%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GRP382-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n014.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 10:17:39 AM UTC 2026
% Result : Unsatisfiable 0.16s 0.48s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 59
% Syntax : Number of formulae : 491 ( 25 unt; 24 def)
% Number of atoms : 2063 ( 622 equ)
% Maximal formula atoms : 17 ( 4 avg)
% Number of connectives : 3138 (1566 ~;1548 |; 0 &)
% ( 24 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 27 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 26 ( 24 usr; 25 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 11 con; 0-2 aty)
% Number of variables : 197 ( 0 sgn 197 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',left_identity) ).
fof(f2,axiom,
! [X0] : multiply(inverse(X0),X0) = identity,
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/GRP004-0.ax',associativity) ).
fof(f5,negated_conjecture,
( inverse(sk_c12) = sk_c11
| multiply(sk_c4,sk_c12) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,plain,
( inverse(sk_c12) = sk_c11
| sk_c11 = multiply(sk_c4,sk_c12) ),
inference(reorient_equations,[],[f5]) ).
fof(f7,negated_conjecture,
( inverse(sk_c12) = sk_c11
| inverse(sk_c4) = sk_c12 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_2) ).
fof(f8,plain,
( inverse(sk_c12) = sk_c11
| sk_c12 = inverse(sk_c4) ),
inference(reorient_equations,[],[f7]) ).
fof(f12,negated_conjecture,
( inverse(sk_c12) = sk_c11
| multiply(sk_c6,sk_c9) = sk_c12 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_5) ).
fof(f13,plain,
( inverse(sk_c12) = sk_c11
| sk_c12 = multiply(sk_c6,sk_c9) ),
inference(reorient_equations,[],[f12]) ).
fof(f14,negated_conjecture,
( inverse(sk_c12) = sk_c11
| inverse(sk_c6) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_6) ).
fof(f15,plain,
( inverse(sk_c12) = sk_c11
| sk_c9 = inverse(sk_c6) ),
inference(reorient_equations,[],[f14]) ).
fof(f16,negated_conjecture,
( inverse(sk_c12) = sk_c11
| multiply(sk_c9,sk_c11) = sk_c12 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_7) ).
fof(f17,plain,
( inverse(sk_c12) = sk_c11
| sk_c12 = multiply(sk_c9,sk_c11) ),
inference(reorient_equations,[],[f16]) ).
fof(f23,negated_conjecture,
( multiply(sk_c11,sk_c10) = sk_c12
| multiply(sk_c4,sk_c12) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_11) ).
fof(f24,plain,
( sk_c12 = multiply(sk_c11,sk_c10)
| sk_c11 = multiply(sk_c4,sk_c12) ),
inference(reorient_equations,[],[f23]) ).
fof(f25,negated_conjecture,
( multiply(sk_c11,sk_c10) = sk_c12
| inverse(sk_c4) = sk_c12 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_12) ).
fof(f26,plain,
( sk_c12 = multiply(sk_c11,sk_c10)
| sk_c12 = inverse(sk_c4) ),
inference(reorient_equations,[],[f25]) ).
fof(f27,negated_conjecture,
( multiply(sk_c11,sk_c10) = sk_c12
| multiply(sk_c5,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_13) ).
fof(f28,plain,
( sk_c12 = multiply(sk_c11,sk_c10)
| multiply(sk_c5,sk_c11) = sk_c10 ),
inference(reorient_equations,[],[f27]) ).
fof(f29,negated_conjecture,
( multiply(sk_c11,sk_c10) = sk_c12
| inverse(sk_c5) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_14) ).
fof(f30,plain,
( sk_c12 = multiply(sk_c11,sk_c10)
| sk_c11 = inverse(sk_c5) ),
inference(reorient_equations,[],[f29]) ).
fof(f31,negated_conjecture,
( multiply(sk_c11,sk_c10) = sk_c12
| multiply(sk_c6,sk_c9) = sk_c12 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_15) ).
fof(f32,plain,
( sk_c12 = multiply(sk_c11,sk_c10)
| sk_c12 = multiply(sk_c6,sk_c9) ),
inference(reorient_equations,[],[f31]) ).
fof(f33,negated_conjecture,
( multiply(sk_c11,sk_c10) = sk_c12
| inverse(sk_c6) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_16) ).
fof(f34,plain,
( sk_c12 = multiply(sk_c11,sk_c10)
| sk_c9 = inverse(sk_c6) ),
inference(reorient_equations,[],[f33]) ).
fof(f35,negated_conjecture,
( multiply(sk_c11,sk_c10) = sk_c12
| multiply(sk_c9,sk_c11) = sk_c12 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_17) ).
fof(f36,plain,
( sk_c12 = multiply(sk_c11,sk_c10)
| sk_c12 = multiply(sk_c9,sk_c11) ),
inference(reorient_equations,[],[f35]) ).
fof(f43,negated_conjecture,
( inverse(sk_c1) = sk_c12
| multiply(sk_c4,sk_c12) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_21) ).
fof(f44,plain,
( sk_c12 = inverse(sk_c1)
| sk_c11 = multiply(sk_c4,sk_c12) ),
inference(reorient_equations,[],[f43]) ).
fof(f45,negated_conjecture,
( inverse(sk_c1) = sk_c12
| inverse(sk_c4) = sk_c12 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_22) ).
fof(f46,plain,
( sk_c12 = inverse(sk_c1)
| sk_c12 = inverse(sk_c4) ),
inference(reorient_equations,[],[f45]) ).
fof(f51,negated_conjecture,
( inverse(sk_c1) = sk_c12
| multiply(sk_c6,sk_c9) = sk_c12 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_25) ).
fof(f52,plain,
( sk_c12 = inverse(sk_c1)
| sk_c12 = multiply(sk_c6,sk_c9) ),
inference(reorient_equations,[],[f51]) ).
fof(f63,negated_conjecture,
( multiply(sk_c1,sk_c11) = sk_c12
| multiply(sk_c4,sk_c12) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_31) ).
fof(f64,plain,
( sk_c12 = multiply(sk_c1,sk_c11)
| sk_c11 = multiply(sk_c4,sk_c12) ),
inference(reorient_equations,[],[f63]) ).
fof(f65,negated_conjecture,
( multiply(sk_c1,sk_c11) = sk_c12
| inverse(sk_c4) = sk_c12 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_32) ).
fof(f66,plain,
( sk_c12 = multiply(sk_c1,sk_c11)
| sk_c12 = inverse(sk_c4) ),
inference(reorient_equations,[],[f65]) ).
fof(f71,negated_conjecture,
( multiply(sk_c1,sk_c11) = sk_c12
| multiply(sk_c6,sk_c9) = sk_c12 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_35) ).
fof(f72,plain,
( sk_c12 = multiply(sk_c1,sk_c11)
| sk_c12 = multiply(sk_c6,sk_c9) ),
inference(reorient_equations,[],[f71]) ).
fof(f83,negated_conjecture,
( multiply(sk_c2,sk_c3) = sk_c11
| multiply(sk_c4,sk_c12) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_41) ).
fof(f84,plain,
( sk_c11 = multiply(sk_c2,sk_c3)
| sk_c11 = multiply(sk_c4,sk_c12) ),
inference(reorient_equations,[],[f83]) ).
fof(f85,negated_conjecture,
( multiply(sk_c2,sk_c3) = sk_c11
| inverse(sk_c4) = sk_c12 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_42) ).
fof(f86,plain,
( sk_c11 = multiply(sk_c2,sk_c3)
| sk_c12 = inverse(sk_c4) ),
inference(reorient_equations,[],[f85]) ).
fof(f93,negated_conjecture,
( multiply(sk_c2,sk_c3) = sk_c11
| inverse(sk_c6) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_46) ).
fof(f94,plain,
( sk_c11 = multiply(sk_c2,sk_c3)
| sk_c9 = inverse(sk_c6) ),
inference(reorient_equations,[],[f93]) ).
fof(f95,negated_conjecture,
( multiply(sk_c2,sk_c3) = sk_c11
| multiply(sk_c9,sk_c11) = sk_c12 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_47) ).
fof(f96,plain,
( sk_c11 = multiply(sk_c2,sk_c3)
| sk_c12 = multiply(sk_c9,sk_c11) ),
inference(reorient_equations,[],[f95]) ).
fof(f103,negated_conjecture,
( inverse(sk_c2) = sk_c3
| multiply(sk_c4,sk_c12) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_51) ).
fof(f104,plain,
( sk_c3 = inverse(sk_c2)
| sk_c11 = multiply(sk_c4,sk_c12) ),
inference(reorient_equations,[],[f103]) ).
fof(f105,negated_conjecture,
( inverse(sk_c2) = sk_c3
| inverse(sk_c4) = sk_c12 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_52) ).
fof(f106,plain,
( sk_c3 = inverse(sk_c2)
| sk_c12 = inverse(sk_c4) ),
inference(reorient_equations,[],[f105]) ).
fof(f113,negated_conjecture,
( inverse(sk_c2) = sk_c3
| inverse(sk_c6) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_56) ).
fof(f114,plain,
( sk_c3 = inverse(sk_c2)
| sk_c9 = inverse(sk_c6) ),
inference(reorient_equations,[],[f113]) ).
fof(f115,negated_conjecture,
( inverse(sk_c2) = sk_c3
| multiply(sk_c9,sk_c11) = sk_c12 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_57) ).
fof(f116,plain,
( sk_c3 = inverse(sk_c2)
| sk_c12 = multiply(sk_c9,sk_c11) ),
inference(reorient_equations,[],[f115]) ).
fof(f123,negated_conjecture,
( multiply(sk_c3,sk_c12) = sk_c11
| multiply(sk_c4,sk_c12) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_61) ).
fof(f124,plain,
( sk_c11 = multiply(sk_c3,sk_c12)
| sk_c11 = multiply(sk_c4,sk_c12) ),
inference(reorient_equations,[],[f123]) ).
fof(f125,negated_conjecture,
( multiply(sk_c3,sk_c12) = sk_c11
| inverse(sk_c4) = sk_c12 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_62) ).
fof(f126,plain,
( sk_c11 = multiply(sk_c3,sk_c12)
| sk_c12 = inverse(sk_c4) ),
inference(reorient_equations,[],[f125]) ).
fof(f131,negated_conjecture,
( multiply(sk_c3,sk_c12) = sk_c11
| multiply(sk_c6,sk_c9) = sk_c12 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_65) ).
fof(f132,plain,
( sk_c11 = multiply(sk_c3,sk_c12)
| sk_c12 = multiply(sk_c6,sk_c9) ),
inference(reorient_equations,[],[f131]) ).
fof(f133,negated_conjecture,
( multiply(sk_c3,sk_c12) = sk_c11
| inverse(sk_c6) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_66) ).
fof(f134,plain,
( sk_c11 = multiply(sk_c3,sk_c12)
| sk_c9 = inverse(sk_c6) ),
inference(reorient_equations,[],[f133]) ).
fof(f135,negated_conjecture,
( multiply(sk_c3,sk_c12) = sk_c11
| multiply(sk_c9,sk_c11) = sk_c12 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_67) ).
fof(f136,plain,
( sk_c11 = multiply(sk_c3,sk_c12)
| sk_c12 = multiply(sk_c9,sk_c11) ),
inference(reorient_equations,[],[f135]) ).
fof(f143,negated_conjecture,
! [X2,X3,X0,X1,X8,X6,X7,X4,X5] :
( inverse(sk_c12) != sk_c11
| multiply(sk_c11,sk_c10) != sk_c12
| inverse(X0) != sk_c12
| multiply(X0,sk_c11) != sk_c12
| multiply(X1,X2) != sk_c11
| inverse(X1) != X2
| multiply(X2,sk_c12) != sk_c11
| 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_71) ).
fof(f144,plain,
! [X2,X3,X0,X1,X8,X6,X7,X4,X5] :
( inverse(sk_c12) != sk_c11
| sk_c12 != multiply(sk_c11,sk_c10)
| inverse(X0) != sk_c12
| sk_c12 != multiply(X0,sk_c11)
| multiply(X1,X2) != sk_c11
| inverse(X1) != X2
| sk_c11 != 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,[],[f143]) ).
fof(f146,definition,
( spl0_1
<=> ! [X5,X7,X6,X8] :
( sk_c12 != multiply(X5,X6)
| multiply(X7,X6) != X8
| inverse(X7) != X8
| inverse(X8) != X6
| sk_c12 != multiply(X6,sk_c11)
| inverse(X5) != X6 ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f147,plain,
( ! [X8,X6,X7,X5] :
( sk_c12 != multiply(X5,X6)
| multiply(X7,X6) != X8
| inverse(X7) != X8
| inverse(X8) != X6
| sk_c12 != multiply(X6,sk_c11)
| inverse(X5) != X6 )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f146]) ).
