%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP317-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 10:13:37 AM UTC 2026
% Result : Unsatisfiable 2.11s 1.31s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 45
% Syntax : Number of formulae : 288 ( 20 unt; 17 def)
% Number of atoms : 1091 ( 293 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 1547 ( 744 ~; 786 |; 0 &)
% ( 17 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 19 ( 17 usr; 18 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 46 ( 0 sgn 46 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_identity) ).
fof(f2,axiom,
! [X0] : multiply(inverse(X0),X0) = identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_inverse) ).
fof(f3,plain,
! [X0] : identity = multiply(inverse(X0),X0),
inference(reorient_equations,[],[f2]) ).
fof(f4,axiom,
! [X2,X0,X1] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity) ).
fof(f7,negated_conjecture,
( multiply(sk_c8,sk_c9) = sk_c7
| inverse(sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_2) ).
fof(f8,plain,
( multiply(sk_c8,sk_c9) = sk_c7
| sk_c7 = inverse(sk_c8) ),
inference(reorient_equations,[],[f7]) ).
fof(f9,negated_conjecture,
( multiply(sk_c8,sk_c9) = sk_c7
| multiply(sk_c5,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_3) ).
fof(f10,plain,
( multiply(sk_c8,sk_c9) = sk_c7
| sk_c9 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f9]) ).
fof(f11,negated_conjecture,
( multiply(sk_c8,sk_c9) = sk_c7
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_4) ).
fof(f12,plain,
( multiply(sk_c8,sk_c9) = sk_c7
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f11]) ).
fof(f13,negated_conjecture,
( multiply(sk_c8,sk_c9) = sk_c7
| multiply(sk_c6,sk_c9) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_5) ).
fof(f14,plain,
( multiply(sk_c8,sk_c9) = sk_c7
| sk_c7 = multiply(sk_c6,sk_c9) ),
inference(reorient_equations,[],[f13]) ).
fof(f15,negated_conjecture,
( multiply(sk_c8,sk_c9) = sk_c7
| inverse(sk_c6) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_6) ).
fof(f16,plain,
( multiply(sk_c8,sk_c9) = sk_c7
| sk_c9 = inverse(sk_c6) ),
inference(reorient_equations,[],[f15]) ).
fof(f17,negated_conjecture,
( multiply(sk_c1,sk_c9) = sk_c8
| multiply(sk_c8,sk_c7) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_7) ).
fof(f18,plain,
( sk_c8 = multiply(sk_c1,sk_c9)
| sk_c9 = multiply(sk_c8,sk_c7) ),
inference(reorient_equations,[],[f17]) ).
fof(f19,negated_conjecture,
( multiply(sk_c1,sk_c9) = sk_c8
| inverse(sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_8) ).
fof(f20,plain,
( sk_c8 = multiply(sk_c1,sk_c9)
| sk_c7 = inverse(sk_c8) ),
inference(reorient_equations,[],[f19]) ).
fof(f25,negated_conjecture,
( multiply(sk_c1,sk_c9) = sk_c8
| multiply(sk_c6,sk_c9) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_11) ).
fof(f26,plain,
( sk_c8 = multiply(sk_c1,sk_c9)
| sk_c7 = multiply(sk_c6,sk_c9) ),
inference(reorient_equations,[],[f25]) ).
fof(f27,negated_conjecture,
( multiply(sk_c1,sk_c9) = sk_c8
| inverse(sk_c6) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_12) ).
fof(f28,plain,
( sk_c8 = multiply(sk_c1,sk_c9)
| sk_c9 = inverse(sk_c6) ),
inference(reorient_equations,[],[f27]) ).
fof(f29,negated_conjecture,
( inverse(sk_c1) = sk_c9
| multiply(sk_c8,sk_c7) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_13) ).
fof(f30,plain,
( sk_c9 = inverse(sk_c1)
| sk_c9 = multiply(sk_c8,sk_c7) ),
inference(reorient_equations,[],[f29]) ).
fof(f31,negated_conjecture,
( inverse(sk_c1) = sk_c9
| inverse(sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_14) ).
fof(f32,plain,
( sk_c9 = inverse(sk_c1)
| sk_c7 = inverse(sk_c8) ),
inference(reorient_equations,[],[f31]) ).
fof(f37,negated_conjecture,
( inverse(sk_c1) = sk_c9
| multiply(sk_c6,sk_c9) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_17) ).
fof(f38,plain,
( sk_c9 = inverse(sk_c1)
| sk_c7 = multiply(sk_c6,sk_c9) ),
inference(reorient_equations,[],[f37]) ).
fof(f39,negated_conjecture,
( inverse(sk_c1) = sk_c9
| inverse(sk_c6) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_18) ).
fof(f40,plain,
( sk_c9 = inverse(sk_c1)
| sk_c9 = inverse(sk_c6) ),
inference(reorient_equations,[],[f39]) ).
fof(f41,negated_conjecture,
( multiply(sk_c9,sk_c7) = sk_c8
| multiply(sk_c8,sk_c7) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_19) ).
fof(f42,plain,
( sk_c8 = multiply(sk_c9,sk_c7)
| sk_c9 = multiply(sk_c8,sk_c7) ),
inference(reorient_equations,[],[f41]) ).
fof(f45,negated_conjecture,
( multiply(sk_c9,sk_c7) = sk_c8
| multiply(sk_c5,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_21) ).
fof(f46,plain,
( sk_c8 = multiply(sk_c9,sk_c7)
| sk_c9 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f45]) ).
fof(f47,negated_conjecture,
( multiply(sk_c9,sk_c7) = sk_c8
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_22) ).
fof(f48,plain,
( sk_c8 = multiply(sk_c9,sk_c7)
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f47]) ).
fof(f49,negated_conjecture,
( multiply(sk_c9,sk_c7) = sk_c8
| multiply(sk_c6,sk_c9) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_23) ).
fof(f50,plain,
( sk_c8 = multiply(sk_c9,sk_c7)
| sk_c7 = multiply(sk_c6,sk_c9) ),
inference(reorient_equations,[],[f49]) ).
fof(f51,negated_conjecture,
( multiply(sk_c9,sk_c7) = sk_c8
| inverse(sk_c6) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_24) ).
fof(f52,plain,
( sk_c8 = multiply(sk_c9,sk_c7)
| sk_c9 = inverse(sk_c6) ),
inference(reorient_equations,[],[f51]) ).
fof(f53,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c9
| multiply(sk_c8,sk_c7) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_25) ).
fof(f54,plain,
( sk_c9 = multiply(sk_c2,sk_c8)
| sk_c9 = multiply(sk_c8,sk_c7) ),
inference(reorient_equations,[],[f53]) ).
fof(f55,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c9
| inverse(sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_26) ).
