%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GRP246-1 : 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 : n019.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 10:17:16 AM UTC 2026
% Result : Unsatisfiable 0.15s 0.47s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 52
% Syntax : Number of formulae : 320 ( 18 unt; 19 def)
% Number of atoms : 1043 ( 322 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 1356 ( 633 ~; 704 |; 0 &)
% ( 19 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 21 ( 19 usr; 20 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 12 con; 0-2 aty)
% Number of variables : 63 ( 0 sgn 63 !; 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,
( multiply(sk_c1,sk_c11) = sk_c10
| multiply(sk_c4,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,plain,
( multiply(sk_c1,sk_c11) = sk_c10
| sk_c10 = multiply(sk_c4,sk_c11) ),
inference(reorient_equations,[],[f5]) ).
fof(f7,negated_conjecture,
( multiply(sk_c1,sk_c11) = sk_c10
| inverse(sk_c4) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_2) ).
fof(f8,plain,
( multiply(sk_c1,sk_c11) = sk_c10
| sk_c11 = inverse(sk_c4) ),
inference(reorient_equations,[],[f7]) ).
fof(f9,negated_conjecture,
( multiply(sk_c1,sk_c11) = sk_c10
| multiply(sk_c5,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_3) ).
fof(f10,negated_conjecture,
( multiply(sk_c1,sk_c11) = sk_c10
| inverse(sk_c5) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_4) ).
fof(f11,plain,
( multiply(sk_c1,sk_c11) = sk_c10
| sk_c10 = inverse(sk_c5) ),
inference(reorient_equations,[],[f10]) ).
fof(f12,negated_conjecture,
( multiply(sk_c1,sk_c11) = sk_c10
| inverse(sk_c6) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_5) ).
fof(f13,plain,
( multiply(sk_c1,sk_c11) = sk_c10
| sk_c11 = inverse(sk_c6) ),
inference(reorient_equations,[],[f12]) ).
fof(f14,negated_conjecture,
( multiply(sk_c1,sk_c11) = sk_c10
| multiply(sk_c6,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_6) ).
fof(f15,plain,
( multiply(sk_c1,sk_c11) = sk_c10
| sk_c11 = multiply(sk_c6,sk_c10) ),
inference(reorient_equations,[],[f14]) ).
fof(f16,negated_conjecture,
( multiply(sk_c1,sk_c11) = sk_c10
| multiply(sk_c7,sk_c8) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_7) ).
fof(f17,plain,
( multiply(sk_c1,sk_c11) = sk_c10
| sk_c10 = multiply(sk_c7,sk_c8) ),
inference(reorient_equations,[],[f16]) ).
fof(f18,negated_conjecture,
( multiply(sk_c1,sk_c11) = sk_c10
| inverse(sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_8) ).
fof(f19,plain,
( multiply(sk_c1,sk_c11) = sk_c10
| sk_c8 = inverse(sk_c7) ),
inference(reorient_equations,[],[f18]) ).
fof(f24,negated_conjecture,
( inverse(sk_c1) = sk_c11
| inverse(sk_c4) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_11) ).
fof(f25,plain,
( sk_c11 = inverse(sk_c1)
| sk_c11 = inverse(sk_c4) ),
inference(reorient_equations,[],[f24]) ).
fof(f34,negated_conjecture,
( inverse(sk_c1) = sk_c11
| multiply(sk_c7,sk_c8) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_16) ).
fof(f35,plain,
( sk_c11 = inverse(sk_c1)
| sk_c10 = multiply(sk_c7,sk_c8) ),
inference(reorient_equations,[],[f34]) ).
fof(f36,negated_conjecture,
( inverse(sk_c1) = sk_c11
| inverse(sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_17) ).
fof(f37,plain,
( sk_c11 = inverse(sk_c1)
| sk_c8 = inverse(sk_c7) ),
inference(reorient_equations,[],[f36]) ).
fof(f44,negated_conjecture,
( multiply(sk_c2,sk_c10) = sk_c9
| multiply(sk_c5,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_21) ).
fof(f45,plain,
( sk_c9 = multiply(sk_c2,sk_c10)
| multiply(sk_c5,sk_c10) = sk_c9 ),
inference(reorient_equations,[],[f44]) ).
fof(f46,negated_conjecture,
( multiply(sk_c2,sk_c10) = sk_c9
| inverse(sk_c5) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_22) ).
fof(f47,plain,
( sk_c9 = multiply(sk_c2,sk_c10)
| sk_c10 = inverse(sk_c5) ),
inference(reorient_equations,[],[f46]) ).
fof(f48,negated_conjecture,
( multiply(sk_c2,sk_c10) = sk_c9
| inverse(sk_c6) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_23) ).
fof(f49,plain,
( sk_c9 = multiply(sk_c2,sk_c10)
| sk_c11 = inverse(sk_c6) ),
inference(reorient_equations,[],[f48]) ).
fof(f50,negated_conjecture,
( multiply(sk_c2,sk_c10) = sk_c9
| multiply(sk_c6,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_24) ).
fof(f51,plain,
( sk_c9 = multiply(sk_c2,sk_c10)
| sk_c11 = multiply(sk_c6,sk_c10) ),
inference(reorient_equations,[],[f50]) ).
fof(f52,negated_conjecture,
( multiply(sk_c2,sk_c10) = sk_c9
| multiply(sk_c7,sk_c8) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_25) ).
fof(f53,plain,
( sk_c9 = multiply(sk_c2,sk_c10)
| sk_c10 = multiply(sk_c7,sk_c8) ),
inference(reorient_equations,[],[f52]) ).
fof(f54,negated_conjecture,
( multiply(sk_c2,sk_c10) = sk_c9
| inverse(sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_26) ).
fof(f55,plain,
( sk_c9 = multiply(sk_c2,sk_c10)
| sk_c8 = inverse(sk_c7) ),
inference(reorient_equations,[],[f54]) ).
fof(f62,negated_conjecture,
( inverse(sk_c2) = sk_c10
| multiply(sk_c5,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_30) ).
fof(f63,plain,
( sk_c10 = inverse(sk_c2)
| multiply(sk_c5,sk_c10) = sk_c9 ),
inference(reorient_equations,[],[f62]) ).
fof(f64,negated_conjecture,
( inverse(sk_c2) = sk_c10
| inverse(sk_c5) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_31) ).
fof(f65,plain,
( sk_c10 = inverse(sk_c2)
| sk_c10 = inverse(sk_c5) ),
inference(reorient_equations,[],[f64]) ).
fof(f70,negated_conjecture,
( inverse(sk_c2) = sk_c10
| multiply(sk_c7,sk_c8) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_34) ).
fof(f71,plain,
( sk_c10 = inverse(sk_c2)
| sk_c10 = multiply(sk_c7,sk_c8) ),
inference(reorient_equations,[],[f70]) ).
fof(f72,negated_conjecture,
( inverse(sk_c2) = sk_c10
| inverse(sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_35) ).