fof(f149,definition,
( spl0_2
<=> ! [X4] :
( sk_c10 != multiply(X4,sk_c11)
| sk_c11 != inverse(X4) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f150,plain,
( ! [X4] :
( sk_c10 != multiply(X4,sk_c11)
| sk_c11 != inverse(X4) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f149]) ).
fof(f152,definition,
( spl0_3
<=> ! [X3] :
( sk_c11 != multiply(X3,sk_c12)
| sk_c12 != inverse(X3) ) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f153,plain,
( ! [X3] :
( sk_c11 != multiply(X3,sk_c12)
| sk_c12 != inverse(X3) )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f152]) ).
fof(f155,definition,
( spl0_4
<=> ! [X2,X1] :
( multiply(X1,X2) != sk_c11
| sk_c11 != multiply(X2,sk_c12)
| inverse(X1) != X2 ) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f156,plain,
( ! [X2,X1] :
( multiply(X1,X2) != sk_c11
| sk_c11 != multiply(X2,sk_c12)
| inverse(X1) != X2 )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f155]) ).
fof(f158,definition,
( spl0_5
<=> ! [X0] :
( inverse(X0) != sk_c12
| sk_c12 != multiply(X0,sk_c11) ) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f159,plain,
( ! [X0] :
( inverse(X0) != sk_c12
| sk_c12 != multiply(X0,sk_c11) )
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f158]) ).
fof(f161,definition,
( spl0_6
<=> sk_c12 = multiply(sk_c11,sk_c10) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f162,plain,
( sk_c12 = multiply(sk_c11,sk_c10)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f161]) ).
fof(f163,plain,
( sk_c12 != multiply(sk_c11,sk_c10)
| spl0_6 ),
inference(avatar_component_clause,[],[f161]) ).
fof(f165,definition,
( spl0_7
<=> inverse(sk_c12) = sk_c11 ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f166,plain,
( inverse(sk_c12) = sk_c11
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f165]) ).
fof(f167,plain,
( inverse(sk_c12) != sk_c11
| spl0_7 ),
inference(avatar_component_clause,[],[f165]) ).
fof(f168,plain,
( spl0_1
| spl0_2
| spl0_3
| spl0_4
| spl0_5
| ~ spl0_6
| ~ spl0_7 ),
inference(avatar_split_clause,[],[f144,f165,f161,f158,f155,f152,f149,f146]) ).
fof(f174,definition,
( spl0_9
<=> sk_c11 = multiply(sk_c3,sk_c12) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f176,plain,
( sk_c11 = multiply(sk_c3,sk_c12)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f174]) ).
fof(f189,definition,
( spl0_12
<=> sk_c12 = multiply(sk_c9,sk_c11) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f191,plain,
( sk_c12 = multiply(sk_c9,sk_c11)
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f189]) ).
fof(f192,plain,
( spl0_12
| spl0_9 ),
inference(avatar_split_clause,[],[f136,f174,f189]) ).
fof(f194,definition,
( spl0_13
<=> sk_c9 = inverse(sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f196,plain,
( sk_c9 = inverse(sk_c6)
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f194]) ).
fof(f197,plain,
( spl0_13
| spl0_9 ),
inference(avatar_split_clause,[],[f134,f174,f194]) ).
fof(f199,definition,
( spl0_14
<=> sk_c12 = multiply(sk_c6,sk_c9) ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
fof(f200,plain,
( sk_c12 != multiply(sk_c6,sk_c9)
| spl0_14 ),
inference(avatar_component_clause,[],[f199]) ).
fof(f201,plain,
( sk_c12 = multiply(sk_c6,sk_c9)
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f199]) ).
fof(f202,plain,
( spl0_14
| spl0_9 ),
inference(avatar_split_clause,[],[f132,f174,f199]) ).
fof(f204,definition,
( spl0_15
<=> sk_c11 = inverse(sk_c5) ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
fof(f206,plain,
( sk_c11 = inverse(sk_c5)
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f204]) ).
fof(f209,definition,
( spl0_16
<=> multiply(sk_c5,sk_c11) = sk_c10 ),
introduced(definition,[new_symbols(definition,[spl0_16])],[avatar_definition]) ).
fof(f211,plain,
( multiply(sk_c5,sk_c11) = sk_c10
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f209]) ).
fof(f214,definition,
( spl0_17
<=> sk_c12 = inverse(sk_c4) ),
introduced(definition,[new_symbols(definition,[spl0_17])],[avatar_definition]) ).
fof(f215,plain,
( sk_c12 != inverse(sk_c4)
| spl0_17 ),
inference(avatar_component_clause,[],[f214]) ).
fof(f216,plain,
( sk_c12 = inverse(sk_c4)
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f214]) ).
fof(f217,plain,
( spl0_17
| spl0_9 ),
inference(avatar_split_clause,[],[f126,f174,f214]) ).
fof(f219,definition,
( spl0_18
<=> sk_c11 = multiply(sk_c4,sk_c12) ),
introduced(definition,[new_symbols(definition,[spl0_18])],[avatar_definition]) ).
fof(f221,plain,
( sk_c11 = multiply(sk_c4,sk_c12)
| ~ spl0_18 ),
inference(avatar_component_clause,[],[f219]) ).
fof(f222,plain,
( spl0_18
| spl0_9 ),
inference(avatar_split_clause,[],[f124,f174,f219]) ).
fof(f224,definition,
( spl0_19
<=> sk_c3 = inverse(sk_c2) ),
introduced(definition,[new_symbols(definition,[spl0_19])],[avatar_definition]) ).
fof(f226,plain,
( sk_c3 = inverse(sk_c2)
| ~ spl0_19 ),
inference(avatar_component_clause,[],[f224]) ).
fof(f230,plain,
( spl0_12
| spl0_19 ),
inference(avatar_split_clause,[],[f116,f224,f189]) ).
fof(f231,plain,
( spl0_13
| spl0_19 ),
inference(avatar_split_clause,[],[f114,f224,f194]) ).
fof(f235,plain,
( spl0_17
| spl0_19 ),
inference(avatar_split_clause,[],[f106,f224,f214]) ).
fof(f236,plain,
( spl0_18
| spl0_19 ),
inference(avatar_split_clause,[],[f104,f224,f219]) ).
fof(f238,definition,
( spl0_20
<=> sk_c11 = multiply(sk_c2,sk_c3) ),
introduced(definition,[new_symbols(definition,[spl0_20])],[avatar_definition]) ).
fof(f240,plain,
( sk_c11 = multiply(sk_c2,sk_c3)
| ~ spl0_20 ),
inference(avatar_component_clause,[],[f238]) ).
fof(f244,plain,
( spl0_12
| spl0_20 ),
inference(avatar_split_clause,[],[f96,f238,f189]) ).
fof(f245,plain,
( spl0_13
| spl0_20 ),
inference(avatar_split_clause,[],[f94,f238,f194]) ).
fof(f249,plain,
( spl0_17
| spl0_20 ),
inference(avatar_split_clause,[],[f86,f238,f214]) ).
fof(f250,plain,
( spl0_18
| spl0_20 ),
inference(avatar_split_clause,[],[f84,f238,f219]) ).
fof(f252,definition,
( spl0_21
<=> sk_c12 = multiply(sk_c1,sk_c11) ),
introduced(definition,[new_symbols(definition,[spl0_21])],[avatar_definition]) ).
fof(f254,plain,
( sk_c12 = multiply(sk_c1,sk_c11)
| ~ spl0_21 ),
inference(avatar_component_clause,[],[f252]) ).
fof(f260,plain,
( spl0_14
| spl0_21 ),
inference(avatar_split_clause,[],[f72,f252,f199]) ).
fof(f263,plain,
( spl0_17
| spl0_21 ),
inference(avatar_split_clause,[],[f66,f252,f214]) ).
fof(f264,plain,
( spl0_18
| spl0_21 ),
inference(avatar_split_clause,[],[f64,f252,f219]) ).
fof(f266,definition,
( spl0_22
<=> sk_c12 = inverse(sk_c1) ),
introduced(definition,[new_symbols(definition,[spl0_22])],[avatar_definition]) ).
fof(f268,plain,
( sk_c12 = inverse(sk_c1)
| ~ spl0_22 ),
inference(avatar_component_clause,[],[f266]) ).
fof(f274,plain,
( spl0_14
| spl0_22 ),
inference(avatar_split_clause,[],[f52,f266,f199]) ).
fof(f277,plain,
( spl0_17
| spl0_22 ),
inference(avatar_split_clause,[],[f46,f266,f214]) ).
fof(f278,plain,
( spl0_18
| spl0_22 ),
inference(avatar_split_clause,[],[f44,f266,f219]) ).
fof(f282,plain,
( spl0_12
| spl0_6 ),
inference(avatar_split_clause,[],[f36,f161,f189]) ).
fof(f283,plain,
( spl0_13
| spl0_6 ),
inference(avatar_split_clause,[],[f34,f161,f194]) ).
fof(f284,plain,
( spl0_14
| spl0_6 ),
inference(avatar_split_clause,[],[f32,f161,f199]) ).
fof(f285,plain,
( spl0_15
| spl0_6 ),
inference(avatar_split_clause,[],[f30,f161,f204]) ).
fof(f286,plain,
( spl0_16
| spl0_6 ),
inference(avatar_split_clause,[],[f28,f161,f209]) ).
fof(f287,plain,
( spl0_17
| spl0_6 ),
inference(avatar_split_clause,[],[f26,f161,f214]) ).
fof(f288,plain,
( spl0_18
| spl0_6 ),
inference(avatar_split_clause,[],[f24,f161,f219]) ).
fof(f292,plain,
( spl0_12
| spl0_7 ),
inference(avatar_split_clause,[],[f17,f165,f189]) ).
fof(f293,plain,
( spl0_13
| spl0_7 ),
inference(avatar_split_clause,[],[f15,f165,f194]) ).
fof(f294,plain,
( spl0_14
| spl0_7 ),
inference(avatar_split_clause,[],[f13,f165,f199]) ).
fof(f297,plain,
( spl0_17
| spl0_7 ),
inference(avatar_split_clause,[],[f8,f165,f214]) ).
fof(f298,plain,
( spl0_18
| spl0_7 ),
inference(avatar_split_clause,[],[f6,f165,f219]) ).
fof(f301,plain,
( sk_c12 = multiply(sk_c6,inverse(sk_c6))
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f201,f196]) ).
fof(f304,plain,
( sk_c12 = multiply(inverse(sk_c6),sk_c11)
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f191,f196]) ).
fof(f305,plain,
( sk_c12 != multiply(sk_c11,multiply(sk_c5,sk_c11))
| spl0_6
| ~ spl0_16 ),
inference(superposition,[],[f163,f211]) ).
fof(f308,plain,
( identity = multiply(sk_c12,sk_c4)
| ~ spl0_17 ),
inference(superposition,[],[f3,f216]) ).
fof(f309,plain,
( identity = multiply(sk_c11,sk_c5)
| ~ spl0_15 ),
inference(superposition,[],[f3,f206]) ).
fof(f311,plain,
! [X0,X1] : multiply(multiply(inverse(X0),X0),X1) = X1,
inference(superposition,[],[f1,f3]) ).
fof(f312,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f311,f4]) ).
fof(f318,plain,
( ! [X0] : multiply(sk_c11,X0) = multiply(sk_c4,multiply(sk_c12,X0))
| ~ spl0_18 ),
inference(superposition,[],[f4,f221]) ).
fof(f319,plain,
( ! [X0] : multiply(sk_c12,X0) = multiply(sk_c6,multiply(inverse(sk_c6),X0))
| ~ spl0_13
| ~ spl0_14 ),
inference(superposition,[],[f4,f301]) ).
fof(f325,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c12,multiply(sk_c4,X0))
| ~ spl0_17 ),
inference(superposition,[],[f4,f308]) ).
fof(f326,plain,
( ! [X0] : multiply(sk_c12,multiply(sk_c4,X0)) = X0
| ~ spl0_17 ),
inference(forward_demodulation,[],[f325,f1]) ).
fof(f327,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c11,multiply(sk_c5,X0))
| ~ spl0_15 ),
inference(superposition,[],[f4,f309]) ).
fof(f328,plain,
( ! [X0] : multiply(sk_c11,multiply(sk_c5,X0)) = X0
| ~ spl0_15 ),
inference(forward_demodulation,[],[f327,f1]) ).
fof(f329,plain,
( sk_c12 = multiply(sk_c12,sk_c11)
| ~ spl0_17
| ~ spl0_18 ),
inference(superposition,[],[f326,f221]) ).