fof(f56,plain,
( sk_c9 = multiply(sk_c2,sk_c8)
| sk_c7 = inverse(sk_c8) ),
inference(reorient_equations,[],[f55]) ).
fof(f65,negated_conjecture,
( inverse(sk_c2) = sk_c8
| multiply(sk_c8,sk_c7) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_31) ).
fof(f66,plain,
( sk_c8 = inverse(sk_c2)
| sk_c9 = multiply(sk_c8,sk_c7) ),
inference(reorient_equations,[],[f65]) ).
fof(f67,negated_conjecture,
( inverse(sk_c2) = sk_c8
| inverse(sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_32) ).
fof(f68,plain,
( sk_c8 = inverse(sk_c2)
| sk_c7 = inverse(sk_c8) ),
inference(reorient_equations,[],[f67]) ).
fof(f73,negated_conjecture,
( inverse(sk_c2) = sk_c8
| multiply(sk_c6,sk_c9) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_35) ).
fof(f74,plain,
( sk_c8 = inverse(sk_c2)
| sk_c7 = multiply(sk_c6,sk_c9) ),
inference(reorient_equations,[],[f73]) ).
fof(f75,negated_conjecture,
( inverse(sk_c2) = sk_c8
| inverse(sk_c6) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_36) ).
fof(f76,plain,
( sk_c8 = inverse(sk_c2)
| sk_c9 = inverse(sk_c6) ),
inference(reorient_equations,[],[f75]) ).
fof(f113,negated_conjecture,
! [X2,X3,X0,X1,X4,X5] :
( multiply(sk_c8,sk_c9) != sk_c7
| multiply(X0,sk_c9) != sk_c8
| inverse(X0) != sk_c9
| multiply(sk_c9,sk_c7) != sk_c8
| multiply(X1,sk_c8) != sk_c9
| inverse(X1) != sk_c8
| inverse(X2) != X3
| inverse(X3) != sk_c9
| multiply(X2,sk_c9) != X3
| multiply(sk_c8,sk_c7) != sk_c9
| inverse(sk_c8) != sk_c7
| multiply(X4,sk_c8) != sk_c9
| inverse(X4) != sk_c8
| multiply(X5,sk_c9) != sk_c7
| inverse(X5) != sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_55) ).
fof(f114,plain,
! [X2,X3,X0,X1,X4,X5] :
( multiply(sk_c8,sk_c9) != sk_c7
| sk_c8 != multiply(X0,sk_c9)
| inverse(X0) != sk_c9
| sk_c8 != multiply(sk_c9,sk_c7)
| sk_c9 != multiply(X1,sk_c8)
| sk_c8 != inverse(X1)
| inverse(X2) != X3
| sk_c9 != inverse(X3)
| multiply(X2,sk_c9) != X3
| sk_c9 != multiply(sk_c8,sk_c7)
| sk_c7 != inverse(sk_c8)
| sk_c9 != multiply(X4,sk_c8)
| sk_c8 != inverse(X4)
| sk_c7 != multiply(X5,sk_c9)
| sk_c9 != inverse(X5) ),
inference(reorient_equations,[],[f113]) ).
fof(f115,plain,
! [X2,X0,X1,X4,X5] :
( multiply(sk_c8,sk_c9) != sk_c7
| sk_c8 != multiply(X0,sk_c9)
| inverse(X0) != sk_c9
| sk_c8 != multiply(sk_c9,sk_c7)
| sk_c9 != multiply(X1,sk_c8)
| sk_c8 != inverse(X1)
| sk_c9 != inverse(inverse(X2))
| inverse(X2) != multiply(X2,sk_c9)
| sk_c9 != multiply(sk_c8,sk_c7)
| sk_c7 != inverse(sk_c8)
| sk_c9 != multiply(X4,sk_c8)
| sk_c8 != inverse(X4)
| sk_c7 != multiply(X5,sk_c9)
| sk_c9 != inverse(X5) ),
inference(equality_resolution,[],[f114]) ).
fof(f117,definition,
( spl0_1
<=> ! [X5] :
( sk_c7 != multiply(X5,sk_c9)
| sk_c9 != inverse(X5) ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f118,plain,
( ! [X5] :
( sk_c7 != multiply(X5,sk_c9)
| sk_c9 != inverse(X5) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f117]) ).
fof(f120,definition,
( spl0_2
<=> ! [X4] :
( sk_c9 != multiply(X4,sk_c8)
| sk_c8 != inverse(X4) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f121,plain,
( ! [X4] :
( sk_c9 != multiply(X4,sk_c8)
| sk_c8 != inverse(X4) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f120]) ).
fof(f123,definition,
( spl0_3
<=> sk_c7 = inverse(sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f124,plain,
( sk_c7 = inverse(sk_c8)
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f123]) ).
fof(f125,plain,
( sk_c7 != inverse(sk_c8)
| spl0_3 ),
inference(avatar_component_clause,[],[f123]) ).
fof(f127,definition,
( spl0_4
<=> sk_c9 = multiply(sk_c8,sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f128,plain,
( sk_c9 = multiply(sk_c8,sk_c7)
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f127]) ).
fof(f129,plain,
( sk_c9 != multiply(sk_c8,sk_c7)
| spl0_4 ),
inference(avatar_component_clause,[],[f127]) ).
fof(f131,definition,
( spl0_5
<=> ! [X2] :
( sk_c9 != inverse(inverse(X2))
| inverse(X2) != multiply(X2,sk_c9) ) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f132,plain,
( ! [X2] :
( sk_c9 != inverse(inverse(X2))
| inverse(X2) != multiply(X2,sk_c9) )
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f131]) ).
fof(f134,definition,
( spl0_6
<=> sk_c8 = multiply(sk_c9,sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f135,plain,
( sk_c8 = multiply(sk_c9,sk_c7)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f134]) ).
fof(f136,plain,
( sk_c8 != multiply(sk_c9,sk_c7)
| spl0_6 ),
inference(avatar_component_clause,[],[f134]) ).
fof(f138,definition,
( spl0_7
<=> ! [X0] :
( sk_c8 != multiply(X0,sk_c9)
| inverse(X0) != sk_c9 ) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f139,plain,
( ! [X0] :
( sk_c8 != multiply(X0,sk_c9)
| inverse(X0) != sk_c9 )
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f138]) ).
fof(f141,definition,
( spl0_8
<=> multiply(sk_c8,sk_c9) = sk_c7 ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f142,plain,
( multiply(sk_c8,sk_c9) = sk_c7
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f141]) ).
fof(f143,plain,
( multiply(sk_c8,sk_c9) != sk_c7
| spl0_8 ),
inference(avatar_component_clause,[],[f141]) ).