fof(f73,plain,
( sk_c10 = inverse(sk_c2)
| sk_c8 = inverse(sk_c7) ),
inference(reorient_equations,[],[f72]) ).
fof(f80,negated_conjecture,
( inverse(sk_c3) = sk_c11
| multiply(sk_c5,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_39) ).
fof(f81,plain,
( sk_c11 = inverse(sk_c3)
| multiply(sk_c5,sk_c10) = sk_c9 ),
inference(reorient_equations,[],[f80]) ).
fof(f82,negated_conjecture,
( inverse(sk_c3) = sk_c11
| inverse(sk_c5) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_40) ).
fof(f83,plain,
( sk_c11 = inverse(sk_c3)
| sk_c10 = inverse(sk_c5) ),
inference(reorient_equations,[],[f82]) ).
fof(f84,negated_conjecture,
( inverse(sk_c3) = sk_c11
| inverse(sk_c6) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_41) ).
fof(f85,plain,
( sk_c11 = inverse(sk_c3)
| sk_c11 = inverse(sk_c6) ),
inference(reorient_equations,[],[f84]) ).
fof(f86,negated_conjecture,
( inverse(sk_c3) = sk_c11
| multiply(sk_c6,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_42) ).
fof(f87,plain,
( sk_c11 = inverse(sk_c3)
| sk_c11 = multiply(sk_c6,sk_c10) ),
inference(reorient_equations,[],[f86]) ).
fof(f88,negated_conjecture,
( inverse(sk_c3) = sk_c11
| multiply(sk_c7,sk_c8) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_43) ).
fof(f89,plain,
( sk_c11 = inverse(sk_c3)
| sk_c10 = multiply(sk_c7,sk_c8) ),
inference(reorient_equations,[],[f88]) ).
fof(f90,negated_conjecture,
( inverse(sk_c3) = sk_c11
| inverse(sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_44) ).
fof(f91,plain,
( sk_c11 = inverse(sk_c3)
| sk_c8 = inverse(sk_c7) ),
inference(reorient_equations,[],[f90]) ).
fof(f102,negated_conjecture,
( multiply(sk_c3,sk_c9) = sk_c11
| inverse(sk_c6) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_50) ).
fof(f103,plain,
( sk_c11 = multiply(sk_c3,sk_c9)
| sk_c11 = inverse(sk_c6) ),
inference(reorient_equations,[],[f102]) ).
fof(f104,negated_conjecture,
( multiply(sk_c3,sk_c9) = sk_c11
| multiply(sk_c6,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_51) ).
fof(f105,plain,
( sk_c11 = multiply(sk_c3,sk_c9)
| sk_c11 = multiply(sk_c6,sk_c10) ),
inference(reorient_equations,[],[f104]) ).
fof(f112,negated_conjecture,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( multiply(X0,sk_c11) != sk_c10
| inverse(X0) != sk_c11
| multiply(X1,sk_c10) != sk_c9
| inverse(X1) != sk_c10
| inverse(X2) != sk_c11
| multiply(X2,sk_c9) != sk_c11
| multiply(X3,sk_c11) != sk_c10
| inverse(X3) != sk_c11
| multiply(X4,sk_c10) != sk_c9
| inverse(X4) != sk_c10
| inverse(X5) != sk_c11
| multiply(X5,sk_c10) != sk_c11
| multiply(X6,X7) != sk_c10
| inverse(X6) != X7
| multiply(X7,sk_c9) != sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_55) ).
fof(f113,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( sk_c10 != multiply(X0,sk_c11)
| inverse(X0) != sk_c11
| sk_c9 != multiply(X1,sk_c10)
| sk_c10 != inverse(X1)
| sk_c11 != inverse(X2)
| sk_c11 != multiply(X2,sk_c9)
| sk_c10 != multiply(X3,sk_c11)
| sk_c11 != inverse(X3)
| sk_c9 != multiply(X4,sk_c10)
| sk_c10 != inverse(X4)
| sk_c11 != inverse(X5)
| sk_c11 != multiply(X5,sk_c10)
| sk_c10 != multiply(X6,X7)
| inverse(X6) != X7
| sk_c10 != multiply(X7,sk_c9) ),
inference(reorient_equations,[],[f112]) ).
fof(f114,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( sk_c10 != multiply(X0,sk_c11)
| inverse(X0) != sk_c11
| sk_c9 != multiply(X1,sk_c10)
| sk_c10 != inverse(X1)
| sk_c11 != inverse(X2)
| sk_c11 != multiply(X2,sk_c9)
| sk_c10 != multiply(X3,sk_c11)
| sk_c11 != inverse(X3)
| sk_c9 != multiply(X4,sk_c10)
| sk_c10 != inverse(X4)
| sk_c11 != inverse(X5)
| sk_c11 != multiply(X5,sk_c10)
| sk_c10 != multiply(X6,inverse(X6))
| sk_c10 != multiply(inverse(X6),sk_c9) ),
inference(equality_resolution,[],[f113]) ).
fof(f116,definition,
( spl0_1
<=> ! [X6] :
( sk_c10 != multiply(X6,inverse(X6))
| sk_c10 != multiply(inverse(X6),sk_c9) ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f117,plain,
( ! [X6] :
( sk_c10 != multiply(X6,inverse(X6))
| sk_c10 != multiply(inverse(X6),sk_c9) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f116]) ).
fof(f119,definition,
( spl0_2
<=> ! [X5] :
( sk_c11 != inverse(X5)
| sk_c11 != multiply(X5,sk_c10) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f120,plain,
( ! [X5] :
( sk_c11 != multiply(X5,sk_c10)
| sk_c11 != inverse(X5) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f119]) ).
fof(f122,definition,
( spl0_3
<=> ! [X4] :
( sk_c9 != multiply(X4,sk_c10)
| sk_c10 != inverse(X4) ) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f123,plain,
( ! [X4] :
( sk_c9 != multiply(X4,sk_c10)
| sk_c10 != inverse(X4) )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f122]) ).
fof(f125,definition,
( spl0_4
<=> ! [X3] :
( sk_c10 != multiply(X3,sk_c11)
| sk_c11 != inverse(X3) ) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f126,plain,
( ! [X3] :
( sk_c10 != multiply(X3,sk_c11)
| sk_c11 != inverse(X3) )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f125]) ).
fof(f128,definition,
( spl0_5
<=> ! [X2] :
( sk_c11 != inverse(X2)
| sk_c11 != multiply(X2,sk_c9) ) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f129,plain,
( ! [X2] :
( sk_c11 != multiply(X2,sk_c9)
| sk_c11 != inverse(X2) )
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f128]) ).
fof(f130,plain,
( spl0_1
| spl0_2
| spl0_3
| spl0_4
| spl0_5
| spl0_3
| spl0_4 ),
inference(avatar_split_clause,[],[f114,f125,f122,f128,f125,f122,f119,f116]) ).
