%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP246-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n008.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 10:13:26 AM UTC 2026
% Result : Unsatisfiable 3.09s 1.35s
% Output : Refutation 3.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 58
% Syntax : Number of formulae : 311 ( 19 unt; 20 def)
% Number of atoms : 901 ( 312 equ)
% Maximal formula atoms : 15 ( 2 avg)
% Number of connectives : 1065 ( 475 ~; 570 |; 0 &)
% ( 20 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 22 ( 20 usr; 21 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 12 con; 0-2 aty)
% Number of variables : 52 ( 0 sgn 52 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_identity) ).
fof(f2,axiom,
! [X0] : multiply(inverse(X0),X0) = identity,
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',associativity) ).
fof(f5,negated_conjecture,
( multiply(sk_c1,sk_c11) = sk_c10
| multiply(sk_c4,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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(f22,negated_conjecture,
( inverse(sk_c1) = sk_c11
| multiply(sk_c4,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_10) ).
fof(f23,plain,
( sk_c11 = inverse(sk_c1)
| sk_c10 = multiply(sk_c4,sk_c11) ),
inference(reorient_equations,[],[f22]) ).
fof(f24,negated_conjecture,
( inverse(sk_c1) = sk_c11
| inverse(sk_c4) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_11) ).
fof(f25,plain,
( sk_c11 = inverse(sk_c1)
| sk_c11 = inverse(sk_c4) ),
inference(reorient_equations,[],[f24]) ).
fof(f26,negated_conjecture,
( inverse(sk_c1) = sk_c11
| multiply(sk_c5,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_12) ).
fof(f27,plain,
( sk_c11 = inverse(sk_c1)
| multiply(sk_c5,sk_c10) = sk_c9 ),
inference(reorient_equations,[],[f26]) ).
fof(f28,negated_conjecture,
( inverse(sk_c1) = sk_c11
| inverse(sk_c5) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_13) ).
fof(f29,plain,
( sk_c11 = inverse(sk_c1)
| sk_c10 = inverse(sk_c5) ),
inference(reorient_equations,[],[f28]) ).
fof(f30,negated_conjecture,
( inverse(sk_c1) = sk_c11
| inverse(sk_c6) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_14) ).
fof(f31,plain,
( sk_c11 = inverse(sk_c1)
| sk_c11 = inverse(sk_c6) ),
inference(reorient_equations,[],[f30]) ).
fof(f32,negated_conjecture,
( inverse(sk_c1) = sk_c11
| multiply(sk_c6,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_15) ).
fof(f33,plain,
( sk_c11 = inverse(sk_c1)
| sk_c11 = multiply(sk_c6,sk_c10) ),
inference(reorient_equations,[],[f32]) ).
fof(f34,negated_conjecture,
( inverse(sk_c1) = sk_c11
| multiply(sk_c7,sk_c8) = sk_c10 ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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(f56,negated_conjecture,
( multiply(sk_c2,sk_c10) = sk_c9
| multiply(sk_c8,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_27) ).
fof(f57,plain,
( sk_c9 = multiply(sk_c2,sk_c10)
| sk_c10 = multiply(sk_c8,sk_c9) ),
inference(reorient_equations,[],[f56]) ).
fof(f62,negated_conjecture,
( inverse(sk_c2) = sk_c10
| multiply(sk_c5,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',prove_this_31) ).
fof(f65,plain,
( sk_c10 = inverse(sk_c2)
| sk_c10 = inverse(sk_c5) ),
inference(reorient_equations,[],[f64]) ).
fof(f66,negated_conjecture,
( inverse(sk_c2) = sk_c10
| inverse(sk_c6) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_32) ).
fof(f67,plain,
( sk_c10 = inverse(sk_c2)
| sk_c11 = inverse(sk_c6) ),
inference(reorient_equations,[],[f66]) ).
fof(f68,negated_conjecture,
( inverse(sk_c2) = sk_c10
| multiply(sk_c6,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_33) ).
fof(f69,plain,
( sk_c10 = inverse(sk_c2)
| sk_c11 = multiply(sk_c6,sk_c10) ),
inference(reorient_equations,[],[f68]) ).
fof(f70,negated_conjecture,
( inverse(sk_c2) = sk_c10
| multiply(sk_c7,sk_c8) = sk_c10 ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',prove_this_35) ).
