%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GRP254-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n015.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 10:17:18 AM UTC 2026
% Result : Unsatisfiable 0.16s 0.49s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 62
% Syntax : Number of formulae : 333 ( 21 unt; 27 def)
% Number of atoms : 955 ( 370 equ)
% Maximal formula atoms : 16 ( 2 avg)
% Number of connectives : 1143 ( 521 ~; 595 |; 0 &)
% ( 27 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 26 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 29 ( 27 usr; 28 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 13 con; 0-2 aty)
% Number of variables : 72 ( 0 sgn 72 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_identity) ).
fof(f2,axiom,
! [X0] : multiply(inverse(X0),X0) = identity,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_inverse) ).
fof(f3,plain,
! [X0] : identity = multiply(inverse(X0),X0),
inference(reorient_equations,[],[f2]) ).
fof(f4,axiom,
! [X2,X0,X1] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',associativity) ).
fof(f5,negated_conjecture,
( multiply(sk_c1,sk_c12) = sk_c11
| multiply(sk_c4,sk_c12) = sk_c11 ),
file('/export/starexec/sandbox2/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/sandbox2/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(f23,negated_conjecture,
( inverse(sk_c1) = sk_c12
| multiply(sk_c4,sk_c12) = sk_c11 ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',prove_this_12) ).
fof(f26,plain,
( sk_c12 = inverse(sk_c1)
| sk_c12 = inverse(sk_c4) ),
inference(reorient_equations,[],[f25]) ).
fof(f47,negated_conjecture,
( multiply(sk_c2,sk_c11) = sk_c10
| multiply(sk_c5,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox2/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/sandbox2/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(f51,negated_conjecture,
( multiply(sk_c2,sk_c11) = sk_c10
| multiply(sk_c6,sk_c9) = sk_c12 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_25) ).
fof(f52,plain,
( sk_c10 = multiply(sk_c2,sk_c11)
| sk_c12 = multiply(sk_c6,sk_c9) ),
inference(reorient_equations,[],[f51]) ).
fof(f53,negated_conjecture,
( multiply(sk_c2,sk_c11) = sk_c10
| inverse(sk_c6) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_26) ).
fof(f54,plain,
( sk_c10 = multiply(sk_c2,sk_c11)
| sk_c9 = inverse(sk_c6) ),
inference(reorient_equations,[],[f53]) ).
fof(f55,negated_conjecture,
( multiply(sk_c2,sk_c11) = sk_c10
| multiply(sk_c9,sk_c11) = sk_c12 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_27) ).
fof(f56,plain,
( sk_c10 = multiply(sk_c2,sk_c11)
| sk_c12 = multiply(sk_c9,sk_c11) ),
inference(reorient_equations,[],[f55]) ).
fof(f67,negated_conjecture,
( inverse(sk_c2) = sk_c11
| multiply(sk_c5,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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(f103,negated_conjecture,
( multiply(sk_c3,sk_c12) = sk_c10
| multiply(sk_c4,sk_c12) = sk_c11 ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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(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/sandbox2/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] :
( inverse(X7) != multiply(X7,inverse(X5))
| sk_c12 != multiply(X5,inverse(X5))
| inverse(X5) != inverse(inverse(X7))
| sk_c12 != multiply(inverse(X5),sk_c11) )
| ~ 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(f150,definition,
( spl0_7
<=> sk_c9 = inverse(sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
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(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(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(f223,definition,
( spl0_18
<=> sk_c10 = multiply(sk_c2,sk_c11) ),
introduced(definition,[new_symbols(definition,[spl0_18])],[avatar_definition]) ).
fof(f225,plain,
( sk_c10 = multiply(sk_c2,sk_c11)
| ~ spl0_18 ),
inference(avatar_component_clause,[],[f223]) ).
fof(f229,plain,
( spl0_9
| spl0_18 ),
inference(avatar_split_clause,[],[f56,f223,f160]) ).
fof(f230,plain,
( spl0_10
| spl0_18 ),
inference(avatar_split_clause,[],[f54,f223,f165]) ).
fof(f231,plain,
( spl0_11
| spl0_18 ),
inference(avatar_split_clause,[],[f52,f223,f170]) ).
