_32 ),
inference(sat_conversion,[],[f1729]) ).
cnf(s286,plain,
spl0_6,
inference(rat,[],[s52,s46,s47,s48,s49,s50,s51]) ).
cnf(s287,plain,
( spl0_8
| ~ spl0_5 ),
inference(rat,[],[s98,s141,s232,s101,s8,s9,s10,s11,s286]) ).
cnf(s288,plain,
( ~ spl0_17
| ~ spl0_16
| ~ spl0_15
| ~ spl0_14
| ~ spl0_5 ),
inference(rat,[],[s141,s98,s217,s286]) ).
cnf(s289,plain,
( spl0_17
| ~ spl0_15
| ~ spl0_14
| ~ spl0_5 ),
inference(rat,[],[s115,s143,s65,s85,s21,s41,s287,s286]) ).
cnf(s290,plain,
( ~ spl0_15
| ~ spl0_14
| ~ spl0_5 ),
inference(rat,[],[s115,s143,s65,s85,s20,s40,s288,s289,s287,s286]) ).
cnf(s291,plain,
( spl0_15
| ~ spl0_5 ),
inference(rat,[],[s281,s116,s88,s143,s65,s85,s19,s29,s39,s287,s286]) ).
cnf(s292,plain,
~ spl0_5,
inference(rat,[],[s281,s116,s88,s143,s65,s85,s18,s28,s38,s290,s291,s287,s286]) ).
cnf(s293,plain,
( spl0_18
| spl0_30
| ~ spl0_15
| ~ spl0_14 ),
inference(rat,[],[s217,s20,s21]) ).
cnf(s294,plain,
( spl0_30
| ~ spl0_15
| ~ spl0_14 ),
inference(rat,[],[s217,s10,s11,s65,s293,s286]) ).
cnf(s295,plain,
( spl0_18
| spl0_25
| ~ spl0_15
| ~ spl0_14 ),
inference(rat,[],[s98,s20,s21,s286]) ).
cnf(s296,plain,
( ~ spl0_30
| ~ spl0_15
| ~ spl0_4
| ~ spl0_14 ),
inference(rat,[],[s98,s10,s11,s122,s295,s124,s286]) ).
cnf(s297,plain,
( ~ spl0_15
| ~ spl0_14
| ~ spl0_4 ),
inference(rat,[],[s296,s294]) ).
cnf(s298,plain,
( spl0_15
| ~ spl0_4 ),
inference(rat,[],[s122,s9,s19]) ).
cnf(s299,plain,
( ~ spl0_15
| ~ spl0_4 ),
inference(rat,[],[s122,s8,s18,s297]) ).
cnf(s300,plain,
~ spl0_4,
inference(rat,[],[s299,s298]) ).
cnf(s301,plain,
( spl0_18
| ~ spl0_3 ),
inference(rat,[],[s61,s20,s21]) ).
cnf(s302,plain,
( ~ spl0_8
| ~ spl0_15
| ~ spl0_14
| ~ spl0_3 ),
inference(rat,[],[s105,s76,s69,s301,s94,s294,s286]) ).
cnf(s303,plain,
( spl0_8
| ~ spl0_3 ),
inference(rat,[],[s61,s10,s11]) ).
cnf(s304,plain,
( spl0_15
| ~ spl0_3 ),
inference(rat,[],[s87,s85,s29,s39,s301,s303]) ).
cnf(s305,plain,
~ spl0_3,
inference(rat,[],[s87,s85,s28,s38,s302,s304,s303,s301]) ).
cnf(s306,plain,
( ~ spl0_15
| ~ spl0_14
| ~ spl0_2 ),
inference(rat,[],[s294,s145]) ).
cnf(s307,plain,
( spl0_15
| ~ spl0_2 ),
inference(rat,[],[s281,s116,s88,s254,s65,s9,s19,s29,s39,s286]) ).
cnf(s308,plain,
( ~ spl0_15
| ~ spl0_2 ),
inference(rat,[],[s281,s116,s88,s254,s65,s8,s18,s28,s38,s306,s286]) ).