fof(f136,definition,
( spl0_7
<=> sk_c11 = multiply(sk_c3,sk_c9) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f137,plain,
( sk_c11 != multiply(sk_c3,sk_c9)
| spl0_7 ),
inference(avatar_component_clause,[],[f136]) ).
fof(f138,plain,
( sk_c11 = multiply(sk_c3,sk_c9)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f136]) ).
fof(f141,definition,
( spl0_8
<=> sk_c8 = inverse(sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f143,plain,
( sk_c8 = inverse(sk_c7)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f141]) ).
fof(f146,definition,
( spl0_9
<=> sk_c10 = multiply(sk_c7,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f148,plain,
( sk_c10 = multiply(sk_c7,sk_c8)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f146]) ).
fof(f151,definition,
( spl0_10
<=> sk_c11 = multiply(sk_c6,sk_c10) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f153,plain,
( sk_c11 = multiply(sk_c6,sk_c10)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f151]) ).
fof(f154,plain,
( spl0_10
| spl0_7 ),
inference(avatar_split_clause,[],[f105,f136,f151]) ).
fof(f156,definition,
( spl0_11
<=> sk_c11 = inverse(sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f158,plain,
( sk_c11 = inverse(sk_c6)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f156]) ).
fof(f159,plain,
( spl0_11
| spl0_7 ),
inference(avatar_split_clause,[],[f103,f136,f156]) ).
fof(f161,definition,
( spl0_12
<=> sk_c10 = inverse(sk_c5) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f163,plain,
( sk_c10 = inverse(sk_c5)
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f161]) ).
fof(f166,definition,
( spl0_13
<=> multiply(sk_c5,sk_c10) = sk_c9 ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f168,plain,
( multiply(sk_c5,sk_c10) = sk_c9
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f166]) ).
fof(f171,definition,
( spl0_14
<=> sk_c11 = inverse(sk_c4) ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
fof(f173,plain,
( sk_c11 = inverse(sk_c4)
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f171]) ).
fof(f176,definition,
( spl0_15
<=> sk_c10 = multiply(sk_c4,sk_c11) ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
fof(f178,plain,
( sk_c10 = multiply(sk_c4,sk_c11)
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f176]) ).
fof(f181,definition,
( spl0_16
<=> sk_c11 = inverse(sk_c3) ),
introduced(definition,[new_symbols(definition,[spl0_16])],[avatar_definition]) ).
fof(f183,plain,
( sk_c11 = inverse(sk_c3)
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f181]) ).
fof(f185,plain,
( spl0_8
| spl0_16 ),
inference(avatar_split_clause,[],[f91,f181,f141]) ).
fof(f186,plain,
( spl0_9
| spl0_16 ),
inference(avatar_split_clause,[],[f89,f181,f146]) ).
fof(f187,plain,
( spl0_10
| spl0_16 ),
inference(avatar_split_clause,[],[f87,f181,f151]) ).
fof(f188,plain,
( spl0_11
| spl0_16 ),
inference(avatar_split_clause,[],[f85,f181,f156]) ).
fof(f189,plain,
( spl0_12
| spl0_16 ),
inference(avatar_split_clause,[],[f83,f181,f161]) ).
fof(f190,plain,
( spl0_13
| spl0_16 ),
inference(avatar_split_clause,[],[f81,f181,f166]) ).
fof(f194,definition,
( spl0_17
<=> sk_c10 = inverse(sk_c2) ),
introduced(definition,[new_symbols(definition,[spl0_17])],[avatar_definition]) ).
fof(f195,plain,
( sk_c10 != inverse(sk_c2)
| spl0_17 ),
inference(avatar_component_clause,[],[f194]) ).
fof(f196,plain,
( sk_c10 = inverse(sk_c2)
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f194]) ).
fof(f198,plain,
( spl0_8
| spl0_17 ),
inference(avatar_split_clause,[],[f73,f194,f141]) ).
fof(f199,plain,
( spl0_9
| spl0_17 ),
inference(avatar_split_clause,[],[f71,f194,f146]) ).
fof(f202,plain,
( spl0_12
| spl0_17 ),
inference(avatar_split_clause,[],[f65,f194,f161]) ).
fof(f203,plain,
( spl0_13
| spl0_17 ),
inference(avatar_split_clause,[],[f63,f194,f166]) ).
fof(f207,definition,
( spl0_18
<=> sk_c9 = multiply(sk_c2,sk_c10) ),
introduced(definition,[new_symbols(definition,[spl0_18])],[avatar_definition]) ).
fof(f209,plain,
( sk_c9 = multiply(sk_c2,sk_c10)
| ~ spl0_18 ),
inference(avatar_component_clause,[],[f207]) ).
fof(f211,plain,
( spl0_8
| spl0_18 ),
inference(avatar_split_clause,[],[f55,f207,f141]) ).
fof(f212,plain,
( spl0_9
| spl0_18 ),
inference(avatar_split_clause,[],[f53,f207,f146]) ).
fof(f213,plain,
( spl0_10
| spl0_18 ),
inference(avatar_split_clause,[],[f51,f207,f151]) ).
fof(f214,plain,
( spl0_11
| spl0_18 ),
inference(avatar_split_clause,[],[f49,f207,f156]) ).
fof(f215,plain,
( spl0_12
| spl0_18 ),
inference(avatar_split_clause,[],[f47,f207,f161]) ).
fof(f216,plain,
( spl0_13
| spl0_18 ),
inference(avatar_split_clause,[],[f45,f207,f166]) ).
fof(f220,definition,
( spl0_19
<=> sk_c11 = inverse(sk_c1) ),
introduced(definition,[new_symbols(definition,[spl0_19])],[avatar_definition]) ).
fof(f221,plain,
( sk_c11 != inverse(sk_c1)
| spl0_19 ),
inference(avatar_component_clause,[],[f220]) ).
fof(f222,plain,
( sk_c11 = inverse(sk_c1)
| ~ spl0_19 ),
inference(avatar_component_clause,[],[f220]) ).
fof(f224,plain,
( spl0_8
| spl0_19 ),
inference(avatar_split_clause,[],[f37,f220,f141]) ).
fof(f225,plain,
( spl0_9
| spl0_19 ),
inference(avatar_split_clause,[],[f35,f220,f146]) ).
fof(f230,plain,
( spl0_14
| spl0_19 ),
inference(avatar_split_clause,[],[f25,f220,f171]) ).
fof(f233,definition,
( spl0_20
<=> multiply(sk_c1,sk_c11) = sk_c10 ),
introduced(definition,[new_symbols(definition,[spl0_20])],[avatar_definition]) ).
fof(f235,plain,
( multiply(sk_c1,sk_c11) = sk_c10
| ~ spl0_20 ),
inference(avatar_component_clause,[],[f233]) ).
fof(f237,plain,
( spl0_8
| spl0_20 ),
inference(avatar_split_clause,[],[f19,f233,f141]) ).
fof(f238,plain,
( spl0_9
| spl0_20 ),
inference(avatar_split_clause,[],[f17,f233,f146]) ).
