%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP238-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n026.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 10:13:24 AM UTC 2026
% Result : Unsatisfiable 3.28s 1.33s
% Output : Refutation 3.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 65
% Syntax : Number of formulae : 390 ( 24 unt; 29 def)
% Number of atoms : 1182 ( 390 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 1483 ( 691 ~; 763 |; 0 &)
% ( 29 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 26 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 31 ( 29 usr; 30 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 12 con; 0-2 aty)
% Number of variables : 78 ( 0 sgn 78 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_identity) ).
fof(f2,axiom,
! [X0] : multiply(inverse(X0),X0) = identity,
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',associativity) ).
fof(f5,negated_conjecture,
( inverse(sk_c11) = sk_c10
| multiply(sk_c4,sk_c5) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,plain,
( inverse(sk_c11) = sk_c10
| sk_c11 = multiply(sk_c4,sk_c5) ),
inference(reorient_equations,[],[f5]) ).
fof(f7,negated_conjecture,
( inverse(sk_c11) = sk_c10
| inverse(sk_c4) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_2) ).
fof(f8,plain,
( inverse(sk_c11) = sk_c10
| sk_c5 = inverse(sk_c4) ),
inference(reorient_equations,[],[f7]) ).
fof(f11,negated_conjecture,
( inverse(sk_c11) = sk_c10
| inverse(sk_c6) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_4) ).
fof(f12,plain,
( inverse(sk_c11) = sk_c10
| sk_c11 = inverse(sk_c6) ),
inference(reorient_equations,[],[f11]) ).
fof(f13,negated_conjecture,
( inverse(sk_c11) = sk_c10
| multiply(sk_c6,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_5) ).
fof(f14,plain,
( inverse(sk_c11) = sk_c10
| sk_c11 = multiply(sk_c6,sk_c10) ),
inference(reorient_equations,[],[f13]) ).
fof(f15,negated_conjecture,
( inverse(sk_c11) = sk_c10
| multiply(sk_c7,sk_c8) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_6) ).
fof(f16,plain,
( inverse(sk_c11) = sk_c10
| sk_c10 = multiply(sk_c7,sk_c8) ),
inference(reorient_equations,[],[f15]) ).
fof(f17,negated_conjecture,
( inverse(sk_c11) = sk_c10
| inverse(sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_7) ).
fof(f18,plain,
( inverse(sk_c11) = sk_c10
| sk_c8 = inverse(sk_c7) ),
inference(reorient_equations,[],[f17]) ).
fof(f19,negated_conjecture,
( inverse(sk_c11) = sk_c10
| multiply(sk_c8,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_8) ).
fof(f20,plain,
( inverse(sk_c11) = sk_c10
| sk_c10 = multiply(sk_c8,sk_c11) ),
inference(reorient_equations,[],[f19]) ).
fof(f29,negated_conjecture,
( inverse(sk_c1) = sk_c11
| multiply(sk_c5,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_13) ).
fof(f30,plain,
( sk_c11 = inverse(sk_c1)
| sk_c11 = multiply(sk_c5,sk_c10) ),
inference(reorient_equations,[],[f29]) ).
fof(f35,negated_conjecture,
( inverse(sk_c1) = sk_c11
| multiply(sk_c7,sk_c8) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_16) ).
fof(f36,plain,
( sk_c11 = inverse(sk_c1)
| sk_c10 = multiply(sk_c7,sk_c8) ),
inference(reorient_equations,[],[f35]) ).
fof(f37,negated_conjecture,
( inverse(sk_c1) = sk_c11
| inverse(sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_17) ).
fof(f38,plain,
( sk_c11 = inverse(sk_c1)
| sk_c8 = inverse(sk_c7) ),
inference(reorient_equations,[],[f37]) ).
fof(f39,negated_conjecture,
( inverse(sk_c1) = sk_c11
| multiply(sk_c8,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_18) ).
fof(f40,plain,
( sk_c11 = inverse(sk_c1)
| sk_c10 = multiply(sk_c8,sk_c11) ),
inference(reorient_equations,[],[f39]) ).
fof(f49,negated_conjecture,
( multiply(sk_c1,sk_c10) = sk_c11
| multiply(sk_c5,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_23) ).
fof(f50,plain,
( sk_c11 = multiply(sk_c1,sk_c10)
| sk_c11 = multiply(sk_c5,sk_c10) ),
inference(reorient_equations,[],[f49]) ).
fof(f55,negated_conjecture,
( multiply(sk_c1,sk_c10) = sk_c11
| multiply(sk_c7,sk_c8) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_26) ).
fof(f56,plain,
( sk_c11 = multiply(sk_c1,sk_c10)
| sk_c10 = multiply(sk_c7,sk_c8) ),
inference(reorient_equations,[],[f55]) ).
fof(f57,negated_conjecture,
( multiply(sk_c1,sk_c10) = sk_c11
| inverse(sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_27) ).
fof(f58,plain,
( sk_c11 = multiply(sk_c1,sk_c10)
| sk_c8 = inverse(sk_c7) ),
inference(reorient_equations,[],[f57]) ).
fof(f59,negated_conjecture,
( multiply(sk_c1,sk_c10) = sk_c11
| multiply(sk_c8,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_28) ).
fof(f60,plain,
( sk_c11 = multiply(sk_c1,sk_c10)
| sk_c10 = multiply(sk_c8,sk_c11) ),
inference(reorient_equations,[],[f59]) ).
fof(f75,negated_conjecture,
( multiply(sk_c11,sk_c3) = sk_c10
| multiply(sk_c7,sk_c8) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_36) ).
fof(f76,plain,
( sk_c10 = multiply(sk_c11,sk_c3)
| sk_c10 = multiply(sk_c7,sk_c8) ),
inference(reorient_equations,[],[f75]) ).
fof(f77,negated_conjecture,
( multiply(sk_c11,sk_c3) = sk_c10
| inverse(sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_37) ).
fof(f78,plain,
( sk_c10 = multiply(sk_c11,sk_c3)
| sk_c8 = inverse(sk_c7) ),
inference(reorient_equations,[],[f77]) ).
fof(f81,negated_conjecture,
( multiply(sk_c11,sk_c3) = sk_c10
| inverse(sk_c9) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_39) ).
fof(f82,plain,
( sk_c10 = multiply(sk_c11,sk_c3)
| sk_c10 = inverse(sk_c9) ),
inference(reorient_equations,[],[f81]) ).
fof(f83,negated_conjecture,
( multiply(sk_c11,sk_c3) = sk_c10
| multiply(sk_c9,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_40) ).
fof(f84,plain,
( sk_c10 = multiply(sk_c11,sk_c3)
| sk_c10 = multiply(sk_c9,sk_c11) ),
inference(reorient_equations,[],[f83]) ).
fof(f95,negated_conjecture,
( multiply(sk_c2,sk_c11) = sk_c3
| multiply(sk_c7,sk_c8) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_46) ).
fof(f96,plain,
( sk_c3 = multiply(sk_c2,sk_c11)
| sk_c10 = multiply(sk_c7,sk_c8) ),
inference(reorient_equations,[],[f95]) ).
fof(f97,negated_conjecture,
( multiply(sk_c2,sk_c11) = sk_c3
| inverse(sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_47) ).
fof(f98,plain,
( sk_c3 = multiply(sk_c2,sk_c11)
| sk_c8 = inverse(sk_c7) ),
inference(reorient_equations,[],[f97]) ).
fof(f101,negated_conjecture,
( multiply(sk_c2,sk_c11) = sk_c3
| inverse(sk_c9) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_49) ).
fof(f102,plain,
( sk_c3 = multiply(sk_c2,sk_c11)
| sk_c10 = inverse(sk_c9) ),
inference(reorient_equations,[],[f101]) ).
fof(f103,negated_conjecture,
( multiply(sk_c2,sk_c11) = sk_c3
| multiply(sk_c9,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_50) ).
fof(f104,plain,
( sk_c3 = multiply(sk_c2,sk_c11)
| sk_c10 = multiply(sk_c9,sk_c11) ),
inference(reorient_equations,[],[f103]) ).
fof(f105,negated_conjecture,
( inverse(sk_c2) = sk_c11
| multiply(sk_c4,sk_c5) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_51) ).
fof(f106,plain,
( sk_c11 = inverse(sk_c2)
| sk_c11 = multiply(sk_c4,sk_c5) ),
inference(reorient_equations,[],[f105]) ).
fof(f107,negated_conjecture,
( inverse(sk_c2) = sk_c11
| inverse(sk_c4) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_52) ).
fof(f108,plain,
( sk_c11 = inverse(sk_c2)
| sk_c5 = inverse(sk_c4) ),
inference(reorient_equations,[],[f107]) ).
fof(f111,negated_conjecture,
( inverse(sk_c2) = sk_c11
| inverse(sk_c6) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_54) ).