fof(f144,plain,
( spl0_1
| spl0_2
| ~ spl0_3
| ~ spl0_4
| spl0_5
| spl0_2
| ~ spl0_6
| spl0_7
| ~ spl0_8 ),
inference(avatar_split_clause,[],[f115,f141,f138,f134,f120,f131,f127,f123,f120,f117]) ).
fof(f146,definition,
( spl0_9
<=> sk_c9 = inverse(sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f148,plain,
( sk_c9 = inverse(sk_c6)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f146]) ).
fof(f155,definition,
( spl0_11
<=> sk_c7 = multiply(sk_c6,sk_c9) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f157,plain,
( sk_c7 = multiply(sk_c6,sk_c9)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f155]) ).
fof(f160,definition,
( spl0_12
<=> sk_c8 = inverse(sk_c5) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f162,plain,
( sk_c8 = inverse(sk_c5)
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f160]) ).
fof(f165,definition,
( spl0_13
<=> sk_c9 = multiply(sk_c5,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f167,plain,
( sk_c9 = multiply(sk_c5,sk_c8)
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f165]) ).
fof(f192,definition,
( spl0_16
<=> sk_c8 = inverse(sk_c2) ),
introduced(definition,[new_symbols(definition,[spl0_16])],[avatar_definition]) ).
fof(f194,plain,
( sk_c8 = inverse(sk_c2)
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f192]) ).
fof(f195,plain,
( spl0_9
| spl0_16 ),
inference(avatar_split_clause,[],[f76,f192,f146]) ).
fof(f196,plain,
( spl0_11
| spl0_16 ),
inference(avatar_split_clause,[],[f74,f192,f155]) ).
fof(f199,plain,
( spl0_3
| spl0_16 ),
inference(avatar_split_clause,[],[f68,f192,f123]) ).
fof(f200,plain,
( spl0_4
| spl0_16 ),
inference(avatar_split_clause,[],[f66,f192,f127]) ).
fof(f202,definition,
( spl0_17
<=> sk_c9 = multiply(sk_c2,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_17])],[avatar_definition]) ).
fof(f204,plain,
( sk_c9 = multiply(sk_c2,sk_c8)
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f202]) ).
fof(f209,plain,
( spl0_3
| spl0_17 ),
inference(avatar_split_clause,[],[f56,f202,f123]) ).
fof(f210,plain,
( spl0_4
| spl0_17 ),
inference(avatar_split_clause,[],[f54,f202,f127]) ).
fof(f211,plain,
( spl0_9
| spl0_6 ),
inference(avatar_split_clause,[],[f52,f134,f146]) ).
fof(f212,plain,
( spl0_11
| spl0_6 ),
inference(avatar_split_clause,[],[f50,f134,f155]) ).
fof(f213,plain,
( spl0_12
| spl0_6 ),
inference(avatar_split_clause,[],[f48,f134,f160]) ).
fof(f214,plain,
( spl0_13
| spl0_6 ),
inference(avatar_split_clause,[],[f46,f134,f165]) ).
fof(f216,plain,
( spl0_4
| spl0_6 ),
inference(avatar_split_clause,[],[f42,f134,f127]) ).
fof(f218,definition,
( spl0_18
<=> sk_c9 = inverse(sk_c1) ),
introduced(definition,[new_symbols(definition,[spl0_18])],[avatar_definition]) ).
fof(f220,plain,
( sk_c9 = inverse(sk_c1)
| ~ spl0_18 ),
inference(avatar_component_clause,[],[f218]) ).
fof(f221,plain,
( spl0_9
| spl0_18 ),
inference(avatar_split_clause,[],[f40,f218,f146]) ).
fof(f222,plain,
( spl0_11
| spl0_18 ),
inference(avatar_split_clause,[],[f38,f218,f155]) ).
fof(f225,plain,
( spl0_3
| spl0_18 ),
inference(avatar_split_clause,[],[f32,f218,f123]) ).
fof(f226,plain,
( spl0_4
| spl0_18 ),
inference(avatar_split_clause,[],[f30,f218,f127]) ).
fof(f228,definition,
( spl0_19
<=> sk_c8 = multiply(sk_c1,sk_c9) ),
introduced(definition,[new_symbols(definition,[spl0_19])],[avatar_definition]) ).
fof(f230,plain,
( sk_c8 = multiply(sk_c1,sk_c9)
| ~ spl0_19 ),
inference(avatar_component_clause,[],[f228]) ).
fof(f231,plain,
( spl0_9
| spl0_19 ),
inference(avatar_split_clause,[],[f28,f228,f146]) ).
fof(f232,plain,
( spl0_11
| spl0_19 ),
inference(avatar_split_clause,[],[f26,f228,f155]) ).
fof(f235,plain,
( spl0_3
| spl0_19 ),
inference(avatar_split_clause,[],[f20,f228,f123]) ).
fof(f236,plain,
( spl0_4
| spl0_19 ),
inference(avatar_split_clause,[],[f18,f228,f127]) ).
fof(f237,plain,
( spl0_9
| spl0_8 ),
inference(avatar_split_clause,[],[f16,f141,f146]) ).
fof(f238,plain,
( spl0_11
| spl0_8 ),
inference(avatar_split_clause,[],[f14,f141,f155]) ).
fof(f239,plain,
( spl0_12
| spl0_8 ),
inference(avatar_split_clause,[],[f12,f141,f160]) ).
fof(f240,plain,
( spl0_13
| spl0_8 ),
inference(avatar_split_clause,[],[f10,f141,f165]) ).
fof(f241,plain,
( spl0_3
| spl0_8 ),
inference(avatar_split_clause,[],[f8,f141,f123]) ).
fof(f243,plain,
( identity = multiply(sk_c7,sk_c8)
| ~ spl0_3 ),
inference(superposition,[],[f3,f124]) ).
fof(f248,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[],[f4,f3]) ).
fof(f252,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f248,f1]) ).
fof(f255,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c7,multiply(sk_c8,X0))
| ~ spl0_3 ),
inference(superposition,[],[f4,f243]) ).
fof(f256,plain,
( ! [X0] : multiply(sk_c7,multiply(sk_c8,X0)) = X0
| ~ spl0_3 ),
inference(forward_demodulation,[],[f255,f1]) ).
fof(f265,plain,
( sk_c7 = multiply(sk_c7,sk_c9)
| ~ spl0_3
| ~ spl0_4 ),
inference(superposition,[],[f256,f128]) ).
fof(f301,plain,
( sk_c8 = multiply(inverse(sk_c7),identity)
| ~ spl0_3 ),
inference(superposition,[],[f252,f243]) ).
fof(f302,plain,
( sk_c9 = multiply(inverse(sk_c7),sk_c7)
| ~ spl0_3
| ~ spl0_4 ),
inference(superposition,[],[f252,f265]) ).