fof(f339,plain,
( sk_c12 != sk_c11
| spl0_6
| ~ spl0_15
| ~ spl0_16 ),
inference(superposition,[],[f305,f328]) ).
fof(f350,plain,
( multiply(sk_c12,sk_c11) = multiply(sk_c6,sk_c12)
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(superposition,[],[f319,f304]) ).
fof(f355,plain,
( sk_c12 = multiply(sk_c6,sk_c12)
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f350,f329]) ).
fof(f364,plain,
( sk_c11 = multiply(inverse(inverse(sk_c6)),sk_c12)
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f312,f304]) ).
fof(f365,plain,
! [X0] : multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[],[f312,f3]) ).
fof(f367,plain,
! [X0,X1] : multiply(X1,X0) = multiply(inverse(inverse(X1)),X0),
inference(superposition,[],[f312,f312]) ).
fof(f368,plain,
( sk_c4 = multiply(inverse(sk_c12),identity)
| ~ spl0_17 ),
inference(superposition,[],[f312,f308]) ).
fof(f369,plain,
( ! [X0] : multiply(sk_c4,X0) = multiply(inverse(sk_c12),X0)
| ~ spl0_17 ),
inference(superposition,[],[f312,f326]) ).
fof(f370,plain,
( sk_c11 = multiply(inverse(sk_c12),sk_c12)
| ~ spl0_17
| ~ spl0_18 ),
inference(superposition,[],[f312,f329]) ).
fof(f373,plain,
( sk_c12 = multiply(inverse(sk_c4),sk_c11)
| ~ spl0_18 ),
inference(superposition,[],[f312,f221]) ).
fof(f378,plain,
( sk_c11 = multiply(inverse(sk_c9),sk_c12)
| ~ spl0_12 ),
inference(superposition,[],[f312,f191]) ).
fof(f384,plain,
( sk_c11 = multiply(inverse(inverse(sk_c6)),sk_c12)
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f378,f196]) ).
fof(f388,plain,
( identity = sk_c11
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f370,f3]) ).
fof(f390,plain,
! [X0] : multiply(X0,identity) = X0,
inference(forward_demodulation,[],[f365,f367]) ).
fof(f391,plain,
( sk_c11 = multiply(sk_c6,sk_c12)
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f364,f367]) ).
fof(f395,plain,
( sk_c11 = multiply(sk_c6,sk_c12)
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f384,f367]) ).
fof(f397,plain,
( sk_c12 = sk_c11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f391,f355]) ).
fof(f399,plain,
( sk_c12 = sk_c11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f395,f355]) ).
fof(f404,plain,
( $false
| spl0_6
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[],[f399,f339]) ).
fof(f405,plain,
( spl0_6
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18 ),
inference(avatar_contradiction_clause,[],[f404]) ).
fof(f408,plain,
( identity != inverse(sk_c12)
| spl0_7
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f167,f388]) ).
fof(f409,plain,
( identity = sk_c12
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f397,f388]) ).
fof(f413,plain,
( sk_c11 = multiply(sk_c4,identity)
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(superposition,[],[f221,f409]) ).
fof(f414,plain,
( identity = multiply(identity,sk_c4)
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(superposition,[],[f308,f409]) ).
fof(f423,plain,
( identity = sk_c4
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f414,f1]) ).
fof(f424,plain,
( sk_c11 = multiply(inverse(sk_c12),identity)
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f413,f369]) ).
fof(f427,plain,
( inverse(sk_c12) = sk_c11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f424,f390]) ).
fof(f430,plain,
( identity = inverse(sk_c12)
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f427,f388]) ).
fof(f433,plain,
( $false
| spl0_7
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[],[f430,f408]) ).
fof(f434,plain,
( spl0_7
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(avatar_contradiction_clause,[],[f433]) ).
fof(f437,plain,
( ! [X2,X1] :
( identity != multiply(X1,X2)
| sk_c11 != multiply(X2,sk_c12)
| inverse(X1) != X2 )
| ~ spl0_4
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f156,f388]) ).
fof(f438,plain,
( identity = inverse(sk_c12)
| ~ spl0_7
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f166,f388]) ).
fof(f440,plain,
( ! [X2,X1] :
( sk_c11 != multiply(X2,identity)
| identity != multiply(X1,X2)
| inverse(X1) != X2 )
| ~ spl0_4
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f437,f409]) ).
fof(f442,plain,
( ! [X2,X1] :
( sk_c11 != X2
| identity != multiply(X1,X2)
| inverse(X1) != X2 )
| ~ spl0_4
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f440,f390]) ).
fof(f443,plain,
( ! [X2,X1] :
( identity != multiply(X1,X2)
| identity != X2
| inverse(X1) != X2 )
| ~ spl0_4
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f442,f388]) ).
fof(f451,plain,
( identity != identity
| identity != sk_c4
| inverse(sk_c12) != sk_c4
| ~ spl0_4
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(superposition,[],[f443,f308]) ).
fof(f467,plain,
( identity != sk_c4
| inverse(sk_c12) != sk_c4
| ~ spl0_4
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(trivial_inequality_removal,[],[f451]) ).
fof(f482,plain,
( inverse(sk_c12) != sk_c4
| ~ spl0_4
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[],[f467,f423]) ).
fof(f499,plain,
( inverse(sk_c12) != multiply(inverse(sk_c12),identity)
| ~ spl0_4
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f482,f368]) ).
fof(f506,plain,
( $false
| ~ spl0_4
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[],[f499,f390]) ).
fof(f507,plain,
( ~ spl0_4
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(avatar_contradiction_clause,[],[f506]) ).
fof(f513,plain,
( sk_c12 != multiply(sk_c6,inverse(sk_c6))
| ~ spl0_13
| spl0_14 ),
inference(forward_demodulation,[],[f200,f196]) ).
fof(f514,plain,
( sk_c11 = multiply(sk_c2,inverse(sk_c2))
| ~ spl0_19
| ~ spl0_20 ),
inference(forward_demodulation,[],[f240,f226]) ).
fof(f515,plain,
( sk_c12 = multiply(sk_c1,identity)
| ~ spl0_17
| ~ spl0_18
| ~ spl0_21 ),
inference(forward_demodulation,[],[f254,f388]) ).
fof(f524,plain,
( sk_c12 = sk_c1
| ~ spl0_17
| ~ spl0_18
| ~ spl0_21 ),
inference(forward_demodulation,[],[f515,f390]) ).
fof(f570,plain,
( identity = multiply(sk_c12,sk_c1)
| ~ spl0_22 ),
inference(superposition,[],[f3,f268]) ).
fof(f622,plain,
( sk_c12 = inverse(sk_c12)
| ~ spl0_17
| ~ spl0_18
| ~ spl0_21
| ~ spl0_22 ),
inference(superposition,[],[f268,f524]) ).
fof(f623,plain,
( identity = sk_c12
| ~ spl0_7
| ~ spl0_17
| ~ spl0_18
| ~ spl0_21
| ~ spl0_22 ),
inference(forward_demodulation,[],[f622,f438]) ).
fof(f652,plain,
( identity = multiply(identity,sk_c12)
| ~ spl0_7
| ~ spl0_17
| ~ spl0_18 ),
inference(superposition,[],[f3,f438]) ).
fof(f653,plain,
( identity = sk_c12
| ~ spl0_7
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f652,f1]) ).
fof(f670,plain,
( sk_c12 = multiply(inverse(sk_c6),identity)
| ~ spl0_12
| ~ spl0_13
| ~ spl0_17
| ~ spl0_18 ),
inference(superposition,[],[f304,f388]) ).
fof(f672,plain,
( sk_c12 = inverse(sk_c6)
| ~ spl0_12
| ~ spl0_13
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f670,f390]) ).
fof(f674,plain,
( identity = inverse(sk_c6)
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13
| ~ spl0_17
| ~ spl0_18
| ~ spl0_21
| ~ spl0_22 ),
inference(forward_demodulation,[],[f672,f623]) ).
fof(f756,plain,
( sk_c12 != multiply(sk_c6,identity)
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13
| spl0_14
| ~ spl0_17
| ~ spl0_18
| ~ spl0_21
| ~ spl0_22 ),
inference(superposition,[],[f513,f674]) ).
fof(f762,plain,
( identity = multiply(identity,sk_c6)
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13
| ~ spl0_17
| ~ spl0_18
| ~ spl0_21
| ~ spl0_22 ),
inference(superposition,[],[f3,f674]) ).
fof(f763,plain,
( identity = sk_c6
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13
| ~ spl0_17
| ~ spl0_18
| ~ spl0_21
| ~ spl0_22 ),
inference(forward_demodulation,[],[f762,f1]) ).
fof(f769,plain,
( sk_c12 != sk_c6
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13
| spl0_14
| ~ spl0_17
| ~ spl0_18
| ~ spl0_21
| ~ spl0_22 ),
inference(forward_demodulation,[],[f756,f390]) ).
fof(f773,plain,
( identity != sk_c12
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13
| spl0_14
| ~ spl0_17
| ~ spl0_18
| ~ spl0_21
| ~ spl0_22 ),
inference(forward_demodulation,[],[f769,f763]) ).
fof(f774,plain,
( $false
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13
| spl0_14
| ~ spl0_17
| ~ spl0_18
| ~ spl0_21
| ~ spl0_22 ),
inference(forward_subsumption_resolution,[],[f773,f623]) ).
fof(f775,plain,
( ~ spl0_7
| ~ spl0_12
| ~ spl0_13
| spl0_14
| ~ spl0_17
| ~ spl0_18
| ~ spl0_21
| ~ spl0_22 ),
inference(avatar_contradiction_clause,[],[f774]) ).
fof(f776,plain,
( sk_c11 = multiply(inverse(sk_c2),sk_c12)
| ~ spl0_9
| ~ spl0_19 ),
inference(forward_demodulation,[],[f176,f226]) ).
fof(f777,plain,
( sk_c12 = multiply(sk_c1,inverse(sk_c12))
| ~ spl0_7
| ~ spl0_21 ),
inference(forward_demodulation,[],[f254,f166]) ).
fof(f780,plain,
( inverse(sk_c12) = multiply(sk_c2,inverse(sk_c2))
| ~ spl0_7
| ~ spl0_19
| ~ spl0_20 ),
inference(forward_demodulation,[],[f514,f166]) ).
fof(f781,plain,
( sk_c12 = multiply(inverse(sk_c12),sk_c10)
| ~ spl0_6
| ~ spl0_7 ),
inference(forward_demodulation,[],[f162,f166]) ).
fof(f784,plain,
( inverse(sk_c12) = multiply(inverse(sk_c2),sk_c12)
| ~ spl0_7
| ~ spl0_9
| ~ spl0_19 ),
inference(forward_demodulation,[],[f776,f166]) ).
fof(f788,plain,
( multiply(sk_c4,identity) = multiply(sk_c11,sk_c1)
| ~ spl0_18
| ~ spl0_22 ),
inference(superposition,[],[f318,f570]) ).
fof(f789,plain,
( sk_c1 = multiply(inverse(sk_c12),identity)
| ~ spl0_22 ),
inference(superposition,[],[f312,f570]) ).
fof(f792,plain,
( inverse(sk_c12) = sk_c1
| ~ spl0_22 ),
inference(forward_demodulation,[],[f789,f390]) ).
fof(f793,plain,
( multiply(sk_c4,identity) = multiply(inverse(sk_c12),sk_c1)
| ~ spl0_7
| ~ spl0_18
| ~ spl0_22 ),
inference(forward_demodulation,[],[f788,f166]) ).
fof(f794,plain,
( multiply(sk_c4,identity) = multiply(inverse(sk_c12),inverse(sk_c12))
| ~ spl0_7
| ~ spl0_18
| ~ spl0_22 ),
inference(forward_demodulation,[],[f793,f792]) ).
fof(f795,plain,
( sk_c4 = multiply(inverse(sk_c12),inverse(sk_c12))
| ~ spl0_7
| ~ spl0_18
| ~ spl0_22 ),
inference(forward_demodulation,[],[f794,f390]) ).
fof(f796,plain,
( inverse(sk_c12) = multiply(inverse(sk_c1),sk_c12)
| ~ spl0_7
| ~ spl0_21 ),
inference(superposition,[],[f312,f777]) ).
fof(f799,plain,
( inverse(sk_c12) = multiply(sk_c12,sk_c12)
| ~ spl0_7
| ~ spl0_21
| ~ spl0_22 ),
inference(forward_demodulation,[],[f796,f268]) ).
fof(f801,plain,
( identity = multiply(sk_c12,inverse(sk_c12))
| ~ spl0_22 ),
inference(superposition,[],[f570,f792]) ).