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(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(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(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(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(f293,plain,
( ! [X0] :
( inverse(X0) != multiply(X0,sk_c9)
| sk_c12 != multiply(sk_c6,sk_c9)
| sk_c9 != inverse(inverse(X0))
| sk_c12 != multiply(sk_c9,sk_c11) )
| ~ spl0_1
| ~ spl0_10 ),
inference(superposition,[],[f129,f167]) ).
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(f337,definition,
( spl0_31
<=> sk_c12 = multiply(sk_c12,sk_c11) ),
introduced(definition,[new_symbols(definition,[spl0_31])],[avatar_definition]) ).
fof(f338,plain,
( sk_c12 = multiply(sk_c12,sk_c11)
| ~ spl0_31 ),
inference(avatar_component_clause,[],[f337]) ).
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(f346,plain,
( sk_c12 != sk_c11
| spl0_33 ),
inference(avatar_component_clause,[],[f344]) ).
fof(f350,plain,
( ! [X0] :
( sk_c12 != multiply(inverse(X0),sk_c11)
| sk_c12 != multiply(X0,inverse(X0))
| inverse(X0) != inverse(inverse(identity))
| inverse(X0) != inverse(identity) )
| ~ spl0_1 ),
inference(superposition,[],[f129,f1]) ).
fof(f351,plain,
( identity = multiply(sk_c12,sk_c1)
| ~ spl0_19 ),
inference(superposition,[],[f3,f239]) ).
fof(f352,plain,
( identity = multiply(sk_c12,sk_c4)
| ~ spl0_14 ),
inference(superposition,[],[f3,f187]) ).
fof(f353,plain,
( identity = multiply(sk_c9,sk_c6)
| ~ spl0_10 ),
inference(superposition,[],[f3,f167]) ).
fof(f356,plain,
( identity = multiply(sk_c11,sk_c2)
| ~ spl0_17 ),
inference(superposition,[],[f3,f211]) ).
fof(f361,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[],[f4,f3]) ).
fof(f364,plain,
( ! [X0] : multiply(sk_c12,X0) = multiply(sk_c6,multiply(sk_c9,X0))
| ~ spl0_11 ),
inference(superposition,[],[f4,f172]) ).
fof(f370,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f361,f1]) ).
fof(f373,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c12,multiply(sk_c1,X0))
| ~ spl0_19 ),
inference(superposition,[],[f4,f351]) ).
fof(f374,plain,
( ! [X0] : multiply(sk_c12,multiply(sk_c1,X0)) = X0
| ~ spl0_19 ),
inference(forward_demodulation,[],[f373,f1]) ).
fof(f375,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c12,multiply(sk_c4,X0))
| ~ spl0_14 ),
inference(superposition,[],[f4,f352]) ).
fof(f376,plain,
( ! [X0] : multiply(sk_c12,multiply(sk_c4,X0)) = X0
| ~ spl0_14 ),
inference(forward_demodulation,[],[f375,f1]) ).
fof(f377,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c9,multiply(sk_c6,X0))
| ~ spl0_10 ),
inference(superposition,[],[f4,f353]) ).
fof(f378,plain,
( ! [X0] : multiply(sk_c9,multiply(sk_c6,X0)) = X0
| ~ spl0_10 ),
inference(forward_demodulation,[],[f377,f1]) ).
fof(f387,plain,
( sk_c12 = multiply(sk_c12,sk_c11)
| ~ spl0_19
| ~ spl0_20 ),
inference(superposition,[],[f374,f253]) ).
fof(f390,plain,
( spl0_31
| ~ spl0_19
| ~ spl0_20 ),
inference(avatar_split_clause,[],[f387,f251,f237,f337]) ).
fof(f392,plain,
( sk_c12 = multiply(sk_c12,sk_c11)
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f376,f192]) ).
fof(f416,plain,
( sk_c9 = multiply(sk_c9,sk_c12)
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f378,f172]) ).
fof(f420,plain,
( multiply(sk_c12,sk_c11) = multiply(sk_c6,sk_c12)
| ~ spl0_9
| ~ spl0_11 ),
inference(superposition,[],[f364,f162]) ).