fof(f303,plain,
( sk_c8 = multiply(inverse(sk_c5),sk_c9)
| ~ spl0_13 ),
inference(superposition,[],[f252,f167]) ).
fof(f305,plain,
( sk_c9 = multiply(inverse(sk_c6),sk_c7)
| ~ spl0_11 ),
inference(superposition,[],[f252,f157]) ).
fof(f310,plain,
( sk_c9 = multiply(sk_c9,sk_c7)
| ~ spl0_9
| ~ spl0_11 ),
inference(forward_demodulation,[],[f305,f148]) ).
fof(f312,plain,
( sk_c8 = multiply(sk_c8,sk_c9)
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f303,f162]) ).
fof(f313,plain,
( identity = sk_c9
| ~ spl0_3
| ~ spl0_4 ),
inference(forward_demodulation,[],[f302,f3]) ).
fof(f321,plain,
( sk_c7 = multiply(inverse(sk_c9),sk_c9)
| ~ spl0_9
| ~ spl0_11 ),
inference(superposition,[],[f252,f310]) ).
fof(f323,plain,
( identity = sk_c7
| ~ spl0_9
| ~ spl0_11 ),
inference(forward_demodulation,[],[f321,f3]) ).
fof(f325,plain,
( sk_c9 = sk_c7
| ~ spl0_3
| ~ spl0_4
| ~ spl0_9
| ~ spl0_11 ),
inference(forward_demodulation,[],[f323,f313]) ).
fof(f335,plain,
( sk_c8 != sk_c7
| spl0_8
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f143,f312]) ).
fof(f343,plain,
( sk_c8 != sk_c9
| ~ spl0_3
| ~ spl0_4
| spl0_8
| ~ spl0_9
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f335,f325]) ).
fof(f354,plain,
( sk_c8 = multiply(inverse(sk_c7),sk_c9)
| ~ spl0_3
| ~ spl0_4 ),
inference(forward_demodulation,[],[f301,f313]) ).
fof(f355,plain,
( sk_c8 = multiply(inverse(sk_c9),sk_c9)
| ~ spl0_3
| ~ spl0_4
| ~ spl0_9
| ~ spl0_11 ),
inference(forward_demodulation,[],[f354,f325]) ).
fof(f356,plain,
( identity = sk_c8
| ~ spl0_3
| ~ spl0_4
| ~ spl0_9
| ~ spl0_11 ),
inference(forward_demodulation,[],[f355,f3]) ).
fof(f357,plain,
( sk_c8 = sk_c9
| ~ spl0_3
| ~ spl0_4
| ~ spl0_9
| ~ spl0_11 ),
inference(forward_demodulation,[],[f356,f313]) ).
fof(f358,plain,
( $false
| ~ spl0_3
| ~ spl0_4
| spl0_8
| ~ spl0_9
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f357,f343]) ).
fof(f359,plain,
( ~ spl0_3
| ~ spl0_4
| spl0_8
| ~ spl0_9
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[],[f358]) ).
fof(f360,plain,
( sk_c8 != sk_c9
| spl0_6
| ~ spl0_9
| ~ spl0_11 ),
inference(forward_demodulation,[],[f136,f310]) ).
fof(f361,plain,
( sk_c9 = multiply(sk_c8,sk_c9)
| ~ spl0_3
| ~ spl0_4
| ~ spl0_8
| ~ spl0_9
| ~ spl0_11 ),
inference(forward_demodulation,[],[f142,f325]) ).
fof(f362,plain,
( sk_c8 = sk_c9
| ~ spl0_3
| ~ spl0_4
| ~ spl0_8
| ~ spl0_9
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f361,f312]) ).
fof(f372,plain,
( $false
| ~ spl0_3
| ~ spl0_4
| spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f362,f360]) ).
fof(f373,plain,
( ~ spl0_3
| ~ spl0_4
| spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[],[f372]) ).
fof(f375,plain,
( sk_c8 = sk_c9
| ~ spl0_6
| ~ spl0_9
| ~ spl0_11 ),
inference(forward_demodulation,[],[f135,f310]) ).
fof(f376,plain,
( sk_c7 = inverse(sk_c9)
| ~ spl0_3
| ~ spl0_6
| ~ spl0_9
| ~ spl0_11 ),
inference(superposition,[],[f124,f375]) ).
fof(f390,plain,
( sk_c9 = inverse(sk_c9)
| ~ spl0_3
| ~ spl0_4
| ~ spl0_6
| ~ spl0_9
| ~ spl0_11 ),
inference(forward_demodulation,[],[f376,f325]) ).
fof(f392,plain,
( ! [X0] :
( inverse(X0) != sk_c9
| sk_c9 != multiply(X0,sk_c9) )
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_11 ),
inference(forward_demodulation,[],[f139,f375]) ).
fof(f393,plain,
( sk_c9 != sk_c7
| sk_c9 != multiply(sk_c8,sk_c9)
| ~ spl0_3
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_11 ),
inference(superposition,[],[f392,f124]) ).
fof(f399,plain,
( sk_c9 != multiply(sk_c8,sk_c9)
| ~ spl0_3
| ~ spl0_4
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f393,f325]) ).
fof(f402,plain,
( $false
| ~ spl0_3
| ~ spl0_4
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f399,f361]) ).
fof(f403,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_11 ),
inference(avatar_contradiction_clause,[],[f402]) ).
fof(f404,plain,
( ! [X5] :
( sk_c9 != inverse(X5)
| sk_c9 != multiply(X5,sk_c9) )
| ~ spl0_1
| ~ spl0_3
| ~ spl0_4
| ~ spl0_9
| ~ spl0_11 ),
inference(forward_demodulation,[],[f118,f325]) ).
fof(f405,plain,
( sk_c9 != sk_c7
| sk_c9 != multiply(sk_c8,sk_c9)
| ~ spl0_1
| ~ spl0_3
| ~ spl0_4
| ~ spl0_9
| ~ spl0_11 ),
inference(superposition,[],[f404,f124]) ).
fof(f411,plain,
( sk_c9 != multiply(sk_c8,sk_c9)
| ~ spl0_1
| ~ spl0_3
| ~ spl0_4
| ~ spl0_9
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f405,f325]) ).
fof(f414,plain,
( $false
| ~ spl0_1
| ~ spl0_3
| ~ spl0_4
| ~ spl0_8
| ~ spl0_9
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f411,f361]) ).
fof(f415,plain,
( ~ spl0_1
| ~ spl0_3
| ~ spl0_4
| ~ spl0_8
| ~ spl0_9
| ~ spl0_11 ),
inference(avatar_contradiction_clause,[],[f414]) ).
fof(f416,plain,
( ! [X4] :
( sk_c9 != multiply(X4,sk_c9)
| sk_c8 != inverse(X4) )
| ~ spl0_2
| ~ spl0_6
| ~ spl0_9
| ~ spl0_11 ),
inference(forward_demodulation,[],[f121,f375]) ).