fof(f802,plain,
( sk_c12 = inverse(inverse(sk_c12))
| ~ spl0_22 ),
inference(superposition,[],[f268,f792]) ).
fof(f803,plain,
( sk_c12 = inverse(multiply(sk_c12,sk_c12))
| ~ spl0_7
| ~ spl0_21
| ~ spl0_22 ),
inference(forward_demodulation,[],[f802,f799]) ).
fof(f804,plain,
( identity = multiply(sk_c12,multiply(sk_c12,sk_c12))
| ~ spl0_7
| ~ spl0_21
| ~ spl0_22 ),
inference(forward_demodulation,[],[f801,f799]) ).
fof(f808,plain,
( sk_c10 = multiply(inverse(inverse(sk_c12)),sk_c12)
| ~ spl0_6
| ~ spl0_7 ),
inference(superposition,[],[f312,f781]) ).
fof(f811,plain,
( sk_c10 = multiply(sk_c12,sk_c12)
| ~ spl0_6
| ~ spl0_7 ),
inference(forward_demodulation,[],[f808,f367]) ).
fof(f829,plain,
( ! [X0] : multiply(inverse(sk_c12),X0) = multiply(sk_c2,multiply(inverse(sk_c2),X0))
| ~ spl0_7
| ~ spl0_19
| ~ spl0_20 ),
inference(superposition,[],[f4,f780]) ).
fof(f830,plain,
( ! [X0] : multiply(sk_c2,multiply(inverse(sk_c2),X0)) = multiply(multiply(sk_c12,sk_c12),X0)
| ~ spl0_7
| ~ spl0_19
| ~ spl0_20
| ~ spl0_21
| ~ spl0_22 ),
inference(forward_demodulation,[],[f829,f799]) ).
fof(f832,plain,
( ! [X0] : multiply(sk_c12,multiply(sk_c12,X0)) = multiply(sk_c2,multiply(inverse(sk_c2),X0))
| ~ spl0_7
| ~ spl0_19
| ~ spl0_20
| ~ spl0_21
| ~ spl0_22 ),
inference(forward_demodulation,[],[f830,f4]) ).
fof(f839,plain,
( sk_c12 = multiply(inverse(inverse(sk_c2)),inverse(sk_c12))
| ~ spl0_7
| ~ spl0_9
| ~ spl0_19 ),
inference(superposition,[],[f312,f784]) ).
fof(f842,plain,
( sk_c12 = multiply(sk_c2,inverse(sk_c12))
| ~ spl0_7
| ~ spl0_9
| ~ spl0_19 ),
inference(forward_demodulation,[],[f839,f367]) ).
fof(f844,plain,
( sk_c12 = multiply(sk_c2,multiply(sk_c12,sk_c12))
| ~ spl0_7
| ~ spl0_9
| ~ spl0_19
| ~ spl0_21
| ~ spl0_22 ),
inference(forward_demodulation,[],[f842,f799]) ).
fof(f866,plain,
( inverse(sk_c12) != sk_c11
| sk_c11 != multiply(inverse(sk_c2),sk_c12)
| inverse(sk_c2) != inverse(sk_c2)
| ~ spl0_4
| ~ spl0_7
| ~ spl0_19
| ~ spl0_20 ),
inference(superposition,[],[f156,f780]) ).
fof(f868,plain,
( inverse(sk_c12) != sk_c11
| sk_c11 != multiply(inverse(sk_c2),sk_c12)
| ~ spl0_4
| ~ spl0_7
| ~ spl0_19
| ~ spl0_20 ),
inference(trivial_inequality_removal,[],[f866]) ).
fof(f871,plain,
( sk_c11 != multiply(inverse(sk_c2),sk_c12)
| ~ spl0_4
| ~ spl0_7
| ~ spl0_19
| ~ spl0_20 ),
inference(forward_subsumption_resolution,[],[f868,f166]) ).
fof(f889,plain,
( inverse(sk_c12) != sk_c11
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_19
| ~ spl0_20 ),
inference(forward_demodulation,[],[f871,f784]) ).
fof(f906,plain,
( $false
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_19
| ~ spl0_20 ),
inference(forward_subsumption_resolution,[],[f889,f166]) ).
fof(f907,plain,
( ~ spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_19
| ~ spl0_20 ),
inference(avatar_contradiction_clause,[],[f906]) ).
fof(f981,definition,
( spl0_25
<=> sk_c12 = multiply(sk_c12,sk_c12) ),
introduced(definition,[new_symbols(definition,[spl0_25])],[avatar_definition]) ).
fof(f982,plain,
( sk_c12 = multiply(sk_c12,sk_c12)
| ~ spl0_25 ),
inference(avatar_component_clause,[],[f981]) ).
fof(f983,plain,
( sk_c12 != multiply(sk_c12,sk_c12)
| spl0_25 ),
inference(avatar_component_clause,[],[f981]) ).
fof(f1046,plain,
( ! [X8,X6,X7,X5] :
( sk_c12 != multiply(X6,inverse(sk_c12))
| sk_c12 != multiply(X5,X6)
| multiply(X7,X6) != X8
| inverse(X7) != X8
| inverse(X8) != X6
| inverse(X5) != X6 )
| ~ spl0_1
| ~ spl0_7 ),
inference(forward_demodulation,[],[f147,f166]) ).
fof(f1047,plain,
( ! [X8,X6,X7,X5] :
( sk_c12 != multiply(X6,multiply(sk_c12,sk_c12))
| sk_c12 != multiply(X5,X6)
| multiply(X7,X6) != X8
| inverse(X7) != X8
| inverse(X8) != X6
| inverse(X5) != X6 )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_21
| ~ spl0_22 ),
inference(forward_demodulation,[],[f1046,f799]) ).
fof(f1050,plain,
( ! [X0] : multiply(multiply(sk_c12,sk_c12),multiply(sk_c12,X0)) = X0
| ~ spl0_7
| ~ spl0_21
| ~ spl0_22 ),
inference(superposition,[],[f312,f799]) ).
fof(f1053,plain,
( ! [X0] : multiply(sk_c12,multiply(sk_c12,multiply(sk_c12,X0))) = X0
| ~ spl0_7
| ~ spl0_21
| ~ spl0_22 ),
inference(forward_demodulation,[],[f1050,f4]) ).
fof(f1060,plain,
( ! [X2,X0,X1] :
( identity != sk_c12
| sk_c12 != multiply(X0,inverse(multiply(sk_c12,sk_c12)))
| multiply(X1,inverse(multiply(sk_c12,sk_c12))) != X2
| inverse(X1) != X2
| inverse(X2) != inverse(multiply(sk_c12,sk_c12))
| inverse(X0) != inverse(multiply(sk_c12,sk_c12)) )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_21
| ~ spl0_22 ),
inference(superposition,[],[f1047,f3]) ).
fof(f1064,plain,
( ! [X2,X0,X1] :
( sk_c12 != multiply(X0,sk_c12)
| identity != sk_c12
| multiply(X1,inverse(multiply(sk_c12,sk_c12))) != X2
| inverse(X1) != X2
| inverse(X2) != inverse(multiply(sk_c12,sk_c12))
| inverse(X0) != inverse(multiply(sk_c12,sk_c12)) )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_21
| ~ spl0_22 ),
inference(forward_demodulation,[],[f1060,f803]) ).
fof(f1068,plain,
( ! [X2,X0,X1] :
( multiply(X1,sk_c12) != X2
| sk_c12 != multiply(X0,sk_c12)
| identity != sk_c12
| inverse(X1) != X2
| inverse(X2) != inverse(multiply(sk_c12,sk_c12))
| inverse(X0) != inverse(multiply(sk_c12,sk_c12)) )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_21
| ~ spl0_22 ),
inference(forward_demodulation,[],[f1064,f803]) ).
fof(f1072,plain,
( ! [X2,X0,X1] :
( sk_c12 != inverse(X2)
| multiply(X1,sk_c12) != X2
| sk_c12 != multiply(X0,sk_c12)
| identity != sk_c12
| inverse(X1) != X2
| inverse(X0) != inverse(multiply(sk_c12,sk_c12)) )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_21
| ~ spl0_22 ),
inference(forward_demodulation,[],[f1068,f803]) ).
fof(f1078,definition,
( spl0_32
<=> ! [X2,X1] :
( X1 != X2
| identity != inverse(X2)
| inverse(X1) != X2 ) ),
introduced(definition,[new_symbols(definition,[spl0_32])],[avatar_definition]) ).
fof(f1079,plain,
( ! [X2,X1] :
( identity != inverse(X2)
| X1 != X2
| inverse(X1) != X2 )
| ~ spl0_32 ),
inference(avatar_component_clause,[],[f1078]) ).
fof(f1082,plain,
( ! [X2,X0,X1] :
( inverse(X0) != sk_c12
| sk_c12 != inverse(X2)
| multiply(X1,sk_c12) != X2
| sk_c12 != multiply(X0,sk_c12)
| identity != sk_c12
| inverse(X1) != X2 )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_21
| ~ spl0_22 ),
inference(forward_demodulation,[],[f1072,f803]) ).
fof(f1086,definition,
( spl0_33
<=> identity = sk_c12 ),
introduced(definition,[new_symbols(definition,[spl0_33])],[avatar_definition]) ).
fof(f1087,plain,
( identity = sk_c12
| ~ spl0_33 ),
inference(avatar_component_clause,[],[f1086]) ).
fof(f1088,plain,
( identity != sk_c12
| spl0_33 ),
inference(avatar_component_clause,[],[f1086]) ).
fof(f1090,definition,
( spl0_34
<=> ! [X2,X1] :
( sk_c12 != inverse(X2)
| inverse(X1) != X2
| multiply(X1,sk_c12) != X2 ) ),
introduced(definition,[new_symbols(definition,[spl0_34])],[avatar_definition]) ).
fof(f1091,plain,
( ! [X2,X1] :
( sk_c12 != inverse(X2)
| inverse(X1) != X2
| multiply(X1,sk_c12) != X2 )
| ~ spl0_34 ),
inference(avatar_component_clause,[],[f1090]) ).
fof(f1093,definition,
( spl0_35
<=> ! [X0] :
( inverse(X0) != sk_c12
| sk_c12 != multiply(X0,sk_c12) ) ),
introduced(definition,[new_symbols(definition,[spl0_35])],[avatar_definition]) ).
fof(f1094,plain,
( ! [X0] :
( inverse(X0) != sk_c12
| sk_c12 != multiply(X0,sk_c12) )
| ~ spl0_35 ),
inference(avatar_component_clause,[],[f1093]) ).
fof(f1095,plain,
( ~ spl0_33
| spl0_34
| spl0_35
| ~ spl0_1
| ~ spl0_7
| ~ spl0_21
| ~ spl0_22 ),
inference(avatar_split_clause,[],[f1082,f266,f252,f165,f146,f1093,f1090,f1086]) ).
fof(f1162,plain,
( multiply(sk_c12,multiply(sk_c12,sk_c12)) = multiply(sk_c2,inverse(sk_c12))
| ~ spl0_7
| ~ spl0_9
| ~ spl0_19
| ~ spl0_20
| ~ spl0_21
| ~ spl0_22 ),
inference(superposition,[],[f832,f784]) ).
fof(f1167,plain,
( multiply(sk_c12,multiply(sk_c12,sk_c12)) = multiply(sk_c2,multiply(sk_c12,sk_c12))
| ~ spl0_7
| ~ spl0_9
| ~ spl0_19
| ~ spl0_20
| ~ spl0_21
| ~ spl0_22 ),
inference(forward_demodulation,[],[f1162,f799]) ).
fof(f1171,plain,
( sk_c12 = multiply(sk_c12,multiply(sk_c12,sk_c12))
| ~ spl0_7
| ~ spl0_9
| ~ spl0_19
| ~ spl0_20
| ~ spl0_21
| ~ spl0_22 ),
inference(forward_demodulation,[],[f1167,f844]) ).
fof(f1173,plain,
( identity = sk_c12
| ~ spl0_7
| ~ spl0_9
| ~ spl0_19
| ~ spl0_20
| ~ spl0_21
| ~ spl0_22 ),
inference(forward_demodulation,[],[f1171,f804]) ).
fof(f1174,plain,
( $false
| ~ spl0_7
| ~ spl0_9
| ~ spl0_19
| ~ spl0_20
| ~ spl0_21
| ~ spl0_22
| spl0_33 ),
inference(forward_subsumption_resolution,[],[f1173,f1088]) ).