fof(f426,plain,
( sk_c12 = multiply(sk_c6,sk_c12)
| ~ spl0_9
| ~ spl0_11
| ~ spl0_31 ),
inference(forward_demodulation,[],[f420,f338]) ).
fof(f428,plain,
( sk_c12 = multiply(sk_c9,sk_c12)
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_31 ),
inference(superposition,[],[f378,f426]) ).
fof(f450,plain,
( sk_c12 = sk_c9
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_31 ),
inference(superposition,[],[f428,f416]) ).
fof(f485,plain,
( ! [X0] :
( inverse(X0) != multiply(X0,sk_c9)
| sk_c12 != multiply(sk_c6,sk_c9)
| sk_c9 != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_subsumption_resolution,[],[f293,f162]) ).
fof(f486,plain,
( ~ spl0_11
| spl0_30
| ~ spl0_1
| ~ spl0_9
| ~ spl0_10 ),
inference(avatar_split_clause,[],[f485,f165,f160,f128,f332,f170]) ).
fof(f490,plain,
( inverse(sk_c8) != sk_c7
| sk_c9 != inverse(inverse(sk_c8))
| ~ spl0_5
| ~ spl0_30 ),
inference(superposition,[],[f333,f143]) ).
fof(f491,plain,
( sk_c9 != inverse(inverse(sk_c8))
| ~ spl0_5
| ~ spl0_8
| ~ spl0_30 ),
inference(forward_subsumption_resolution,[],[f490,f157]) ).
fof(f510,plain,
( sk_c9 != inverse(sk_c7)
| ~ spl0_5
| ~ spl0_8
| ~ spl0_30 ),
inference(forward_demodulation,[],[f491,f157]) ).
fof(f513,plain,
( ~ spl0_7
| ~ spl0_5
| ~ spl0_8
| ~ spl0_30 ),
inference(avatar_split_clause,[],[f510,f332,f155,f141,f150]) ).
fof(f534,definition,
( spl0_41
<=> identity = sk_c12 ),
introduced(definition,[new_symbols(definition,[spl0_41])],[avatar_definition]) ).
fof(f535,plain,
( identity = sk_c12
| ~ spl0_41 ),
inference(avatar_component_clause,[],[f534]) ).
fof(f619,plain,
( sk_c11 = multiply(inverse(sk_c12),sk_c12)
| ~ spl0_31 ),
inference(superposition,[],[f370,f338]) ).
fof(f634,plain,
( sk_c11 = multiply(inverse(sk_c2),sk_c10)
| ~ spl0_18 ),
inference(superposition,[],[f370,f225]) ).
fof(f636,plain,
( sk_c12 = multiply(inverse(sk_c3),sk_c10)
| ~ spl0_6 ),
inference(superposition,[],[f370,f147]) ).
fof(f643,plain,
( sk_c12 = multiply(sk_c10,sk_c10)
| ~ spl0_6
| ~ spl0_16 ),
inference(forward_demodulation,[],[f636,f197]) ).
fof(f645,plain,
( sk_c11 = multiply(sk_c11,sk_c10)
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f634,f211]) ).
fof(f652,plain,
( identity = sk_c11
| ~ spl0_31 ),
inference(forward_demodulation,[],[f619,f3]) ).
fof(f660,plain,
( identity != sk_c12
| ~ spl0_31
| spl0_33 ),
inference(superposition,[],[f346,f652]) ).
fof(f662,plain,
( identity = multiply(identity,sk_c2)
| ~ spl0_17
| ~ spl0_31 ),
inference(superposition,[],[f356,f652]) ).
fof(f672,plain,
( identity = sk_c2
| ~ spl0_17
| ~ spl0_31 ),
inference(forward_demodulation,[],[f662,f1]) ).
fof(f673,plain,
( ~ spl0_41
| ~ spl0_31
| spl0_33 ),
inference(avatar_split_clause,[],[f660,f344,f337,f534]) ).
fof(f676,plain,
( identity = multiply(identity,sk_c10)
| ~ spl0_17
| ~ spl0_18
| ~ spl0_31 ),
inference(forward_demodulation,[],[f645,f652]) ).