fof(f239,plain,
( spl0_10
| spl0_20 ),
inference(avatar_split_clause,[],[f15,f233,f151]) ).
fof(f240,plain,
( spl0_11
| spl0_20 ),
inference(avatar_split_clause,[],[f13,f233,f156]) ).
fof(f241,plain,
( spl0_12
| spl0_20 ),
inference(avatar_split_clause,[],[f11,f233,f161]) ).
fof(f242,plain,
( spl0_13
| spl0_20 ),
inference(avatar_split_clause,[],[f9,f233,f166]) ).
fof(f243,plain,
( spl0_14
| spl0_20 ),
inference(avatar_split_clause,[],[f8,f233,f171]) ).
fof(f244,plain,
( spl0_15
| spl0_20 ),
inference(avatar_split_clause,[],[f6,f233,f176]) ).
fof(f246,plain,
( sk_c11 != sk_c11
| sk_c11 != inverse(sk_c6)
| ~ spl0_2
| ~ spl0_10 ),
inference(superposition,[],[f120,f153]) ).
fof(f247,plain,
( sk_c11 != inverse(sk_c6)
| ~ spl0_2
| ~ spl0_10 ),
inference(trivial_inequality_removal,[],[f246]) ).
fof(f248,plain,
( $false
| ~ spl0_2
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f247,f158]) ).
fof(f249,plain,
( ~ spl0_2
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_contradiction_clause,[],[f248]) ).
fof(f263,plain,
( identity = multiply(sk_c11,sk_c1)
| ~ spl0_19 ),
inference(superposition,[],[f3,f222]) ).
fof(f264,plain,
( identity = multiply(sk_c11,sk_c4)
| ~ spl0_14 ),
inference(superposition,[],[f3,f173]) ).
fof(f265,plain,
( identity = multiply(sk_c10,sk_c5)
| ~ spl0_12 ),
inference(superposition,[],[f3,f163]) ).
fof(f266,plain,
( identity = multiply(sk_c11,sk_c6)
| ~ spl0_11 ),
inference(superposition,[],[f3,f158]) ).
fof(f269,plain,
( identity = multiply(sk_c11,sk_c3)
| ~ spl0_16 ),
inference(superposition,[],[f3,f183]) ).
fof(f282,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[],[f4,f3]) ).
fof(f283,plain,
( ! [X0] : multiply(sk_c1,multiply(sk_c11,X0)) = multiply(sk_c10,X0)
| ~ spl0_20 ),
inference(superposition,[],[f4,f235]) ).
fof(f284,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c11,multiply(sk_c1,X0))
| ~ spl0_19 ),
inference(superposition,[],[f4,f263]) ).
fof(f292,plain,
( ! [X0] : multiply(sk_c11,multiply(sk_c1,X0)) = X0
| ~ spl0_19 ),
inference(forward_demodulation,[],[f284,f1]) ).
fof(f293,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f282,f1]) ).
fof(f298,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c10,multiply(sk_c5,X0))
| ~ spl0_12 ),
inference(superposition,[],[f4,f265]) ).
fof(f299,plain,
( ! [X0] : multiply(sk_c10,multiply(sk_c5,X0)) = X0
| ~ spl0_12 ),
inference(forward_demodulation,[],[f298,f1]) ).
fof(f309,plain,
( multiply(sk_c1,identity) = multiply(sk_c10,sk_c4)
| ~ spl0_14
| ~ spl0_20 ),
inference(superposition,[],[f283,f264]) ).
fof(f317,plain,
( sk_c11 = multiply(sk_c11,sk_c10)
| ~ spl0_19
| ~ spl0_20 ),
inference(superposition,[],[f292,f235]) ).
fof(f334,plain,
( multiply(sk_c1,sk_c11) = multiply(sk_c10,sk_c10)
| ~ spl0_19
| ~ spl0_20 ),
inference(superposition,[],[f283,f317]) ).
fof(f335,plain,
( sk_c11 != sk_c11
| sk_c11 != inverse(sk_c11)
| ~ spl0_2
| ~ spl0_19
| ~ spl0_20 ),
inference(superposition,[],[f120,f317]) ).
fof(f337,plain,
( sk_c11 != inverse(sk_c11)
| ~ spl0_2
| ~ spl0_19
| ~ spl0_20 ),
inference(trivial_inequality_removal,[],[f335]) ).
fof(f338,plain,
( sk_c10 = multiply(sk_c10,sk_c10)
| ~ spl0_19
| ~ spl0_20 ),
inference(forward_demodulation,[],[f334,f235]) ).
fof(f384,plain,
( sk_c10 = multiply(sk_c10,sk_c9)
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f299,f168]) ).
fof(f444,plain,
! [X0] : multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[],[f293,f3]) ).
fof(f445,plain,
! [X0,X1] : multiply(X1,X0) = multiply(inverse(inverse(X1)),X0),
inference(superposition,[],[f293,f293]) ).
fof(f450,plain,
( sk_c1 = multiply(inverse(sk_c11),identity)
| ~ spl0_19 ),
inference(superposition,[],[f293,f263]) ).
fof(f453,plain,
( sk_c6 = multiply(inverse(sk_c11),identity)
| ~ spl0_11 ),
inference(superposition,[],[f293,f266]) ).
fof(f454,plain,
( sk_c3 = multiply(inverse(sk_c11),identity)
| ~ spl0_16 ),
inference(superposition,[],[f293,f269]) ).
fof(f456,plain,
( sk_c10 = multiply(inverse(sk_c10),sk_c10)
| ~ spl0_19
| ~ spl0_20 ),
inference(superposition,[],[f293,f338]) ).
fof(f458,plain,
( sk_c9 = multiply(inverse(sk_c10),sk_c10)
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f293,f384]) ).
fof(f465,plain,
( sk_c8 = multiply(inverse(sk_c7),sk_c10)
| ~ spl0_9 ),
inference(superposition,[],[f293,f148]) ).
fof(f470,plain,
( sk_c10 = multiply(inverse(sk_c2),sk_c9)
| ~ spl0_18 ),
inference(superposition,[],[f293,f209]) ).
fof(f480,plain,
( sk_c10 = multiply(sk_c10,sk_c9)
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f470,f196]) ).
fof(f482,plain,
( sk_c8 = multiply(sk_c8,sk_c10)
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f465,f143]) ).
fof(f488,plain,
( identity = sk_c9
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f458,f3]) ).
fof(f490,plain,
( identity = sk_c10
| ~ spl0_19
| ~ spl0_20 ),
inference(forward_demodulation,[],[f456,f3]) ).
fof(f491,plain,
( sk_c6 = sk_c3
| ~ spl0_11
| ~ spl0_16 ),
inference(forward_demodulation,[],[f453,f454]) ).
fof(f497,plain,
! [X0] : multiply(X0,identity) = X0,
inference(forward_demodulation,[],[f444,f445]) ).
fof(f529,plain,
( sk_c10 = multiply(inverse(sk_c8),sk_c8)
| ~ spl0_8
| ~ spl0_9 ),
inference(superposition,[],[f293,f482]) ).
