%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP254-1 : 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 : 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 10:13:27 AM UTC 2026
% Result : Unsatisfiable 2.77s 1.31s
% Output : Refutation 3.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 73
% Syntax : Number of formulae : 406 ( 24 unt; 29 def)
% Number of atoms : 1198 ( 425 equ)
% Maximal formula atoms : 16 ( 2 avg)
% Number of connectives : 1452 ( 660 ~; 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 : 15 ( 15 usr; 13 con; 0-2 aty)
% Number of variables : 74 ( 0 sgn 74 !; 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,
( multiply(sk_c1,sk_c12) = sk_c11
| multiply(sk_c4,sk_c12) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,plain,
( multiply(sk_c1,sk_c12) = sk_c11
| sk_c11 = multiply(sk_c4,sk_c12) ),
inference(reorient_equations,[],[f5]) ).
fof(f7,negated_conjecture,
( multiply(sk_c1,sk_c12) = sk_c11
| inverse(sk_c4) = sk_c12 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_2) ).
fof(f8,plain,
( multiply(sk_c1,sk_c12) = sk_c11
| sk_c12 = inverse(sk_c4) ),
inference(reorient_equations,[],[f7]) ).
fof(f21,negated_conjecture,
( multiply(sk_c1,sk_c12) = sk_c11
| multiply(sk_c8,sk_c9) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_10) ).
fof(f22,plain,
( multiply(sk_c1,sk_c12) = sk_c11
| sk_c7 = multiply(sk_c8,sk_c9) ),
inference(reorient_equations,[],[f21]) ).
fof(f23,negated_conjecture,
( inverse(sk_c1) = sk_c12
| multiply(sk_c4,sk_c12) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_11) ).
fof(f24,plain,
( sk_c12 = inverse(sk_c1)
| sk_c11 = multiply(sk_c4,sk_c12) ),
inference(reorient_equations,[],[f23]) ).
fof(f25,negated_conjecture,
( inverse(sk_c1) = sk_c12
| inverse(sk_c4) = sk_c12 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_12) ).
fof(f26,plain,
( sk_c12 = inverse(sk_c1)
| sk_c12 = inverse(sk_c4) ),
inference(reorient_equations,[],[f25]) ).
fof(f41,negated_conjecture,
( inverse(sk_c1) = sk_c12
| multiply(sk_c8,sk_c9) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_20) ).
fof(f42,plain,
( sk_c12 = inverse(sk_c1)
| sk_c7 = multiply(sk_c8,sk_c9) ),
inference(reorient_equations,[],[f41]) ).
fof(f43,negated_conjecture,
( multiply(sk_c2,sk_c11) = sk_c10
| multiply(sk_c4,sk_c12) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_21) ).
fof(f44,plain,
( sk_c10 = multiply(sk_c2,sk_c11)
| sk_c11 = multiply(sk_c4,sk_c12) ),
inference(reorient_equations,[],[f43]) ).
fof(f45,negated_conjecture,
( multiply(sk_c2,sk_c11) = sk_c10
| inverse(sk_c4) = sk_c12 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_22) ).
fof(f46,plain,
( sk_c10 = multiply(sk_c2,sk_c11)
| sk_c12 = inverse(sk_c4) ),
inference(reorient_equations,[],[f45]) ).
fof(f47,negated_conjecture,
( multiply(sk_c2,sk_c11) = sk_c10
| multiply(sk_c5,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_23) ).
fof(f48,plain,
( sk_c10 = multiply(sk_c2,sk_c11)
| multiply(sk_c5,sk_c11) = sk_c10 ),
inference(reorient_equations,[],[f47]) ).
fof(f49,negated_conjecture,
( multiply(sk_c2,sk_c11) = sk_c10
| inverse(sk_c5) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_24) ).
fof(f50,plain,
( sk_c10 = multiply(sk_c2,sk_c11)
| sk_c11 = inverse(sk_c5) ),
inference(reorient_equations,[],[f49]) ).
fof(f61,negated_conjecture,
( multiply(sk_c2,sk_c11) = sk_c10
| multiply(sk_c8,sk_c9) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_30) ).
fof(f62,plain,
( sk_c10 = multiply(sk_c2,sk_c11)
| sk_c7 = multiply(sk_c8,sk_c9) ),
inference(reorient_equations,[],[f61]) ).
fof(f63,negated_conjecture,
( inverse(sk_c2) = sk_c11
| multiply(sk_c4,sk_c12) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_31) ).
fof(f64,plain,
( sk_c11 = inverse(sk_c2)
| sk_c11 = multiply(sk_c4,sk_c12) ),
inference(reorient_equations,[],[f63]) ).
fof(f67,negated_conjecture,
( inverse(sk_c2) = sk_c11
| multiply(sk_c5,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_33) ).
fof(f68,plain,
( sk_c11 = inverse(sk_c2)
| multiply(sk_c5,sk_c11) = sk_c10 ),
inference(reorient_equations,[],[f67]) ).
fof(f69,negated_conjecture,
( inverse(sk_c2) = sk_c11
| inverse(sk_c5) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_34) ).
fof(f70,plain,
( sk_c11 = inverse(sk_c2)
| sk_c11 = inverse(sk_c5) ),
inference(reorient_equations,[],[f69]) ).
fof(f71,negated_conjecture,
( inverse(sk_c2) = sk_c11
| multiply(sk_c6,sk_c9) = sk_c12 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_35) ).
fof(f72,plain,
( sk_c11 = inverse(sk_c2)
| sk_c12 = multiply(sk_c6,sk_c9) ),
inference(reorient_equations,[],[f71]) ).
fof(f73,negated_conjecture,
( inverse(sk_c2) = sk_c11
| inverse(sk_c6) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_36) ).
fof(f74,plain,
( sk_c11 = inverse(sk_c2)
| sk_c9 = inverse(sk_c6) ),
inference(reorient_equations,[],[f73]) ).
fof(f75,negated_conjecture,
( inverse(sk_c2) = sk_c11
| multiply(sk_c9,sk_c11) = sk_c12 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_37) ).
fof(f76,plain,
( sk_c11 = inverse(sk_c2)
| sk_c12 = multiply(sk_c9,sk_c11) ),
inference(reorient_equations,[],[f75]) ).
fof(f77,negated_conjecture,
( inverse(sk_c2) = sk_c11
| inverse(sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_38) ).
fof(f78,plain,
( sk_c11 = inverse(sk_c2)
| inverse(sk_c8) = sk_c7 ),
inference(reorient_equations,[],[f77]) ).
fof(f79,negated_conjecture,
( inverse(sk_c2) = sk_c11
| inverse(sk_c7) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_39) ).
fof(f80,plain,
( sk_c11 = inverse(sk_c2)
| sk_c9 = inverse(sk_c7) ),
inference(reorient_equations,[],[f79]) ).
fof(f81,negated_conjecture,
( inverse(sk_c2) = sk_c11
| multiply(sk_c8,sk_c9) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_40) ).
fof(f82,plain,
( sk_c11 = inverse(sk_c2)
| sk_c7 = multiply(sk_c8,sk_c9) ),
inference(reorient_equations,[],[f81]) ).
fof(f83,negated_conjecture,
( inverse(sk_c3) = sk_c10
| multiply(sk_c4,sk_c12) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_41) ).
fof(f84,plain,
( sk_c10 = inverse(sk_c3)
| sk_c11 = multiply(sk_c4,sk_c12) ),
inference(reorient_equations,[],[f83]) ).
fof(f85,negated_conjecture,
( inverse(sk_c3) = sk_c10
| inverse(sk_c4) = sk_c12 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_42) ).
fof(f86,plain,
( sk_c10 = inverse(sk_c3)
| sk_c12 = inverse(sk_c4) ),
inference(reorient_equations,[],[f85]) ).
fof(f87,negated_conjecture,
( inverse(sk_c3) = sk_c10
| multiply(sk_c5,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_43) ).
fof(f88,plain,
( sk_c10 = inverse(sk_c3)
| multiply(sk_c5,sk_c11) = sk_c10 ),
inference(reorient_equations,[],[f87]) ).
fof(f89,negated_conjecture,
( inverse(sk_c3) = sk_c10
| inverse(sk_c5) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_44) ).
fof(f90,plain,
( sk_c10 = inverse(sk_c3)
| sk_c11 = inverse(sk_c5) ),
inference(reorient_equations,[],[f89]) ).
fof(f91,negated_conjecture,
( inverse(sk_c3) = sk_c10
| multiply(sk_c6,sk_c9) = sk_c12 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_45) ).
fof(f92,plain,
( sk_c10 = inverse(sk_c3)
| sk_c12 = multiply(sk_c6,sk_c9) ),
inference(reorient_equations,[],[f91]) ).
fof(f93,negated_conjecture,
( inverse(sk_c3) = sk_c10
| inverse(sk_c6) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_46) ).
fof(f94,plain,
( sk_c10 = inverse(sk_c3)
| sk_c9 = inverse(sk_c6) ),
inference(reorient_equations,[],[f93]) ).
fof(f95,negated_conjecture,
( inverse(sk_c3) = sk_c10
| multiply(sk_c9,sk_c11) = sk_c12 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_47) ).