cnf(s309,plain,
~ spl0_2,
inference(rat,[],[s308,s307]) ).
cnf(s310,plain,
spl0_1,
inference(rat,[],[s1,s286,s300,s292,s305,s309]) ).
cnf(s311,plain,
( ~ spl0_35
| ~ spl0_25
| ~ spl0_18
| ~ spl0_36
| ~ spl0_8 ),
inference(rat,[],[s144,s36,s37,s40,s41,s85,s187,s190]) ).
cnf(s312,plain,
( ~ spl0_18
| ~ spl0_8
| ~ spl0_15
| ~ spl0_14 ),
inference(rat,[],[s311,s174,s203,s69,s94,s294,s310]) ).
cnf(s313,plain,
( spl0_18
| ~ spl0_15
| ~ spl0_14 ),
inference(rat,[],[s185,s174,s144,s268,s100,s295,s16,s17,s20,s21,s294,s310]) ).
cnf(s314,plain,
( ~ spl0_15
| ~ spl0_14 ),
inference(rat,[],[s185,s174,s144,s268,s98,s100,s6,s7,s10,s11,s312,s313,s294,s286,s310]) ).
cnf(s315,plain,
( ~ spl0_25
| ~ spl0_8
| ~ spl0_18
| ~ spl0_36 ),
inference(rat,[],[s172,s311,s310]) ).
cnf(s316,plain,
spl0_15,
inference(rat,[],[s315,s203,s116,s281,s88,s65,s9,s19,s29,s39,s286]) ).
cnf(s317,plain,
~ spl0_14,
inference(rat,[],[s314,s316]) ).
cnf(s318,plain,
spl0_20,
inference(rat,[],[s38,s317]) ).
cnf(s319,plain,
spl0_19,
inference(rat,[],[s28,s317]) ).
cnf(s320,plain,
spl0_18,
inference(rat,[],[s18,s317]) ).
cnf(s321,plain,
spl0_8,
inference(rat,[],[s8,s317]) ).
cnf(s325,plain,
spl0_30,
inference(rat,[],[s65,s320,s286,s321]) ).
cnf(s328,plain,
spl0_32,
inference(rat,[],[s88,s318,s319,s286,s325]) ).
cnf(s329,plain,
spl0_27,
inference(rat,[],[s281,s328]) ).
cnf(s330,plain,
spl0_25,
inference(rat,[],[s116,s321,s320,s329]) ).
cnf(s332,plain,
spl0_36,
inference(rat,[],[s203,s328,s330]) ).
cnf(s333,plain,
$false,
inference(rat,[],[s315,s321,s320,s332,s330]) ).
fof(f1734,plain,
$false,
inference(avatar_sat_refutation,[],[s333]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP338-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.40 % Computer : n009.cluster.edu
% 0.11/0.40 % Model : x86_64 x86_64
% 0.11/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.40 % Memory : 8046.5625MB
% 0.11/0.40 % OS : Linux 6.8.0-71-generic
% 0.11/0.40 % CPULimit : 300
% 0.11/0.40 % WCLimit : 300
% 0.11/0.40 % DateTime : Sun Sep 27 09:54:15 UTC 2026
% 0.11/0.40 % CPUTime :
% 0.11/0.40 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.44 Running first-order theorem proving
% 0.11/0.44 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.75/1.35 % (1786051)Input is clausal, will run a generic CNF schedule.
% 2.75/1.35 % (1786060)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1252781405:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.75/1.35 % (1786060)Instruction limit reached!