fof(f112,plain,
( sk_c11 = inverse(sk_c2)
| sk_c11 = inverse(sk_c6) ),
inference(reorient_equations,[],[f111]) ).
fof(f113,negated_conjecture,
( inverse(sk_c2) = sk_c11
| multiply(sk_c6,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_55) ).
fof(f114,plain,
( sk_c11 = inverse(sk_c2)
| sk_c11 = multiply(sk_c6,sk_c10) ),
inference(reorient_equations,[],[f113]) ).
fof(f115,negated_conjecture,
( inverse(sk_c2) = sk_c11
| multiply(sk_c7,sk_c8) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_56) ).
fof(f116,plain,
( sk_c11 = inverse(sk_c2)
| sk_c10 = multiply(sk_c7,sk_c8) ),
inference(reorient_equations,[],[f115]) ).
fof(f117,negated_conjecture,
( inverse(sk_c2) = sk_c11
| inverse(sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_57) ).
fof(f118,plain,
( sk_c11 = inverse(sk_c2)
| sk_c8 = inverse(sk_c7) ),
inference(reorient_equations,[],[f117]) ).
fof(f119,negated_conjecture,
( inverse(sk_c2) = sk_c11
| multiply(sk_c8,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_58) ).
fof(f120,plain,
( sk_c11 = inverse(sk_c2)
| sk_c10 = multiply(sk_c8,sk_c11) ),
inference(reorient_equations,[],[f119]) ).
fof(f121,negated_conjecture,
( inverse(sk_c2) = sk_c11
| inverse(sk_c9) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_59) ).
fof(f122,plain,
( sk_c11 = inverse(sk_c2)
| sk_c10 = inverse(sk_c9) ),
inference(reorient_equations,[],[f121]) ).
fof(f123,negated_conjecture,
( inverse(sk_c2) = sk_c11
| multiply(sk_c9,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_60) ).
fof(f124,plain,
( sk_c11 = inverse(sk_c2)
| sk_c10 = multiply(sk_c9,sk_c11) ),
inference(reorient_equations,[],[f123]) ).
fof(f125,negated_conjecture,
! [X2,X3,X0,X1,X8,X6,X7,X4,X5] :
( inverse(sk_c11) != sk_c10
| inverse(X0) != sk_c11
| multiply(X0,sk_c10) != sk_c11
| multiply(sk_c11,X1) != sk_c10
| multiply(X2,sk_c11) != X1
| inverse(X2) != sk_c11
| multiply(X3,X4) != sk_c11
| inverse(X3) != X4
| multiply(X4,sk_c10) != sk_c11
| inverse(X5) != sk_c11
| multiply(X5,sk_c10) != sk_c11
| multiply(X6,X7) != sk_c10
| inverse(X6) != X7
| multiply(X7,sk_c11) != sk_c10
| inverse(X8) != sk_c10
| multiply(X8,sk_c11) != sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_61) ).
fof(f126,plain,
! [X2,X3,X0,X1,X8,X6,X7,X4,X5] :
( inverse(sk_c11) != sk_c10
| inverse(X0) != sk_c11
| sk_c11 != multiply(X0,sk_c10)
| sk_c10 != multiply(sk_c11,X1)
| multiply(X2,sk_c11) != X1
| sk_c11 != inverse(X2)
| sk_c11 != multiply(X3,X4)
| inverse(X3) != X4
| sk_c11 != multiply(X4,sk_c10)
| sk_c11 != inverse(X5)
| sk_c11 != multiply(X5,sk_c10)
| sk_c10 != multiply(X6,X7)
| inverse(X6) != X7
| sk_c10 != multiply(X7,sk_c11)
| sk_c10 != inverse(X8)
| sk_c10 != multiply(X8,sk_c11) ),
inference(reorient_equations,[],[f125]) ).
fof(f127,plain,
! [X2,X3,X0,X8,X6,X7,X4,X5] :
( inverse(sk_c11) != sk_c10
| inverse(X0) != sk_c11
| sk_c11 != multiply(X0,sk_c10)
| sk_c10 != multiply(sk_c11,multiply(X2,sk_c11))
| sk_c11 != inverse(X2)
| sk_c11 != multiply(X3,X4)
| inverse(X3) != X4
| sk_c11 != multiply(X4,sk_c10)
| sk_c11 != inverse(X5)
| sk_c11 != multiply(X5,sk_c10)
| sk_c10 != multiply(X6,X7)
| inverse(X6) != X7
| sk_c10 != multiply(X7,sk_c11)
| sk_c10 != inverse(X8)
| sk_c10 != multiply(X8,sk_c11) ),
inference(equality_resolution,[],[f126]) ).
fof(f128,plain,
! [X2,X3,X0,X8,X6,X7,X5] :
( inverse(sk_c11) != sk_c10
| inverse(X0) != sk_c11
| sk_c11 != multiply(X0,sk_c10)
| sk_c10 != multiply(sk_c11,multiply(X2,sk_c11))
| sk_c11 != inverse(X2)
| sk_c11 != multiply(X3,inverse(X3))
| sk_c11 != multiply(inverse(X3),sk_c10)
| sk_c11 != inverse(X5)
| sk_c11 != multiply(X5,sk_c10)
| sk_c10 != multiply(X6,X7)
| inverse(X6) != X7
| sk_c10 != multiply(X7,sk_c11)
| sk_c10 != inverse(X8)
| sk_c10 != multiply(X8,sk_c11) ),
inference(equality_resolution,[],[f127]) ).
fof(f129,plain,
! [X2,X3,X0,X8,X6,X5] :
( inverse(sk_c11) != sk_c10
| inverse(X0) != sk_c11
| sk_c11 != multiply(X0,sk_c10)
| sk_c10 != multiply(sk_c11,multiply(X2,sk_c11))
| sk_c11 != inverse(X2)
| sk_c11 != multiply(X3,inverse(X3))
| sk_c11 != multiply(inverse(X3),sk_c10)
| sk_c11 != inverse(X5)
| sk_c11 != multiply(X5,sk_c10)
| sk_c10 != multiply(X6,inverse(X6))
| sk_c10 != multiply(inverse(X6),sk_c11)
| sk_c10 != inverse(X8)
| sk_c10 != multiply(X8,sk_c11) ),
inference(equality_resolution,[],[f128]) ).
fof(f131,definition,
( spl0_1
<=> ! [X8] :
( sk_c10 != inverse(X8)
| sk_c10 != multiply(X8,sk_c11) ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f132,plain,
( ! [X8] :
( sk_c10 != inverse(X8)
| sk_c10 != multiply(X8,sk_c11) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f131]) ).
fof(f134,definition,
( spl0_2
<=> ! [X6] :
( sk_c10 != multiply(X6,inverse(X6))
| sk_c10 != multiply(inverse(X6),sk_c11) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f135,plain,
( ! [X6] :
( sk_c10 != multiply(inverse(X6),sk_c11)
| sk_c10 != multiply(X6,inverse(X6)) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f134]) ).
fof(f137,definition,
( spl0_3
<=> ! [X5] :
( sk_c11 != inverse(X5)
| sk_c11 != multiply(X5,sk_c10) ) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f138,plain,
( ! [X5] :
( sk_c11 != inverse(X5)
| sk_c11 != multiply(X5,sk_c10) )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f137]) ).
fof(f140,definition,
( spl0_4
<=> ! [X3] :
( sk_c11 != multiply(X3,inverse(X3))
| sk_c11 != multiply(inverse(X3),sk_c10) ) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f141,plain,
( ! [X3] :
( sk_c11 != multiply(X3,inverse(X3))
| sk_c11 != multiply(inverse(X3),sk_c10) )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f140]) ).
fof(f143,definition,
( spl0_5
<=> ! [X2] :
( sk_c10 != multiply(sk_c11,multiply(X2,sk_c11))
| sk_c11 != inverse(X2) ) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f144,plain,
( ! [X2] :
( sk_c10 != multiply(sk_c11,multiply(X2,sk_c11))
| sk_c11 != inverse(X2) )
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f143]) ).
fof(f146,definition,
( spl0_6
<=> inverse(sk_c11) = sk_c10 ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f147,plain,
( inverse(sk_c11) = sk_c10
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f146]) ).
fof(f148,plain,
( inverse(sk_c11) != sk_c10
| spl0_6 ),
inference(avatar_component_clause,[],[f146]) ).
fof(f149,plain,
( spl0_1
| spl0_2
| spl0_3
| spl0_4
| spl0_5
| spl0_3
| ~ spl0_6 ),
inference(avatar_split_clause,[],[f129,f146,f137,f143,f140,f137,f134,f131]) ).
fof(f151,definition,
( spl0_7
<=> sk_c10 = multiply(sk_c9,sk_c11) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f153,plain,
( sk_c10 = multiply(sk_c9,sk_c11)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f151]) ).