fof(f1175,plain,
( ~ spl0_7
| ~ spl0_9
| ~ spl0_19
| ~ spl0_20
| ~ spl0_21
| ~ spl0_22
| spl0_33 ),
inference(avatar_contradiction_clause,[],[f1174]) ).
fof(f1176,plain,
( ! [X0] :
( identity != inverse(X0)
| sk_c12 != multiply(X0,sk_c12) )
| ~ spl0_33
| ~ spl0_35 ),
inference(forward_demodulation,[],[f1094,f1087]) ).
fof(f1177,plain,
( ! [X0] :
( identity != multiply(X0,identity)
| identity != inverse(X0) )
| ~ spl0_33
| ~ spl0_35 ),
inference(forward_demodulation,[],[f1176,f1087]) ).
fof(f1178,plain,
( ! [X0] :
( identity != inverse(X0)
| identity != X0 )
| ~ spl0_33
| ~ spl0_35 ),
inference(forward_demodulation,[],[f1177,f390]) ).
fof(f1179,plain,
( sk_c11 = multiply(sk_c4,identity)
| ~ spl0_18
| ~ spl0_33 ),
inference(superposition,[],[f221,f1087]) ).
fof(f1181,plain,
( identity = multiply(identity,sk_c1)
| ~ spl0_22
| ~ spl0_33 ),
inference(superposition,[],[f570,f1087]) ).
fof(f1189,plain,
( identity != multiply(identity,identity)
| spl0_25
| ~ spl0_33 ),
inference(superposition,[],[f983,f1087]) ).
fof(f1192,plain,
( $false
| spl0_25
| ~ spl0_33 ),
inference(forward_subsumption_resolution,[],[f1189,f1]) ).
fof(f1193,plain,
( spl0_25
| ~ spl0_33 ),
inference(avatar_contradiction_clause,[],[f1192]) ).
fof(f1201,plain,
( identity = sk_c1
| ~ spl0_22
| ~ spl0_33 ),
inference(forward_demodulation,[],[f1181,f1]) ).
fof(f1203,plain,
( sk_c11 = sk_c4
| ~ spl0_18
| ~ spl0_33 ),
inference(forward_demodulation,[],[f1179,f390]) ).
fof(f1209,plain,
( sk_c11 = multiply(inverse(sk_c12),inverse(sk_c12))
| ~ spl0_7
| ~ spl0_18
| ~ spl0_22
| ~ spl0_33 ),
inference(forward_demodulation,[],[f1203,f795]) ).
fof(f1212,plain,
( sk_c11 = multiply(multiply(sk_c12,sk_c12),multiply(sk_c12,sk_c12))
| ~ spl0_7
| ~ spl0_18
| ~ spl0_21
| ~ spl0_22
| ~ spl0_33 ),
inference(forward_demodulation,[],[f1209,f799]) ).
fof(f1215,plain,
( sk_c11 = multiply(sk_c12,multiply(sk_c12,multiply(sk_c12,sk_c12)))
| ~ spl0_7
| ~ spl0_18
| ~ spl0_21
| ~ spl0_22
| ~ spl0_33 ),
inference(forward_demodulation,[],[f1212,f4]) ).
fof(f1217,plain,
( sk_c12 = sk_c11
| ~ spl0_7
| ~ spl0_18
| ~ spl0_21
| ~ spl0_22
| ~ spl0_33 ),
inference(forward_demodulation,[],[f1215,f1053]) ).
fof(f1219,plain,
( identity = sk_c11
| ~ spl0_7
| ~ spl0_18
| ~ spl0_21
| ~ spl0_22
| ~ spl0_33 ),
inference(forward_demodulation,[],[f1217,f1087]) ).
fof(f1223,plain,
( ! [X3] :
( sk_c11 != multiply(X3,identity)
| sk_c12 != inverse(X3) )
| ~ spl0_3
| ~ spl0_33 ),
inference(forward_demodulation,[],[f153,f1087]) ).
fof(f1225,plain,
( ! [X3] :
( sk_c11 != X3
| sk_c12 != inverse(X3) )
| ~ spl0_3
| ~ spl0_33 ),
inference(forward_demodulation,[],[f1223,f390]) ).
fof(f1226,plain,
( ! [X3] :
( inverse(sk_c12) != X3
| sk_c12 != inverse(X3) )
| ~ spl0_3
| ~ spl0_7
| ~ spl0_33 ),
inference(forward_demodulation,[],[f1225,f166]) ).
fof(f1227,plain,
( ! [X3] :
( multiply(sk_c12,sk_c12) != X3
| sk_c12 != inverse(X3) )
| ~ spl0_3
| ~ spl0_7
| ~ spl0_21
| ~ spl0_22
| ~ spl0_33 ),
inference(forward_demodulation,[],[f1226,f799]) ).
fof(f1228,plain,
( ! [X3] :
( multiply(identity,identity) != X3
| sk_c12 != inverse(X3) )
| ~ spl0_3
| ~ spl0_7
| ~ spl0_21
| ~ spl0_22
| ~ spl0_33 ),
inference(forward_demodulation,[],[f1227,f1087]) ).
fof(f1229,plain,
( ! [X3] :
( identity != X3
| sk_c12 != inverse(X3) )
| ~ spl0_3
| ~ spl0_7
| ~ spl0_21
| ~ spl0_22
| ~ spl0_33 ),
inference(forward_demodulation,[],[f1228,f1]) ).
fof(f1230,plain,
( ! [X3] :
( identity != inverse(X3)
| identity != X3 )
| ~ spl0_3
| ~ spl0_7
| ~ spl0_21
| ~ spl0_22
| ~ spl0_33 ),
inference(forward_demodulation,[],[f1229,f1087]) ).
fof(f1237,plain,
( identity != sk_c12
| identity != sk_c1
| ~ spl0_22
| ~ spl0_33
| ~ spl0_35 ),
inference(superposition,[],[f1178,f268]) ).
fof(f1238,plain,
( identity != sk_c1
| ~ spl0_22
| ~ spl0_33
| ~ spl0_35 ),
inference(forward_subsumption_resolution,[],[f1237,f1087]) ).
fof(f1244,plain,
( $false
| ~ spl0_22
| ~ spl0_33
| ~ spl0_35 ),
inference(forward_subsumption_resolution,[],[f1238,f1201]) ).
fof(f1245,plain,
( ~ spl0_22
| ~ spl0_33
| ~ spl0_35 ),
inference(avatar_contradiction_clause,[],[f1244]) ).
fof(f1283,plain,
( identity != sk_c12
| identity != multiply(sk_c12,sk_c12)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_21
| ~ spl0_22
| ~ spl0_33 ),
inference(superposition,[],[f1230,f803]) ).
fof(f1292,plain,
( identity != multiply(sk_c12,sk_c12)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_21
| ~ spl0_22
| ~ spl0_33 ),
inference(forward_subsumption_resolution,[],[f1283,f1087]) ).
fof(f1299,plain,
( identity != multiply(identity,identity)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_21
| ~ spl0_22
| ~ spl0_33 ),
inference(forward_demodulation,[],[f1292,f1087]) ).
fof(f1306,plain,
( $false
| ~ spl0_3
| ~ spl0_7
| ~ spl0_21
| ~ spl0_22
| ~ spl0_33 ),
inference(forward_subsumption_resolution,[],[f1299,f1]) ).
fof(f1307,plain,
( ~ spl0_3
| ~ spl0_7
| ~ spl0_21
| ~ spl0_22
| ~ spl0_33 ),
inference(avatar_contradiction_clause,[],[f1306]) ).
fof(f1319,plain,
( ! [X0] :
( identity != inverse(X0)
| sk_c12 != multiply(X0,sk_c11) )
| ~ spl0_5
| ~ spl0_33 ),
inference(forward_demodulation,[],[f159,f1087]) ).
fof(f1320,plain,
( ! [X0] :
( sk_c12 != multiply(X0,inverse(sk_c12))
| identity != inverse(X0) )
| ~ spl0_5
| ~ spl0_7
| ~ spl0_33 ),
inference(forward_demodulation,[],[f1319,f166]) ).
fof(f1321,plain,
( ! [X0] :
( sk_c12 != multiply(X0,multiply(sk_c12,sk_c12))
| identity != inverse(X0) )
| ~ spl0_5
| ~ spl0_7
| ~ spl0_21
| ~ spl0_22
| ~ spl0_33 ),
inference(forward_demodulation,[],[f1320,f799]) ).
fof(f1322,plain,
( ! [X0] :
( identity != multiply(X0,multiply(identity,identity))
| identity != inverse(X0) )
| ~ spl0_5
| ~ spl0_7
| ~ spl0_21
| ~ spl0_22
| ~ spl0_33 ),
inference(forward_demodulation,[],[f1321,f1087]) ).
fof(f1323,plain,
( ! [X0] :
( identity != multiply(X0,identity)
| identity != inverse(X0) )
| ~ spl0_5
| ~ spl0_7
| ~ spl0_21
| ~ spl0_22
| ~ spl0_33 ),
inference(forward_demodulation,[],[f1322,f1]) ).
fof(f1324,plain,
( ! [X0] :
( identity != inverse(X0)
| identity != X0 )
| ~ spl0_5
| ~ spl0_7
| ~ spl0_21
| ~ spl0_22
| ~ spl0_33 ),
inference(forward_demodulation,[],[f1323,f390]) ).
fof(f1338,plain,
( identity != sk_c12
| identity != multiply(sk_c12,sk_c12)
| ~ spl0_5
| ~ spl0_7
| ~ spl0_21
| ~ spl0_22
| ~ spl0_33 ),
inference(superposition,[],[f1324,f803]) ).
fof(f1347,plain,
( identity != multiply(sk_c12,sk_c12)
| ~ spl0_5
| ~ spl0_7
| ~ spl0_21
| ~ spl0_22
| ~ spl0_33 ),
inference(forward_subsumption_resolution,[],[f1338,f1087]) ).
fof(f1354,plain,
( identity != multiply(identity,identity)
| ~ spl0_5
| ~ spl0_7
| ~ spl0_21
| ~ spl0_22
| ~ spl0_33 ),
inference(forward_demodulation,[],[f1347,f1087]) ).
fof(f1361,plain,
( $false
| ~ spl0_5
| ~ spl0_7
| ~ spl0_21
| ~ spl0_22
| ~ spl0_33 ),
inference(forward_subsumption_resolution,[],[f1354,f1]) ).
fof(f1362,plain,
( ~ spl0_5
| ~ spl0_7
| ~ spl0_21
| ~ spl0_22
| ~ spl0_33 ),
inference(avatar_contradiction_clause,[],[f1361]) ).
fof(f1374,plain,
( ! [X4] :
( sk_c10 != multiply(X4,inverse(sk_c12))
| sk_c11 != inverse(X4) )
| ~ spl0_2
| ~ spl0_7 ),
inference(forward_demodulation,[],[f150,f166]) ).
fof(f1375,plain,
( ! [X4] :
( sk_c10 != multiply(X4,multiply(sk_c12,sk_c12))
| sk_c11 != inverse(X4) )
| ~ spl0_2
| ~ spl0_7
| ~ spl0_21
| ~ spl0_22 ),
inference(forward_demodulation,[],[f1374,f799]) ).
fof(f1376,plain,
( ! [X4] :
( sk_c10 != multiply(X4,multiply(identity,identity))
| sk_c11 != inverse(X4) )
| ~ spl0_2
| ~ spl0_7
| ~ spl0_21
| ~ spl0_22
| ~ spl0_33 ),
inference(forward_demodulation,[],[f1375,f1087]) ).
fof(f1377,plain,
( ! [X4] :
( sk_c10 != multiply(X4,identity)
| sk_c11 != inverse(X4) )
| ~ spl0_2
| ~ spl0_7
| ~ spl0_21
| ~ spl0_22
| ~ spl0_33 ),
inference(forward_demodulation,[],[f1376,f1]) ).
fof(f1378,plain,
( ! [X4] :
( sk_c10 != X4
| sk_c11 != inverse(X4) )
| ~ spl0_2
| ~ spl0_7
| ~ spl0_21
| ~ spl0_22
| ~ spl0_33 ),
inference(forward_demodulation,[],[f1377,f390]) ).
fof(f1379,plain,
( ! [X4] :
( multiply(sk_c12,sk_c12) != X4
| sk_c11 != inverse(X4) )
| ~ spl0_2
| ~ spl0_6
| ~ spl0_7
| ~ spl0_21
| ~ spl0_22
| ~ spl0_33 ),
inference(forward_demodulation,[],[f1378,f811]) ).
fof(f1380,plain,
( ! [X4] :
( multiply(identity,identity) != X4
| sk_c11 != inverse(X4) )
| ~ spl0_2
| ~ spl0_6
| ~ spl0_7
| ~ spl0_21
| ~ spl0_22
| ~ spl0_33 ),
inference(forward_demodulation,[],[f1379,f1087]) ).