fof(f417,plain,
( ! [X4] :
( sk_c9 != inverse(X4)
| sk_c9 != multiply(X4,sk_c9) )
| ~ spl0_2
| ~ spl0_6
| ~ spl0_9
| ~ spl0_11 ),
inference(forward_demodulation,[],[f416,f375]) ).
fof(f418,plain,
( sk_c9 != sk_c7
| sk_c9 != multiply(sk_c8,sk_c9)
| ~ spl0_2
| ~ spl0_3
| ~ spl0_6
| ~ spl0_9
| ~ spl0_11 ),
inference(superposition,[],[f417,f124]) ).
fof(f424,plain,
( sk_c9 != multiply(sk_c8,sk_c9)
| ~ spl0_2
| ~ spl0_3
| ~ spl0_4
| ~ spl0_6
| ~ spl0_9
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f418,f325]) ).
fof(f427,plain,
( $false
| ~ spl0_2
| ~ spl0_3
| ~ spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f424,f361]) ).
fof(f428,plain,
( ~ spl0_2
| ~ spl0_3
| ~ spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_11 ),
inference(avatar_contradiction_clause,[],[f427]) ).
fof(f430,plain,
( sk_c9 != inverse(sk_c7)
| multiply(sk_c8,sk_c9) != sk_c7
| ~ spl0_3
| ~ spl0_5 ),
inference(superposition,[],[f132,f124]) ).
fof(f431,plain,
( sk_c9 != inverse(sk_c9)
| sk_c9 != multiply(sk_c6,sk_c9)
| ~ spl0_5
| ~ spl0_9 ),
inference(superposition,[],[f132,f148]) ).
fof(f434,plain,
( sk_c9 != sk_c7
| sk_c9 != inverse(sk_c9)
| ~ spl0_5
| ~ spl0_9
| ~ spl0_11 ),
inference(forward_demodulation,[],[f431,f157]) ).
fof(f437,plain,
( sk_c9 != inverse(sk_c9)
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_9
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f434,f325]) ).
fof(f455,plain,
( $false
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_9
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f437,f390]) ).
fof(f456,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_9
| ~ spl0_11 ),
inference(avatar_contradiction_clause,[],[f455]) ).
fof(f540,plain,
( identity = multiply(sk_c8,sk_c2)
| ~ spl0_16 ),
inference(superposition,[],[f3,f194]) ).
fof(f543,plain,
( sk_c8 = multiply(inverse(sk_c2),sk_c9)
| ~ spl0_17 ),
inference(superposition,[],[f252,f204]) ).
fof(f545,plain,
( sk_c8 = multiply(sk_c8,sk_c9)
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f543,f194]) ).
fof(f546,plain,
( sk_c9 = multiply(inverse(sk_c1),sk_c8)
| ~ spl0_19 ),
inference(superposition,[],[f252,f230]) ).
fof(f548,plain,
( sk_c9 = multiply(sk_c9,sk_c8)
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_demodulation,[],[f546,f220]) ).
fof(f627,plain,
( sk_c8 = multiply(inverse(sk_c9),sk_c9)
| ~ spl0_18
| ~ spl0_19 ),
inference(superposition,[],[f252,f548]) ).
fof(f629,plain,
( identity = sk_c8
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_demodulation,[],[f627,f3]) ).
fof(f691,plain,
( sk_c8 = multiply(sk_c8,sk_c2)
| ~ spl0_16
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_demodulation,[],[f540,f629]) ).
fof(f709,plain,
( sk_c2 = multiply(inverse(sk_c8),sk_c8)
| ~ spl0_16
| ~ spl0_18
| ~ spl0_19 ),
inference(superposition,[],[f252,f691]) ).
fof(f711,plain,
( identity = sk_c2
| ~ spl0_16
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_demodulation,[],[f709,f3]) ).
fof(f713,plain,
( sk_c8 = sk_c2
| ~ spl0_16
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_demodulation,[],[f711,f629]) ).
fof(f717,plain,
( sk_c8 = inverse(sk_c8)
| ~ spl0_16
| ~ spl0_18
| ~ spl0_19 ),
inference(superposition,[],[f194,f713]) ).
fof(f719,plain,
( sk_c8 != sk_c7
| spl0_3
| ~ spl0_16
| ~ spl0_18
| ~ spl0_19 ),
inference(superposition,[],[f125,f717]) ).
fof(f759,plain,
( sk_c8 = sk_c7
| ~ spl0_8
| ~ spl0_16
| ~ spl0_17 ),
inference(superposition,[],[f545,f142]) ).
fof(f768,plain,
( $false
| spl0_3
| ~ spl0_8
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_subsumption_resolution,[],[f759,f719]) ).
fof(f769,plain,
( spl0_3
| ~ spl0_8
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19 ),
inference(avatar_contradiction_clause,[],[f768]) ).
fof(f770,plain,
( sk_c8 = sk_c7
| ~ spl0_3
| ~ spl0_16
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_demodulation,[],[f124,f717]) ).
fof(f774,plain,
( sk_c8 = multiply(sk_c9,sk_c8)
| ~ spl0_3
| ~ spl0_6
| ~ spl0_16
| ~ spl0_18
| ~ spl0_19 ),
inference(superposition,[],[f135,f770]) ).
fof(f777,plain,
( sk_c8 = sk_c9
| ~ spl0_3
| ~ spl0_6
| ~ spl0_16
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_demodulation,[],[f774,f548]) ).
fof(f781,plain,
( sk_c9 = multiply(sk_c2,sk_c9)
| ~ spl0_3
| ~ spl0_6
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19 ),
inference(superposition,[],[f204,f777]) ).
fof(f795,plain,
( sk_c9 = multiply(sk_c8,sk_c9)
| ~ spl0_3
| ~ spl0_6
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_demodulation,[],[f781,f713]) ).
fof(f802,plain,
( sk_c9 = multiply(sk_c9,sk_c9)
| ~ spl0_3
| ~ spl0_6
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_demodulation,[],[f795,f777]) ).
fof(f804,plain,
( ! [X4] :
( sk_c9 != multiply(X4,sk_c9)
| sk_c8 != inverse(X4) )
| ~ spl0_2
| ~ spl0_3
| ~ spl0_6
| ~ spl0_16
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_demodulation,[],[f121,f777]) ).
fof(f805,plain,
( ! [X4] :
( sk_c9 != inverse(X4)
| sk_c9 != multiply(X4,sk_c9) )
| ~ spl0_2
| ~ spl0_3
| ~ spl0_6
| ~ spl0_16
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_demodulation,[],[f804,f777]) ).