fof(f677,plain,
( identity = sk_c10
| ~ spl0_17
| ~ spl0_18
| ~ spl0_31 ),
inference(forward_demodulation,[],[f676,f1]) ).
fof(f678,plain,
( sk_c12 = multiply(identity,identity)
| ~ spl0_6
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| ~ spl0_31 ),
inference(superposition,[],[f643,f677]) ).
fof(f686,plain,
( identity = sk_c12
| ~ spl0_6
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| ~ spl0_31 ),
inference(forward_demodulation,[],[f678,f1]) ).
fof(f692,plain,
( spl0_41
| ~ spl0_6
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| ~ spl0_31 ),
inference(avatar_split_clause,[],[f686,f337,f223,f209,f195,f145,f534]) ).
fof(f771,definition,
( spl0_48
<=> identity = inverse(identity) ),
introduced(definition,[new_symbols(definition,[spl0_48])],[avatar_definition]) ).
fof(f772,plain,
( identity = inverse(identity)
| ~ spl0_48 ),
inference(avatar_component_clause,[],[f771]) ).
fof(f804,plain,
( ! [X3] :
( identity != multiply(X3,sk_c12)
| sk_c12 != inverse(X3) )
| ~ spl0_3
| ~ spl0_31 ),
inference(forward_demodulation,[],[f135,f652]) ).
fof(f808,plain,
( identity != sk_c11
| sk_c12 != inverse(sk_c1)
| ~ spl0_3
| ~ spl0_20
| ~ spl0_31 ),
inference(superposition,[],[f804,f253]) ).
fof(f809,plain,
( identity != sk_c11
| sk_c12 != inverse(sk_c4)
| ~ spl0_3
| ~ spl0_15
| ~ spl0_31 ),
inference(superposition,[],[f804,f192]) ).
fof(f813,plain,
( sk_c12 != inverse(sk_c4)
| ~ spl0_3
| ~ spl0_15
| ~ spl0_31 ),
inference(forward_subsumption_resolution,[],[f809,f652]) ).
fof(f814,plain,
( sk_c12 != inverse(sk_c1)
| ~ spl0_3
| ~ spl0_20
| ~ spl0_31 ),
inference(forward_subsumption_resolution,[],[f808,f652]) ).
fof(f817,plain,
( $false
| ~ spl0_3
| ~ spl0_14
| ~ spl0_15
| ~ spl0_31 ),
inference(forward_subsumption_resolution,[],[f813,f187]) ).
fof(f818,plain,
( ~ spl0_3
| ~ spl0_14
| ~ spl0_15
| ~ spl0_31 ),
inference(avatar_contradiction_clause,[],[f817]) ).
fof(f819,plain,
( $false
| ~ spl0_3
| ~ spl0_19
| ~ spl0_20
| ~ spl0_31 ),
inference(forward_subsumption_resolution,[],[f814,f239]) ).
fof(f820,plain,
( ~ spl0_3
| ~ spl0_19
| ~ spl0_20
| ~ spl0_31 ),
inference(avatar_contradiction_clause,[],[f819]) ).
fof(f835,plain,
( ! [X0] :
( sk_c12 != multiply(inverse(X0),identity)
| sk_c12 != multiply(X0,inverse(X0))
| inverse(X0) != inverse(inverse(identity))
| inverse(X0) != inverse(identity) )
| ~ spl0_1
| ~ spl0_31 ),
inference(forward_demodulation,[],[f350,f652]) ).
fof(f1028,plain,
( sk_c11 = inverse(identity)
| ~ spl0_17
| ~ spl0_31 ),
inference(superposition,[],[f211,f672]) ).
fof(f1029,plain,
( identity = inverse(identity)
| ~ spl0_17
| ~ spl0_31 ),
inference(forward_demodulation,[],[f1028,f652]) ).
fof(f1033,plain,
( spl0_48
| ~ spl0_17
| ~ spl0_31 ),
inference(avatar_split_clause,[],[f1029,f337,f209,f771]) ).