fof(f1381,plain,
( ! [X4] :
( identity != X4
| sk_c11 != inverse(X4) )
| ~ spl0_2
| ~ spl0_6
| ~ spl0_7
| ~ spl0_21
| ~ spl0_22
| ~ spl0_33 ),
inference(forward_demodulation,[],[f1380,f1]) ).
fof(f1382,plain,
( ! [X4] :
( inverse(sk_c12) != inverse(X4)
| identity != X4 )
| ~ spl0_2
| ~ spl0_6
| ~ spl0_7
| ~ spl0_21
| ~ spl0_22
| ~ spl0_33 ),
inference(forward_demodulation,[],[f1381,f166]) ).
fof(f1383,plain,
( ! [X4] :
( inverse(X4) != multiply(sk_c12,sk_c12)
| identity != X4 )
| ~ spl0_2
| ~ spl0_6
| ~ spl0_7
| ~ spl0_21
| ~ spl0_22
| ~ spl0_33 ),
inference(forward_demodulation,[],[f1382,f799]) ).
fof(f1384,plain,
( ! [X4] :
( inverse(X4) != multiply(identity,identity)
| identity != X4 )
| ~ spl0_2
| ~ spl0_6
| ~ spl0_7
| ~ spl0_21
| ~ spl0_22
| ~ spl0_33 ),
inference(forward_demodulation,[],[f1383,f1087]) ).
fof(f1385,plain,
( ! [X4] :
( identity != inverse(X4)
| identity != X4 )
| ~ spl0_2
| ~ spl0_6
| ~ spl0_7
| ~ spl0_21
| ~ spl0_22
| ~ spl0_33 ),
inference(forward_demodulation,[],[f1384,f1]) ).
fof(f1390,plain,
( sk_c12 = multiply(inverse(sk_c4),identity)
| ~ spl0_7
| ~ spl0_18
| ~ spl0_21
| ~ spl0_22
| ~ spl0_33 ),
inference(superposition,[],[f373,f1219]) ).
fof(f1391,plain,
( sk_c12 = inverse(sk_c4)
| ~ spl0_7
| ~ spl0_18
| ~ spl0_21
| ~ spl0_22
| ~ spl0_33 ),
inference(forward_demodulation,[],[f1390,f390]) ).
fof(f1396,plain,
( $false
| ~ spl0_7
| spl0_17
| ~ spl0_18
| ~ spl0_21
| ~ spl0_22
| ~ spl0_33 ),
inference(forward_subsumption_resolution,[],[f1391,f215]) ).
fof(f1397,plain,
( ~ spl0_7
| spl0_17
| ~ spl0_18
| ~ spl0_21
| ~ spl0_22
| ~ spl0_33 ),
inference(avatar_contradiction_clause,[],[f1396]) ).
fof(f1417,plain,
( identity = inverse(identity)
| ~ spl0_7
| ~ spl0_17
| ~ spl0_18
| ~ spl0_33 ),
inference(forward_demodulation,[],[f438,f1087]) ).
fof(f1474,plain,
( identity != sk_c12
| identity != multiply(sk_c12,sk_c12)
| ~ spl0_2
| ~ spl0_6
| ~ spl0_7
| ~ spl0_21
| ~ spl0_22
| ~ spl0_33 ),
inference(superposition,[],[f1385,f803]) ).
fof(f1483,plain,
( identity != multiply(sk_c12,sk_c12)
| ~ spl0_2
| ~ spl0_6
| ~ spl0_7
| ~ spl0_21
| ~ spl0_22
| ~ spl0_33 ),
inference(forward_subsumption_resolution,[],[f1474,f1087]) ).
fof(f1490,plain,
( identity != multiply(identity,identity)
| ~ spl0_2
| ~ spl0_6
| ~ spl0_7
| ~ spl0_21
| ~ spl0_22
| ~ spl0_33 ),
inference(forward_demodulation,[],[f1483,f1087]) ).
fof(f1497,plain,
( $false
| ~ spl0_2
| ~ spl0_6
| ~ spl0_7
| ~ spl0_21
| ~ spl0_22
| ~ spl0_33 ),
inference(forward_subsumption_resolution,[],[f1490,f1]) ).
fof(f1498,plain,
( ~ spl0_2
| ~ spl0_6
| ~ spl0_7
| ~ spl0_21
| ~ spl0_22
| ~ spl0_33 ),
inference(avatar_contradiction_clause,[],[f1497]) ).
fof(f1512,plain,
( ! [X8,X6,X7,X5] :
( identity != multiply(X5,X6)
| multiply(X7,X6) != X8
| inverse(X7) != X8
| inverse(X8) != X6
| sk_c12 != multiply(X6,sk_c11)
| inverse(X5) != X6 )
| ~ spl0_1
| ~ spl0_33 ),
inference(forward_demodulation,[],[f147,f1087]) ).
fof(f1516,plain,
( ! [X2,X1] :
( identity != inverse(X2)
| inverse(X1) != X2
| multiply(X1,sk_c12) != X2 )
| ~ spl0_33
| ~ spl0_34 ),
inference(forward_demodulation,[],[f1091,f1087]) ).
fof(f1520,plain,
( ! [X2,X1] :
( multiply(X1,identity) != X2
| identity != inverse(X2)
| inverse(X1) != X2 )
| ~ spl0_33
| ~ spl0_34 ),
inference(forward_demodulation,[],[f1516,f1087]) ).
fof(f1524,plain,
( ! [X2,X1] :
( X1 != X2
| identity != inverse(X2)
| inverse(X1) != X2 )
| ~ spl0_33
| ~ spl0_34 ),
inference(forward_demodulation,[],[f1520,f390]) ).
fof(f1557,plain,
( ! [X0] :
( identity != multiply(sk_c12,sk_c12)
| sk_c12 != X0
| inverse(X0) != sk_c12 )
| ~ spl0_7
| ~ spl0_21
| ~ spl0_22
| ~ spl0_32 ),
inference(superposition,[],[f1079,f799]) ).
fof(f1564,plain,
( ! [X0] :
( identity != multiply(identity,identity)
| sk_c12 != X0
| inverse(X0) != sk_c12 )
| ~ spl0_7
| ~ spl0_21
| ~ spl0_22
| ~ spl0_32
| ~ spl0_33 ),
inference(forward_demodulation,[],[f1557,f1087]) ).
fof(f1570,plain,
( ! [X0] :
( sk_c12 != X0
| inverse(X0) != sk_c12 )
| ~ spl0_7
| ~ spl0_21
| ~ spl0_22
| ~ spl0_32
| ~ spl0_33 ),
inference(forward_subsumption_resolution,[],[f1564,f1]) ).
fof(f1576,plain,
( ! [X0] :
( identity != X0
| inverse(X0) != sk_c12 )
| ~ spl0_7
| ~ spl0_21
| ~ spl0_22
| ~ spl0_32
| ~ spl0_33 ),
inference(forward_demodulation,[],[f1570,f1087]) ).
fof(f1582,plain,
( ! [X0] :
( identity != inverse(X0)
| identity != X0 )
| ~ spl0_7
| ~ spl0_21
| ~ spl0_22
| ~ spl0_32
| ~ spl0_33 ),
inference(forward_demodulation,[],[f1576,f1087]) ).
fof(f2889,plain,
( identity != sk_c12
| identity != multiply(sk_c12,sk_c12)
| ~ spl0_7
| ~ spl0_21
| ~ spl0_22
| ~ spl0_32
| ~ spl0_33 ),
inference(superposition,[],[f1582,f803]) ).
fof(f2901,plain,
( identity != multiply(sk_c12,sk_c12)
| ~ spl0_7
| ~ spl0_21
| ~ spl0_22
| ~ spl0_32
| ~ spl0_33 ),
inference(forward_subsumption_resolution,[],[f2889,f1087]) ).
fof(f2905,plain,
( identity != multiply(identity,identity)
| ~ spl0_7
| ~ spl0_21
| ~ spl0_22
| ~ spl0_32
| ~ spl0_33 ),
inference(forward_demodulation,[],[f2901,f1087]) ).
fof(f2908,plain,
( $false
| ~ spl0_7
| ~ spl0_21
| ~ spl0_22
| ~ spl0_32
| ~ spl0_33 ),
inference(forward_subsumption_resolution,[],[f2905,f1]) ).
fof(f2909,plain,
( ~ spl0_7
| ~ spl0_21
| ~ spl0_22
| ~ spl0_32
| ~ spl0_33 ),
inference(avatar_contradiction_clause,[],[f2908]) ).
fof(f2912,plain,
( spl0_32
| ~ spl0_33
| ~ spl0_34 ),
inference(avatar_split_clause,[],[f1524,f1090,f1086,f1078]) ).
fof(f2947,plain,
( $false
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18
| spl0_33 ),
inference(forward_subsumption_resolution,[],[f409,f1088]) ).
fof(f2948,plain,
( ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18
| spl0_33 ),
inference(avatar_contradiction_clause,[],[f2947]) ).
fof(f2953,plain,
( $false
| ~ spl0_7
| ~ spl0_17
| ~ spl0_18
| spl0_33 ),
inference(forward_subsumption_resolution,[],[f653,f1088]) ).
fof(f2954,plain,
( ~ spl0_7
| ~ spl0_17
| ~ spl0_18
| spl0_33 ),
inference(avatar_contradiction_clause,[],[f2953]) ).
fof(f3097,plain,
( ! [X4] :
( sk_c10 != multiply(X4,inverse(sk_c12))
| sk_c11 != inverse(X4) )
| ~ spl0_2
| ~ spl0_7 ),
inference(forward_demodulation,[],[f150,f166]) ).
fof(f3139,plain,
( ! [X4] :
( sk_c10 != multiply(X4,identity)
| sk_c11 != inverse(X4) )
| ~ spl0_2
| ~ spl0_7
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f3097,f438]) ).
fof(f3168,plain,
( ! [X4] :
( sk_c10 != X4
| sk_c11 != inverse(X4) )
| ~ spl0_2
| ~ spl0_7
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f3139,f390]) ).
fof(f3185,plain,
( ! [X4] :
( multiply(sk_c12,sk_c12) != X4
| sk_c11 != inverse(X4) )
| ~ spl0_2
| ~ spl0_6
| ~ spl0_7
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f3168,f811]) ).
fof(f3195,plain,
( ! [X4] :
( sk_c12 != X4
| sk_c11 != inverse(X4) )
| ~ spl0_2
| ~ spl0_6
| ~ spl0_7
| ~ spl0_17
| ~ spl0_18
| ~ spl0_25 ),
inference(forward_demodulation,[],[f3185,f982]) ).
fof(f3200,plain,
( ! [X4] :
( identity != X4
| sk_c11 != inverse(X4) )
| ~ spl0_2
| ~ spl0_6
| ~ spl0_7
| ~ spl0_17
| ~ spl0_18
| ~ spl0_25
| ~ spl0_33 ),
inference(forward_demodulation,[],[f3195,f1087]) ).
fof(f3206,plain,
( ! [X4] :
( inverse(sk_c12) != inverse(X4)
| identity != X4 )
| ~ spl0_2
| ~ spl0_6
| ~ spl0_7
| ~ spl0_17
| ~ spl0_18
| ~ spl0_25
| ~ spl0_33 ),
inference(forward_demodulation,[],[f3200,f166]) ).
fof(f3208,plain,
( ! [X4] :
( identity != inverse(X4)
| identity != X4 )
| ~ spl0_2
| ~ spl0_6
| ~ spl0_7
| ~ spl0_17
| ~ spl0_18
| ~ spl0_25
| ~ spl0_33 ),
inference(forward_demodulation,[],[f3206,f438]) ).
fof(f3279,plain,
( ! [X0] : multiply(inverse(X0),X0) = inverse(multiply(inverse(X0),X0))
| ~ spl0_7
| ~ spl0_17
| ~ spl0_18
| ~ spl0_33 ),
inference(superposition,[],[f1417,f3]) ).
fof(f3364,plain,
( identity != identity
| identity != sk_c12
| ~ spl0_2
| ~ spl0_6
| ~ spl0_7
| ~ spl0_17
| ~ spl0_18
| ~ spl0_25
| ~ spl0_33 ),
inference(superposition,[],[f3208,f438]) ).
fof(f3371,plain,
( identity != sk_c12
| ~ spl0_2
| ~ spl0_6
| ~ spl0_7
| ~ spl0_17
| ~ spl0_18
| ~ spl0_25
| ~ spl0_33 ),
inference(trivial_inequality_removal,[],[f3364]) ).