fof(f96,plain,
( sk_c10 = inverse(sk_c3)
| sk_c12 = multiply(sk_c9,sk_c11) ),
inference(reorient_equations,[],[f95]) ).
fof(f97,negated_conjecture,
( inverse(sk_c3) = sk_c10
| inverse(sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_48) ).
fof(f98,plain,
( sk_c10 = inverse(sk_c3)
| inverse(sk_c8) = sk_c7 ),
inference(reorient_equations,[],[f97]) ).
fof(f99,negated_conjecture,
( inverse(sk_c3) = sk_c10
| inverse(sk_c7) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_49) ).
fof(f100,plain,
( sk_c10 = inverse(sk_c3)
| sk_c9 = inverse(sk_c7) ),
inference(reorient_equations,[],[f99]) ).
fof(f101,negated_conjecture,
( inverse(sk_c3) = sk_c10
| multiply(sk_c8,sk_c9) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_50) ).
fof(f102,plain,
( sk_c10 = inverse(sk_c3)
| sk_c7 = multiply(sk_c8,sk_c9) ),
inference(reorient_equations,[],[f101]) ).
fof(f103,negated_conjecture,
( multiply(sk_c3,sk_c12) = sk_c10
| multiply(sk_c4,sk_c12) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_51) ).
fof(f104,plain,
( sk_c10 = multiply(sk_c3,sk_c12)
| sk_c11 = multiply(sk_c4,sk_c12) ),
inference(reorient_equations,[],[f103]) ).
fof(f105,negated_conjecture,
( multiply(sk_c3,sk_c12) = sk_c10
| inverse(sk_c4) = sk_c12 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_52) ).
fof(f106,plain,
( sk_c10 = multiply(sk_c3,sk_c12)
| sk_c12 = inverse(sk_c4) ),
inference(reorient_equations,[],[f105]) ).
fof(f107,negated_conjecture,
( multiply(sk_c3,sk_c12) = sk_c10
| multiply(sk_c5,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_53) ).
fof(f108,plain,
( sk_c10 = multiply(sk_c3,sk_c12)
| multiply(sk_c5,sk_c11) = sk_c10 ),
inference(reorient_equations,[],[f107]) ).
fof(f109,negated_conjecture,
( multiply(sk_c3,sk_c12) = sk_c10
| inverse(sk_c5) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_54) ).
fof(f110,plain,
( sk_c10 = multiply(sk_c3,sk_c12)
| sk_c11 = inverse(sk_c5) ),
inference(reorient_equations,[],[f109]) ).
fof(f111,negated_conjecture,
( multiply(sk_c3,sk_c12) = sk_c10
| multiply(sk_c6,sk_c9) = sk_c12 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_55) ).
fof(f112,plain,
( sk_c10 = multiply(sk_c3,sk_c12)
| sk_c12 = multiply(sk_c6,sk_c9) ),
inference(reorient_equations,[],[f111]) ).
fof(f113,negated_conjecture,
( multiply(sk_c3,sk_c12) = sk_c10
| inverse(sk_c6) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_56) ).
fof(f114,plain,
( sk_c10 = multiply(sk_c3,sk_c12)
| sk_c9 = inverse(sk_c6) ),
inference(reorient_equations,[],[f113]) ).
fof(f115,negated_conjecture,
( multiply(sk_c3,sk_c12) = sk_c10
| multiply(sk_c9,sk_c11) = sk_c12 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_57) ).
fof(f116,plain,
( sk_c10 = multiply(sk_c3,sk_c12)
| sk_c12 = multiply(sk_c9,sk_c11) ),
inference(reorient_equations,[],[f115]) ).
fof(f117,negated_conjecture,
( multiply(sk_c3,sk_c12) = sk_c10
| inverse(sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_58) ).
fof(f118,plain,
( sk_c10 = multiply(sk_c3,sk_c12)
| inverse(sk_c8) = sk_c7 ),
inference(reorient_equations,[],[f117]) ).
fof(f119,negated_conjecture,
( multiply(sk_c3,sk_c12) = sk_c10
| inverse(sk_c7) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_59) ).
fof(f120,plain,
( sk_c10 = multiply(sk_c3,sk_c12)
| sk_c9 = inverse(sk_c7) ),
inference(reorient_equations,[],[f119]) ).
fof(f121,negated_conjecture,
( multiply(sk_c3,sk_c12) = sk_c10
| multiply(sk_c8,sk_c9) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_60) ).
fof(f122,plain,
( sk_c10 = multiply(sk_c3,sk_c12)
| sk_c7 = multiply(sk_c8,sk_c9) ),
inference(reorient_equations,[],[f121]) ).
fof(f123,negated_conjecture,
! [X2,X3,X0,X1,X8,X6,X7,X4,X5] :
( multiply(X0,sk_c12) != sk_c11
| inverse(X0) != sk_c12
| multiply(X1,sk_c11) != sk_c10
| inverse(X1) != sk_c11
| inverse(X2) != sk_c10
| multiply(X2,sk_c12) != sk_c10
| multiply(X3,sk_c12) != sk_c11
| inverse(X3) != sk_c12
| multiply(X4,sk_c11) != sk_c10
| inverse(X4) != sk_c11
| multiply(X5,X6) != sk_c12
| inverse(X5) != X6
| multiply(X6,sk_c11) != sk_c12
| inverse(X7) != X8
| inverse(X8) != X6
| multiply(X7,X6) != X8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_61) ).
fof(f124,plain,
! [X2,X3,X0,X1,X8,X6,X7,X4,X5] :
( sk_c11 != multiply(X0,sk_c12)
| inverse(X0) != sk_c12
| sk_c10 != multiply(X1,sk_c11)
| sk_c11 != inverse(X1)
| sk_c10 != inverse(X2)
| sk_c10 != multiply(X2,sk_c12)
| sk_c11 != multiply(X3,sk_c12)
| sk_c12 != inverse(X3)
| sk_c10 != multiply(X4,sk_c11)
| sk_c11 != inverse(X4)
| sk_c12 != multiply(X5,X6)
| inverse(X5) != X6
| sk_c12 != multiply(X6,sk_c11)
| inverse(X7) != X8
| inverse(X8) != X6
| multiply(X7,X6) != X8 ),
inference(reorient_equations,[],[f123]) ).
fof(f125,plain,
! [X2,X3,X0,X1,X8,X7,X4,X5] :
( sk_c11 != multiply(X0,sk_c12)
| inverse(X0) != sk_c12
| sk_c10 != multiply(X1,sk_c11)
| sk_c11 != inverse(X1)
| sk_c10 != inverse(X2)
| sk_c10 != multiply(X2,sk_c12)
| sk_c11 != multiply(X3,sk_c12)
| sk_c12 != inverse(X3)
| sk_c10 != multiply(X4,sk_c11)
| sk_c11 != inverse(X4)
| sk_c12 != multiply(X5,inverse(X5))
| sk_c12 != multiply(inverse(X5),sk_c11)
| inverse(X7) != X8
| inverse(X5) != inverse(X8)
| multiply(X7,inverse(X5)) != X8 ),
inference(equality_resolution,[],[f124]) ).
fof(f126,plain,
! [X2,X3,X0,X1,X7,X4,X5] :
( sk_c11 != multiply(X0,sk_c12)
| inverse(X0) != sk_c12
| sk_c10 != multiply(X1,sk_c11)
| sk_c11 != inverse(X1)
| sk_c10 != inverse(X2)
| sk_c10 != multiply(X2,sk_c12)
| sk_c11 != multiply(X3,sk_c12)
| sk_c12 != inverse(X3)
| sk_c10 != multiply(X4,sk_c11)
| sk_c11 != inverse(X4)
| sk_c12 != multiply(X5,inverse(X5))
| sk_c12 != multiply(inverse(X5),sk_c11)
| inverse(X5) != inverse(inverse(X7))
| inverse(X7) != multiply(X7,inverse(X5)) ),
inference(equality_resolution,[],[f125]) ).
fof(f128,definition,
( spl0_1
<=> ! [X5,X7] :
( sk_c12 != multiply(X5,inverse(X5))
| inverse(X7) != multiply(X7,inverse(X5))
| inverse(X5) != inverse(inverse(X7))
| sk_c12 != multiply(inverse(X5),sk_c11) ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f129,plain,
( ! [X7,X5] :
( sk_c12 != multiply(inverse(X5),sk_c11)
| inverse(X7) != multiply(X7,inverse(X5))
| inverse(X5) != inverse(inverse(X7))
| sk_c12 != multiply(X5,inverse(X5)) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f128]) ).
fof(f131,definition,
( spl0_2
<=> ! [X4] :
( sk_c10 != multiply(X4,sk_c11)
| sk_c11 != inverse(X4) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f132,plain,
( ! [X4] :
( sk_c10 != multiply(X4,sk_c11)
| sk_c11 != inverse(X4) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f131]) ).
fof(f134,definition,
( spl0_3
<=> ! [X3] :
( sk_c11 != multiply(X3,sk_c12)
| sk_c12 != inverse(X3) ) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f135,plain,
( ! [X3] :
( sk_c11 != multiply(X3,sk_c12)
| sk_c12 != inverse(X3) )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f134]) ).