fof(f531,plain,
( identity = sk_c10
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f529,f3]) ).
fof(f555,plain,
( sk_c9 = multiply(inverse(sk_c10),sk_c10)
| ~ spl0_17
| ~ spl0_18 ),
inference(superposition,[],[f293,f480]) ).
fof(f557,plain,
( identity = sk_c9
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f555,f3]) ).
fof(f576,plain,
( ! [X0] : multiply(X0,sk_c10) = X0
| ~ spl0_19
| ~ spl0_20 ),
inference(forward_demodulation,[],[f497,f490]) ).
fof(f577,plain,
( sk_c10 = sk_c9
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19
| ~ spl0_20 ),
inference(forward_demodulation,[],[f557,f490]) ).
fof(f579,plain,
( sk_c11 = multiply(sk_c3,sk_c10)
| ~ spl0_7
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19
| ~ spl0_20 ),
inference(superposition,[],[f138,f577]) ).
fof(f587,plain,
( sk_c11 = sk_c3
| ~ spl0_7
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19
| ~ spl0_20 ),
inference(forward_demodulation,[],[f579,f576]) ).
fof(f599,plain,
( sk_c9 = sk_c2
| ~ spl0_18
| ~ spl0_19
| ~ spl0_20 ),
inference(superposition,[],[f576,f209]) ).
fof(f617,plain,
( sk_c9 = sk_c2
| ~ spl0_18
| ~ spl0_19
| ~ spl0_20 ),
inference(superposition,[],[f209,f576]) ).
fof(f618,plain,
( sk_c10 = sk_c2
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19
| ~ spl0_20 ),
inference(forward_demodulation,[],[f617,f577]) ).
fof(f643,plain,
( sk_c1 = sk_c3
| ~ spl0_16
| ~ spl0_19 ),
inference(superposition,[],[f450,f454]) ).
fof(f648,plain,
( sk_c1 = sk_c11
| ~ spl0_7
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19
| ~ spl0_20 ),
inference(forward_demodulation,[],[f643,f587]) ).
fof(f661,plain,
( sk_c11 = inverse(sk_c11)
| ~ spl0_7
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19
| ~ spl0_20 ),
inference(superposition,[],[f222,f648]) ).
fof(f662,plain,
( $false
| ~ spl0_2
| ~ spl0_7
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19
| ~ spl0_20 ),
inference(forward_subsumption_resolution,[],[f661,f337]) ).
fof(f663,plain,
( ~ spl0_2
| ~ spl0_7
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19
| ~ spl0_20 ),
inference(avatar_contradiction_clause,[],[f662]) ).
fof(f666,plain,
( ! [X6] :
( sk_c10 != multiply(inverse(X6),sk_c10)
| sk_c10 != multiply(X6,inverse(X6)) )
| ~ spl0_1
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19
| ~ spl0_20 ),
inference(forward_demodulation,[],[f117,f577]) ).
fof(f667,plain,
( sk_c11 = sk_c6
| ~ spl0_10
| ~ spl0_19
| ~ spl0_20 ),
inference(forward_demodulation,[],[f153,f576]) ).
fof(f668,plain,
( ! [X6] :
( sk_c10 != multiply(X6,inverse(X6))
| sk_c10 != inverse(X6) )
| ~ spl0_1
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19
| ~ spl0_20 ),
inference(forward_demodulation,[],[f666,f576]) ).
fof(f680,plain,
( sk_c10 != multiply(sk_c2,sk_c10)
| sk_c10 != sk_c10
| ~ spl0_1
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19
| ~ spl0_20 ),
inference(superposition,[],[f668,f196]) ).
fof(f685,plain,
( sk_c10 != multiply(sk_c2,sk_c10)
| ~ spl0_1
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19
| ~ spl0_20 ),
inference(trivial_inequality_removal,[],[f680]) ).
fof(f687,plain,
( sk_c10 != sk_c9
| ~ spl0_1
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19
| ~ spl0_20 ),
inference(forward_demodulation,[],[f685,f209]) ).
fof(f691,plain,
( $false
| ~ spl0_1
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19
| ~ spl0_20 ),
inference(forward_subsumption_resolution,[],[f687,f577]) ).
fof(f692,plain,
( ~ spl0_1
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19
| ~ spl0_20 ),
inference(avatar_contradiction_clause,[],[f691]) ).
fof(f709,plain,
( sk_c10 != sk_c10
| sk_c11 != inverse(sk_c1)
| ~ spl0_4
| ~ spl0_20 ),
inference(superposition,[],[f126,f235]) ).
fof(f711,plain,
( sk_c10 != sk_c10
| sk_c11 != inverse(sk_c4)
| ~ spl0_4
| ~ spl0_15 ),
inference(superposition,[],[f126,f178]) ).
fof(f712,plain,
( sk_c11 != inverse(sk_c4)
| ~ spl0_4
| ~ spl0_15 ),
inference(trivial_inequality_removal,[],[f711]) ).
fof(f713,plain,
( sk_c11 != inverse(sk_c1)
| ~ spl0_4
| ~ spl0_20 ),
inference(trivial_inequality_removal,[],[f709]) ).
fof(f714,plain,
( $false
| ~ spl0_4
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f712,f173]) ).
fof(f715,plain,
( ~ spl0_4
| ~ spl0_14
| ~ spl0_15 ),
inference(avatar_contradiction_clause,[],[f714]) ).
fof(f717,plain,
( $false
| ~ spl0_4
| ~ spl0_19
| ~ spl0_20 ),
inference(forward_subsumption_resolution,[],[f713,f222]) ).
fof(f718,plain,
( ~ spl0_4
| ~ spl0_19
| ~ spl0_20 ),
inference(avatar_contradiction_clause,[],[f717]) ).
fof(f725,plain,
( ! [X4] :
( sk_c9 != X4
| sk_c10 != inverse(X4) )
| ~ spl0_3
| ~ spl0_19
| ~ spl0_20 ),
inference(forward_demodulation,[],[f123,f576]) ).
fof(f726,plain,
( ! [X4] :
( sk_c10 != inverse(X4)
| sk_c10 != X4 )
| ~ spl0_3
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19
| ~ spl0_20 ),
inference(forward_demodulation,[],[f725,f577]) ).
fof(f739,plain,
( sk_c10 != sk_c10
| sk_c10 != sk_c2
| ~ spl0_3
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19
| ~ spl0_20 ),
inference(superposition,[],[f726,f196]) ).
fof(f741,plain,
( sk_c10 != sk_c2
| ~ spl0_3
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19
| ~ spl0_20 ),
inference(trivial_inequality_removal,[],[f739]) ).
fof(f742,plain,
( $false
| ~ spl0_3
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19
| ~ spl0_20 ),
inference(forward_subsumption_resolution,[],[f741,f618]) ).
fof(f743,plain,
( ~ spl0_3
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19
| ~ spl0_20 ),
inference(avatar_contradiction_clause,[],[f742]) ).