fof(f3374,plain,
( $false
| ~ spl0_2
| ~ spl0_6
| ~ spl0_7
| ~ spl0_17
| ~ spl0_18
| ~ spl0_25
| ~ spl0_33 ),
inference(forward_subsumption_resolution,[],[f3371,f1087]) ).
fof(f3375,plain,
( ~ spl0_2
| ~ spl0_6
| ~ spl0_7
| ~ spl0_17
| ~ spl0_18
| ~ spl0_25
| ~ spl0_33 ),
inference(avatar_contradiction_clause,[],[f3374]) ).
fof(f3378,plain,
( ! [X3] :
( identity != X3
| sk_c12 != inverse(X3) )
| ~ spl0_3
| ~ spl0_7
| ~ spl0_17
| ~ spl0_18
| ~ spl0_33 ),
inference(forward_demodulation,[],[f1226,f438]) ).
fof(f3381,plain,
( ! [X3] :
( identity != inverse(X3)
| identity != X3 )
| ~ spl0_3
| ~ spl0_7
| ~ spl0_17
| ~ spl0_18
| ~ spl0_33 ),
inference(forward_demodulation,[],[f3378,f1087]) ).
fof(f3398,plain,
( identity != identity
| identity != sk_c12
| ~ spl0_3
| ~ spl0_7
| ~ spl0_17
| ~ spl0_18
| ~ spl0_33 ),
inference(superposition,[],[f3381,f438]) ).
fof(f3403,plain,
( identity != sk_c12
| ~ spl0_3
| ~ spl0_7
| ~ spl0_17
| ~ spl0_18
| ~ spl0_33 ),
inference(trivial_inequality_removal,[],[f3398]) ).
fof(f3411,plain,
( $false
| ~ spl0_3
| ~ spl0_7
| ~ spl0_17
| ~ spl0_18
| ~ spl0_33 ),
inference(forward_subsumption_resolution,[],[f3403,f1087]) ).
fof(f3412,plain,
( ~ spl0_3
| ~ spl0_7
| ~ spl0_17
| ~ spl0_18
| ~ spl0_33 ),
inference(avatar_contradiction_clause,[],[f3411]) ).
fof(f3414,plain,
( ! [X0] :
( sk_c12 != multiply(X0,inverse(sk_c12))
| identity != inverse(X0) )
| ~ spl0_5
| ~ spl0_7
| ~ spl0_33 ),
inference(forward_demodulation,[],[f1319,f166]) ).
fof(f3416,plain,
( ! [X0] :
( sk_c12 != multiply(X0,identity)
| identity != inverse(X0) )
| ~ spl0_5
| ~ spl0_7
| ~ spl0_17
| ~ spl0_18
| ~ spl0_33 ),
inference(forward_demodulation,[],[f3414,f438]) ).
fof(f3418,plain,
( ! [X0] :
( sk_c12 != X0
| identity != inverse(X0) )
| ~ spl0_5
| ~ spl0_7
| ~ spl0_17
| ~ spl0_18
| ~ spl0_33 ),
inference(forward_demodulation,[],[f3416,f390]) ).
fof(f3420,plain,
( ! [X0] :
( identity != inverse(X0)
| identity != X0 )
| ~ spl0_5
| ~ spl0_7
| ~ spl0_17
| ~ spl0_18
| ~ spl0_33 ),
inference(forward_demodulation,[],[f3418,f1087]) ).
fof(f3431,plain,
( identity != identity
| identity != sk_c12
| ~ spl0_5
| ~ spl0_7
| ~ spl0_17
| ~ spl0_18
| ~ spl0_33 ),
inference(superposition,[],[f3420,f438]) ).
fof(f3436,plain,
( identity != sk_c12
| ~ spl0_5
| ~ spl0_7
| ~ spl0_17
| ~ spl0_18
| ~ spl0_33 ),
inference(trivial_inequality_removal,[],[f3431]) ).
fof(f3444,plain,
( $false
| ~ spl0_5
| ~ spl0_7
| ~ spl0_17
| ~ spl0_18
| ~ spl0_33 ),
inference(forward_subsumption_resolution,[],[f3436,f1087]) ).
fof(f3445,plain,
( ~ spl0_5
| ~ spl0_7
| ~ spl0_17
| ~ spl0_18
| ~ spl0_33 ),
inference(avatar_contradiction_clause,[],[f3444]) ).
fof(f3447,plain,
( ! [X8,X6,X7,X5] :
( sk_c12 != multiply(X6,inverse(sk_c12))
| identity != multiply(X5,X6)
| multiply(X7,X6) != X8
| inverse(X7) != X8
| inverse(X8) != X6
| inverse(X5) != X6 )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_33 ),
inference(forward_demodulation,[],[f1512,f166]) ).
fof(f3449,plain,
( ! [X8,X6,X7,X5] :
( sk_c12 != multiply(X6,identity)
| identity != multiply(X5,X6)
| multiply(X7,X6) != X8
| inverse(X7) != X8
| inverse(X8) != X6
| inverse(X5) != X6 )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_17
| ~ spl0_18
| ~ spl0_33 ),
inference(forward_demodulation,[],[f3447,f438]) ).
fof(f3451,plain,
( ! [X8,X6,X7,X5] :
( sk_c12 != X6
| identity != multiply(X5,X6)
| multiply(X7,X6) != X8
| inverse(X7) != X8
| inverse(X8) != X6
| inverse(X5) != X6 )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_17
| ~ spl0_18
| ~ spl0_33 ),
inference(forward_demodulation,[],[f3449,f390]) ).
fof(f3453,plain,
( ! [X8,X6,X7,X5] :
( identity != multiply(X5,X6)
| identity != X6
| multiply(X7,X6) != X8
| inverse(X7) != X8
| inverse(X8) != X6
| inverse(X5) != X6 )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_17
| ~ spl0_18
| ~ spl0_33 ),
inference(forward_demodulation,[],[f3451,f1087]) ).
fof(f3513,plain,
( ! [X0,X1] :
( identity != sk_c12
| identity != sk_c12
| multiply(X0,sk_c12) != X1
| inverse(X0) != X1
| sk_c12 != inverse(X1)
| sk_c12 != inverse(sk_c12) )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_17
| ~ spl0_18
| ~ spl0_25
| ~ spl0_33 ),
inference(superposition,[],[f3453,f982]) ).
fof(f3520,plain,
( ! [X0,X1] :
( identity != sk_c12
| multiply(X0,sk_c12) != X1
| inverse(X0) != X1
| sk_c12 != inverse(X1)
| sk_c12 != inverse(sk_c12) )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_17
| ~ spl0_18
| ~ spl0_25
| ~ spl0_33 ),
inference(duplicate_literal_removal,[],[f3513]) ).
fof(f3529,plain,
( ! [X0,X1] :
( multiply(X0,sk_c12) != X1
| inverse(X0) != X1
| sk_c12 != inverse(X1)
| sk_c12 != inverse(sk_c12) )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_17
| ~ spl0_18
| ~ spl0_25
| ~ spl0_33 ),
inference(forward_subsumption_resolution,[],[f3520,f1087]) ).
fof(f3545,plain,
( ! [X0,X1] :
( multiply(X0,identity) != X1
| inverse(X0) != X1
| sk_c12 != inverse(X1)
| sk_c12 != inverse(sk_c12) )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_17
| ~ spl0_18
| ~ spl0_25
| ~ spl0_33 ),
inference(forward_demodulation,[],[f3529,f1087]) ).
fof(f3549,plain,
( ! [X0,X1] :
( X0 != X1
| inverse(X0) != X1
| sk_c12 != inverse(X1)
| sk_c12 != inverse(sk_c12) )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_17
| ~ spl0_18
| ~ spl0_25
| ~ spl0_33 ),
inference(forward_demodulation,[],[f3545,f390]) ).
fof(f3553,plain,
( ! [X0,X1] :
( identity != inverse(X1)
| X0 != X1
| inverse(X0) != X1
| sk_c12 != inverse(sk_c12) )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_17
| ~ spl0_18
| ~ spl0_25
| ~ spl0_33 ),
inference(forward_demodulation,[],[f3549,f1087]) ).
fof(f3557,plain,
( ! [X0,X1] :
( identity != sk_c12
| identity != inverse(X1)
| X0 != X1
| inverse(X0) != X1 )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_17
| ~ spl0_18
| ~ spl0_25
| ~ spl0_33 ),
inference(forward_demodulation,[],[f3553,f438]) ).
fof(f3561,plain,
( ! [X0,X1] :
( identity != inverse(X1)
| X0 != X1
| inverse(X0) != X1 )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_17
| ~ spl0_18
| ~ spl0_25
| ~ spl0_33 ),
inference(forward_subsumption_resolution,[],[f3557,f1087]) ).
fof(f3565,plain,
( spl0_32
| ~ spl0_1
| ~ spl0_7
| ~ spl0_17
| ~ spl0_18
| ~ spl0_25
| ~ spl0_33 ),
inference(avatar_split_clause,[],[f3561,f1086,f981,f219,f214,f165,f146,f1078]) ).
fof(f3671,plain,
( ! [X0] :
( identity != identity
| identity != X0
| identity != inverse(X0) )
| ~ spl0_7
| ~ spl0_17
| ~ spl0_18
| ~ spl0_32
| ~ spl0_33 ),
inference(superposition,[],[f1079,f1417]) ).
fof(f3679,plain,
( ! [X0] :
( identity != inverse(X0)
| identity != X0 )
| ~ spl0_7
| ~ spl0_17
| ~ spl0_18
| ~ spl0_32
| ~ spl0_33 ),
inference(trivial_inequality_removal,[],[f3671]) ).
fof(f3689,plain,
( ! [X0] :
( identity != multiply(inverse(X0),X0)
| identity != multiply(inverse(X0),X0) )
| ~ spl0_7
| ~ spl0_17
| ~ spl0_18
| ~ spl0_32
| ~ spl0_33 ),
inference(superposition,[],[f3679,f3279]) ).
fof(f3696,plain,
( ! [X0] : identity != multiply(inverse(X0),X0)
| ~ spl0_7
| ~ spl0_17
| ~ spl0_18
| ~ spl0_32
| ~ spl0_33 ),
inference(duplicate_literal_removal,[],[f3689]) ).
fof(f3706,plain,
( $false
| ~ spl0_7
| ~ spl0_17
| ~ spl0_18
| ~ spl0_32
| ~ spl0_33 ),
inference(forward_subsumption_resolution,[],[f3696,f3]) ).
fof(f3707,plain,
( ~ spl0_7
| ~ spl0_17
| ~ spl0_18
| ~ spl0_32
| ~ spl0_33 ),
inference(avatar_contradiction_clause,[],[f3706]) ).
cnf(s1,plain,
( spl0_1
| spl0_2
| spl0_3
| spl0_4
| spl0_5
| ~ spl0_6
| ~ spl0_7 ),
inference(sat_conversion,[],[f168]) ).
cnf(s5,plain,
( spl0_9
| spl0_12 ),
inference(sat_conversion,[],[f192]) ).
cnf(s6,plain,
( spl0_9
| spl0_13 ),
inference(sat_conversion,[],[f197]) ).
cnf(s7,plain,
( spl0_9
| spl0_14 ),
inference(sat_conversion,[],[f202]) ).
cnf(s10,plain,
( spl0_9
| spl0_17 ),
inference(sat_conversion,[],[f217]) ).
cnf(s11,plain,
( spl0_9
| spl0_18 ),
inference(sat_conversion,[],[f222]) ).
cnf(s15,plain,
( spl0_12
| spl0_19 ),
inference(sat_conversion,[],[f230]) ).
cnf(s16,plain,
( spl0_13
| spl0_19 ),
inference(sat_conversion,[],[f231]) ).
cnf(s20,plain,
( spl0_17
| spl0_19 ),
inference(sat_conversion,[],[f235]) ).
cnf(s21,plain,
( spl0_18
| spl0_19 ),
inference(sat_conversion,[],[f236]) ).
cnf(s25,plain,
( spl0_12
| spl0_20 ),
inference(sat_conversion,[],[f244]) ).
cnf(s26,plain,
( spl0_13
| spl0_20 ),
inference(sat_conversion,[],[f245]) ).
cnf(s30,plain,
( spl0_17
| spl0_20 ),
inference(sat_conversion,[],[f249]) ).
cnf(s31,plain,
( spl0_18
| spl0_20 ),
inference(sat_conversion,[],[f250]) ).
cnf(s37,plain,
( spl0_14
| spl0_21 ),
inference(sat_conversion,[],[f260]) ).
cnf(s40,plain,
( spl0_17
| spl0_21 ),
inference(sat_conversion,[],[f263]) ).