fof(f137,definition,
( spl0_4
<=> ! [X2] :
( sk_c10 != inverse(X2)
| sk_c10 != multiply(X2,sk_c12) ) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f138,plain,
( ! [X2] :
( sk_c10 != multiply(X2,sk_c12)
| sk_c10 != inverse(X2) )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f137]) ).
fof(f139,plain,
( spl0_1
| spl0_2
| spl0_3
| spl0_4
| spl0_2
| spl0_3 ),
inference(avatar_split_clause,[],[f126,f134,f131,f137,f134,f131,f128]) ).
fof(f141,definition,
( spl0_5
<=> sk_c7 = multiply(sk_c8,sk_c9) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f143,plain,
( sk_c7 = multiply(sk_c8,sk_c9)
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f141]) ).
fof(f145,definition,
( spl0_6
<=> sk_c10 = multiply(sk_c3,sk_c12) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f147,plain,
( sk_c10 = multiply(sk_c3,sk_c12)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f145]) ).
fof(f148,plain,
( spl0_5
| spl0_6 ),
inference(avatar_split_clause,[],[f122,f145,f141]) ).
fof(f150,definition,
( spl0_7
<=> sk_c9 = inverse(sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f152,plain,
( sk_c9 = inverse(sk_c7)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f150]) ).
fof(f153,plain,
( spl0_7
| spl0_6 ),
inference(avatar_split_clause,[],[f120,f145,f150]) ).
fof(f155,definition,
( spl0_8
<=> inverse(sk_c8) = sk_c7 ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f157,plain,
( inverse(sk_c8) = sk_c7
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f155]) ).
fof(f158,plain,
( spl0_8
| spl0_6 ),
inference(avatar_split_clause,[],[f118,f145,f155]) ).
fof(f160,definition,
( spl0_9
<=> sk_c12 = multiply(sk_c9,sk_c11) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f162,plain,
( sk_c12 = multiply(sk_c9,sk_c11)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f160]) ).
fof(f163,plain,
( spl0_9
| spl0_6 ),
inference(avatar_split_clause,[],[f116,f145,f160]) ).
fof(f165,definition,
( spl0_10
<=> sk_c9 = inverse(sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f167,plain,
( sk_c9 = inverse(sk_c6)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f165]) ).
fof(f168,plain,
( spl0_10
| spl0_6 ),
inference(avatar_split_clause,[],[f114,f145,f165]) ).
fof(f170,definition,
( spl0_11
<=> sk_c12 = multiply(sk_c6,sk_c9) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f172,plain,
( sk_c12 = multiply(sk_c6,sk_c9)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f170]) ).
fof(f173,plain,
( spl0_11
| spl0_6 ),
inference(avatar_split_clause,[],[f112,f145,f170]) ).
fof(f175,definition,
( spl0_12
<=> sk_c11 = inverse(sk_c5) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f177,plain,
( sk_c11 = inverse(sk_c5)
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f175]) ).
fof(f178,plain,
( spl0_12
| spl0_6 ),
inference(avatar_split_clause,[],[f110,f145,f175]) ).
fof(f180,definition,
( spl0_13
<=> multiply(sk_c5,sk_c11) = sk_c10 ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f182,plain,
( multiply(sk_c5,sk_c11) = sk_c10
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f180]) ).
fof(f183,plain,
( spl0_13
| spl0_6 ),
inference(avatar_split_clause,[],[f108,f145,f180]) ).
fof(f185,definition,
( spl0_14
<=> sk_c12 = inverse(sk_c4) ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
fof(f187,plain,
( sk_c12 = inverse(sk_c4)
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f185]) ).
fof(f188,plain,
( spl0_14
| spl0_6 ),
inference(avatar_split_clause,[],[f106,f145,f185]) ).
fof(f190,definition,
( spl0_15
<=> sk_c11 = multiply(sk_c4,sk_c12) ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
fof(f192,plain,
( sk_c11 = multiply(sk_c4,sk_c12)
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f190]) ).
fof(f193,plain,
( spl0_15
| spl0_6 ),
inference(avatar_split_clause,[],[f104,f145,f190]) ).
fof(f195,definition,
( spl0_16
<=> sk_c10 = inverse(sk_c3) ),
introduced(definition,[new_symbols(definition,[spl0_16])],[avatar_definition]) ).
fof(f197,plain,
( sk_c10 = inverse(sk_c3)
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f195]) ).
fof(f198,plain,
( spl0_5
| spl0_16 ),
inference(avatar_split_clause,[],[f102,f195,f141]) ).
fof(f199,plain,
( spl0_7
| spl0_16 ),
inference(avatar_split_clause,[],[f100,f195,f150]) ).
fof(f200,plain,
( spl0_8
| spl0_16 ),
inference(avatar_split_clause,[],[f98,f195,f155]) ).
fof(f201,plain,
( spl0_9
| spl0_16 ),
inference(avatar_split_clause,[],[f96,f195,f160]) ).
fof(f202,plain,
( spl0_10
| spl0_16 ),
inference(avatar_split_clause,[],[f94,f195,f165]) ).
fof(f203,plain,
( spl0_11
| spl0_16 ),
inference(avatar_split_clause,[],[f92,f195,f170]) ).
fof(f204,plain,
( spl0_12
| spl0_16 ),
inference(avatar_split_clause,[],[f90,f195,f175]) ).
fof(f205,plain,
( spl0_13
| spl0_16 ),
inference(avatar_split_clause,[],[f88,f195,f180]) ).
fof(f206,plain,
( spl0_14
| spl0_16 ),
inference(avatar_split_clause,[],[f86,f195,f185]) ).
fof(f207,plain,
( spl0_15
| spl0_16 ),
inference(avatar_split_clause,[],[f84,f195,f190]) ).
fof(f209,definition,
( spl0_17
<=> sk_c11 = inverse(sk_c2) ),
introduced(definition,[new_symbols(definition,[spl0_17])],[avatar_definition]) ).
fof(f211,plain,
( sk_c11 = inverse(sk_c2)
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f209]) ).
fof(f212,plain,
( spl0_5
| spl0_17 ),
inference(avatar_split_clause,[],[f82,f209,f141]) ).
fof(f213,plain,
( spl0_7
| spl0_17 ),
inference(avatar_split_clause,[],[f80,f209,f150]) ).
fof(f214,plain,
( spl0_8
| spl0_17 ),
inference(avatar_split_clause,[],[f78,f209,f155]) ).
fof(f215,plain,
( spl0_9
| spl0_17 ),
inference(avatar_split_clause,[],[f76,f209,f160]) ).
fof(f216,plain,
( spl0_10
| spl0_17 ),
inference(avatar_split_clause,[],[f74,f209,f165]) ).
fof(f217,plain,
( spl0_11
| spl0_17 ),
inference(avatar_split_clause,[],[f72,f209,f170]) ).
fof(f218,plain,
( spl0_12
| spl0_17 ),
inference(avatar_split_clause,[],[f70,f209,f175]) ).
fof(f219,plain,
( spl0_13
| spl0_17 ),
inference(avatar_split_clause,[],[f68,f209,f180]) ).
fof(f221,plain,
( spl0_15
| spl0_17 ),
inference(avatar_split_clause,[],[f64,f209,f190]) ).
fof(f223,definition,
( spl0_18
<=> sk_c10 = multiply(sk_c2,sk_c11) ),
introduced(definition,[new_symbols(definition,[spl0_18])],[avatar_definition]) ).
fof(f224,plain,
( sk_c10 != multiply(sk_c2,sk_c11)
| spl0_18 ),
inference(avatar_component_clause,[],[f223]) ).
fof(f225,plain,
( sk_c10 = multiply(sk_c2,sk_c11)
| ~ spl0_18 ),
inference(avatar_component_clause,[],[f223]) ).
fof(f226,plain,
( spl0_5
| spl0_18 ),
inference(avatar_split_clause,[],[f62,f223,f141]) ).
fof(f232,plain,
( spl0_12
| spl0_18 ),
inference(avatar_split_clause,[],[f50,f223,f175]) ).
fof(f233,plain,
( spl0_13
| spl0_18 ),
inference(avatar_split_clause,[],[f48,f223,f180]) ).
fof(f234,plain,
( spl0_14
| spl0_18 ),
inference(avatar_split_clause,[],[f46,f223,f185]) ).
fof(f235,plain,
( spl0_15
| spl0_18 ),
inference(avatar_split_clause,[],[f44,f223,f190]) ).
fof(f237,definition,
( spl0_19
<=> sk_c12 = inverse(sk_c1) ),
introduced(definition,[new_symbols(definition,[spl0_19])],[avatar_definition]) ).
fof(f239,plain,
( sk_c12 = inverse(sk_c1)
| ~ spl0_19 ),
inference(avatar_component_clause,[],[f237]) ).
fof(f240,plain,
( spl0_5
| spl0_19 ),
inference(avatar_split_clause,[],[f42,f237,f141]) ).
fof(f248,plain,
( spl0_14
| spl0_19 ),
inference(avatar_split_clause,[],[f26,f237,f185]) ).
fof(f249,plain,
( spl0_15
| spl0_19 ),
inference(avatar_split_clause,[],[f24,f237,f190]) ).