fof(f155,definition,
( spl0_8
<=> sk_c11 = inverse(sk_c2) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f157,plain,
( sk_c11 = inverse(sk_c2)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f155]) ).
fof(f158,plain,
( spl0_7
| spl0_8 ),
inference(avatar_split_clause,[],[f124,f155,f151]) ).
fof(f160,definition,
( spl0_9
<=> sk_c10 = inverse(sk_c9) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f162,plain,
( sk_c10 = inverse(sk_c9)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f160]) ).
fof(f163,plain,
( spl0_9
| spl0_8 ),
inference(avatar_split_clause,[],[f122,f155,f160]) ).
fof(f165,definition,
( spl0_10
<=> sk_c10 = multiply(sk_c8,sk_c11) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f167,plain,
( sk_c10 = multiply(sk_c8,sk_c11)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f165]) ).
fof(f168,plain,
( spl0_10
| spl0_8 ),
inference(avatar_split_clause,[],[f120,f155,f165]) ).
fof(f170,definition,
( spl0_11
<=> sk_c8 = inverse(sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f172,plain,
( sk_c8 = inverse(sk_c7)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f170]) ).
fof(f173,plain,
( spl0_11
| spl0_8 ),
inference(avatar_split_clause,[],[f118,f155,f170]) ).
fof(f175,definition,
( spl0_12
<=> sk_c10 = multiply(sk_c7,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f177,plain,
( sk_c10 = multiply(sk_c7,sk_c8)
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f175]) ).
fof(f178,plain,
( spl0_12
| spl0_8 ),
inference(avatar_split_clause,[],[f116,f155,f175]) ).
fof(f180,definition,
( spl0_13
<=> sk_c11 = multiply(sk_c6,sk_c10) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f182,plain,
( sk_c11 = multiply(sk_c6,sk_c10)
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f180]) ).
fof(f183,plain,
( spl0_13
| spl0_8 ),
inference(avatar_split_clause,[],[f114,f155,f180]) ).
fof(f185,definition,
( spl0_14
<=> sk_c11 = inverse(sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
fof(f187,plain,
( sk_c11 = inverse(sk_c6)
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f185]) ).
fof(f188,plain,
( spl0_14
| spl0_8 ),
inference(avatar_split_clause,[],[f112,f155,f185]) ).
fof(f190,definition,
( spl0_15
<=> sk_c11 = multiply(sk_c5,sk_c10) ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
fof(f192,plain,
( sk_c11 = multiply(sk_c5,sk_c10)
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f190]) ).
fof(f195,definition,
( spl0_16
<=> sk_c5 = inverse(sk_c4) ),
introduced(definition,[new_symbols(definition,[spl0_16])],[avatar_definition]) ).
fof(f197,plain,
( sk_c5 = inverse(sk_c4)
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f195]) ).
fof(f198,plain,
( spl0_16
| spl0_8 ),
inference(avatar_split_clause,[],[f108,f155,f195]) ).
fof(f200,definition,
( spl0_17
<=> sk_c11 = multiply(sk_c4,sk_c5) ),
introduced(definition,[new_symbols(definition,[spl0_17])],[avatar_definition]) ).
fof(f202,plain,
( sk_c11 = multiply(sk_c4,sk_c5)
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f200]) ).
fof(f203,plain,
( spl0_17
| spl0_8 ),
inference(avatar_split_clause,[],[f106,f155,f200]) ).
fof(f205,definition,
( spl0_18
<=> sk_c3 = multiply(sk_c2,sk_c11) ),
introduced(definition,[new_symbols(definition,[spl0_18])],[avatar_definition]) ).
fof(f207,plain,
( sk_c3 = multiply(sk_c2,sk_c11)
| ~ spl0_18 ),
inference(avatar_component_clause,[],[f205]) ).
fof(f208,plain,
( spl0_7
| spl0_18 ),
inference(avatar_split_clause,[],[f104,f205,f151]) ).
fof(f209,plain,
( spl0_9
| spl0_18 ),
inference(avatar_split_clause,[],[f102,f205,f160]) ).
fof(f211,plain,
( spl0_11
| spl0_18 ),
inference(avatar_split_clause,[],[f98,f205,f170]) ).
fof(f212,plain,
( spl0_12
| spl0_18 ),
inference(avatar_split_clause,[],[f96,f205,f175]) ).
fof(f219,definition,
( spl0_19
<=> sk_c10 = multiply(sk_c11,sk_c3) ),
introduced(definition,[new_symbols(definition,[spl0_19])],[avatar_definition]) ).
fof(f221,plain,
( sk_c10 = multiply(sk_c11,sk_c3)
| ~ spl0_19 ),
inference(avatar_component_clause,[],[f219]) ).
fof(f222,plain,
( spl0_7
| spl0_19 ),
inference(avatar_split_clause,[],[f84,f219,f151]) ).
fof(f223,plain,
( spl0_9
| spl0_19 ),
inference(avatar_split_clause,[],[f82,f219,f160]) ).
fof(f225,plain,
( spl0_11
| spl0_19 ),
inference(avatar_split_clause,[],[f78,f219,f170]) ).
fof(f226,plain,
( spl0_12
| spl0_19 ),
inference(avatar_split_clause,[],[f76,f219,f175]) ).
fof(f233,definition,
( spl0_20
<=> sk_c11 = multiply(sk_c1,sk_c10) ),
introduced(definition,[new_symbols(definition,[spl0_20])],[avatar_definition]) ).
fof(f235,plain,
( sk_c11 = multiply(sk_c1,sk_c10)
| ~ spl0_20 ),
inference(avatar_component_clause,[],[f233]) ).
fof(f238,plain,
( spl0_10
| spl0_20 ),
inference(avatar_split_clause,[],[f60,f233,f165]) ).
fof(f239,plain,
( spl0_11
| spl0_20 ),
inference(avatar_split_clause,[],[f58,f233,f170]) ).
fof(f240,plain,
( spl0_12
| spl0_20 ),
inference(avatar_split_clause,[],[f56,f233,f175]) ).
fof(f243,plain,
( spl0_15
| spl0_20 ),
inference(avatar_split_clause,[],[f50,f233,f190]) ).
fof(f247,definition,
( spl0_21
<=> sk_c11 = inverse(sk_c1) ),
introduced(definition,[new_symbols(definition,[spl0_21])],[avatar_definition]) ).
fof(f249,plain,
( sk_c11 = inverse(sk_c1)
| ~ spl0_21 ),
inference(avatar_component_clause,[],[f247]) ).
fof(f252,plain,
( spl0_10
| spl0_21 ),
inference(avatar_split_clause,[],[f40,f247,f165]) ).
fof(f253,plain,
( spl0_11
| spl0_21 ),
inference(avatar_split_clause,[],[f38,f247,f170]) ).
fof(f254,plain,
( spl0_12
| spl0_21 ),
inference(avatar_split_clause,[],[f36,f247,f175]) ).
fof(f257,plain,
( spl0_15
| spl0_21 ),
inference(avatar_split_clause,[],[f30,f247,f190]) ).
fof(f262,plain,
( spl0_10
| spl0_6 ),
inference(avatar_split_clause,[],[f20,f146,f165]) ).
fof(f263,plain,
( spl0_11
| spl0_6 ),
inference(avatar_split_clause,[],[f18,f146,f170]) ).
fof(f264,plain,
( spl0_12
| spl0_6 ),
inference(avatar_split_clause,[],[f16,f146,f175]) ).
fof(f265,plain,
( spl0_13
| spl0_6 ),
inference(avatar_split_clause,[],[f14,f146,f180]) ).
fof(f266,plain,
( spl0_14
| spl0_6 ),
inference(avatar_split_clause,[],[f12,f146,f185]) ).
fof(f268,plain,
( spl0_16
| spl0_6 ),
inference(avatar_split_clause,[],[f8,f146,f195]) ).
fof(f269,plain,
( spl0_17
| spl0_6 ),
inference(avatar_split_clause,[],[f6,f146,f200]) ).
fof(f270,plain,
( identity = multiply(sk_c5,sk_c4)
| ~ spl0_16 ),
inference(superposition,[],[f3,f197]) ).
fof(f271,plain,
( identity = multiply(sk_c11,sk_c6)
| ~ spl0_14 ),
inference(superposition,[],[f3,f187]) ).
fof(f272,plain,
( identity = multiply(sk_c8,sk_c7)
| ~ spl0_11 ),
inference(superposition,[],[f3,f172]) ).
fof(f275,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[],[f4,f3]) ).
fof(f278,plain,
( ! [X0] : multiply(sk_c10,X0) = multiply(sk_c8,multiply(sk_c11,X0))
| ~ spl0_10 ),
inference(superposition,[],[f4,f167]) ).
fof(f280,plain,
( ! [X0] : multiply(sk_c11,X0) = multiply(sk_c5,multiply(sk_c10,X0))
| ~ spl0_15 ),
inference(superposition,[],[f4,f192]) ).