fof(f1161,plain,
( ! [X0] :
( identity != multiply(inverse(X0),identity)
| sk_c12 != multiply(X0,inverse(X0))
| inverse(X0) != inverse(inverse(identity))
| inverse(X0) != inverse(identity) )
| ~ spl0_1
| ~ spl0_31
| ~ spl0_41 ),
inference(forward_demodulation,[],[f835,f535]) ).
fof(f1162,plain,
( ! [X0] :
( identity != multiply(X0,inverse(X0))
| identity != multiply(inverse(X0),identity)
| inverse(X0) != inverse(inverse(identity))
| inverse(X0) != inverse(identity) )
| ~ spl0_1
| ~ spl0_31
| ~ spl0_41 ),
inference(forward_demodulation,[],[f1161,f535]) ).
fof(f1163,plain,
( ! [X0] :
( inverse(X0) != inverse(identity)
| identity != multiply(X0,inverse(X0))
| identity != multiply(inverse(X0),identity)
| inverse(X0) != inverse(identity) )
| ~ spl0_1
| ~ spl0_31
| ~ spl0_41
| ~ spl0_48 ),
inference(forward_demodulation,[],[f1162,f772]) ).
fof(f1164,plain,
( ! [X0] :
( inverse(X0) != inverse(identity)
| identity != multiply(X0,inverse(X0))
| identity != multiply(inverse(X0),identity) )
| ~ spl0_1
| ~ spl0_31
| ~ spl0_41
| ~ spl0_48 ),
inference(duplicate_literal_removal,[],[f1163]) ).
fof(f1165,plain,
( ! [X0] :
( identity != multiply(inverse(X0),identity)
| identity != multiply(X0,inverse(X0))
| identity != inverse(X0) )
| ~ spl0_1
| ~ spl0_31
| ~ spl0_41
| ~ spl0_48 ),
inference(forward_demodulation,[],[f1164,f772]) ).
fof(f1173,plain,
( identity != identity
| identity != multiply(identity,inverse(identity))
| identity != inverse(identity)
| ~ spl0_1
| ~ spl0_31
| ~ spl0_41
| ~ spl0_48 ),
inference(superposition,[],[f1165,f3]) ).
fof(f1174,plain,
( identity != multiply(identity,inverse(identity))
| identity != inverse(identity)
| ~ spl0_1
| ~ spl0_31
| ~ spl0_41
| ~ spl0_48 ),
inference(trivial_inequality_removal,[],[f1173]) ).
fof(f1177,plain,
( identity != multiply(identity,inverse(identity))
| ~ spl0_1
| ~ spl0_31
| ~ spl0_41
| ~ spl0_48 ),
inference(forward_subsumption_resolution,[],[f1174,f772]) ).
fof(f1184,plain,
( identity != inverse(identity)
| ~ spl0_1
| ~ spl0_31
| ~ spl0_41
| ~ spl0_48 ),
inference(forward_demodulation,[],[f1177,f1]) ).
fof(f1189,plain,
( $false
| ~ spl0_1
| ~ spl0_31
| ~ spl0_41
| ~ spl0_48 ),
inference(forward_subsumption_resolution,[],[f1184,f772]) ).
fof(f1190,plain,
( ~ spl0_1
| ~ spl0_31
| ~ spl0_41
| ~ spl0_48 ),
inference(avatar_contradiction_clause,[],[f1189]) ).
fof(f1227,plain,
( identity = inverse(sk_c5)
| ~ spl0_12
| ~ spl0_31 ),
inference(forward_demodulation,[],[f177,f652]) ).
fof(f1308,plain,
( identity = multiply(identity,sk_c5)
| ~ spl0_12
| ~ spl0_31 ),
inference(superposition,[],[f3,f1227]) ).
fof(f1309,plain,
( identity = sk_c5
| ~ spl0_12
| ~ spl0_31 ),
inference(forward_demodulation,[],[f1308,f1]) ).
fof(f1312,plain,
( sk_c12 = multiply(sk_c6,sk_c12)
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_31 ),
inference(forward_demodulation,[],[f172,f450]) ).
fof(f1315,plain,
( sk_c12 = multiply(inverse(sk_c6),sk_c12)
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_31 ),
inference(superposition,[],[f370,f1312]) ).