fof(f251,definition,
( spl0_20
<=> multiply(sk_c1,sk_c12) = sk_c11 ),
introduced(definition,[new_symbols(definition,[spl0_20])],[avatar_definition]) ).
fof(f253,plain,
( multiply(sk_c1,sk_c12) = sk_c11
| ~ spl0_20 ),
inference(avatar_component_clause,[],[f251]) ).
fof(f254,plain,
( spl0_5
| spl0_20 ),
inference(avatar_split_clause,[],[f22,f251,f141]) ).
fof(f262,plain,
( spl0_14
| spl0_20 ),
inference(avatar_split_clause,[],[f8,f251,f185]) ).
fof(f263,plain,
( spl0_15
| spl0_20 ),
inference(avatar_split_clause,[],[f6,f251,f190]) ).
fof(f264,plain,
( sk_c10 != sk_c10
| sk_c11 != inverse(sk_c5)
| ~ spl0_2
| ~ spl0_13 ),
inference(superposition,[],[f132,f182]) ).
fof(f266,plain,
( sk_c11 != inverse(sk_c5)
| ~ spl0_2
| ~ spl0_13 ),
inference(trivial_inequality_removal,[],[f264]) ).
fof(f272,definition,
( spl0_22
<=> sk_c12 = sk_c10 ),
introduced(definition,[new_symbols(definition,[spl0_22])],[avatar_definition]) ).
fof(f274,plain,
( sk_c12 != sk_c10
| spl0_22 ),
inference(avatar_component_clause,[],[f272]) ).
fof(f278,plain,
( ~ spl0_12
| ~ spl0_2
| ~ spl0_13 ),
inference(avatar_split_clause,[],[f266,f180,f131,f175]) ).
fof(f279,plain,
( sk_c10 != sk_c10
| sk_c11 != inverse(sk_c2)
| ~ spl0_2
| ~ spl0_18 ),
inference(superposition,[],[f132,f225]) ).
fof(f280,plain,
( sk_c11 != inverse(sk_c2)
| ~ spl0_2
| ~ spl0_18 ),
inference(trivial_inequality_removal,[],[f279]) ).
fof(f281,plain,
( $false
| ~ spl0_2
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[],[f280,f211]) ).
fof(f282,plain,
( ~ spl0_2
| ~ spl0_17
| ~ spl0_18 ),
inference(avatar_contradiction_clause,[],[f281]) ).
fof(f283,plain,
( sk_c11 != sk_c10
| sk_c10 != inverse(sk_c1)
| ~ spl0_4
| ~ spl0_20 ),
inference(superposition,[],[f138,f253]) ).
fof(f284,plain,
( sk_c11 != sk_c10
| inverse(sk_c4) != sk_c10
| ~ spl0_4
| ~ spl0_15 ),
inference(superposition,[],[f138,f192]) ).
fof(f285,plain,
( sk_c10 != sk_c10
| sk_c10 != inverse(sk_c3)
| ~ spl0_4
| ~ spl0_6 ),
inference(superposition,[],[f138,f147]) ).
fof(f286,plain,
( sk_c10 != inverse(sk_c3)
| ~ spl0_4
| ~ spl0_6 ),
inference(trivial_inequality_removal,[],[f285]) ).
fof(f287,plain,
( $false
| ~ spl0_4
| ~ spl0_6
| ~ spl0_16 ),
inference(forward_subsumption_resolution,[],[f286,f197]) ).
fof(f288,plain,
( ~ spl0_4
| ~ spl0_6
| ~ spl0_16 ),
inference(avatar_contradiction_clause,[],[f287]) ).
fof(f290,plain,
( sk_c12 != sk_c10
| sk_c11 != sk_c10
| ~ spl0_4
| ~ spl0_19
| ~ spl0_20 ),
inference(forward_demodulation,[],[f283,f239]) ).
fof(f291,plain,
( ! [X0] :
( sk_c12 != multiply(sk_c12,sk_c11)
| inverse(X0) != multiply(X0,sk_c12)
| sk_c12 != inverse(inverse(X0))
| sk_c12 != multiply(sk_c1,sk_c12) )
| ~ spl0_1
| ~ spl0_19 ),
inference(superposition,[],[f129,f239]) ).
fof(f292,plain,
( ! [X0] :
( sk_c12 != multiply(sk_c12,sk_c11)
| inverse(X0) != multiply(X0,sk_c12)
| sk_c12 != inverse(inverse(X0))
| sk_c12 != multiply(sk_c4,sk_c12) )
| ~ spl0_1
| ~ spl0_14 ),
inference(superposition,[],[f129,f187]) ).
fof(f293,plain,
( ! [X0] :
( sk_c12 != multiply(sk_c9,sk_c11)
| inverse(X0) != multiply(X0,sk_c9)
| sk_c9 != inverse(inverse(X0))
| sk_c12 != multiply(sk_c6,sk_c9) )
| ~ spl0_1
| ~ spl0_10 ),
inference(superposition,[],[f129,f167]) ).
fof(f324,plain,
( ! [X0] :
( inverse(X0) != multiply(X0,sk_c9)
| sk_c9 != inverse(inverse(X0))
| sk_c12 != multiply(sk_c6,sk_c9) )
| ~ spl0_1
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_subsumption_resolution,[],[f293,f162]) ).
fof(f325,plain,
( ! [X0] :
( sk_c12 != sk_c11
| sk_c12 != multiply(sk_c12,sk_c11)
| inverse(X0) != multiply(X0,sk_c12)
| sk_c12 != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f292,f192]) ).
fof(f326,plain,
( ! [X0] :
( sk_c12 != sk_c11
| sk_c12 != multiply(sk_c12,sk_c11)
| inverse(X0) != multiply(X0,sk_c12)
| sk_c12 != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_19
| ~ spl0_20 ),
inference(forward_demodulation,[],[f291,f253]) ).
fof(f332,definition,
( spl0_30
<=> ! [X0] :
( inverse(X0) != multiply(X0,sk_c9)
| sk_c9 != inverse(inverse(X0)) ) ),
introduced(definition,[new_symbols(definition,[spl0_30])],[avatar_definition]) ).
fof(f333,plain,
( ! [X0] :
( inverse(X0) != multiply(X0,sk_c9)
| sk_c9 != inverse(inverse(X0)) )
| ~ spl0_30 ),
inference(avatar_component_clause,[],[f332]) ).
fof(f335,plain,
( ! [X0] :
( inverse(X0) != multiply(X0,sk_c9)
| sk_c9 != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f324,f172]) ).
fof(f337,definition,
( spl0_31
<=> ! [X0] :
( inverse(X0) != multiply(X0,sk_c12)
| sk_c12 != inverse(inverse(X0)) ) ),
introduced(definition,[new_symbols(definition,[spl0_31])],[avatar_definition]) ).
fof(f338,plain,
( ! [X0] :
( sk_c12 != inverse(inverse(X0))
| inverse(X0) != multiply(X0,sk_c12) )
| ~ spl0_31 ),
inference(avatar_component_clause,[],[f337]) ).
fof(f340,definition,
( spl0_32
<=> sk_c12 = multiply(sk_c12,sk_c11) ),
introduced(definition,[new_symbols(definition,[spl0_32])],[avatar_definition]) ).
fof(f341,plain,
( sk_c12 = multiply(sk_c12,sk_c11)
| ~ spl0_32 ),
inference(avatar_component_clause,[],[f340]) ).
fof(f344,definition,
( spl0_33
<=> sk_c12 = sk_c11 ),
introduced(definition,[new_symbols(definition,[spl0_33])],[avatar_definition]) ).
fof(f345,plain,
( sk_c12 = sk_c11
| ~ spl0_33 ),
inference(avatar_component_clause,[],[f344]) ).
fof(f347,plain,
( spl0_31
| ~ spl0_32
| ~ spl0_33
| ~ spl0_1
| ~ spl0_14
| ~ spl0_15 ),
inference(avatar_split_clause,[],[f325,f190,f185,f128,f344,f340,f337]) ).
fof(f348,plain,
( spl0_31
| ~ spl0_32
| ~ spl0_33
| ~ spl0_1
| ~ spl0_19
| ~ spl0_20 ),
inference(avatar_split_clause,[],[f326,f251,f237,f128,f344,f340,f337]) ).
fof(f349,plain,
( spl0_30
| ~ spl0_1
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_split_clause,[],[f335,f170,f165,f160,f128,f332]) ).
fof(f351,plain,
( inverse(sk_c8) != sk_c7
| sk_c9 != inverse(inverse(sk_c8))
| ~ spl0_5
| ~ spl0_30 ),
inference(superposition,[],[f333,f143]) ).
fof(f352,plain,
( sk_c9 != inverse(inverse(sk_c8))
| ~ spl0_5
| ~ spl0_8
| ~ spl0_30 ),
inference(forward_subsumption_resolution,[],[f351,f157]) ).
fof(f354,plain,
( sk_c9 != inverse(sk_c7)
| ~ spl0_5
| ~ spl0_8
| ~ spl0_30 ),
inference(forward_demodulation,[],[f352,f157]) ).
fof(f356,plain,
( $false
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_30 ),
inference(forward_subsumption_resolution,[],[f354,f152]) ).
fof(f357,plain,
( ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_30 ),
inference(avatar_contradiction_clause,[],[f356]) ).