fof(f281,plain,
( ! [X0] : multiply(sk_c11,X0) = multiply(sk_c4,multiply(sk_c5,X0))
| ~ spl0_17 ),
inference(superposition,[],[f4,f202]) ).
fof(f284,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f275,f1]) ).
fof(f286,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c5,multiply(sk_c4,X0))
| ~ spl0_16 ),
inference(superposition,[],[f4,f270]) ).
fof(f287,plain,
( ! [X0] : multiply(sk_c5,multiply(sk_c4,X0)) = X0
| ~ spl0_16 ),
inference(forward_demodulation,[],[f286,f1]) ).
fof(f288,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c11,multiply(sk_c6,X0))
| ~ spl0_14 ),
inference(superposition,[],[f4,f271]) ).
fof(f289,plain,
( ! [X0] : multiply(sk_c11,multiply(sk_c6,X0)) = X0
| ~ spl0_14 ),
inference(forward_demodulation,[],[f288,f1]) ).
fof(f290,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c8,multiply(sk_c7,X0))
| ~ spl0_11 ),
inference(superposition,[],[f4,f272]) ).
fof(f291,plain,
( ! [X0] : multiply(sk_c8,multiply(sk_c7,X0)) = X0
| ~ spl0_11 ),
inference(forward_demodulation,[],[f290,f1]) ).
fof(f294,plain,
( sk_c5 = multiply(sk_c5,sk_c11)
| ~ spl0_16
| ~ spl0_17 ),
inference(superposition,[],[f287,f202]) ).
fof(f306,plain,
( sk_c10 = multiply(sk_c11,sk_c11)
| ~ spl0_13
| ~ spl0_14 ),
inference(superposition,[],[f289,f182]) ).
fof(f323,plain,
( sk_c8 = multiply(sk_c8,sk_c10)
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f291,f177]) ).
fof(f328,plain,
( multiply(sk_c4,sk_c5) = multiply(sk_c11,sk_c11)
| ~ spl0_16
| ~ spl0_17 ),
inference(superposition,[],[f281,f294]) ).
fof(f334,plain,
( sk_c10 = multiply(sk_c4,sk_c5)
| ~ spl0_13
| ~ spl0_14
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f328,f306]) ).
fof(f336,plain,
( sk_c11 = sk_c10
| ~ spl0_13
| ~ spl0_14
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f334,f202]) ).
fof(f343,plain,
( sk_c8 = multiply(sk_c8,sk_c11)
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f323,f336]) ).
fof(f344,plain,
( sk_c10 = sk_c8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f343,f167]) ).
fof(f345,plain,
( sk_c11 = sk_c8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f344,f336]) ).
fof(f381,plain,
( ! [X0] : multiply(sk_c11,X0) = multiply(inverse(sk_c8),multiply(sk_c10,X0))
| ~ spl0_10 ),
inference(superposition,[],[f284,f278]) ).
fof(f387,plain,
( sk_c11 = multiply(inverse(sk_c8),sk_c10)
| ~ spl0_10 ),
inference(superposition,[],[f284,f167]) ).
fof(f395,plain,
( sk_c8 = multiply(inverse(sk_c7),sk_c10)
| ~ spl0_12 ),
inference(superposition,[],[f284,f177]) ).
fof(f406,plain,
( sk_c11 = multiply(inverse(sk_c8),sk_c11)
| ~ spl0_10
| ~ spl0_13
| ~ spl0_14
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f387,f336]) ).
fof(f411,plain,
( ! [X0] : multiply(sk_c11,X0) = multiply(inverse(sk_c8),multiply(sk_c11,X0))
| ~ spl0_10
| ~ spl0_13
| ~ spl0_14
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f381,f336]) ).
fof(f419,plain,
( sk_c11 = multiply(inverse(sk_c11),sk_c11)
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f406,f345]) ).
fof(f422,plain,
( ! [X0] : multiply(sk_c11,X0) = multiply(inverse(sk_c11),multiply(sk_c11,X0))
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f411,f345]) ).
fof(f427,plain,
( identity = sk_c11
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f419,f3]) ).
fof(f429,plain,
( ! [X0] : multiply(sk_c11,X0) = X0
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f422,f284]) ).
fof(f458,plain,
( identity = sk_c6
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_16
| ~ spl0_17 ),
inference(superposition,[],[f271,f429]) ).
fof(f459,plain,
( sk_c11 = sk_c6
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f458,f427]) ).
fof(f468,plain,
( sk_c11 = inverse(sk_c11)
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_16
| ~ spl0_17 ),
inference(superposition,[],[f187,f459]) ).
fof(f478,plain,
( sk_c11 != sk_c10
| spl0_6
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_16
| ~ spl0_17 ),
inference(superposition,[],[f148,f468]) ).
fof(f483,plain,
( $false
| spl0_6
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f478,f336]) ).
fof(f484,plain,
( spl0_6
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_16
| ~ spl0_17 ),
inference(avatar_contradiction_clause,[],[f483]) ).
fof(f517,plain,
( sk_c8 = multiply(sk_c8,sk_c10)
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f395,f172]) ).
fof(f522,plain,
( identity = multiply(sk_c10,sk_c11)
| ~ spl0_6 ),
inference(superposition,[],[f3,f147]) ).
fof(f530,plain,
( sk_c11 = multiply(inverse(sk_c2),sk_c3)
| ~ spl0_18 ),
inference(superposition,[],[f284,f207]) ).
fof(f532,plain,
( sk_c11 = multiply(sk_c11,sk_c3)
| ~ spl0_8
| ~ spl0_18 ),
inference(forward_demodulation,[],[f530,f157]) ).
fof(f546,plain,
( sk_c11 != sk_c10
| sk_c11 != multiply(sk_c11,sk_c10)
| ~ spl0_3
| ~ spl0_6 ),
inference(superposition,[],[f138,f147]) ).
fof(f550,plain,
( sk_c11 != sk_c11
| sk_c11 != multiply(sk_c1,sk_c10)
| ~ spl0_3
| ~ spl0_21 ),
inference(superposition,[],[f138,f249]) ).
fof(f553,plain,
( sk_c11 != multiply(sk_c1,sk_c10)
| ~ spl0_3
| ~ spl0_21 ),
inference(trivial_inequality_removal,[],[f550]) ).
fof(f554,plain,
( $false
| ~ spl0_3
| ~ spl0_20
| ~ spl0_21 ),
inference(forward_subsumption_resolution,[],[f553,f235]) ).
fof(f555,plain,
( ~ spl0_3
| ~ spl0_20
| ~ spl0_21 ),
inference(avatar_contradiction_clause,[],[f554]) ).
fof(f557,definition,
( spl0_24
<=> sk_c11 = multiply(sk_c9,sk_c10) ),
introduced(definition,[new_symbols(definition,[spl0_24])],[avatar_definition]) ).
fof(f558,plain,
( sk_c11 = multiply(sk_c9,sk_c10)
| ~ spl0_24 ),
inference(avatar_component_clause,[],[f557]) ).
fof(f559,plain,
( sk_c11 != multiply(sk_c9,sk_c10)
| spl0_24 ),
inference(avatar_component_clause,[],[f557]) ).
fof(f561,definition,
( spl0_25
<=> sk_c11 = sk_c10 ),
introduced(definition,[new_symbols(definition,[spl0_25])],[avatar_definition]) ).
fof(f562,plain,
( sk_c11 = sk_c10
| ~ spl0_25 ),
inference(avatar_component_clause,[],[f561]) ).
fof(f563,plain,
( sk_c11 != sk_c10
| spl0_25 ),
inference(avatar_component_clause,[],[f561]) ).
fof(f580,definition,
( spl0_29
<=> sk_c11 = multiply(sk_c11,sk_c10) ),
introduced(definition,[new_symbols(definition,[spl0_29])],[avatar_definition]) ).
fof(f582,plain,
( sk_c11 != multiply(sk_c11,sk_c10)
| spl0_29 ),
inference(avatar_component_clause,[],[f580]) ).
fof(f583,plain,
( ~ spl0_29
| ~ spl0_25
| ~ spl0_3
| ~ spl0_6 ),
inference(avatar_split_clause,[],[f546,f146,f137,f561,f580]) ).
fof(f585,plain,
( spl0_25
| ~ spl0_13
| ~ spl0_14
| ~ spl0_16
| ~ spl0_17 ),
inference(avatar_split_clause,[],[f336,f200,f195,f185,f180,f561]) ).
fof(f590,plain,
( sk_c11 = multiply(sk_c6,sk_c11)
| ~ spl0_13
| ~ spl0_25 ),
inference(superposition,[],[f182,f562]) ).
fof(f615,plain,
( ! [X3] :
( sk_c11 != multiply(inverse(X3),sk_c11)
| sk_c11 != multiply(X3,inverse(X3)) )
| ~ spl0_4
| ~ spl0_25 ),
inference(forward_demodulation,[],[f141,f562]) ).