fof(f1317,plain,
( sk_c12 = multiply(sk_c9,sk_c12)
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_31 ),
inference(forward_demodulation,[],[f1315,f167]) ).
fof(f1319,plain,
( sk_c12 = multiply(sk_c12,sk_c12)
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_31 ),
inference(forward_demodulation,[],[f1317,f450]) ).
fof(f1417,plain,
( sk_c12 = multiply(inverse(sk_c12),sk_c12)
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_31 ),
inference(superposition,[],[f370,f1319]) ).
fof(f1419,plain,
( identity = sk_c12
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_31 ),
inference(forward_demodulation,[],[f1417,f3]) ).
fof(f1426,plain,
( spl0_31
| ~ spl0_14
| ~ spl0_15 ),
inference(avatar_split_clause,[],[f392,f190,f185,f337]) ).
fof(f1434,definition,
( spl0_58
<=> sk_c11 = sk_c10 ),
introduced(definition,[new_symbols(definition,[spl0_58])],[avatar_definition]) ).
fof(f1436,plain,
( sk_c11 != sk_c10
| spl0_58 ),
inference(avatar_component_clause,[],[f1434]) ).
fof(f1438,plain,
( sk_c12 != sk_c10
| sk_c11 != sk_c10
| ~ spl0_4
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f284,f187]) ).
fof(f1451,plain,
( ~ spl0_58
| ~ spl0_22
| ~ spl0_4
| ~ spl0_14
| ~ spl0_15 ),
inference(avatar_split_clause,[],[f1438,f190,f185,f137,f272,f1434]) ).
fof(f1457,plain,
( spl0_41
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_31 ),
inference(avatar_split_clause,[],[f1419,f337,f170,f165,f160,f534]) ).
fof(f1484,plain,
( sk_c12 != sk_c10
| ~ spl0_33
| spl0_58 ),
inference(forward_demodulation,[],[f1436,f345]) ).
fof(f1485,plain,
( ~ spl0_22
| ~ spl0_33
| spl0_58 ),
inference(avatar_split_clause,[],[f1484,f1434,f344,f272]) ).
fof(f1490,plain,
( sk_c10 = multiply(sk_c5,sk_c12)
| ~ spl0_13
| ~ spl0_33 ),
inference(forward_demodulation,[],[f182,f345]) ).
fof(f1491,plain,
( sk_c10 = multiply(identity,sk_c12)
| ~ spl0_12
| ~ spl0_13
| ~ spl0_31
| ~ spl0_33 ),
inference(forward_demodulation,[],[f1490,f1309]) ).
fof(f1492,plain,
( sk_c12 = sk_c10
| ~ spl0_12
| ~ spl0_13
| ~ spl0_31
| ~ spl0_33 ),
inference(forward_demodulation,[],[f1491,f1]) ).
fof(f1493,plain,
( $false
| ~ spl0_12
| ~ spl0_13
| spl0_22
| ~ spl0_31
| ~ spl0_33 ),
inference(forward_subsumption_resolution,[],[f1492,f274]) ).
fof(f1494,plain,
( ~ spl0_12
| ~ spl0_13
| spl0_22
| ~ spl0_31
| ~ spl0_33 ),
inference(avatar_contradiction_clause,[],[f1493]) ).
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(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(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(s36,plain,
( spl0_9
| spl0_18 ),
inference(sat_conversion,[],[f229]) ).
cnf(s37,plain,
( spl0_10
| spl0_18 ),
inference(sat_conversion,[],[f230]) ).
cnf(s38,plain,
( spl0_11
| spl0_18 ),
inference(sat_conversion,[],[f231]) ).
cnf(s39,plain,
( spl0_12
| spl0_18 ),
inference(sat_conversion,[],[f232]) ).
cnf(s40,plain,
( spl0_13
| spl0_18 ),
inference(sat_conversion,[],[f233]) ).
cnf(s51,plain,
( spl0_14
| spl0_19 ),
inference(sat_conversion,[],[f248]) ).
cnf(s52,plain,
( spl0_15
| spl0_19 ),
inference(sat_conversion,[],[f249]) ).