fof(f359,definition,
( spl0_34
<=> sk_c12 = sk_c9 ),
introduced(definition,[new_symbols(definition,[spl0_34])],[avatar_definition]) ).
fof(f360,plain,
( sk_c12 = sk_c9
| ~ spl0_34 ),
inference(avatar_component_clause,[],[f359]) ).
fof(f382,plain,
( identity = multiply(sk_c12,sk_c1)
| ~ spl0_19 ),
inference(superposition,[],[f3,f239]) ).
fof(f383,plain,
( identity = multiply(sk_c12,sk_c4)
| ~ spl0_14 ),
inference(superposition,[],[f3,f187]) ).
fof(f384,plain,
( identity = multiply(sk_c9,sk_c6)
| ~ spl0_10 ),
inference(superposition,[],[f3,f167]) ).
fof(f386,plain,
( identity = multiply(sk_c11,sk_c2)
| ~ spl0_17 ),
inference(superposition,[],[f3,f211]) ).
fof(f413,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[],[f4,f3]) ).
fof(f416,plain,
( ! [X0] : multiply(sk_c12,X0) = multiply(sk_c6,multiply(sk_c9,X0))
| ~ spl0_11 ),
inference(superposition,[],[f4,f172]) ).
fof(f422,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f413,f1]) ).
fof(f425,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c12,multiply(sk_c1,X0))
| ~ spl0_19 ),
inference(superposition,[],[f4,f382]) ).
fof(f426,plain,
( ! [X0] : multiply(sk_c12,multiply(sk_c1,X0)) = X0
| ~ spl0_19 ),
inference(forward_demodulation,[],[f425,f1]) ).
fof(f427,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c12,multiply(sk_c4,X0))
| ~ spl0_14 ),
inference(superposition,[],[f4,f383]) ).
fof(f428,plain,
( ! [X0] : multiply(sk_c12,multiply(sk_c4,X0)) = X0
| ~ spl0_14 ),
inference(forward_demodulation,[],[f427,f1]) ).
fof(f429,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c9,multiply(sk_c6,X0))
| ~ spl0_10 ),
inference(superposition,[],[f4,f384]) ).
fof(f430,plain,
( ! [X0] : multiply(sk_c9,multiply(sk_c6,X0)) = X0
| ~ spl0_10 ),
inference(forward_demodulation,[],[f429,f1]) ).
fof(f442,plain,
( sk_c12 = multiply(sk_c12,sk_c11)
| ~ spl0_19
| ~ spl0_20 ),
inference(superposition,[],[f426,f253]) ).
fof(f447,plain,
( spl0_32
| ~ spl0_19
| ~ spl0_20 ),
inference(avatar_split_clause,[],[f442,f251,f237,f340]) ).
fof(f449,plain,
( ! [X0] : multiply(sk_c12,X0) = multiply(sk_c12,multiply(sk_c11,X0))
| ~ spl0_32 ),
inference(superposition,[],[f4,f341]) ).
fof(f460,plain,
( sk_c12 = multiply(sk_c12,sk_c11)
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f428,f192]) ).
fof(f466,plain,
( multiply(sk_c12,sk_c11) = multiply(sk_c6,sk_c12)
| ~ spl0_9
| ~ spl0_11 ),
inference(superposition,[],[f416,f162]) ).
fof(f471,plain,
( sk_c12 = multiply(sk_c6,sk_c12)
| ~ spl0_9
| ~ spl0_11
| ~ spl0_32 ),
inference(forward_demodulation,[],[f466,f341]) ).
fof(f481,plain,
( sk_c9 = multiply(sk_c9,sk_c12)
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f430,f172]) ).
fof(f483,plain,
( sk_c12 = multiply(sk_c9,sk_c12)
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_32 ),
inference(superposition,[],[f430,f471]) ).
fof(f507,plain,
( sk_c12 = sk_c9
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_32 ),
inference(superposition,[],[f481,f483]) ).
fof(f512,plain,
( spl0_34
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_32 ),
inference(avatar_split_clause,[],[f507,f340,f170,f165,f160,f359]) ).
fof(f518,definition,
( spl0_45
<=> sk_c12 = inverse(sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_45])],[avatar_definition]) ).
fof(f519,plain,
( sk_c12 = inverse(sk_c6)
| ~ spl0_45 ),
inference(avatar_component_clause,[],[f518]) ).
fof(f606,plain,
( ! [X0] : multiply(sk_c11,X0) = multiply(inverse(sk_c12),multiply(sk_c12,X0))
| ~ spl0_32 ),
inference(superposition,[],[f422,f449]) ).
fof(f608,plain,
( sk_c11 = multiply(inverse(sk_c12),sk_c12)
| ~ spl0_32 ),
inference(superposition,[],[f422,f341]) ).
fof(f616,plain,
( sk_c9 = multiply(inverse(sk_c6),sk_c12)
| ~ spl0_11 ),
inference(superposition,[],[f422,f172]) ).
fof(f625,plain,
( sk_c11 = multiply(inverse(sk_c2),sk_c10)
| ~ spl0_18 ),
inference(superposition,[],[f422,f225]) ).
fof(f627,plain,
( sk_c12 = multiply(inverse(sk_c3),sk_c10)
| ~ spl0_6 ),
inference(superposition,[],[f422,f147]) ).
fof(f634,plain,
( sk_c12 = multiply(sk_c10,sk_c10)
| ~ spl0_6
| ~ spl0_16 ),
inference(forward_demodulation,[],[f627,f197]) ).
fof(f636,plain,
( sk_c11 = multiply(sk_c11,sk_c10)
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f625,f211]) ).
fof(f641,plain,
( identity = sk_c11
| ~ spl0_32 ),
inference(forward_demodulation,[],[f608,f3]) ).
fof(f642,plain,
( ! [X0] : multiply(sk_c11,X0) = X0
| ~ spl0_32 ),
inference(forward_demodulation,[],[f606,f422]) ).
fof(f654,plain,
( sk_c10 = multiply(inverse(sk_c11),sk_c11)
| ~ spl0_17
| ~ spl0_18 ),
inference(superposition,[],[f422,f636]) ).
fof(f656,plain,
( identity = sk_c10
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f654,f3]) ).
fof(f660,plain,
( sk_c11 = sk_c10
| ~ spl0_17
| ~ spl0_18
| ~ spl0_32 ),
inference(forward_demodulation,[],[f656,f641]) ).
fof(f666,plain,
( identity = sk_c2
| ~ spl0_17
| ~ spl0_32 ),
inference(superposition,[],[f386,f642]) ).
fof(f682,plain,
( sk_c11 = sk_c2
| ~ spl0_17
| ~ spl0_32 ),
inference(forward_demodulation,[],[f666,f641]) ).
fof(f689,plain,
( sk_c12 = multiply(sk_c11,sk_c11)
| ~ spl0_6
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| ~ spl0_32 ),
inference(superposition,[],[f634,f660]) ).
fof(f691,plain,
( sk_c12 = sk_c11
| ~ spl0_6
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| ~ spl0_32 ),
inference(forward_demodulation,[],[f689,f642]) ).
fof(f698,plain,
( spl0_33
| ~ spl0_6
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| ~ spl0_32 ),
inference(avatar_split_clause,[],[f691,f340,f223,f209,f195,f145,f344]) ).
fof(f767,plain,
( sk_c12 != inverse(sk_c10)
| sk_c10 != multiply(sk_c3,sk_c12)
| ~ spl0_16
| ~ spl0_31 ),
inference(superposition,[],[f338,f197]) ).
fof(f768,plain,
( sk_c12 != inverse(sk_c10)
| ~ spl0_6
| ~ spl0_16
| ~ spl0_31 ),
inference(forward_subsumption_resolution,[],[f767,f147]) ).
fof(f781,plain,
( sk_c12 != inverse(sk_c11)
| ~ spl0_6
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| ~ spl0_31
| ~ spl0_32 ),
inference(forward_demodulation,[],[f768,f660]) ).
fof(f785,plain,
( sk_c12 != inverse(sk_c12)
| ~ spl0_6
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| ~ spl0_31
| ~ spl0_32
| ~ spl0_33 ),
inference(forward_demodulation,[],[f781,f345]) ).
fof(f787,definition,
( spl0_51
<=> sk_c12 = inverse(sk_c12) ),
introduced(definition,[new_symbols(definition,[spl0_51])],[avatar_definition]) ).
fof(f788,plain,
( sk_c12 = inverse(sk_c12)
| ~ spl0_51 ),
inference(avatar_component_clause,[],[f787]) ).
fof(f789,plain,
( sk_c12 != inverse(sk_c12)
| spl0_51 ),
inference(avatar_component_clause,[],[f787]) ).
fof(f797,plain,
( ~ spl0_51
| ~ spl0_6
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| ~ spl0_31
| ~ spl0_32
| ~ spl0_33 ),
inference(avatar_split_clause,[],[f785,f344,f340,f337,f223,f209,f195,f145,f787]) ).
fof(f800,plain,
( sk_c12 = sk_c2
| ~ spl0_17
| ~ spl0_32
| ~ spl0_33 ),
inference(forward_demodulation,[],[f682,f345]) ).