fof(f625,plain,
( sk_c11 != multiply(sk_c8,sk_c11)
| sk_c11 != multiply(sk_c7,sk_c8)
| ~ spl0_4
| ~ spl0_11
| ~ spl0_25 ),
inference(superposition,[],[f615,f172]) ).
fof(f627,plain,
( sk_c11 != multiply(sk_c11,sk_c11)
| sk_c11 != multiply(sk_c1,sk_c11)
| ~ spl0_4
| ~ spl0_21
| ~ spl0_25 ),
inference(superposition,[],[f615,f249]) ).
fof(f634,definition,
( spl0_30
<=> sk_c11 = multiply(sk_c1,sk_c11) ),
introduced(definition,[new_symbols(definition,[spl0_30])],[avatar_definition]) ).
fof(f635,plain,
( sk_c11 = multiply(sk_c1,sk_c11)
| ~ spl0_30 ),
inference(avatar_component_clause,[],[f634]) ).
fof(f638,definition,
( spl0_31
<=> sk_c11 = multiply(sk_c11,sk_c11) ),
introduced(definition,[new_symbols(definition,[spl0_31])],[avatar_definition]) ).
fof(f640,plain,
( sk_c11 != multiply(sk_c11,sk_c11)
| spl0_31 ),
inference(avatar_component_clause,[],[f638]) ).
fof(f641,plain,
( ~ spl0_30
| ~ spl0_31
| ~ spl0_4
| ~ spl0_21
| ~ spl0_25 ),
inference(avatar_split_clause,[],[f627,f561,f247,f140,f638,f634]) ).
fof(f643,plain,
( sk_c11 != sk_c10
| sk_c11 != multiply(sk_c7,sk_c8)
| ~ spl0_4
| ~ spl0_10
| ~ spl0_11
| ~ spl0_25 ),
inference(forward_demodulation,[],[f625,f167]) ).
fof(f656,plain,
( sk_c11 != multiply(sk_c7,sk_c8)
| ~ spl0_4
| ~ spl0_10
| ~ spl0_11
| ~ spl0_25 ),
inference(forward_subsumption_resolution,[],[f643,f562]) ).
fof(f662,plain,
( sk_c11 != sk_c10
| ~ spl0_4
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_25 ),
inference(forward_demodulation,[],[f656,f177]) ).
fof(f667,plain,
( $false
| ~ spl0_4
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_25 ),
inference(forward_subsumption_resolution,[],[f662,f562]) ).
fof(f668,plain,
( ~ spl0_4
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_25 ),
inference(avatar_contradiction_clause,[],[f667]) ).
fof(f669,plain,
( ! [X2] :
( sk_c11 != inverse(X2)
| sk_c11 != multiply(sk_c11,multiply(X2,sk_c11)) )
| ~ spl0_5
| ~ spl0_25 ),
inference(forward_demodulation,[],[f144,f562]) ).
fof(f676,plain,
( sk_c11 != sk_c10
| sk_c11 != multiply(sk_c11,multiply(sk_c9,sk_c11))
| ~ spl0_5
| ~ spl0_9
| ~ spl0_25 ),
inference(superposition,[],[f669,f162]) ).
fof(f678,plain,
( sk_c11 != sk_c11
| sk_c11 != multiply(sk_c11,multiply(sk_c2,sk_c11))
| ~ spl0_5
| ~ spl0_8
| ~ spl0_25 ),
inference(superposition,[],[f669,f157]) ).
fof(f679,plain,
( sk_c11 != multiply(sk_c11,multiply(sk_c2,sk_c11))
| ~ spl0_5
| ~ spl0_8
| ~ spl0_25 ),
inference(trivial_inequality_removal,[],[f678]) ).
fof(f683,plain,
( sk_c11 != multiply(sk_c11,sk_c3)
| ~ spl0_5
| ~ spl0_8
| ~ spl0_18
| ~ spl0_25 ),
inference(forward_demodulation,[],[f679,f207]) ).
fof(f684,plain,
( sk_c11 != multiply(sk_c11,multiply(sk_c9,sk_c11))
| ~ spl0_5
| ~ spl0_9
| ~ spl0_25 ),
inference(forward_subsumption_resolution,[],[f676,f562]) ).
fof(f693,plain,
( sk_c11 != sk_c10
| ~ spl0_5
| ~ spl0_8
| ~ spl0_18
| ~ spl0_19
| ~ spl0_25 ),
inference(forward_demodulation,[],[f683,f221]) ).
fof(f694,plain,
( sk_c11 != multiply(sk_c11,sk_c10)
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_25 ),
inference(forward_demodulation,[],[f684,f153]) ).
fof(f695,plain,
( $false
| ~ spl0_5
| ~ spl0_8
| ~ spl0_18
| ~ spl0_19
| ~ spl0_25 ),
inference(forward_subsumption_resolution,[],[f693,f562]) ).
fof(f696,plain,
( ~ spl0_5
| ~ spl0_8
| ~ spl0_18
| ~ spl0_19
| ~ spl0_25 ),
inference(avatar_contradiction_clause,[],[f695]) ).
fof(f697,plain,
( sk_c11 != multiply(sk_c11,sk_c11)
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_25 ),
inference(forward_demodulation,[],[f694,f562]) ).
fof(f698,plain,
( ~ spl0_31
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_25 ),
inference(avatar_split_clause,[],[f697,f561,f160,f151,f143,f638]) ).
fof(f713,plain,
( ! [X8] :
( sk_c11 != inverse(X8)
| sk_c10 != multiply(X8,sk_c11) )
| ~ spl0_1
| ~ spl0_25 ),
inference(forward_demodulation,[],[f132,f562]) ).
fof(f715,plain,
( ! [X8] :
( sk_c11 != inverse(X8)
| sk_c11 != multiply(X8,sk_c11) )
| ~ spl0_1
| ~ spl0_25 ),
inference(forward_demodulation,[],[f713,f562]) ).
fof(f717,plain,
( sk_c11 != sk_c10
| sk_c11 != multiply(sk_c11,sk_c11)
| ~ spl0_1
| ~ spl0_6
| ~ spl0_25 ),
inference(superposition,[],[f715,f147]) ).
fof(f722,plain,
( sk_c11 != sk_c11
| sk_c11 != multiply(sk_c1,sk_c11)
| ~ spl0_1
| ~ spl0_21
| ~ spl0_25 ),
inference(superposition,[],[f715,f249]) ).
fof(f725,plain,
( sk_c11 != multiply(sk_c1,sk_c11)
| ~ spl0_1
| ~ spl0_21
| ~ spl0_25 ),
inference(trivial_inequality_removal,[],[f722]) ).
fof(f729,plain,
( ~ spl0_30
| ~ spl0_1
| ~ spl0_21
| ~ spl0_25 ),
inference(avatar_split_clause,[],[f725,f561,f247,f131,f634]) ).
fof(f734,plain,
( sk_c11 != multiply(sk_c11,sk_c11)
| ~ spl0_1
| ~ spl0_6
| ~ spl0_25 ),
inference(forward_subsumption_resolution,[],[f717,f562]) ).
fof(f739,plain,
( ~ spl0_31
| ~ spl0_1
| ~ spl0_6
| ~ spl0_25 ),
inference(avatar_split_clause,[],[f734,f561,f146,f131,f638]) ).
fof(f742,plain,
( ! [X6] :
( sk_c11 != multiply(X6,inverse(X6))
| sk_c10 != multiply(inverse(X6),sk_c11) )
| ~ spl0_2
| ~ spl0_25 ),
inference(forward_demodulation,[],[f135,f562]) ).
fof(f743,plain,
( ! [X6] :
( sk_c11 != multiply(inverse(X6),sk_c11)
| sk_c11 != multiply(X6,inverse(X6)) )
| ~ spl0_2
| ~ spl0_25 ),
inference(forward_demodulation,[],[f742,f562]) ).
fof(f749,plain,
( sk_c11 != multiply(sk_c10,sk_c11)
| sk_c11 != multiply(sk_c11,sk_c10)
| ~ spl0_2
| ~ spl0_6
| ~ spl0_25 ),
inference(superposition,[],[f743,f147]) ).
fof(f824,plain,
( sk_c11 = multiply(sk_c11,sk_c11)
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_16
| ~ spl0_17
| ~ spl0_25 ),
inference(forward_demodulation,[],[f590,f459]) ).
fof(f825,plain,
( $false
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_16
| ~ spl0_17
| ~ spl0_25
| spl0_31 ),
inference(forward_subsumption_resolution,[],[f824,f640]) ).
fof(f826,plain,
( ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_16
| ~ spl0_17
| ~ spl0_25
| spl0_31 ),
inference(avatar_contradiction_clause,[],[f825]) ).