fof(f810,plain,
( sk_c8 != sk_c9
| sk_c9 != multiply(sk_c2,sk_c9)
| ~ spl0_2
| ~ spl0_3
| ~ spl0_6
| ~ spl0_16
| ~ spl0_18
| ~ spl0_19 ),
inference(superposition,[],[f805,f194]) ).
fof(f817,plain,
( sk_c9 != multiply(sk_c2,sk_c9)
| ~ spl0_2
| ~ spl0_3
| ~ spl0_6
| ~ spl0_16
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_subsumption_resolution,[],[f810,f777]) ).
fof(f821,definition,
( spl0_20
<=> sk_c9 = multiply(sk_c9,sk_c9) ),
introduced(definition,[new_symbols(definition,[spl0_20])],[avatar_definition]) ).
fof(f831,plain,
( sk_c9 != multiply(sk_c8,sk_c9)
| ~ spl0_2
| ~ spl0_3
| ~ spl0_6
| ~ spl0_16
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_demodulation,[],[f817,f713]) ).
fof(f835,plain,
( sk_c9 != sk_c7
| ~ spl0_2
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_16
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_demodulation,[],[f831,f142]) ).
fof(f837,plain,
( sk_c8 != sk_c9
| ~ spl0_2
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_16
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_demodulation,[],[f835,f770]) ).
fof(f840,plain,
( $false
| ~ spl0_2
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_16
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_subsumption_resolution,[],[f837,f777]) ).
fof(f841,plain,
( ~ spl0_2
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_16
| ~ spl0_18
| ~ spl0_19 ),
inference(avatar_contradiction_clause,[],[f840]) ).
fof(f842,plain,
( sk_c9 != multiply(sk_c8,sk_c8)
| ~ spl0_3
| spl0_4
| ~ spl0_16
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_demodulation,[],[f129,f770]) ).
fof(f847,plain,
( sk_c9 != multiply(sk_c9,sk_c9)
| ~ spl0_3
| spl0_4
| ~ spl0_6
| ~ spl0_16
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_demodulation,[],[f842,f777]) ).
fof(f851,plain,
( ~ spl0_20
| ~ spl0_3
| spl0_4
| ~ spl0_6
| ~ spl0_16
| ~ spl0_18
| ~ spl0_19 ),
inference(avatar_split_clause,[],[f847,f228,f218,f192,f134,f127,f123,f821]) ).
fof(f852,plain,
( spl0_20
| ~ spl0_3
| ~ spl0_6
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19 ),
inference(avatar_split_clause,[],[f802,f228,f218,f202,f192,f134,f123,f821]) ).
fof(f860,plain,
( ! [X0] :
( sk_c9 != multiply(X0,sk_c9)
| inverse(X0) != sk_c9 )
| ~ spl0_3
| ~ spl0_6
| ~ spl0_7
| ~ spl0_16
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_demodulation,[],[f139,f777]) ).
fof(f870,plain,
( sk_c9 != sk_c9
| sk_c9 != inverse(identity)
| ~ spl0_3
| ~ spl0_6
| ~ spl0_7
| ~ spl0_16
| ~ spl0_18
| ~ spl0_19 ),
inference(superposition,[],[f860,f1]) ).
fof(f877,plain,
( sk_c9 != inverse(identity)
| ~ spl0_3
| ~ spl0_6
| ~ spl0_7
| ~ spl0_16
| ~ spl0_18
| ~ spl0_19 ),
inference(trivial_inequality_removal,[],[f870]) ).
fof(f884,plain,
( sk_c9 != inverse(sk_c8)
| ~ spl0_3
| ~ spl0_6
| ~ spl0_7
| ~ spl0_16
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_demodulation,[],[f877,f629]) ).
fof(f891,plain,
( sk_c8 != sk_c9
| ~ spl0_3
| ~ spl0_6
| ~ spl0_7
| ~ spl0_16
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_demodulation,[],[f884,f717]) ).
fof(f897,plain,
( $false
| ~ spl0_3
| ~ spl0_6
| ~ spl0_7
| ~ spl0_16
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_subsumption_resolution,[],[f891,f777]) ).
fof(f898,plain,
( ~ spl0_3
| ~ spl0_6
| ~ spl0_7
| ~ spl0_16
| ~ spl0_18
| ~ spl0_19 ),
inference(avatar_contradiction_clause,[],[f897]) ).
fof(f901,plain,
( sk_c9 != inverse(sk_c7)
| ~ spl0_3
| ~ spl0_5
| ~ spl0_8 ),
inference(forward_subsumption_resolution,[],[f430,f142]) ).
fof(f904,plain,
( sk_c9 != inverse(sk_c8)
| ~ spl0_3
| ~ spl0_5
| ~ spl0_8
| ~ spl0_16
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_demodulation,[],[f901,f770]) ).
fof(f907,plain,
( sk_c8 != sk_c9
| ~ spl0_3
| ~ spl0_5
| ~ spl0_8
| ~ spl0_16
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_demodulation,[],[f904,f717]) ).
fof(f910,plain,
( $false
| ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_16
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_subsumption_resolution,[],[f907,f777]) ).
fof(f911,plain,
( ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_16
| ~ spl0_18
| ~ spl0_19 ),
inference(avatar_contradiction_clause,[],[f910]) ).
fof(f912,plain,
( ! [X5] :
( sk_c8 != multiply(X5,sk_c9)
| sk_c9 != inverse(X5) )
| ~ spl0_1
| ~ spl0_3
| ~ spl0_16
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_demodulation,[],[f118,f770]) ).
fof(f913,plain,
( ! [X5] :
( sk_c9 != inverse(X5)
| sk_c9 != multiply(X5,sk_c9) )
| ~ spl0_1
| ~ spl0_3
| ~ spl0_6
| ~ spl0_16
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_demodulation,[],[f912,f777]) ).
fof(f923,plain,
( sk_c8 != sk_c9
| sk_c9 != multiply(sk_c2,sk_c9)
| ~ spl0_1
| ~ spl0_3
| ~ spl0_6
| ~ spl0_16
| ~ spl0_18
| ~ spl0_19 ),
inference(superposition,[],[f913,f194]) ).
fof(f930,plain,
( sk_c9 != multiply(sk_c2,sk_c9)
| ~ spl0_1
| ~ spl0_3
| ~ spl0_6
| ~ spl0_16
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_subsumption_resolution,[],[f923,f777]) ).
fof(f936,plain,
( sk_c9 != multiply(sk_c8,sk_c9)
| ~ spl0_1
| ~ spl0_3
| ~ spl0_6
| ~ spl0_16
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_demodulation,[],[f930,f713]) ).
fof(f941,plain,
( sk_c9 != sk_c7
| ~ spl0_1
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_16
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_demodulation,[],[f936,f142]) ).