fof(f807,plain,
( sk_c11 = inverse(sk_c12)
| ~ spl0_17
| ~ spl0_32
| ~ spl0_33 ),
inference(superposition,[],[f211,f800]) ).
fof(f808,plain,
( sk_c12 = inverse(sk_c12)
| ~ spl0_17
| ~ spl0_32
| ~ spl0_33 ),
inference(forward_demodulation,[],[f807,f345]) ).
fof(f812,plain,
( spl0_51
| ~ spl0_17
| ~ spl0_32
| ~ spl0_33 ),
inference(avatar_split_clause,[],[f808,f344,f340,f209,f787]) ).
fof(f855,plain,
( identity = multiply(sk_c7,sk_c8)
| ~ spl0_8 ),
inference(superposition,[],[f3,f157]) ).
fof(f856,plain,
( sk_c11 = multiply(sk_c7,sk_c8)
| ~ spl0_8
| ~ spl0_32 ),
inference(forward_demodulation,[],[f855,f641]) ).
fof(f857,plain,
( sk_c7 = multiply(sk_c8,sk_c12)
| ~ spl0_5
| ~ spl0_34 ),
inference(superposition,[],[f143,f360]) ).
fof(f877,plain,
( sk_c12 = inverse(sk_c6)
| ~ spl0_10
| ~ spl0_34 ),
inference(forward_demodulation,[],[f167,f360]) ).
fof(f878,plain,
( spl0_45
| ~ spl0_10
| ~ spl0_34 ),
inference(avatar_split_clause,[],[f877,f359,f165,f518]) ).
fof(f887,plain,
( identity = multiply(sk_c11,sk_c5)
| ~ spl0_12 ),
inference(superposition,[],[f3,f177]) ).
fof(f888,plain,
( identity = sk_c5
| ~ spl0_12
| ~ spl0_32 ),
inference(forward_demodulation,[],[f887,f642]) ).
fof(f890,plain,
( sk_c11 = sk_c5
| ~ spl0_12
| ~ spl0_32 ),
inference(forward_demodulation,[],[f888,f641]) ).
fof(f903,plain,
( sk_c11 != sk_c11
| sk_c12 != inverse(sk_c1)
| ~ spl0_3
| ~ spl0_20 ),
inference(superposition,[],[f135,f253]) ).
fof(f905,plain,
( sk_c11 != sk_c11
| sk_c12 != inverse(sk_c4)
| ~ spl0_3
| ~ spl0_15 ),
inference(superposition,[],[f135,f192]) ).
fof(f907,plain,
( sk_c12 != inverse(sk_c4)
| ~ spl0_3
| ~ spl0_15 ),
inference(trivial_inequality_removal,[],[f905]) ).
fof(f908,plain,
( sk_c12 != inverse(sk_c1)
| ~ spl0_3
| ~ spl0_20 ),
inference(trivial_inequality_removal,[],[f903]) ).
fof(f909,plain,
( $false
| ~ spl0_3
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f907,f187]) ).
fof(f910,plain,
( ~ spl0_3
| ~ spl0_14
| ~ spl0_15 ),
inference(avatar_contradiction_clause,[],[f909]) ).
fof(f911,plain,
( $false
| ~ spl0_3
| ~ spl0_19
| ~ spl0_20 ),
inference(forward_subsumption_resolution,[],[f908,f239]) ).
fof(f912,plain,
( ~ spl0_3
| ~ spl0_19
| ~ spl0_20 ),
inference(avatar_contradiction_clause,[],[f911]) ).
fof(f918,plain,
( sk_c12 != sk_c10
| ~ spl0_4
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19
| ~ spl0_20
| ~ spl0_32 ),
inference(forward_subsumption_resolution,[],[f290,f660]) ).
fof(f923,plain,
( sk_c12 != sk_c11
| ~ spl0_4
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19
| ~ spl0_20
| ~ spl0_32 ),
inference(forward_demodulation,[],[f918,f660]) ).
fof(f971,plain,
( sk_c8 = multiply(inverse(sk_c7),sk_c11)
| ~ spl0_8
| ~ spl0_32 ),
inference(superposition,[],[f422,f856]) ).
fof(f974,plain,
( multiply(sk_c9,sk_c11) = sk_c8
| ~ spl0_7
| ~ spl0_8
| ~ spl0_32 ),
inference(forward_demodulation,[],[f971,f152]) ).
fof(f976,plain,
( sk_c12 = sk_c8
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_32 ),
inference(forward_demodulation,[],[f974,f162]) ).
fof(f978,plain,
( sk_c7 = inverse(sk_c12)
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_32 ),
inference(superposition,[],[f157,f976]) ).
fof(f983,plain,
( sk_c12 = sk_c7
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_32
| ~ spl0_51 ),
inference(forward_demodulation,[],[f978,f788]) ).
fof(f1028,plain,
( sk_c11 = multiply(sk_c12,sk_c8)
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_32
| ~ spl0_51 ),
inference(superposition,[],[f856,f983]) ).
fof(f1029,plain,
( sk_c11 = multiply(sk_c12,sk_c12)
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_32
| ~ spl0_51 ),
inference(forward_demodulation,[],[f1028,f976]) ).
fof(f1037,plain,
( sk_c7 = multiply(sk_c12,sk_c12)
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_32
| ~ spl0_34 ),
inference(forward_demodulation,[],[f857,f976]) ).
fof(f1097,plain,
( sk_c12 != sk_c7
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_32
| spl0_51 ),
inference(superposition,[],[f789,f978]) ).
fof(f1175,plain,
( sk_c9 = multiply(sk_c12,sk_c12)
| ~ spl0_11
| ~ spl0_45 ),
inference(forward_demodulation,[],[f616,f519]) ).
fof(f1176,plain,
( sk_c12 = multiply(sk_c12,sk_c12)
| ~ spl0_11
| ~ spl0_34
| ~ spl0_45 ),
inference(forward_demodulation,[],[f1175,f360]) ).
fof(f1177,plain,
( sk_c12 = sk_c7
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_11
| ~ spl0_32
| ~ spl0_34
| ~ spl0_45 ),
inference(superposition,[],[f1176,f1037]) ).
fof(f1190,plain,
( $false
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_11
| ~ spl0_32
| ~ spl0_34
| ~ spl0_45
| spl0_51 ),
inference(forward_subsumption_resolution,[],[f1177,f1097]) ).
fof(f1191,plain,
( ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_11
| ~ spl0_32
| ~ spl0_34
| ~ spl0_45
| spl0_51 ),
inference(avatar_contradiction_clause,[],[f1190]) ).
fof(f1231,plain,
( sk_c12 = sk_c11
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_11
| ~ spl0_32
| ~ spl0_34
| ~ spl0_45
| ~ spl0_51 ),
inference(forward_demodulation,[],[f1029,f1176]) ).
fof(f1239,plain,
( ~ spl0_33
| ~ spl0_4
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19
| ~ spl0_20
| ~ spl0_32 ),
inference(avatar_split_clause,[],[f923,f340,f251,f237,f223,f209,f137,f344]) ).
fof(f1267,plain,
( spl0_33
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_11
| ~ spl0_32
| ~ spl0_34
| ~ spl0_45
| ~ spl0_51 ),
inference(avatar_split_clause,[],[f1231,f787,f518,f359,f340,f170,f160,f155,f150,f344]) ).
fof(f1291,plain,
( sk_c10 != multiply(sk_c11,sk_c11)
| ~ spl0_17
| spl0_18
| ~ spl0_32 ),
inference(forward_demodulation,[],[f224,f682]) ).
fof(f1294,plain,
( sk_c10 = multiply(sk_c11,sk_c11)
| ~ spl0_12
| ~ spl0_13
| ~ spl0_32 ),
inference(forward_demodulation,[],[f182,f890]) ).
fof(f1296,plain,
( sk_c12 != sk_c10
| sk_c11 != sk_c10
| ~ spl0_4
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f284,f187]) ).
fof(f1298,definition,
( spl0_54
<=> sk_c11 = sk_c10 ),
introduced(definition,[new_symbols(definition,[spl0_54])],[avatar_definition]) ).
fof(f1299,plain,
( sk_c11 = sk_c10
| ~ spl0_54 ),
inference(avatar_component_clause,[],[f1298]) ).
fof(f1308,plain,
( ~ spl0_54
| ~ spl0_22
| ~ spl0_4
| ~ spl0_14
| ~ spl0_15 ),
inference(avatar_split_clause,[],[f1296,f190,f185,f137,f272,f1298]) ).
fof(f1319,plain,
( sk_c11 != sk_c10
| ~ spl0_17
| spl0_18
| ~ spl0_32 ),
inference(forward_demodulation,[],[f1291,f642]) ).
fof(f1320,plain,
( sk_c11 = sk_c10
| ~ spl0_12
| ~ spl0_13
| ~ spl0_32 ),
inference(forward_demodulation,[],[f1294,f642]) ).
fof(f1321,plain,
( ~ spl0_54
| ~ spl0_17
| spl0_18
| ~ spl0_32 ),
inference(avatar_split_clause,[],[f1319,f340,f223,f209,f1298]) ).
fof(f1322,plain,
( spl0_54
| ~ spl0_12
| ~ spl0_13
| ~ spl0_32 ),
inference(avatar_split_clause,[],[f1320,f340,f180,f175,f1298]) ).