fof(f747,plain,
( ! [X2] :
( sk_c11 != multiply(X2,sk_c10)
| sk_c11 != inverse(X2) )
| ~ spl0_5
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19
| ~ spl0_20 ),
inference(forward_demodulation,[],[f129,f577]) ).
fof(f748,plain,
( ! [X2] :
( sk_c11 != inverse(X2)
| sk_c11 != X2 )
| ~ spl0_5
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19
| ~ spl0_20 ),
inference(forward_demodulation,[],[f747,f576]) ).
fof(f751,plain,
( sk_c11 != sk_c11
| sk_c1 != sk_c11
| ~ spl0_5
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19
| ~ spl0_20 ),
inference(superposition,[],[f748,f222]) ).
fof(f758,plain,
( sk_c1 != sk_c11
| ~ spl0_5
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19
| ~ spl0_20 ),
inference(trivial_inequality_removal,[],[f751]) ).
fof(f763,plain,
( $false
| ~ spl0_5
| ~ spl0_7
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19
| ~ spl0_20 ),
inference(forward_subsumption_resolution,[],[f758,f648]) ).
fof(f764,plain,
( ~ spl0_5
| ~ spl0_7
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19
| ~ spl0_20 ),
inference(avatar_contradiction_clause,[],[f763]) ).
fof(f767,plain,
( sk_c11 != multiply(sk_c3,sk_c10)
| spl0_7
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19
| ~ spl0_20 ),
inference(forward_demodulation,[],[f137,f577]) ).
fof(f769,plain,
( sk_c11 = sk_c3
| ~ spl0_10
| ~ spl0_11
| ~ spl0_16
| ~ spl0_19
| ~ spl0_20 ),
inference(forward_demodulation,[],[f491,f667]) ).
fof(f776,plain,
( sk_c11 != sk_c3
| spl0_7
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19
| ~ spl0_20 ),
inference(forward_demodulation,[],[f767,f576]) ).
fof(f778,plain,
( $false
| spl0_7
| ~ spl0_10
| ~ spl0_11
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19
| ~ spl0_20 ),
inference(forward_subsumption_resolution,[],[f776,f769]) ).
fof(f779,plain,
( spl0_7
| ~ spl0_10
| ~ spl0_11
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19
| ~ spl0_20 ),
inference(avatar_contradiction_clause,[],[f778]) ).
fof(f786,plain,
( sk_c10 = sk_c9
| ~ spl0_8
| ~ spl0_9
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f488,f531]) ).
fof(f796,plain,
( identity = multiply(sk_c10,sk_c5)
| ~ spl0_12 ),
inference(superposition,[],[f3,f163]) ).
fof(f802,plain,
( ! [X0] : multiply(sk_c10,X0) = X0
| ~ spl0_8
| ~ spl0_9 ),
inference(superposition,[],[f1,f531]) ).
fof(f949,plain,
( identity = sk_c5
| ~ spl0_8
| ~ spl0_9
| ~ spl0_12 ),
inference(forward_demodulation,[],[f796,f802]) ).
fof(f952,plain,
( sk_c10 = sk_c5
| ~ spl0_8
| ~ spl0_9
| ~ spl0_12 ),
inference(forward_demodulation,[],[f949,f531]) ).
fof(f954,plain,
( sk_c10 = inverse(sk_c10)
| ~ spl0_8
| ~ spl0_9
| ~ spl0_12 ),
inference(superposition,[],[f163,f952]) ).
fof(f963,plain,
( sk_c4 = multiply(sk_c1,identity)
| ~ spl0_8
| ~ spl0_9
| ~ spl0_14
| ~ spl0_20 ),
inference(forward_demodulation,[],[f309,f802]) ).
fof(f969,plain,
( sk_c1 = sk_c4
| ~ spl0_8
| ~ spl0_9
| ~ spl0_14
| ~ spl0_20 ),
inference(forward_demodulation,[],[f963,f497]) ).
fof(f974,plain,
( sk_c11 = inverse(sk_c1)
| ~ spl0_8
| ~ spl0_9
| ~ spl0_14
| ~ spl0_20 ),
inference(superposition,[],[f173,f969]) ).
fof(f975,plain,
( $false
| ~ spl0_8
| ~ spl0_9
| ~ spl0_14
| spl0_19
| ~ spl0_20 ),
inference(forward_subsumption_resolution,[],[f974,f221]) ).
fof(f976,plain,
( ~ spl0_8
| ~ spl0_9
| ~ spl0_14
| spl0_19
| ~ spl0_20 ),
inference(avatar_contradiction_clause,[],[f975]) ).
fof(f978,plain,
( sk_c10 = sk_c2
| ~ spl0_8
| ~ spl0_9
| ~ spl0_12
| ~ spl0_13
| ~ spl0_18
| ~ spl0_19
| ~ spl0_20 ),
inference(forward_demodulation,[],[f599,f786]) ).
fof(f985,plain,
( sk_c10 != inverse(sk_c10)
| ~ spl0_8
| ~ spl0_9
| ~ spl0_12
| ~ spl0_13
| spl0_17
| ~ spl0_18
| ~ spl0_19
| ~ spl0_20 ),
inference(superposition,[],[f195,f978]) ).
fof(f990,plain,
( $false
| ~ spl0_8
| ~ spl0_9
| ~ spl0_12
| ~ spl0_13
| spl0_17
| ~ spl0_18
| ~ spl0_19
| ~ spl0_20 ),
inference(forward_subsumption_resolution,[],[f985,f954]) ).
fof(f991,plain,
( ~ spl0_8
| ~ spl0_9
| ~ spl0_12
| ~ spl0_13
| spl0_17
| ~ spl0_18
| ~ spl0_19
| ~ spl0_20 ),
inference(avatar_contradiction_clause,[],[f990]) ).
fof(f1019,plain,
( ! [X0] :
( sk_c11 != multiply(X0,sk_c10)
| inverse(X0) != sk_c11 )
| ~ spl0_5
| ~ spl0_8
| ~ spl0_9
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f129,f786]) ).
fof(f1025,plain,
( spl0_2
| ~ spl0_5
| ~ spl0_8
| ~ spl0_9
| ~ spl0_12
| ~ spl0_13 ),
inference(avatar_split_clause,[],[f1019,f166,f161,f146,f141,f128,f119]) ).
fof(f1026,plain,
( ! [X4] :
( sk_c10 != multiply(X4,sk_c10)
| sk_c10 != inverse(X4) )
| ~ spl0_3
| ~ spl0_8
| ~ spl0_9
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f123,f786]) ).
fof(f1032,plain,
( identity != sk_c10
| sk_c10 != inverse(inverse(sk_c10))
| ~ spl0_3
| ~ spl0_8
| ~ spl0_9
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f1026,f3]) ).
fof(f1040,plain,
( sk_c10 != inverse(inverse(sk_c10))
| ~ spl0_3
| ~ spl0_8
| ~ spl0_9
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f1032,f531]) ).