fof(f857,plain,
( sk_c10 != multiply(sk_c8,sk_c11)
| sk_c10 != multiply(sk_c7,sk_c8)
| ~ spl0_2
| ~ spl0_11 ),
inference(superposition,[],[f135,f172]) ).
fof(f868,definition,
( spl0_35
<=> sk_c10 = multiply(sk_c10,sk_c11) ),
introduced(definition,[new_symbols(definition,[spl0_35])],[avatar_definition]) ).
fof(f869,plain,
( sk_c10 = multiply(sk_c10,sk_c11)
| ~ spl0_35 ),
inference(avatar_component_clause,[],[f868]) ).
fof(f870,plain,
( sk_c10 != multiply(sk_c10,sk_c11)
| spl0_35 ),
inference(avatar_component_clause,[],[f868]) ).
fof(f872,plain,
( sk_c10 != multiply(sk_c8,sk_c11)
| ~ spl0_2
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f857,f177]) ).
fof(f888,definition,
( spl0_39
<=> identity = sk_c10 ),
introduced(definition,[new_symbols(definition,[spl0_39])],[avatar_definition]) ).
fof(f889,plain,
( identity = sk_c10
| ~ spl0_39 ),
inference(avatar_component_clause,[],[f888]) ).
fof(f903,plain,
( ~ spl0_10
| ~ spl0_2
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_split_clause,[],[f872,f175,f170,f134,f165]) ).
fof(f917,plain,
( sk_c11 = multiply(inverse(sk_c10),sk_c10)
| ~ spl0_35 ),
inference(superposition,[],[f284,f869]) ).
fof(f919,plain,
( identity = sk_c11
| ~ spl0_35 ),
inference(forward_demodulation,[],[f917,f3]) ).
fof(f921,plain,
( identity = sk_c10
| ~ spl0_6
| ~ spl0_35 ),
inference(forward_demodulation,[],[f522,f869]) ).
fof(f957,plain,
( sk_c11 = multiply(sk_c1,sk_c11)
| ~ spl0_20
| ~ spl0_25 ),
inference(superposition,[],[f235,f562]) ).
fof(f975,plain,
( sk_c11 != multiply(sk_c11,sk_c11)
| sk_c11 != multiply(sk_c11,sk_c10)
| ~ spl0_2
| ~ spl0_6
| ~ spl0_25 ),
inference(forward_demodulation,[],[f749,f562]) ).
fof(f986,plain,
( spl0_30
| ~ spl0_20
| ~ spl0_25 ),
inference(avatar_split_clause,[],[f957,f561,f233,f634]) ).
fof(f988,plain,
( sk_c11 != multiply(sk_c11,sk_c11)
| sk_c11 != multiply(sk_c11,sk_c11)
| ~ spl0_2
| ~ spl0_6
| ~ spl0_25 ),
inference(forward_demodulation,[],[f975,f562]) ).
fof(f989,plain,
( sk_c11 != multiply(sk_c11,sk_c11)
| ~ spl0_2
| ~ spl0_6
| ~ spl0_25 ),
inference(duplicate_literal_removal,[],[f988]) ).
fof(f997,plain,
( ~ spl0_31
| ~ spl0_2
| ~ spl0_6
| ~ spl0_25 ),
inference(avatar_split_clause,[],[f989,f561,f146,f134,f638]) ).
fof(f1001,definition,
( spl0_43
<=> identity = sk_c11 ),
introduced(definition,[new_symbols(definition,[spl0_43])],[avatar_definition]) ).
fof(f1002,plain,
( identity = sk_c11
| ~ spl0_43 ),
inference(avatar_component_clause,[],[f1001]) ).
fof(f1003,plain,
( identity != sk_c11
| spl0_43 ),
inference(avatar_component_clause,[],[f1001]) ).
fof(f1009,plain,
( sk_c11 != multiply(sk_c9,sk_c11)
| spl0_24
| ~ spl0_25 ),
inference(forward_demodulation,[],[f559,f562]) ).
fof(f1010,plain,
( sk_c11 != sk_c10
| ~ spl0_7
| spl0_24
| ~ spl0_25 ),
inference(forward_demodulation,[],[f1009,f153]) ).
fof(f1011,plain,
( $false
| ~ spl0_7
| spl0_24
| ~ spl0_25 ),
inference(forward_subsumption_resolution,[],[f1010,f562]) ).
fof(f1012,plain,
( ~ spl0_7
| spl0_24
| ~ spl0_25 ),
inference(avatar_contradiction_clause,[],[f1011]) ).
fof(f1015,plain,
( sk_c11 != multiply(sk_c11,sk_c11)
| ~ spl0_25
| spl0_29 ),
inference(forward_demodulation,[],[f582,f562]) ).
fof(f1016,plain,
( ~ spl0_31
| ~ spl0_25
| spl0_29 ),
inference(avatar_split_clause,[],[f1015,f580,f561,f638]) ).
fof(f1018,plain,
( sk_c11 = multiply(inverse(sk_c1),sk_c11)
| ~ spl0_30 ),
inference(superposition,[],[f284,f635]) ).
fof(f1020,plain,
( sk_c11 = multiply(sk_c11,sk_c11)
| ~ spl0_21
| ~ spl0_30 ),
inference(forward_demodulation,[],[f1018,f249]) ).
fof(f1023,plain,
( spl0_31
| ~ spl0_21
| ~ spl0_30 ),
inference(avatar_split_clause,[],[f1020,f634,f247,f638]) ).
fof(f1030,plain,
( sk_c10 = multiply(inverse(sk_c9),sk_c11)
| ~ spl0_24 ),
inference(superposition,[],[f284,f558]) ).
fof(f1032,plain,
( sk_c10 = multiply(sk_c10,sk_c11)
| ~ spl0_9
| ~ spl0_24 ),
inference(forward_demodulation,[],[f1030,f162]) ).
fof(f1033,plain,
( spl0_35
| ~ spl0_9
| ~ spl0_24 ),
inference(avatar_split_clause,[],[f1032,f557,f160,f868]) ).
fof(f1038,plain,
( identity != sk_c10
| ~ spl0_6
| spl0_35 ),
inference(superposition,[],[f870,f522]) ).
fof(f1053,plain,
( sk_c10 = multiply(inverse(sk_c8),sk_c8)
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f284,f517]) ).
fof(f1055,plain,
( identity = sk_c10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f1053,f3]) ).
fof(f1058,plain,
( ~ spl0_39
| ~ spl0_6
| spl0_35 ),
inference(avatar_split_clause,[],[f1038,f868,f146,f888]) ).
fof(f1059,plain,
( spl0_39
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_split_clause,[],[f1055,f175,f170,f888]) ).
fof(f1060,plain,
( $false
| ~ spl0_35
| spl0_43 ),
inference(forward_subsumption_resolution,[],[f919,f1003]) ).
fof(f1061,plain,
( ~ spl0_35
| spl0_43 ),
inference(avatar_contradiction_clause,[],[f1060]) ).
fof(f1062,plain,
( spl0_39
| ~ spl0_6
| ~ spl0_35 ),
inference(avatar_split_clause,[],[f921,f868,f146,f888]) ).
fof(f1063,plain,
( spl0_43
| ~ spl0_35 ),
inference(avatar_split_clause,[],[f919,f868,f1001]) ).
fof(f1067,plain,
( multiply(sk_c5,sk_c10) = multiply(sk_c11,sk_c11)
| ~ spl0_15
| ~ spl0_35 ),
inference(superposition,[],[f280,f869]) ).
fof(f1071,plain,
( sk_c11 = multiply(sk_c11,sk_c11)
| ~ spl0_15
| ~ spl0_35 ),
inference(forward_demodulation,[],[f1067,f192]) ).
fof(f1072,plain,
( $false
| ~ spl0_15
| spl0_31
| ~ spl0_35 ),
inference(forward_subsumption_resolution,[],[f1071,f640]) ).
fof(f1073,plain,
( ~ spl0_15
| spl0_31
| ~ spl0_35 ),
inference(avatar_contradiction_clause,[],[f1072]) ).
fof(f1074,plain,
( sk_c11 = sk_c10
| ~ spl0_39
| ~ spl0_43 ),
inference(superposition,[],[f1002,f889]) ).
fof(f1079,plain,
( $false
| spl0_25
| ~ spl0_39
| ~ spl0_43 ),
inference(forward_subsumption_resolution,[],[f1074,f563]) ).
fof(f1080,plain,
( spl0_25
| ~ spl0_39
| ~ spl0_43 ),
inference(avatar_contradiction_clause,[],[f1079]) ).
fof(f1096,plain,
( sk_c11 = sk_c10
| ~ spl0_8
| ~ spl0_18
| ~ spl0_19 ),
inference(superposition,[],[f532,f221]) ).
fof(f1107,plain,
( $false
| ~ spl0_8
| ~ spl0_18
| ~ spl0_19
| spl0_25 ),
inference(forward_subsumption_resolution,[],[f1096,f563]) ).