cnf(s41,plain,
( spl0_18
| spl0_21 ),
inference(sat_conversion,[],[f264]) ).
cnf(s47,plain,
( spl0_14
| spl0_22 ),
inference(sat_conversion,[],[f274]) ).
cnf(s50,plain,
( spl0_17
| spl0_22 ),
inference(sat_conversion,[],[f277]) ).
cnf(s51,plain,
( spl0_18
| spl0_22 ),
inference(sat_conversion,[],[f278]) ).
cnf(s55,plain,
( spl0_6
| spl0_12 ),
inference(sat_conversion,[],[f282]) ).
cnf(s56,plain,
( spl0_6
| spl0_13 ),
inference(sat_conversion,[],[f283]) ).
cnf(s57,plain,
( spl0_6
| spl0_14 ),
inference(sat_conversion,[],[f284]) ).
cnf(s58,plain,
( spl0_6
| spl0_15 ),
inference(sat_conversion,[],[f285]) ).
cnf(s59,plain,
( spl0_6
| spl0_16 ),
inference(sat_conversion,[],[f286]) ).
cnf(s60,plain,
( spl0_6
| spl0_17 ),
inference(sat_conversion,[],[f287]) ).
cnf(s61,plain,
( spl0_6
| spl0_18 ),
inference(sat_conversion,[],[f288]) ).
cnf(s65,plain,
( spl0_7
| spl0_12 ),
inference(sat_conversion,[],[f292]) ).
cnf(s66,plain,
( spl0_7
| spl0_13 ),
inference(sat_conversion,[],[f293]) ).
cnf(s67,plain,
( spl0_7
| spl0_14 ),
inference(sat_conversion,[],[f294]) ).
cnf(s70,plain,
( spl0_7
| spl0_17 ),
inference(sat_conversion,[],[f297]) ).
cnf(s71,plain,
( spl0_7
| spl0_18 ),
inference(sat_conversion,[],[f298]) ).
cnf(s73,plain,
( spl0_6
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18 ),
inference(sat_conversion,[],[f405]) ).
cnf(s74,plain,
( spl0_7
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(sat_conversion,[],[f434]) ).
cnf(s77,plain,
( ~ spl0_4
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(sat_conversion,[],[f507]) ).
cnf(s80,plain,
( ~ spl0_7
| ~ spl0_12
| ~ spl0_13
| spl0_14
| ~ spl0_17
| ~ spl0_18
| ~ spl0_21
| ~ spl0_22 ),
inference(sat_conversion,[],[f775]) ).
cnf(s81,plain,
( ~ spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_19
| ~ spl0_20 ),
inference(sat_conversion,[],[f907]) ).
cnf(s93,plain,
( ~ spl0_1
| ~ spl0_7
| ~ spl0_21
| ~ spl0_22
| ~ spl0_33
| spl0_34
| spl0_35 ),
inference(sat_conversion,[],[f1095]) ).
cnf(s96,plain,
( ~ spl0_7
| ~ spl0_9
| ~ spl0_19
| ~ spl0_20
| ~ spl0_21
| ~ spl0_22
| spl0_33 ),
inference(sat_conversion,[],[f1175]) ).
cnf(s97,plain,
( spl0_25
| ~ spl0_33 ),
inference(sat_conversion,[],[f1193]) ).
cnf(s98,plain,
( ~ spl0_22
| ~ spl0_33
| ~ spl0_35 ),
inference(sat_conversion,[],[f1245]) ).
cnf(s105,plain,
( ~ spl0_3
| ~ spl0_7
| ~ spl0_21
| ~ spl0_22
| ~ spl0_33 ),
inference(sat_conversion,[],[f1307]) ).
cnf(s109,plain,
( ~ spl0_5
| ~ spl0_7
| ~ spl0_21
| ~ spl0_22
| ~ spl0_33 ),
inference(sat_conversion,[],[f1362]) ).
cnf(s110,plain,
( ~ spl0_7
| spl0_17
| ~ spl0_18
| ~ spl0_21
| ~ spl0_22
| ~ spl0_33 ),
inference(sat_conversion,[],[f1397]) ).
cnf(s114,plain,
( ~ spl0_2
| ~ spl0_6
| ~ spl0_7
| ~ spl0_21
| ~ spl0_22
| ~ spl0_33 ),
inference(sat_conversion,[],[f1498]) ).
cnf(s132,plain,
( ~ spl0_7
| ~ spl0_21
| ~ spl0_22
| ~ spl0_32
| ~ spl0_33 ),
inference(sat_conversion,[],[f2909]) ).
cnf(s133,plain,
( spl0_32
| ~ spl0_33
| ~ spl0_34 ),
inference(sat_conversion,[],[f2912]) ).
cnf(s136,plain,
( ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18
| spl0_33 ),
inference(sat_conversion,[],[f2948]) ).
cnf(s137,plain,
( ~ spl0_7
| ~ spl0_17
| ~ spl0_18
| spl0_33 ),
inference(sat_conversion,[],[f2954]) ).
cnf(s156,plain,
( ~ spl0_2
| ~ spl0_6
| ~ spl0_7
| ~ spl0_17
| ~ spl0_18
| ~ spl0_25
| ~ spl0_33 ),
inference(sat_conversion,[],[f3375]) ).
cnf(s160,plain,
( ~ spl0_3
| ~ spl0_7
| ~ spl0_17
| ~ spl0_18
| ~ spl0_33 ),
inference(sat_conversion,[],[f3412]) ).
cnf(s164,plain,
( ~ spl0_5
| ~ spl0_7
| ~ spl0_17
| ~ spl0_18
| ~ spl0_33 ),
inference(sat_conversion,[],[f3445]) ).
cnf(s165,plain,
( ~ spl0_1
| ~ spl0_7
| ~ spl0_17
| ~ spl0_18
| ~ spl0_25
| spl0_32
| ~ spl0_33 ),
inference(sat_conversion,[],[f3565]) ).
cnf(s173,plain,
( ~ spl0_7
| ~ spl0_17
| ~ spl0_18
| ~ spl0_32
| ~ spl0_33 ),
inference(sat_conversion,[],[f3707]) ).
cnf(s174,plain,
spl0_6,
inference(rat,[],[s73,s55,s56,s57,s58,s59,s60,s61]) ).
cnf(s175,plain,
spl0_7,
inference(rat,[],[s74,s65,s66,s67,s70,s71]) ).
cnf(s176,plain,
( spl0_9
| ~ spl0_5 ),
inference(rat,[],[s164,s136,s5,s6,s7,s10,s11,s175]) ).
cnf(s178,plain,
( spl0_18
| ~ spl0_5 ),
inference(rat,[],[s96,s109,s21,s31,s41,s51,s176,s175]) ).
cnf(s179,plain,
( spl0_17
| ~ spl0_5 ),
inference(rat,[],[s96,s109,s20,s30,s40,s50,s176,s175]) ).
cnf(s180,plain,
~ spl0_5,
inference(rat,[],[s164,s137,s179,s178,s175]) ).
cnf(s181,plain,
( spl0_18
| ~ spl0_4 ),
inference(rat,[],[s81,s11,s21,s31,s175]) ).
cnf(s182,plain,
( spl0_17
| ~ spl0_4 ),
inference(rat,[],[s81,s10,s20,s30,s175]) ).
cnf(s183,plain,
( ~ spl0_13
| ~ spl0_12
| ~ spl0_4
| ~ spl0_17
| ~ spl0_18 ),
inference(rat,[],[s80,s37,s47,s77,s175]) ).
cnf(s184,plain,
( spl0_13
| ~ spl0_4 ),
inference(rat,[],[s81,s6,s16,s26,s175]) ).
cnf(s185,plain,
( ~ spl0_13
| ~ spl0_18
| ~ spl0_4
| ~ spl0_17 ),
inference(rat,[],[s81,s5,s15,s25,s183,s175]) ).
cnf(s186,plain,
~ spl0_4,
inference(rat,[],[s185,s184,s182,s181]) ).
cnf(s187,plain,
( ~ spl0_18
| ~ spl0_17
| ~ spl0_3 ),
inference(rat,[],[s137,s160,s175]) ).
cnf(s188,plain,
( spl0_18
| ~ spl0_3 ),
inference(rat,[],[s96,s105,s11,s21,s31,s41,s51,s175]) ).
cnf(s189,plain,
( ~ spl0_18
| ~ spl0_3 ),
inference(rat,[],[s96,s110,s10,s20,s30,s40,s50,s187,s175]) ).
cnf(s190,plain,
~ spl0_3,
inference(rat,[],[s189,s188]) ).
cnf(s191,plain,
( ~ spl0_18
| ~ spl0_17
| ~ spl0_2 ),
inference(rat,[],[s156,s97,s137,s174,s175]) ).
cnf(s192,plain,
( spl0_18
| ~ spl0_2 ),
inference(rat,[],[s96,s114,s11,s21,s31,s41,s51,s175,s174]) ).
cnf(s193,plain,
( ~ spl0_18
| ~ spl0_2 ),
inference(rat,[],[s96,s110,s10,s20,s30,s40,s50,s191,s175]) ).
cnf(s194,plain,
~ spl0_2,
inference(rat,[],[s193,s192]) ).
cnf(s195,plain,
spl0_1,
inference(rat,[],[s1,s174,s180,s186,s175,s190,s194]) ).
cnf(s196,plain,
( ~ spl0_33
| ~ spl0_18
| ~ spl0_25
| ~ spl0_17 ),
inference(rat,[],[s173,s165,s195,s175]) ).
cnf(s197,plain,
( ~ spl0_18
| ~ spl0_17 ),
inference(rat,[],[s196,s97,s137,s175]) ).
cnf(s198,plain,
( ~ spl0_19
| ~ spl0_20
| ~ spl0_9
| ~ spl0_21
| ~ spl0_22 ),
inference(rat,[],[s133,s93,s132,s98,s96,s175,s195]) ).
cnf(s199,plain,
spl0_18,
inference(rat,[],[s198,s11,s21,s31,s41,s51]) ).
cnf(s200,plain,
~ spl0_17,
inference(rat,[],[s197,s199]) ).
cnf(s201,plain,
spl0_22,
inference(rat,[],[s50,s200]) ).
cnf(s202,plain,
spl0_21,
inference(rat,[],[s40,s200]) ).
cnf(s203,plain,
spl0_20,
inference(rat,[],[s30,s200]) ).
cnf(s204,plain,
spl0_19,
inference(rat,[],[s20,s200]) ).
cnf(s205,plain,
spl0_9,
inference(rat,[],[s10,s200]) ).
cnf(s207,plain,
$false,
inference(rat,[],[s198,s201,s202,s205,s203,s204]) ).
fof(f3708,plain,
$false,
inference(avatar_sat_refutation,[],[s207]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP382-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.37 % Computer : n014.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 27 10:00:02 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.41 Running first-order model finding
% 0.10/0.41 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/0.48 % (558257)Will run a generic schedule for satisfiability detection.
% 0.16/0.48 % (558267)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3776484530:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.16/0.48 % (558263)% WARNING: option uhcvi not known.
% 0.16/0.48 % (558265)dis+10_1_sil=32000:sp=arity:random_seed=2944015920:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.16/0.48 % (558262)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=454856126_2999 on theBenchmark for (2999ds/0Mi)
% 0.16/0.48 % (558263)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1124444310:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.16/0.48 % (558264)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=710410798:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.16/0.48 % (558266)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=391306609:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.16/0.48 % (558268)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2240964196:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.16/0.48 % TRYING [1]
% 0.16/0.48 % TRYING [2]
% 0.16/0.48 % TRYING [3]
% 0.16/0.48 % TRYING [4]
% 0.16/0.48 % (558267) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-558257-558267"...
% 0.16/0.48 % (558265) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-558257-558265"...
% 0.16/0.48 % (558267)...printing done.
% 0.16/0.48 % (558267)Refutation found. Thanks to Tanya!
% 0.16/0.48 % SZS status Unsatisfiable for theBenchmark
% 0.16/0.48 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.49 % (558267)------------------------------
% 0.16/0.49 % (558267)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.16/0.49 % (558267)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/0.49 % (558267)CaDiCaL version: 2.1.3
% 0.16/0.49 % (558267)Termination reason: Refutation
% 0.16/0.49 % (558267)Time elapsed: 0.030 s
% 0.16/0.49 % (558267)Peak memory usage: 13 MB
% 0.16/0.49 % (558267)Instructions burned: 96 (million)
% 0.16/0.49 % (558257)Success in time 0.06 s
% 0.16/0.49 % Vampire exiting
%------------------------------------------------------------------------------