fof(f1044,plain,
( sk_c10 != inverse(sk_c10)
| ~ spl0_3
| ~ spl0_8
| ~ spl0_9
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f1040,f954]) ).
fof(f1047,plain,
( $false
| ~ spl0_3
| ~ spl0_8
| ~ spl0_9
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f1044,f954]) ).
fof(f1048,plain,
( ~ spl0_3
| ~ spl0_8
| ~ spl0_9
| ~ spl0_12
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[],[f1047]) ).
fof(f1049,plain,
( ! [X6] :
( sk_c10 != multiply(inverse(X6),sk_c10)
| sk_c10 != multiply(X6,inverse(X6)) )
| ~ spl0_1
| ~ spl0_8
| ~ spl0_9
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f117,f786]) ).
fof(f1063,plain,
( identity != sk_c10
| sk_c10 != multiply(sk_c10,inverse(sk_c10))
| ~ spl0_1
| ~ spl0_8
| ~ spl0_9
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f1049,f3]) ).
fof(f1083,plain,
( sk_c10 != multiply(sk_c10,inverse(sk_c10))
| ~ spl0_1
| ~ spl0_8
| ~ spl0_9
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f1063,f531]) ).
fof(f1100,plain,
( sk_c10 != inverse(sk_c10)
| ~ spl0_1
| ~ spl0_8
| ~ spl0_9
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f1083,f802]) ).
fof(f1109,plain,
( $false
| ~ spl0_1
| ~ spl0_8
| ~ spl0_9
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f1100,f954]) ).
fof(f1110,plain,
( ~ spl0_1
| ~ spl0_8
| ~ spl0_9
| ~ spl0_12
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[],[f1109]) ).
cnf(s1,plain,
( spl0_3
| spl0_4
| spl0_1
| spl0_3
| spl0_2
| spl0_4
| spl0_5 ),
inference(sat_conversion,[],[f130]) ).
cnf(s2,plain,
( spl0_1
| spl0_2
| spl0_3
| spl0_4
| spl0_5 ),
inference(rat,[],[s1]) ).
cnf(s6,plain,
( spl0_7
| spl0_10 ),
inference(sat_conversion,[],[f154]) ).
cnf(s7,plain,
( spl0_7
| spl0_11 ),
inference(sat_conversion,[],[f159]) ).
cnf(s13,plain,
( spl0_8
| spl0_16 ),
inference(sat_conversion,[],[f185]) ).
cnf(s14,plain,
( spl0_9
| spl0_16 ),
inference(sat_conversion,[],[f186]) ).
cnf(s15,plain,
( spl0_10
| spl0_16 ),
inference(sat_conversion,[],[f187]) ).
cnf(s16,plain,
( spl0_11
| spl0_16 ),
inference(sat_conversion,[],[f188]) ).
cnf(s17,plain,
( spl0_12
| spl0_16 ),
inference(sat_conversion,[],[f189]) ).
cnf(s18,plain,
( spl0_13
| spl0_16 ),
inference(sat_conversion,[],[f190]) ).
cnf(s22,plain,
( spl0_8
| spl0_17 ),
inference(sat_conversion,[],[f198]) ).
cnf(s23,plain,
( spl0_9
| spl0_17 ),
inference(sat_conversion,[],[f199]) ).
cnf(s26,plain,
( spl0_12
| spl0_17 ),
inference(sat_conversion,[],[f202]) ).
cnf(s27,plain,
( spl0_13
| spl0_17 ),
inference(sat_conversion,[],[f203]) ).
cnf(s31,plain,
( spl0_8
| spl0_18 ),
inference(sat_conversion,[],[f211]) ).
cnf(s32,plain,
( spl0_9
| spl0_18 ),
inference(sat_conversion,[],[f212]) ).
cnf(s33,plain,
( spl0_10
| spl0_18 ),
inference(sat_conversion,[],[f213]) ).
cnf(s34,plain,
( spl0_11
| spl0_18 ),
inference(sat_conversion,[],[f214]) ).
cnf(s35,plain,
( spl0_12
| spl0_18 ),
inference(sat_conversion,[],[f215]) ).
cnf(s36,plain,
( spl0_13
| spl0_18 ),
inference(sat_conversion,[],[f216]) ).
cnf(s40,plain,
( spl0_8
| spl0_19 ),
inference(sat_conversion,[],[f224]) ).
cnf(s41,plain,
( spl0_9
| spl0_19 ),
inference(sat_conversion,[],[f225]) ).
cnf(s46,plain,
( spl0_14
| spl0_19 ),
inference(sat_conversion,[],[f230]) ).
cnf(s49,plain,
( spl0_8
| spl0_20 ),
inference(sat_conversion,[],[f237]) ).
cnf(s50,plain,
( spl0_9
| spl0_20 ),
inference(sat_conversion,[],[f238]) ).
cnf(s51,plain,
( spl0_10
| spl0_20 ),
inference(sat_conversion,[],[f239]) ).
cnf(s52,plain,
( spl0_11
| spl0_20 ),
inference(sat_conversion,[],[f240]) ).
cnf(s53,plain,
( spl0_12
| spl0_20 ),
inference(sat_conversion,[],[f241]) ).
cnf(s54,plain,
( spl0_13
| spl0_20 ),
inference(sat_conversion,[],[f242]) ).
cnf(s55,plain,
( spl0_14
| spl0_20 ),
inference(sat_conversion,[],[f243]) ).
cnf(s56,plain,
( spl0_15
| spl0_20 ),
inference(sat_conversion,[],[f244]) ).
cnf(s57,plain,
( ~ spl0_2
| ~ spl0_10
| ~ spl0_11 ),
inference(sat_conversion,[],[f249]) ).
cnf(s66,plain,
( ~ spl0_2
| ~ spl0_7
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19
| ~ spl0_20 ),
inference(sat_conversion,[],[f663]) ).
cnf(s68,plain,
( ~ spl0_1
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19
| ~ spl0_20 ),
inference(sat_conversion,[],[f692]) ).
cnf(s70,plain,
( ~ spl0_4
| ~ spl0_14
| ~ spl0_15 ),
inference(sat_conversion,[],[f715]) ).
cnf(s71,plain,
( ~ spl0_4
| ~ spl0_19
| ~ spl0_20 ),
inference(sat_conversion,[],[f718]) ).
cnf(s74,plain,
( ~ spl0_3
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19
| ~ spl0_20 ),
inference(sat_conversion,[],[f743]) ).
cnf(s77,plain,
( ~ spl0_5
| ~ spl0_7
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19
| ~ spl0_20 ),
inference(sat_conversion,[],[f764]) ).
cnf(s79,plain,
( spl0_7
| ~ spl0_10
| ~ spl0_11
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19
| ~ spl0_20 ),
inference(sat_conversion,[],[f779]) ).