fof(f1338,plain,
( sk_c12 = sk_c10
| ~ spl0_33
| ~ spl0_54 ),
inference(forward_demodulation,[],[f1299,f345]) ).
fof(f1339,plain,
( $false
| spl0_22
| ~ spl0_33
| ~ spl0_54 ),
inference(forward_subsumption_resolution,[],[f1338,f274]) ).
fof(f1340,plain,
( spl0_22
| ~ spl0_33
| ~ spl0_54 ),
inference(avatar_contradiction_clause,[],[f1339]) ).
fof(f1493,plain,
( spl0_32
| ~ spl0_14
| ~ spl0_15 ),
inference(avatar_split_clause,[],[f460,f190,f185,f340]) ).
cnf(s1,plain,
( spl0_2
| spl0_3
| spl0_2
| spl0_1
| spl0_3
| spl0_4 ),
inference(sat_conversion,[],[f139]) ).
cnf(s2,plain,
( spl0_1
| spl0_2
| spl0_3
| spl0_4 ),
inference(rat,[],[s1]) ).
cnf(s3,plain,
( spl0_5
| spl0_6 ),
inference(sat_conversion,[],[f148]) ).
cnf(s4,plain,
( spl0_6
| spl0_7 ),
inference(sat_conversion,[],[f153]) ).
cnf(s5,plain,
( spl0_6
| spl0_8 ),
inference(sat_conversion,[],[f158]) ).
cnf(s6,plain,
( spl0_6
| spl0_9 ),
inference(sat_conversion,[],[f163]) ).
cnf(s7,plain,
( spl0_6
| spl0_10 ),
inference(sat_conversion,[],[f168]) ).
cnf(s8,plain,
( spl0_6
| spl0_11 ),
inference(sat_conversion,[],[f173]) ).
cnf(s9,plain,
( spl0_6
| spl0_12 ),
inference(sat_conversion,[],[f178]) ).
cnf(s10,plain,
( spl0_6
| spl0_13 ),
inference(sat_conversion,[],[f183]) ).
cnf(s11,plain,
( spl0_6
| spl0_14 ),
inference(sat_conversion,[],[f188]) ).
cnf(s12,plain,
( spl0_6
| spl0_15 ),
inference(sat_conversion,[],[f193]) ).
cnf(s13,plain,
( spl0_5
| spl0_16 ),
inference(sat_conversion,[],[f198]) ).
cnf(s14,plain,
( spl0_7
| spl0_16 ),
inference(sat_conversion,[],[f199]) ).
cnf(s15,plain,
( spl0_8
| spl0_16 ),
inference(sat_conversion,[],[f200]) ).
cnf(s16,plain,
( spl0_9
| spl0_16 ),
inference(sat_conversion,[],[f201]) ).
cnf(s17,plain,
( spl0_10
| spl0_16 ),
inference(sat_conversion,[],[f202]) ).
cnf(s18,plain,
( spl0_11
| spl0_16 ),
inference(sat_conversion,[],[f203]) ).
cnf(s19,plain,
( spl0_12
| spl0_16 ),
inference(sat_conversion,[],[f204]) ).
cnf(s20,plain,
( spl0_13
| spl0_16 ),
inference(sat_conversion,[],[f205]) ).
cnf(s21,plain,
( spl0_14
| spl0_16 ),
inference(sat_conversion,[],[f206]) ).
cnf(s22,plain,
( spl0_15
| spl0_16 ),
inference(sat_conversion,[],[f207]) ).
cnf(s23,plain,
( spl0_5
| spl0_17 ),
inference(sat_conversion,[],[f212]) ).
cnf(s24,plain,
( spl0_7
| spl0_17 ),
inference(sat_conversion,[],[f213]) ).
cnf(s25,plain,
( spl0_8
| spl0_17 ),
inference(sat_conversion,[],[f214]) ).
cnf(s26,plain,
( spl0_9
| spl0_17 ),
inference(sat_conversion,[],[f215]) ).
cnf(s27,plain,
( spl0_10
| spl0_17 ),
inference(sat_conversion,[],[f216]) ).
cnf(s28,plain,
( spl0_11
| spl0_17 ),
inference(sat_conversion,[],[f217]) ).
cnf(s29,plain,
( spl0_12
| spl0_17 ),
inference(sat_conversion,[],[f218]) ).
cnf(s30,plain,
( spl0_13
| spl0_17 ),
inference(sat_conversion,[],[f219]) ).
cnf(s32,plain,
( spl0_15
| spl0_17 ),
inference(sat_conversion,[],[f221]) ).
cnf(s33,plain,
( spl0_5
| spl0_18 ),
inference(sat_conversion,[],[f226]) ).
cnf(s39,plain,
( spl0_12
| spl0_18 ),
inference(sat_conversion,[],[f232]) ).
cnf(s40,plain,
( spl0_13
| spl0_18 ),
inference(sat_conversion,[],[f233]) ).
cnf(s41,plain,
( spl0_14
| spl0_18 ),
inference(sat_conversion,[],[f234]) ).
cnf(s42,plain,
( spl0_15
| spl0_18 ),
inference(sat_conversion,[],[f235]) ).
cnf(s43,plain,
( spl0_5
| spl0_19 ),
inference(sat_conversion,[],[f240]) ).
cnf(s51,plain,
( spl0_14
| spl0_19 ),
inference(sat_conversion,[],[f248]) ).
cnf(s52,plain,
( spl0_15
| spl0_19 ),
inference(sat_conversion,[],[f249]) ).
cnf(s53,plain,
( spl0_5
| spl0_20 ),
inference(sat_conversion,[],[f254]) ).
cnf(s61,plain,
( spl0_14
| spl0_20 ),
inference(sat_conversion,[],[f262]) ).
cnf(s62,plain,
( spl0_15
| spl0_20 ),
inference(sat_conversion,[],[f263]) ).
cnf(s65,plain,
( ~ spl0_2
| ~ spl0_12
| ~ spl0_13 ),
inference(sat_conversion,[],[f278]) ).
cnf(s66,plain,
( ~ spl0_2
| ~ spl0_17
| ~ spl0_18 ),
inference(sat_conversion,[],[f282]) ).
cnf(s67,plain,
( ~ spl0_4
| ~ spl0_6
| ~ spl0_16 ),
inference(sat_conversion,[],[f288]) ).
cnf(s71,plain,
( ~ spl0_1
| ~ spl0_14
| ~ spl0_15
| spl0_31
| ~ spl0_32
| ~ spl0_33 ),
inference(sat_conversion,[],[f347]) ).
cnf(s72,plain,
( ~ spl0_1
| ~ spl0_19
| ~ spl0_20
| spl0_31
| ~ spl0_32
| ~ spl0_33 ),
inference(sat_conversion,[],[f348]) ).
cnf(s73,plain,
( ~ spl0_1
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| spl0_30 ),
inference(sat_conversion,[],[f349]) ).
cnf(s74,plain,
( ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_30 ),
inference(sat_conversion,[],[f357]) ).
cnf(s80,plain,
( ~ spl0_19
| ~ spl0_20
| spl0_32 ),
inference(sat_conversion,[],[f447]) ).
cnf(s81,plain,
( ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_32
| spl0_34 ),
inference(sat_conversion,[],[f512]) ).
cnf(s88,plain,
( ~ spl0_6
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| ~ spl0_32
| spl0_33 ),
inference(sat_conversion,[],[f698]) ).
cnf(s101,plain,
( ~ spl0_6
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| ~ spl0_31
| ~ spl0_32
| ~ spl0_33
| ~ spl0_51 ),
inference(sat_conversion,[],[f797]) ).
cnf(s103,plain,
( ~ spl0_17
| ~ spl0_32
| ~ spl0_33
| spl0_51 ),
inference(sat_conversion,[],[f812]) ).
cnf(s124,plain,
( ~ spl0_10
| ~ spl0_34
| spl0_45 ),
inference(sat_conversion,[],[f878]) ).
cnf(s125,plain,
( ~ spl0_3
| ~ spl0_14
| ~ spl0_15 ),
inference(sat_conversion,[],[f910]) ).
cnf(s126,plain,
( ~ spl0_3
| ~ spl0_19
| ~ spl0_20 ),
inference(sat_conversion,[],[f912]) ).
cnf(s144,plain,
( ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_11
| ~ spl0_32
| ~ spl0_34
| ~ spl0_45
| spl0_51 ),
inference(sat_conversion,[],[f1191]) ).
cnf(s168,plain,
( ~ spl0_4
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19
| ~ spl0_20
| ~ spl0_32
| ~ spl0_33 ),
inference(sat_conversion,[],[f1239]) ).
cnf(s184,plain,
( ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_11
| ~ spl0_32
| spl0_33
| ~ spl0_34
| ~ spl0_45
| ~ spl0_51 ),
inference(sat_conversion,[],[f1267]) ).
cnf(s209,plain,
( ~ spl0_4
| ~ spl0_14
| ~ spl0_15
| ~ spl0_22
| ~ spl0_54 ),
inference(sat_conversion,[],[f1308]) ).