fof(f944,plain,
( sk_c8 != sk_c9
| ~ spl0_1
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_16
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_demodulation,[],[f941,f770]) ).
fof(f947,plain,
( $false
| ~ spl0_1
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_16
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_subsumption_resolution,[],[f944,f777]) ).
fof(f948,plain,
( ~ spl0_1
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_16
| ~ spl0_18
| ~ spl0_19 ),
inference(avatar_contradiction_clause,[],[f947]) ).
cnf(s1,plain,
( spl0_2
| spl0_1
| spl0_2
| ~ spl0_3
| ~ spl0_4
| spl0_5
| ~ spl0_6
| spl0_7
| ~ spl0_8 ),
inference(sat_conversion,[],[f144]) ).
cnf(s2,plain,
( spl0_1
| spl0_2
| ~ spl0_3
| ~ spl0_4
| spl0_5
| ~ spl0_6
| spl0_7
| ~ spl0_8 ),
inference(rat,[],[s1]) ).
cnf(s21,plain,
( spl0_9
| spl0_16 ),
inference(sat_conversion,[],[f195]) ).
cnf(s22,plain,
( spl0_11
| spl0_16 ),
inference(sat_conversion,[],[f196]) ).
cnf(s25,plain,
( spl0_3
| spl0_16 ),
inference(sat_conversion,[],[f199]) ).
cnf(s26,plain,
( spl0_4
| spl0_16 ),
inference(sat_conversion,[],[f200]) ).
cnf(s31,plain,
( spl0_3
| spl0_17 ),
inference(sat_conversion,[],[f209]) ).
cnf(s32,plain,
( spl0_4
| spl0_17 ),
inference(sat_conversion,[],[f210]) ).
cnf(s33,plain,
( spl0_6
| spl0_9 ),
inference(sat_conversion,[],[f211]) ).
cnf(s34,plain,
( spl0_6
| spl0_11 ),
inference(sat_conversion,[],[f212]) ).
cnf(s35,plain,
( spl0_6
| spl0_12 ),
inference(sat_conversion,[],[f213]) ).
cnf(s36,plain,
( spl0_6
| spl0_13 ),
inference(sat_conversion,[],[f214]) ).
cnf(s38,plain,
( spl0_4
| spl0_6 ),
inference(sat_conversion,[],[f216]) ).
cnf(s39,plain,
( spl0_9
| spl0_18 ),
inference(sat_conversion,[],[f221]) ).
cnf(s40,plain,
( spl0_11
| spl0_18 ),
inference(sat_conversion,[],[f222]) ).
cnf(s43,plain,
( spl0_3
| spl0_18 ),
inference(sat_conversion,[],[f225]) ).
cnf(s44,plain,
( spl0_4
| spl0_18 ),
inference(sat_conversion,[],[f226]) ).
cnf(s45,plain,
( spl0_9
| spl0_19 ),
inference(sat_conversion,[],[f231]) ).
cnf(s46,plain,
( spl0_11
| spl0_19 ),
inference(sat_conversion,[],[f232]) ).
cnf(s49,plain,
( spl0_3
| spl0_19 ),
inference(sat_conversion,[],[f235]) ).
cnf(s50,plain,
( spl0_4
| spl0_19 ),
inference(sat_conversion,[],[f236]) ).
cnf(s51,plain,
( spl0_8
| spl0_9 ),
inference(sat_conversion,[],[f237]) ).
cnf(s52,plain,
( spl0_8
| spl0_11 ),
inference(sat_conversion,[],[f238]) ).
cnf(s53,plain,
( spl0_8
| spl0_12 ),
inference(sat_conversion,[],[f239]) ).
cnf(s54,plain,
( spl0_8
| spl0_13 ),
inference(sat_conversion,[],[f240]) ).
cnf(s55,plain,
( spl0_3
| spl0_8 ),
inference(sat_conversion,[],[f241]) ).
cnf(s57,plain,
( ~ spl0_3
| ~ spl0_4
| spl0_8
| ~ spl0_9
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(sat_conversion,[],[f359]) ).
cnf(s59,plain,
( ~ spl0_3
| ~ spl0_4
| spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(sat_conversion,[],[f373]) ).
cnf(s61,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_11 ),
inference(sat_conversion,[],[f403]) ).
cnf(s63,plain,
( ~ spl0_1
| ~ spl0_3
| ~ spl0_4
| ~ spl0_8
| ~ spl0_9
| ~ spl0_11 ),
inference(sat_conversion,[],[f415]) ).
cnf(s65,plain,
( ~ spl0_2
| ~ spl0_3
| ~ spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_11 ),
inference(sat_conversion,[],[f428]) ).
cnf(s66,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_9
| ~ spl0_11 ),
inference(sat_conversion,[],[f456]) ).
cnf(s70,plain,
( spl0_3
| ~ spl0_8
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19 ),
inference(sat_conversion,[],[f769]) ).
cnf(s75,plain,
( ~ spl0_2
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_16
| ~ spl0_18
| ~ spl0_19 ),
inference(sat_conversion,[],[f841]) ).
cnf(s76,plain,
( ~ spl0_3
| spl0_4
| ~ spl0_6
| ~ spl0_16
| ~ spl0_18
| ~ spl0_19
| ~ spl0_20 ),
inference(sat_conversion,[],[f851]) ).
cnf(s77,plain,
( ~ spl0_3
| ~ spl0_6
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19
| spl0_20 ),
inference(sat_conversion,[],[f852]) ).
cnf(s85,plain,
( ~ spl0_3
| ~ spl0_6
| ~ spl0_7
| ~ spl0_16
| ~ spl0_18
| ~ spl0_19 ),
inference(sat_conversion,[],[f898]) ).
cnf(s87,plain,
( ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_16
| ~ spl0_18
| ~ spl0_19 ),
inference(sat_conversion,[],[f911]) ).
cnf(s93,plain,
( ~ spl0_1
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_16
| ~ spl0_18
| ~ spl0_19 ),
inference(sat_conversion,[],[f948]) ).
cnf(s94,plain,
spl0_3,
inference(rat,[],[s70,s25,s31,s43,s49,s55]) ).
cnf(s95,plain,
spl0_4,
inference(rat,[],[s76,s77,s26,s32,s38,s44,s50,s94]) ).
cnf(s97,plain,
spl0_8,
inference(rat,[],[s57,s51,s52,s53,s54,s94,s95]) ).
cnf(s98,plain,
( spl0_11
| ~ spl0_7
| ~ spl0_6 ),
inference(rat,[],[s85,s22,s40,s46,s94]) ).
cnf(s99,plain,
( ~ spl0_11
| ~ spl0_6
| ~ spl0_7 ),
inference(rat,[],[s85,s21,s39,s45,s61,s95,s97,s94]) ).