% 2.75/1.35 % (1786060)------------------------------
% 2.75/1.35 % (1786060)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.75/1.35 % (1786060)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.75/1.35 % (1786060)CaDiCaL version: 2.1.3
% 2.75/1.35 % (1786060)Termination reason: Instruction limit
% 2.75/1.35 % (1786060)Termination phase: Saturation
% 2.75/1.35 % (1786060)Time elapsed: 0.036 s
% 2.75/1.35 % (1786060)Peak memory usage: 89 MB
% 2.75/1.35 % (1786060)Instructions burned: 115 (million)
% 2.75/1.35 % (1786056)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=3337502123:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.75/1.35 % (1786058)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=3373976564:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.75/1.35 % (1786057)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=1154091327:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.75/1.35 % (1786059)lrs+10_1_sil=8000:sp=occurrence:random_seed=1705951605:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.75/1.35 % (1786059)Refutation not found, incomplete strategy
% 2.75/1.35 % (1786059)------------------------------
% 2.75/1.35 % (1786059)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.75/1.35 % (1786059)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.75/1.35 % (1786059)CaDiCaL version: 2.1.3
% 2.75/1.35 % (1786059)Termination reason: Refutation not found, incomplete strategy
% 2.75/1.35 % (1786059)Time elapsed: 0.004 s
% 2.75/1.35 % (1786059)Peak memory usage: 88 MB
% 2.75/1.35 % (1786059)Instructions burned: 5 (million)
% 2.75/1.35 % (1786061)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=4111991125:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.75/1.35 % (1786062)dis-21_1_sil=8000:lcm=predicate:random_seed=1093561795: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)
% 2.75/1.35 % (1786062)Refutation not found, incomplete strategy
% 2.75/1.35 % (1786062)------------------------------
% 2.75/1.35 % (1786062)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.75/1.35 % (1786062)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.75/1.35 % (1786062)CaDiCaL version: 2.1.3
% 2.75/1.35 % (1786062)Termination reason: Refutation not found, incomplete strategy
% 2.75/1.35 % (1786062)Time elapsed: 0.002 s
% 2.75/1.35 % (1786062)Peak memory usage: 88 MB
% 2.75/1.35 % (1786062)Instructions burned: 2 (million)
% 2.75/1.35 % (1786061)First to succeed.
% 2.75/1.35 % (1786061)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1786051"
% 2.75/1.35 % (1786068)dis+1010_3_sil=8000:plsq=on:drc=off:fde=none:plsqc=1:bsd=on:plsqr=7,2:sos=on:spb=goal_then_units:random_seed=1825602441:i=143:sd=2:aac=none:ss=axioms:sgt=16_2998 on theBenchmark for (2998ds/143Mi)
% 2.75/1.35 % (1786068)Refutation not found, incomplete strategy
% 2.75/1.35 % (1786068)------------------------------
% 2.75/1.35 % (1786068)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.75/1.35 % (1786068)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.75/1.35 % (1786068)CaDiCaL version: 2.1.3
% 2.75/1.35 % (1786068)Termination reason: Refutation not found, incomplete strategy
% 2.75/1.35 % (1786068)Time elapsed: 0.002 s
% 2.75/1.35 % (1786068)Peak memory usage: 88 MB
% 2.75/1.35 % (1786068)Instructions burned: 5 (million)
% 2.75/1.35 % (1786059)------------------------------
% 2.75/1.35 % (1786059)------------------------------
% 2.75/1.35 % (1786062)------------------------------
% 2.75/1.35 % (1786062)------------------------------
% 2.75/1.35 % (1786068)------------------------------
% 2.75/1.35 % (1786068)------------------------------
% 2.75/1.35 % (1786061)Refutation found. Thanks to Tanya!
% 2.75/1.35 % SZS status Unsatisfiable for theBenchmark
% 2.75/1.35 % SZS output start Proof for theBenchmark
% See solution above
% 3.91/1.54 % (1786061)------------------------------
% 3.91/1.54 % (1786061)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.91/1.54 % (1786061)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.91/1.54 % (1786061)CaDiCaL version: 2.1.3
% 3.91/1.54 % (1786061)Termination reason: Refutation
% 3.91/1.54 % (1786061)Time elapsed: 0.036 s
% 3.91/1.54 % (1786061)Peak memory usage: 90 MB
% 3.91/1.54 % (1786061)Instructions burned: 57 (million)
% 3.91/1.54 % (1786061)------------------------------
% 3.91/1.54 % (1786061)------------------------------
% 3.91/1.54 % (1786051)Success in time 0.466 s
% 3.91/1.54 % Vampire exiting
%------------------------------------------------------------------------------