cnf(s95,plain,
( ~ spl0_8
| ~ spl0_9
| ~ spl0_14
| spl0_19
| ~ spl0_20 ),
inference(sat_conversion,[],[f976]) ).
cnf(s96,plain,
( ~ spl0_8
| ~ spl0_9
| ~ spl0_12
| ~ spl0_13
| spl0_17
| ~ spl0_18
| ~ spl0_19
| ~ spl0_20 ),
inference(sat_conversion,[],[f991]) ).
cnf(s97,plain,
( spl0_2
| ~ spl0_5
| ~ spl0_8
| ~ spl0_9
| ~ spl0_12
| ~ spl0_13 ),
inference(sat_conversion,[],[f1025]) ).
cnf(s101,plain,
( ~ spl0_3
| ~ spl0_8
| ~ spl0_9
| ~ spl0_12
| ~ spl0_13 ),
inference(sat_conversion,[],[f1048]) ).
cnf(s108,plain,
( ~ spl0_1
| ~ spl0_8
| ~ spl0_9
| ~ spl0_12
| ~ spl0_13 ),
inference(sat_conversion,[],[f1110]) ).
cnf(s110,plain,
( spl0_20
| ~ spl0_5
| spl0_2 ),
inference(rat,[],[s97,s49,s50,s53,s54]) ).
cnf(s111,plain,
( spl0_19
| ~ spl0_20 ),
inference(rat,[],[s95,s40,s41,s46]) ).
cnf(s112,plain,
( spl0_18
| ~ spl0_5
| spl0_2 ),
inference(rat,[],[s97,s31,s32,s35,s36]) ).
cnf(s113,plain,
( spl0_17
| ~ spl0_18
| ~ spl0_20 ),
inference(rat,[],[s96,s22,s23,s26,s27,s111]) ).
cnf(s114,plain,
( spl0_16
| ~ spl0_5
| spl0_2 ),
inference(rat,[],[s97,s13,s14,s17,s18]) ).
cnf(s115,plain,
( ~ spl0_16
| ~ spl0_20
| ~ spl0_5
| ~ spl0_17
| ~ spl0_19
| ~ spl0_18 ),
inference(rat,[],[s79,s6,s7,s77]) ).
cnf(s116,plain,
( ~ spl0_5
| spl0_2 ),
inference(rat,[],[s115,s114,s113,s112,s111,s110]) ).
cnf(s117,plain,
( spl0_20
| ~ spl0_4 ),
inference(rat,[],[s70,s55,s56]) ).
cnf(s118,plain,
~ spl0_4,
inference(rat,[],[s71,s111,s117]) ).
cnf(s119,plain,
( spl0_20
| ~ spl0_3 ),
inference(rat,[],[s101,s49,s50,s53,s54]) ).
cnf(s120,plain,
( spl0_18
| ~ spl0_3 ),
inference(rat,[],[s101,s31,s32,s35,s36]) ).
cnf(s121,plain,
( ~ spl0_18
| ~ spl0_20
| ~ spl0_3
| ~ spl0_17 ),
inference(rat,[],[s111,s74]) ).
cnf(s122,plain,
~ spl0_3,
inference(rat,[],[s121,s113,s120,s119]) ).
cnf(s123,plain,
( spl0_20
| spl0_1 ),
inference(rat,[],[s2,s97,s57,s49,s50,s51,s52,s53,s54,s122,s118]) ).
cnf(s124,plain,
( spl0_16
| ~ spl0_2 ),
inference(rat,[],[s57,s15,s16]) ).
cnf(s125,plain,
( spl0_18
| ~ spl0_2 ),
inference(rat,[],[s57,s33,s34]) ).
cnf(s126,plain,
( ~ spl0_5
| ~ spl0_20 ),
inference(rat,[],[s115,s113,s125,s124,s116,s111]) ).
cnf(s127,plain,
( ~ spl0_17
| ~ spl0_20
| ~ spl0_2
| ~ spl0_16
| ~ spl0_18
| ~ spl0_19 ),
inference(rat,[],[s79,s6,s7,s66]) ).
cnf(s128,plain,
spl0_1,
inference(rat,[],[s127,s113,s125,s124,s2,s126,s111,s123,s122,s118]) ).
cnf(s129,plain,
spl0_20,
inference(rat,[],[s108,s49,s50,s53,s54,s128]) ).
cnf(s130,plain,
spl0_19,
inference(rat,[],[s111,s129]) ).
cnf(s132,plain,
spl0_18,
inference(rat,[],[s108,s31,s32,s35,s36,s128]) ).
cnf(s133,plain,
spl0_17,
inference(rat,[],[s113,s129,s132]) ).
cnf(s134,plain,
$false,
inference(rat,[],[s68,s129,s130,s128,s132,s133]) ).
fof(f1111,plain,
$false,
inference(avatar_sat_refutation,[],[s134]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP246-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.39 % Computer : n019.cluster.edu
% 0.10/0.39 % Model : x86_64 x86_64
% 0.10/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.39 % Memory : 8046.5625MB
% 0.10/0.39 % OS : Linux 6.8.0-71-generic
% 0.10/0.39 % CPULimit : 300
% 0.10/0.39 % WCLimit : 300
% 0.10/0.39 % DateTime : Sun Sep 27 09:39:07 UTC 2026
% 0.10/0.39 % CPUTime :
% 0.10/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.42 Running first-order model finding
% 0.10/0.42 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
% 0.15/0.47 % (2841257)Will run a generic schedule for satisfiability detection.
% 0.15/0.47 % (2841266)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=156839604:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.15/0.47 % (2841263)% WARNING: option uhcvi not known.
% 0.15/0.47 % (2841262)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2548322097_2999 on theBenchmark for (2999ds/0Mi)
% 0.15/0.47 % (2841263)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1833336584:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.15/0.47 % (2841264)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=747733522:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.15/0.47 % (2841265)dis+10_1_sil=32000:sp=arity:random_seed=2085800406:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.15/0.47 % (2841267)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2649736707:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.15/0.47 % (2841268)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3576064849:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.15/0.47 % (2841266) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2841257-2841266"...
% 0.15/0.47 % TRYING [1]
% 0.15/0.47 % TRYING [2]
% 0.15/0.47 % (2841266)...printing done.
% 0.15/0.47 % (2841266)Refutation found. Thanks to Tanya!
% 0.15/0.47 % SZS status Unsatisfiable for theBenchmark
% 0.15/0.47 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.48 % (2841266)------------------------------
% 0.15/0.48 % (2841266)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.15/0.48 % (2841266)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.15/0.48 % (2841266)CaDiCaL version: 2.1.3
% 0.15/0.48 % (2841266)Termination reason: Refutation
% 0.15/0.48 % (2841266)Time elapsed: 0.013 s
% 0.15/0.48 % (2841266)Peak memory usage: 12 MB
% 0.15/0.48 % (2841266)Instructions burned: 35 (million)
% 0.15/0.48 % (2841257)Success in time 0.042 s
% 0.15/0.48 % Vampire exiting
%------------------------------------------------------------------------------