cnf(s100,plain,
( ~ spl0_7
| ~ spl0_6 ),
inference(rat,[],[s99,s98]) ).
cnf(s101,plain,
( ~ spl0_6
| spl0_5
| spl0_1
| spl0_2 ),
inference(rat,[],[s100,s2,s97,s95,s94]) ).
cnf(s102,plain,
spl0_6,
inference(rat,[],[s59,s33,s34,s35,s36,s94,s95,s97]) ).
cnf(s104,plain,
( spl0_11
| ~ spl0_5 ),
inference(rat,[],[s87,s22,s40,s46,s97,s94,s102]) ).
cnf(s105,plain,
( ~ spl0_11
| ~ spl0_5 ),
inference(rat,[],[s87,s21,s39,s45,s66,s95,s102,s94,s97]) ).
cnf(s106,plain,
~ spl0_5,
inference(rat,[],[s105,s104]) ).
cnf(s107,plain,
( spl0_11
| ~ spl0_2 ),
inference(rat,[],[s75,s22,s40,s46,s94,s97,s102]) ).
cnf(s108,plain,
( ~ spl0_11
| ~ spl0_2 ),
inference(rat,[],[s75,s21,s39,s45,s65,s95,s102,s97,s94]) ).
cnf(s109,plain,
~ spl0_2,
inference(rat,[],[s108,s107]) ).
cnf(s110,plain,
spl0_1,
inference(rat,[],[s101,s102,s106,s109]) ).
cnf(s111,plain,
spl0_11,
inference(rat,[],[s93,s22,s40,s46,s94,s97,s102,s110]) ).
cnf(s112,plain,
~ spl0_9,
inference(rat,[],[s63,s95,s97,s94,s110,s111]) ).
cnf(s113,plain,
spl0_19,
inference(rat,[],[s45,s112]) ).
cnf(s114,plain,
spl0_18,
inference(rat,[],[s39,s112]) ).
cnf(s116,plain,
spl0_16,
inference(rat,[],[s21,s112]) ).
cnf(s120,plain,
$false,
inference(rat,[],[s93,s110,s102,s97,s94,s116,s113,s114]) ).
fof(f949,plain,
$false,
inference(avatar_sat_refutation,[],[s120]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP317-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n013.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 09:48:51 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.11/1.31 % (4164781)Input is clausal, will run a generic CNF schedule.
% 2.11/1.31 % (4164786)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=1779620719:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.11/1.31 % (4164790)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=4210352860:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.11/1.31 % (4164788)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=1932016802:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.11/1.31 % (4164789)lrs+10_1_sil=8000:sp=occurrence:random_seed=2921203286:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.11/1.31 % (4164791)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3482520516:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.11/1.31 % (4164792)dis-21_1_sil=8000:lcm=predicate:random_seed=1685532608:st=5:avsq=on:i=117:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/117Mi)
% 2.11/1.31 % (4164787)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=1044988401:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.11/1.31 % (4164792)Refutation not found, incomplete strategy
% 2.11/1.31 % (4164792)------------------------------
% 2.11/1.31 % (4164792)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.11/1.31 % (4164792)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.11/1.31 % (4164792)CaDiCaL version: 2.1.3
% 2.11/1.31 % (4164792)Termination reason: Refutation not found, incomplete strategy
% 2.11/1.31 % (4164792)Time elapsed: 0.002 s
% 2.11/1.31 % (4164792)Peak memory usage: 88 MB
% 2.11/1.31 % (4164792)Instructions burned: 3 (million)
% 2.11/1.31 % (4164789)Refutation not found, incomplete strategy
% 2.11/1.31 % (4164789)------------------------------
% 2.11/1.31 % (4164789)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.11/1.31 % (4164789)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.11/1.31 % (4164789)CaDiCaL version: 2.1.3
% 2.11/1.31 % (4164789)Termination reason: Refutation not found, incomplete strategy
% 2.11/1.31 % (4164789)Time elapsed: 0.003 s
% 2.11/1.31 % (4164789)Peak memory usage: 88 MB
% 2.11/1.31 % (4164789)Instructions burned: 4 (million)
% 2.11/1.31 % (4164791)First to succeed.
% 2.11/1.31 % (4164791)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-4164781"
% 2.11/1.31 % (4164790)Instruction limit reached!
% 2.11/1.31 % (4164790)------------------------------
% 2.11/1.31 % (4164790)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.11/1.31 % (4164790)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.11/1.31 % (4164790)CaDiCaL version: 2.1.3
% 2.11/1.31 % (4164790)Termination reason: Instruction limit
% 2.11/1.31 % (4164790)Termination phase: Saturation
% 2.11/1.31 % (4164790)Time elapsed: 0.067 s
% 2.11/1.31 % (4164790)Peak memory usage: 89 MB
% 2.11/1.31 % (4164790)Instructions burned: 115 (million)
% 2.11/1.31 % (4164800)dis+1010_3_sil=8000:plsq=on:drc=off:fde=none:plsqc=1:bsd=on:plsqr=7,2:sos=on:spb=goal_then_units:random_seed=369481075:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 2.11/1.31 % (4164789)------------------------------
% 2.11/1.31 % (4164789)------------------------------
% 2.11/1.31 % (4164792)------------------------------
% 2.11/1.31 % (4164792)------------------------------
% 2.11/1.31 % (4164800)Refutation not found, incomplete strategy
% 2.11/1.31 % (4164800)------------------------------
% 2.11/1.31 % (4164800)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.11/1.31 % (4164800)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.11/1.31 % (4164800)CaDiCaL version: 2.1.3
% 2.11/1.31 % (4164800)Termination reason: Refutation not found, incomplete strategy
% 2.11/1.31 % (4164800)Time elapsed: 0.004 s
% 2.11/1.31 % (4164800)Peak memory usage: 88 MB
% 2.11/1.31 % (4164800)Instructions burned: 4 (million)
% 2.11/1.31 % (4164791)Refutation found. Thanks to Tanya!
% 2.11/1.31 % SZS status Unsatisfiable for theBenchmark
% 2.11/1.31 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/1.50 % (4164791)------------------------------
% 0.17/1.50 % (4164791)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.17/1.50 % (4164791)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/1.50 % (4164791)CaDiCaL version: 2.1.3
% 0.17/1.50 % (4164791)Termination reason: Refutation
% 0.17/1.50 % (4164791)Time elapsed: 0.020 s
% 0.17/1.50 % (4164791)Peak memory usage: 90 MB
% 0.17/1.50 % (4164791)Instructions burned: 32 (million)
% 0.17/1.50 % (4164791)------------------------------
% 0.17/1.50 % (4164791)------------------------------
% 0.17/1.50 % (4164781)Success in time 0.458 s
% 0.17/1.50 % Vampire exiting
%------------------------------------------------------------------------------