cnf(s214,plain,
( ~ spl0_17
| spl0_18
| ~ spl0_32
| ~ spl0_54 ),
inference(sat_conversion,[],[f1321]) ).
cnf(s215,plain,
( ~ spl0_12
| ~ spl0_13
| ~ spl0_32
| spl0_54 ),
inference(sat_conversion,[],[f1322]) ).
cnf(s221,plain,
( spl0_22
| ~ spl0_33
| ~ spl0_54 ),
inference(sat_conversion,[],[f1340]) ).
cnf(s232,plain,
( ~ spl0_14
| ~ spl0_15
| spl0_32 ),
inference(sat_conversion,[],[f1493]) ).
cnf(s235,plain,
( spl0_5
| ~ spl0_4 ),
inference(rat,[],[s88,s168,s80,s3,s13,s23,s33,s43,s53]) ).
cnf(s236,plain,
( spl0_16
| ~ spl0_4 ),
inference(rat,[],[s184,s144,s221,s124,s209,s81,s215,s232,s14,s15,s16,s17,s18,s19,s20,s21,s22,s235]) ).
cnf(s237,plain,
~ spl0_4,
inference(rat,[],[s184,s144,s221,s124,s209,s81,s215,s232,s4,s5,s6,s7,s8,s9,s10,s11,s12,s67,s236,s235]) ).
cnf(s239,plain,
( spl0_15
| ~ spl0_3 ),
inference(rat,[],[s126,s52,s62]) ).
cnf(s240,plain,
( ~ spl0_15
| ~ spl0_3 ),
inference(rat,[],[s126,s51,s61,s125]) ).
cnf(s241,plain,
~ spl0_3,
inference(rat,[],[s240,s239]) ).
cnf(s242,plain,
( spl0_15
| ~ spl0_2 ),
inference(rat,[],[s66,s32,s42]) ).
cnf(s243,plain,
( spl0_18
| ~ spl0_17
| ~ spl0_32 ),
inference(rat,[],[s215,s39,s40,s214]) ).
cnf(s244,plain,
( ~ spl0_17
| ~ spl0_32
| ~ spl0_2 ),
inference(rat,[],[s243,s66]) ).
cnf(s245,plain,
( spl0_17
| ~ spl0_2 ),
inference(rat,[],[s65,s29,s30]) ).
cnf(s246,plain,
~ spl0_2,
inference(rat,[],[s232,s41,s244,s66,s245,s242]) ).
cnf(s247,plain,
spl0_1,
inference(rat,[],[s2,s237,s241,s246]) ).
cnf(s249,plain,
spl0_6,
inference(rat,[],[s74,s73,s3,s4,s5,s6,s7,s8,s247]) ).
cnf(s250,plain,
spl0_16,
inference(rat,[],[s74,s73,s13,s14,s15,s16,s17,s18,s247]) ).
cnf(s251,plain,
( ~ spl0_17
| ~ spl0_14
| ~ spl0_15 ),
inference(rat,[],[s101,s103,s71,s88,s243,s232,s249,s250,s247]) ).
cnf(s252,plain,
spl0_17,
inference(rat,[],[s74,s73,s23,s24,s25,s26,s27,s28,s247]) ).
cnf(s253,plain,
spl0_14,
inference(rat,[],[s72,s101,s103,s88,s80,s41,s51,s61,s247,s249,s250,s252]) ).
cnf(s254,plain,
~ spl0_15,
inference(rat,[],[s251,s252,s253]) ).
cnf(s255,plain,
spl0_20,
inference(rat,[],[s62,s254]) ).
cnf(s256,plain,
spl0_19,
inference(rat,[],[s52,s254]) ).
cnf(s257,plain,
spl0_18,
inference(rat,[],[s42,s254]) ).
cnf(s258,plain,
spl0_32,
inference(rat,[],[s80,s255,s256]) ).
cnf(s259,plain,
spl0_33,
inference(rat,[],[s88,s257,s252,s250,s249,s258]) ).
cnf(s261,plain,
spl0_51,
inference(rat,[],[s103,s252,s258,s259]) ).
cnf(s263,plain,
~ spl0_31,
inference(rat,[],[s101,s261,s252,s258,s250,s257,s249,s259]) ).
cnf(s265,plain,
$false,
inference(rat,[],[s72,s255,s258,s256,s247,s259,s263]) ).
fof(f1500,plain,
$false,
inference(avatar_sat_refutation,[],[s265]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP254-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/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 09:42:51 UTC 2026
% 0.11/0.40 % CPUTime :
% 0.11/0.40 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.44 Running first-order theorem proving
% 0.11/0.44 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.77/1.31 % (1781105)Input is clausal, will run a generic CNF schedule.
% 2.77/1.31 % (1781111)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=2222255995:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.77/1.31 % (1781110)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=3519008411:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.77/1.31 % (1781113)lrs+10_1_sil=8000:sp=occurrence:random_seed=3854120735:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.77/1.31 % (1781114)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=4160917534:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.77/1.31 % (1781116)dis-21_1_sil=8000:lcm=predicate:random_seed=4037285224: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)
% 2.77/1.31 % (1781112)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=1259792683:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.77/1.31 % (1781115)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2100559779:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.77/1.31 % (1781116)Refutation not found, incomplete strategy
% 2.77/1.31 % (1781116)------------------------------
% 2.77/1.31 % (1781116)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.77/1.31 % (1781116)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.77/1.31 % (1781116)CaDiCaL version: 2.1.3
% 2.77/1.31 % (1781116)Termination reason: Refutation not found, incomplete strategy
% 2.77/1.31 % (1781116)Time elapsed: 0.003 s
% 2.77/1.31 % (1781116)Peak memory usage: 88 MB
% 2.77/1.31 % (1781116)Instructions burned: 4 (million)
% 2.77/1.31 % (1781115)First to succeed.
% 2.77/1.31 % (1781115)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1781105"
% 2.77/1.31 % (1781113)Instruction limit reached!
% 2.77/1.31 % (1781113)------------------------------
% 2.77/1.31 % (1781113)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.77/1.31 % (1781113)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.77/1.31 % (1781113)CaDiCaL version: 2.1.3
% 2.77/1.31 % (1781113)Termination reason: Instruction limit
% 2.77/1.31 % (1781113)Termination phase: Saturation
% 2.77/1.31 % (1781113)Time elapsed: 0.048 s
% 2.77/1.31 % (1781113)Peak memory usage: 89 MB
% 2.77/1.31 % (1781113)Instructions burned: 109 (million)
% 2.77/1.31 % (1781114)Instruction limit reached!
% 2.77/1.31 % (1781114)------------------------------
% 2.77/1.31 % (1781114)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.77/1.31 % (1781114)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.77/1.31 % (1781114)CaDiCaL version: 2.1.3
% 2.77/1.31 % (1781114)Termination reason: Instruction limit
% 2.77/1.31 % (1781114)Termination phase: Saturation
% 2.77/1.31 % (1781114)Time elapsed: 0.065 s
% 2.77/1.31 % (1781114)Peak memory usage: 89 MB
% 2.77/1.31 % (1781114)Instructions burned: 114 (million)
% 2.77/1.31 % (1781124)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=3056423901:i=143:sd=2:aac=none:ss=axioms:sgt=16_2998 on theBenchmark for (2998ds/143Mi)
% 2.77/1.31 % (1781125)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=2815135085:st=3:avsq=on:s2a=on:i=189:s2at=1.2:avsqr=1,16:sd=2:bd=all:nm=64:ss=axioms:sgt=30_2997 on theBenchmark for (2997ds/189Mi)
% 2.77/1.31 % (1781116)------------------------------
% 2.77/1.31 % (1781116)------------------------------
% 2.77/1.31 % (1781124)Instruction limit reached!
% 2.77/1.31 % (1781124)------------------------------
% 2.77/1.31 % (1781124)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.77/1.31 % (1781124)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.77/1.31 % (1781124)CaDiCaL version: 2.1.3
% 2.77/1.31 % (1781124)Termination reason: Instruction limit
% 2.77/1.31 % (1781124)Termination phase: Saturation
% 2.77/1.31 % (1781124)Time elapsed: 0.063 s
% 2.77/1.31 % (1781124)Peak memory usage: 89 MB
% 2.77/1.31 % (1781124)Instructions burned: 143 (million)
% 2.77/1.31 % (1781115)Refutation found. Thanks to Tanya!
% 2.77/1.31 % SZS status Unsatisfiable for theBenchmark
% 2.77/1.31 % SZS output start Proof for theBenchmark
% See solution above
% 3.61/1.41 % (1781115)------------------------------
% 3.61/1.41 % (1781115)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.61/1.41 % (1781115)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.61/1.41 % (1781115)CaDiCaL version: 2.1.3
% 3.61/1.41 % (1781115)Termination reason: Refutation
% 3.61/1.41 % (1781115)Time elapsed: 0.033 s
% 3.61/1.41 % (1781115)Peak memory usage: 90 MB
% 3.61/1.41 % (1781115)Instructions burned: 51 (million)
% 3.61/1.41 % (1781115)------------------------------
% 3.61/1.41 % (1781115)------------------------------
% 3.61/1.41 % (1781105)Success in time 0.436 s
% 3.61/1.41 % Vampire exiting
%------------------------------------------------------------------------------