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(s74,plain,
( ~ spl0_19
| ~ spl0_20
| spl0_31 ),
inference(sat_conversion,[],[f390]) ).
cnf(s76,plain,
( ~ spl0_1
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| spl0_30 ),
inference(sat_conversion,[],[f486]) ).
cnf(s80,plain,
( ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_30 ),
inference(sat_conversion,[],[f513]) ).
cnf(s83,plain,
( ~ spl0_31
| spl0_33
| ~ spl0_41 ),
inference(sat_conversion,[],[f673]) ).
cnf(s86,plain,
( ~ spl0_6
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| ~ spl0_31
| spl0_41 ),
inference(sat_conversion,[],[f692]) ).
cnf(s106,plain,
( ~ spl0_3
| ~ spl0_14
| ~ spl0_15
| ~ spl0_31 ),
inference(sat_conversion,[],[f818]) ).
cnf(s107,plain,
( ~ spl0_3
| ~ spl0_19
| ~ spl0_20
| ~ spl0_31 ),
inference(sat_conversion,[],[f820]) ).
cnf(s156,plain,
( ~ spl0_17
| ~ spl0_31
| spl0_48 ),
inference(sat_conversion,[],[f1033]) ).
cnf(s177,plain,
( ~ spl0_1
| ~ spl0_31
| ~ spl0_41
| ~ spl0_48 ),
inference(sat_conversion,[],[f1190]) ).
cnf(s215,plain,
( ~ spl0_14
| ~ spl0_15
| spl0_31 ),
inference(sat_conversion,[],[f1426]) ).
cnf(s220,plain,
( ~ spl0_4
| ~ spl0_14
| ~ spl0_15
| ~ spl0_22
| ~ spl0_58 ),
inference(sat_conversion,[],[f1451]) ).
cnf(s222,plain,
( ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_31
| spl0_41 ),
inference(sat_conversion,[],[f1457]) ).
cnf(s231,plain,
( ~ spl0_22
| ~ spl0_33
| spl0_58 ),
inference(sat_conversion,[],[f1485]) ).
cnf(s232,plain,
( ~ spl0_12
| ~ spl0_13
| spl0_22
| ~ spl0_31
| ~ spl0_33 ),
inference(sat_conversion,[],[f1494]) ).
cnf(s234,plain,
( spl0_16
| ~ spl0_4 ),
inference(rat,[],[s231,s220,s232,s83,s222,s215,s16,s17,s18,s19,s20,s21,s22]) ).
cnf(s235,plain,
( ~ spl0_16
| ~ spl0_4 ),
inference(rat,[],[s231,s220,s232,s83,s222,s215,s6,s7,s8,s9,s10,s11,s12,s67]) ).
cnf(s236,plain,
~ spl0_4,
inference(rat,[],[s235,s234]) ).
cnf(s238,plain,
( spl0_15
| ~ spl0_31
| ~ spl0_3 ),
inference(rat,[],[s107,s52,s62]) ).
cnf(s239,plain,
( ~ spl0_15
| ~ spl0_31
| ~ spl0_3 ),
inference(rat,[],[s107,s51,s61,s106]) ).
cnf(s240,plain,
( ~ spl0_31
| ~ spl0_3 ),
inference(rat,[],[s239,s238]) ).
cnf(s241,plain,
( spl0_15
| spl0_31 ),
inference(rat,[],[s74,s52,s62]) ).
cnf(s242,plain,
( ~ spl0_15
| spl0_31 ),
inference(rat,[],[s74,s51,s61,s215]) ).
cnf(s243,plain,
spl0_31,
inference(rat,[],[s242,s241]) ).
cnf(s245,plain,
~ spl0_3,
inference(rat,[],[s240,s243]) ).
cnf(s247,plain,
( spl0_18
| ~ spl0_2 ),
inference(rat,[],[s65,s39,s40]) ).
cnf(s248,plain,
( ~ spl0_18
| ~ spl0_2 ),
inference(rat,[],[s65,s29,s30,s66]) ).
cnf(s249,plain,
~ spl0_2,
inference(rat,[],[s248,s247]) ).