fof(f1108,plain,
( ~ spl0_8
| ~ spl0_18
| ~ spl0_19
| spl0_25 ),
inference(avatar_contradiction_clause,[],[f1107]) ).
cnf(s1,plain,
( spl0_3
| spl0_2
| spl0_1
| spl0_3
| spl0_4
| spl0_5
| ~ spl0_6 ),
inference(sat_conversion,[],[f149]) ).
cnf(s2,plain,
( spl0_1
| spl0_2
| spl0_3
| spl0_4
| spl0_5
| ~ spl0_6 ),
inference(rat,[],[s1]) ).
cnf(s3,plain,
( spl0_7
| spl0_8 ),
inference(sat_conversion,[],[f158]) ).
cnf(s4,plain,
( spl0_8
| spl0_9 ),
inference(sat_conversion,[],[f163]) ).
cnf(s5,plain,
( spl0_8
| spl0_10 ),
inference(sat_conversion,[],[f168]) ).
cnf(s6,plain,
( spl0_8
| spl0_11 ),
inference(sat_conversion,[],[f173]) ).
cnf(s7,plain,
( spl0_8
| spl0_12 ),
inference(sat_conversion,[],[f178]) ).
cnf(s8,plain,
( spl0_8
| spl0_13 ),
inference(sat_conversion,[],[f183]) ).
cnf(s9,plain,
( spl0_8
| spl0_14 ),
inference(sat_conversion,[],[f188]) ).
cnf(s11,plain,
( spl0_8
| spl0_16 ),
inference(sat_conversion,[],[f198]) ).
cnf(s12,plain,
( spl0_8
| spl0_17 ),
inference(sat_conversion,[],[f203]) ).
cnf(s13,plain,
( spl0_7
| spl0_18 ),
inference(sat_conversion,[],[f208]) ).
cnf(s14,plain,
( spl0_9
| spl0_18 ),
inference(sat_conversion,[],[f209]) ).
cnf(s16,plain,
( spl0_11
| spl0_18 ),
inference(sat_conversion,[],[f211]) ).
cnf(s17,plain,
( spl0_12
| spl0_18 ),
inference(sat_conversion,[],[f212]) ).
cnf(s23,plain,
( spl0_7
| spl0_19 ),
inference(sat_conversion,[],[f222]) ).
cnf(s24,plain,
( spl0_9
| spl0_19 ),
inference(sat_conversion,[],[f223]) ).
cnf(s26,plain,
( spl0_11
| spl0_19 ),
inference(sat_conversion,[],[f225]) ).
cnf(s27,plain,
( spl0_12
| spl0_19 ),
inference(sat_conversion,[],[f226]) ).
cnf(s35,plain,
( spl0_10
| spl0_20 ),
inference(sat_conversion,[],[f238]) ).
cnf(s36,plain,
( spl0_11
| spl0_20 ),
inference(sat_conversion,[],[f239]) ).
cnf(s37,plain,
( spl0_12
| spl0_20 ),
inference(sat_conversion,[],[f240]) ).
cnf(s40,plain,
( spl0_15
| spl0_20 ),
inference(sat_conversion,[],[f243]) ).
cnf(s45,plain,
( spl0_10
| spl0_21 ),
inference(sat_conversion,[],[f252]) ).
cnf(s46,plain,
( spl0_11
| spl0_21 ),
inference(sat_conversion,[],[f253]) ).
cnf(s47,plain,
( spl0_12
| spl0_21 ),
inference(sat_conversion,[],[f254]) ).
cnf(s50,plain,
( spl0_15
| spl0_21 ),
inference(sat_conversion,[],[f257]) ).
cnf(s55,plain,
( spl0_6
| spl0_10 ),
inference(sat_conversion,[],[f262]) ).
cnf(s56,plain,
( spl0_6
| spl0_11 ),
inference(sat_conversion,[],[f263]) ).
cnf(s57,plain,
( spl0_6
| spl0_12 ),
inference(sat_conversion,[],[f264]) ).
cnf(s58,plain,
( spl0_6
| spl0_13 ),
inference(sat_conversion,[],[f265]) ).
cnf(s59,plain,
( spl0_6
| spl0_14 ),
inference(sat_conversion,[],[f266]) ).
cnf(s61,plain,
( spl0_6
| spl0_16 ),
inference(sat_conversion,[],[f268]) ).
cnf(s62,plain,
( spl0_6
| spl0_17 ),
inference(sat_conversion,[],[f269]) ).
cnf(s63,plain,
( spl0_6
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_16
| ~ spl0_17 ),
inference(sat_conversion,[],[f484]) ).
cnf(s69,plain,
( ~ spl0_3
| ~ spl0_20
| ~ spl0_21 ),
inference(sat_conversion,[],[f555]) ).
cnf(s73,plain,
( ~ spl0_3
| ~ spl0_6
| ~ spl0_25
| ~ spl0_29 ),
inference(sat_conversion,[],[f583]) ).
cnf(s74,plain,
( ~ spl0_13
| ~ spl0_14
| ~ spl0_16
| ~ spl0_17
| spl0_25 ),
inference(sat_conversion,[],[f585]) ).
cnf(s76,plain,
( ~ spl0_4
| ~ spl0_21
| ~ spl0_25
| ~ spl0_30
| ~ spl0_31 ),
inference(sat_conversion,[],[f641]) ).
cnf(s84,plain,
( ~ spl0_4
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_25 ),
inference(sat_conversion,[],[f668]) ).
cnf(s86,plain,
( ~ spl0_5
| ~ spl0_8
| ~ spl0_18
| ~ spl0_19
| ~ spl0_25 ),
inference(sat_conversion,[],[f696]) ).
cnf(s87,plain,
( ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_25
| ~ spl0_31 ),
inference(sat_conversion,[],[f698]) ).
cnf(s90,plain,
( ~ spl0_1
| ~ spl0_21
| ~ spl0_25
| ~ spl0_30 ),
inference(sat_conversion,[],[f729]) ).
cnf(s95,plain,
( ~ spl0_1
| ~ spl0_6
| ~ spl0_25
| ~ spl0_31 ),
inference(sat_conversion,[],[f739]) ).
cnf(s113,plain,
( ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_16
| ~ spl0_17
| ~ spl0_25
| spl0_31 ),
inference(sat_conversion,[],[f826]) ).
cnf(s124,plain,
( ~ spl0_2
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(sat_conversion,[],[f903]) ).
cnf(s147,plain,
( ~ spl0_20
| ~ spl0_25
| spl0_30 ),
inference(sat_conversion,[],[f986]) ).
cnf(s149,plain,
( ~ spl0_2
| ~ spl0_6
| ~ spl0_25
| ~ spl0_31 ),
inference(sat_conversion,[],[f997]) ).
cnf(s155,plain,
( ~ spl0_7
| spl0_24
| ~ spl0_25 ),
inference(sat_conversion,[],[f1012]) ).
cnf(s157,plain,
( ~ spl0_25
| spl0_29
| ~ spl0_31 ),
inference(sat_conversion,[],[f1016]) ).
cnf(s159,plain,
( ~ spl0_21
| ~ spl0_30
| spl0_31 ),
inference(sat_conversion,[],[f1023]) ).
cnf(s161,plain,
( ~ spl0_9
| ~ spl0_24
| spl0_35 ),
inference(sat_conversion,[],[f1033]) ).
cnf(s163,plain,
( ~ spl0_6
| spl0_35
| ~ spl0_39 ),
inference(sat_conversion,[],[f1058]) ).
cnf(s164,plain,
( ~ spl0_11
| ~ spl0_12
| spl0_39 ),
inference(sat_conversion,[],[f1059]) ).
cnf(s165,plain,
( ~ spl0_35
| spl0_43 ),
inference(sat_conversion,[],[f1061]) ).
cnf(s166,plain,
( ~ spl0_6
| ~ spl0_35
| spl0_39 ),
inference(sat_conversion,[],[f1062]) ).
cnf(s167,plain,
( ~ spl0_35
| spl0_43 ),
inference(sat_conversion,[],[f1063]) ).
cnf(s169,plain,
( ~ spl0_15
| spl0_31
| ~ spl0_35 ),
inference(sat_conversion,[],[f1073]) ).
cnf(s171,plain,
( spl0_25
| ~ spl0_39
| ~ spl0_43 ),
inference(sat_conversion,[],[f1080]) ).
cnf(s175,plain,
( ~ spl0_8
| ~ spl0_18
| ~ spl0_19
| spl0_25 ),
inference(sat_conversion,[],[f1108]) ).
cnf(s176,plain,
spl0_6,
inference(rat,[],[s63,s55,s56,s57,s58,s59,s61,s62]) ).