cnf(s250,plain,
spl0_1,
inference(rat,[],[s2,s236,s245,s249]) ).
cnf(s251,plain,
( spl0_18
| spl0_41 ),
inference(rat,[],[s222,s36,s37,s38,s243]) ).
cnf(s252,plain,
( spl0_6
| spl0_41 ),
inference(rat,[],[s222,s6,s7,s8,s243]) ).
cnf(s253,plain,
( ~ spl0_6
| ~ spl0_17
| spl0_41
| ~ spl0_18 ),
inference(rat,[],[s222,s16,s17,s18,s86,s243]) ).
cnf(s254,plain,
~ spl0_17,
inference(rat,[],[s253,s252,s251,s177,s156,s243,s250]) ).
cnf(s257,plain,
spl0_11,
inference(rat,[],[s28,s254]) ).
cnf(s258,plain,
spl0_10,
inference(rat,[],[s27,s254]) ).
cnf(s259,plain,
spl0_9,
inference(rat,[],[s26,s254]) ).
cnf(s260,plain,
spl0_8,
inference(rat,[],[s25,s254]) ).
cnf(s261,plain,
spl0_7,
inference(rat,[],[s24,s254]) ).
cnf(s262,plain,
spl0_5,
inference(rat,[],[s23,s254]) ).
cnf(s264,plain,
spl0_30,
inference(rat,[],[s76,s258,s257,s250,s259]) ).
cnf(s265,plain,
$false,
inference(rat,[],[s80,s260,s262,s264,s261]) ).
fof(f1495,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.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.38 % Computer : n015.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sun Sep 27 09:46:06 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.41 Running first-order model finding
% 0.11/0.41 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.49 % (1410286)Will run a generic schedule for satisfiability detection.
% 0.16/0.49 % (1410295)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=355285228:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.16/0.49 % (1410292)% WARNING: option uhcvi not known.
% 0.16/0.49 % (1410291)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3146201663_2999 on theBenchmark for (2999ds/0Mi)
% 0.16/0.49 % (1410292)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2097096384:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.16/0.49 % (1410293)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=735680370:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.16/0.49 % (1410294)dis+10_1_sil=32000:sp=arity:random_seed=436869977:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.16/0.49 % (1410297)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=4006679028:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.16/0.49 % (1410296)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=4276457229:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.16/0.49 % TRYING [1]
% 0.16/0.49 % TRYING [2]
% 0.16/0.49 % TRYING [3]
% 0.16/0.49 % TRYING [4]
% 0.16/0.49 % (1410294) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1410286-1410294"...
% 0.16/0.49 % (1410295)Instruction limit reached!
% 0.16/0.49 % (1410295)------------------------------
% 0.16/0.49 % (1410295)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.16/0.49 % (1410295)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/0.49 % (1410295)CaDiCaL version: 2.1.3
% 0.16/0.49 % (1410295)Termination reason: Instruction limit
% 0.16/0.49 % (1410295)Termination phase: Saturation
% 0.16/0.49 % (1410295)Time elapsed: 0.034 s
% 0.16/0.49 % (1410295)Peak memory usage: 12 MB
% 0.16/0.49 % (1410295)Instructions burned: 117 (million)
% 0.16/0.49 % TRYING [5]
% 0.16/0.49 % (1410294)...printing done.
% 0.16/0.49 % (1410294)Refutation found. Thanks to Tanya!
% 0.16/0.49 % SZS status Unsatisfiable for theBenchmark
% 0.16/0.49 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.49 % (1410294)------------------------------
% 0.16/0.49 % (1410294)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.16/0.49 % (1410294)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/0.49 % (1410294)CaDiCaL version: 2.1.3
% 0.16/0.49 % (1410294)Termination reason: Refutation
% 0.16/0.49 % (1410294)Time elapsed: 0.030 s
% 0.16/0.49 % (1410294)Peak memory usage: 13 MB
% 0.16/0.49 % (1410294)Instructions burned: 51 (million)
% 0.16/0.49 % (1410286)Success in time 0.067 s
% 0.16/0.49 % Vampire exiting
%------------------------------------------------------------------------------