cnf(s177,plain,
( spl0_8
| ~ spl0_7
| ~ spl0_5 ),
inference(rat,[],[s87,s113,s74,s4,s5,s6,s7,s8,s9,s11,s12]) ).
cnf(s178,plain,
( ~ spl0_39
| ~ spl0_9
| ~ spl0_7
| ~ spl0_5 ),
inference(rat,[],[s147,s159,s40,s50,s169,s87,s171,s167,s163,s176]) ).
cnf(s179,plain,
( spl0_12
| spl0_25
| ~ spl0_8 ),
inference(rat,[],[s175,s17,s27]) ).
cnf(s180,plain,
( ~ spl0_9
| ~ spl0_7
| ~ spl0_5 ),
inference(rat,[],[s175,s16,s26,s164,s179,s155,s161,s166,s178,s177,s176]) ).
cnf(s181,plain,
( ~ spl0_7
| ~ spl0_5 ),
inference(rat,[],[s86,s175,s14,s24,s180,s177]) ).
cnf(s182,plain,
~ spl0_5,
inference(rat,[],[s86,s175,s3,s13,s23,s181]) ).
cnf(s183,plain,
( spl0_10
| ~ spl0_25
| ~ spl0_4 ),
inference(rat,[],[s76,s159,s147,s35,s45]) ).
cnf(s184,plain,
( spl0_12
| ~ spl0_25
| ~ spl0_4 ),
inference(rat,[],[s76,s159,s147,s37,s47]) ).
cnf(s185,plain,
( ~ spl0_12
| ~ spl0_25
| ~ spl0_4
| ~ spl0_10 ),
inference(rat,[],[s76,s159,s147,s36,s46,s84]) ).
cnf(s186,plain,
( ~ spl0_25
| ~ spl0_4 ),
inference(rat,[],[s185,s184,s183]) ).
cnf(s187,plain,
( ~ spl0_39
| spl0_25 ),
inference(rat,[],[s165,s171,s163,s176]) ).
cnf(s188,plain,
( spl0_11
| spl0_25 ),
inference(rat,[],[s175,s6,s16,s26]) ).
cnf(s189,plain,
spl0_25,
inference(rat,[],[s179,s7,s164,s188,s187]) ).
cnf(s190,plain,
~ spl0_4,
inference(rat,[],[s186,s189]) ).
cnf(s191,plain,
( spl0_15
| ~ spl0_3 ),
inference(rat,[],[s69,s40,s50]) ).
cnf(s192,plain,
( spl0_11
| ~ spl0_3 ),
inference(rat,[],[s69,s36,s46]) ).
cnf(s193,plain,
~ spl0_3,
inference(rat,[],[s69,s37,s47,s164,s192,s163,s169,s191,s157,s73,s176,s189]) ).
cnf(s194,plain,
( spl0_10
| spl0_31 ),
inference(rat,[],[s147,s159,s35,s45,s189]) ).
cnf(s195,plain,
( spl0_11
| spl0_31 ),
inference(rat,[],[s147,s159,s36,s46,s189]) ).
cnf(s196,plain,
~ spl0_2,
inference(rat,[],[s147,s159,s37,s47,s124,s195,s194,s149,s189,s176]) ).
cnf(s197,plain,
spl0_1,
inference(rat,[],[s2,s176,s182,s190,s193,s196]) ).
cnf(s198,plain,
~ spl0_31,
inference(rat,[],[s95,s189,s176,s197]) ).
cnf(s200,plain,
spl0_11,
inference(rat,[],[s195,s198]) ).
cnf(s201,plain,
spl0_15,
inference(rat,[],[s147,s90,s40,s50,s189,s197]) ).
cnf(s202,plain,
~ spl0_35,
inference(rat,[],[s169,s198,s201]) ).
cnf(s203,plain,
~ spl0_39,
inference(rat,[],[s163,s176,s202]) ).
cnf(s205,plain,
~ spl0_12,
inference(rat,[],[s164,s200,s203]) ).
cnf(s206,plain,
spl0_21,
inference(rat,[],[s47,s205]) ).
cnf(s207,plain,
spl0_20,
inference(rat,[],[s37,s205]) ).
cnf(s211,plain,
~ spl0_30,
inference(rat,[],[s90,s197,s189,s206]) ).
cnf(s212,plain,
$false,
inference(rat,[],[s147,s189,s207,s211]) ).
fof(f1109,plain,
$false,
inference(avatar_sat_refutation,[],[s212]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP238-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.39 % Computer : n026.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Sun Sep 27 09:40:42 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.43 Running first-order theorem proving
% 0.12/0.43 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
% 3.28/1.33 % (2582355)Input is clausal, will run a generic CNF schedule.
% 3.28/1.33 % (2582361)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=749891813:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.28/1.33 % (2582366)dis-21_1_sil=8000:lcm=predicate:random_seed=3772028576: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)
% 3.28/1.33 % (2582364)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=2447109572:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.28/1.33 % (2582363)lrs+10_1_sil=8000:sp=occurrence:random_seed=2665157622:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.28/1.33 % (2582362)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=699323533:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.28/1.33 % (2582360)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=3457982657:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.28/1.33 % (2582365)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=4002764512:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.28/1.33 % (2582366)Refutation not found, incomplete strategy
% 3.28/1.33 % (2582366)------------------------------
% 3.28/1.33 % (2582366)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.28/1.33 % (2582366)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.28/1.33 % (2582366)CaDiCaL version: 2.1.3
% 3.28/1.33 % (2582366)Termination reason: Refutation not found, incomplete strategy
% 3.28/1.33 % (2582366)Time elapsed: 0.002 s
% 3.28/1.33 % (2582366)Peak memory usage: 88 MB
% 3.28/1.33 % (2582366)Instructions burned: 3 (million)
% 3.28/1.33 % (2582363)Refutation not found, incomplete strategy
% 3.28/1.33 % (2582363)------------------------------
% 3.28/1.33 % (2582363)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.28/1.33 % (2582363)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.28/1.33 % (2582363)CaDiCaL version: 2.1.3
% 3.28/1.33 % (2582363)Termination reason: Refutation not found, incomplete strategy
% 3.28/1.33 % (2582363)Time elapsed: 0.004 s
% 3.28/1.33 % (2582363)Peak memory usage: 88 MB
% 3.28/1.33 % (2582363)Instructions burned: 6 (million)
% 3.28/1.33 % (2582365)First to succeed.
% 3.28/1.33 % (2582365)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2582355"
% 3.28/1.33 % (2582364)Instruction limit reached!
% 3.28/1.33 % (2582364)------------------------------
% 3.28/1.33 % (2582364)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.28/1.33 % (2582364)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.28/1.33 % (2582364)CaDiCaL version: 2.1.3
% 3.28/1.33 % (2582364)Termination reason: Instruction limit
% 3.28/1.33 % (2582364)Termination phase: Saturation
% 3.28/1.33 % (2582364)Time elapsed: 0.066 s
% 3.28/1.33 % (2582364)Peak memory usage: 89 MB
% 3.28/1.33 % (2582364)Instructions burned: 115 (million)
% 3.28/1.33 % (2582374)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=3886345962:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 3.28/1.33 % (2582374)Refutation not found, incomplete strategy
% 3.28/1.33 % (2582374)------------------------------
% 3.28/1.33 % (2582374)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.28/1.33 % (2582374)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.28/1.33 % (2582374)CaDiCaL version: 2.1.3
% 3.28/1.33 % (2582374)Termination reason: Refutation not found, incomplete strategy
% 3.28/1.33 % (2582374)Time elapsed: 0.004 s
% 3.28/1.33 % (2582374)Peak memory usage: 88 MB
% 3.28/1.33 % (2582374)Instructions burned: 6 (million)
% 3.28/1.33 % (2582363)------------------------------
% 3.28/1.33 % (2582363)------------------------------
% 3.28/1.33 % (2582366)------------------------------
% 3.28/1.33 % (2582366)------------------------------
% 3.28/1.33 % (2582365)Refutation found. Thanks to Tanya!
% 3.28/1.33 % SZS status Unsatisfiable for theBenchmark
% 3.28/1.33 % SZS output start Proof for theBenchmark
% See solution above
% 3.88/1.53 % (2582365)------------------------------
% 3.88/1.53 % (2582365)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.88/1.53 % (2582365)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.88/1.53 % (2582365)CaDiCaL version: 2.1.3
% 3.88/1.53 % (2582365)Termination reason: Refutation
% 3.88/1.53 % (2582365)Time elapsed: 0.026 s
% 3.88/1.53 % (2582365)Peak memory usage: 90 MB
% 3.88/1.53 % (2582365)Instructions burned: 38 (million)
% 3.88/1.53 % (2582365)------------------------------
% 3.88/1.53 % (2582365)------------------------------
% 3.88/1.53 % (2582355)Success in time 0.459 s
% 3.88/1.53 % Vampire exiting
%------------------------------------------------------------------------------