fof(f73,plain,
( sk_c10 = inverse(sk_c2)
| sk_c8 = inverse(sk_c7) ),
inference(reorient_equations,[],[f72]) ).
fof(f74,negated_conjecture,
( inverse(sk_c2) = sk_c10
| multiply(sk_c8,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_36) ).
fof(f75,plain,
( sk_c10 = inverse(sk_c2)
| sk_c10 = multiply(sk_c8,sk_c9) ),
inference(reorient_equations,[],[f74]) ).
fof(f84,negated_conjecture,
( inverse(sk_c3) = sk_c11
| inverse(sk_c6) = sk_c11 ),
file('/export/starexec/sandbox2/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/sandbox2/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(f102,negated_conjecture,
( multiply(sk_c3,sk_c9) = sk_c11
| inverse(sk_c6) = sk_c11 ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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(inverse(X6),sk_c9)
| sk_c10 != multiply(X6,inverse(X6)) )
| ~ 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_c10 != inverse(X4)
| sk_c9 != multiply(X4,sk_c10) )
| ~ 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 != inverse(X2)
| sk_c11 != multiply(X2,sk_c9) )
| ~ 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(f132,definition,
( spl0_6
<=> sk_c10 = multiply(sk_c8,sk_c9) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f134,plain,
( sk_c10 = multiply(sk_c8,sk_c9)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f132]) ).
fof(f136,definition,
( spl0_7
<=> sk_c11 = multiply(sk_c3,sk_c9) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
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(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(f194,definition,
( spl0_17
<=> sk_c10 = inverse(sk_c2) ),
introduced(definition,[new_symbols(definition,[spl0_17])],[avatar_definition]) ).
fof(f196,plain,
( sk_c10 = inverse(sk_c2)
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f194]) ).
fof(f197,plain,
( spl0_6
| spl0_17 ),
inference(avatar_split_clause,[],[f75,f194,f132]) ).
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(f200,plain,
( spl0_10
| spl0_17 ),
inference(avatar_split_clause,[],[f69,f194,f151]) ).
fof(f201,plain,
( spl0_11
| spl0_17 ),
inference(avatar_split_clause,[],[f67,f194,f156]) ).
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(f210,plain,
( spl0_6
| spl0_18 ),
inference(avatar_split_clause,[],[f57,f207,f132]) ).
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(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(f226,plain,
( spl0_10
| spl0_19 ),
inference(avatar_split_clause,[],[f33,f220,f151]) ).
fof(f227,plain,
( spl0_11
| spl0_19 ),
inference(avatar_split_clause,[],[f31,f220,f156]) ).
fof(f228,plain,
( spl0_12
| spl0_19 ),
inference(avatar_split_clause,[],[f29,f220,f161]) ).
fof(f229,plain,
( spl0_13
| spl0_19 ),
inference(avatar_split_clause,[],[f27,f220,f166]) ).
fof(f230,plain,
( spl0_14
| spl0_19 ),
inference(avatar_split_clause,[],[f25,f220,f171]) ).
fof(f231,plain,
( spl0_15
| spl0_19 ),
inference(avatar_split_clause,[],[f23,f220,f176]) ).
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(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(f285,plain,
( ! [X0] : multiply(sk_c10,X0) = multiply(sk_c4,multiply(sk_c11,X0))
| ~ spl0_15 ),
inference(superposition,[],[f4,f178]) ).
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(f315,plain,
( sk_c11 = multiply(sk_c11,sk_c10)
| ~ spl0_19
| ~ spl0_20 ),
inference(superposition,[],[f292,f235]) ).
fof(f329,plain,
( multiply(sk_c1,sk_c11) = multiply(sk_c10,sk_c10)
| ~ spl0_19
| ~ spl0_20 ),
inference(superposition,[],[f283,f315]) ).
fof(f333,plain,
( sk_c10 = multiply(sk_c10,sk_c10)
| ~ spl0_19
| ~ spl0_20 ),
inference(forward_demodulation,[],[f329,f235]) ).
fof(f429,plain,
( sk_c1 = multiply(inverse(sk_c11),identity)
| ~ spl0_19 ),
inference(superposition,[],[f293,f263]) ).
fof(f430,plain,
( sk_c10 = multiply(inverse(sk_c11),sk_c11)
| ~ spl0_19
| ~ spl0_20 ),
inference(superposition,[],[f293,f315]) ).
fof(f433,plain,
( sk_c3 = multiply(inverse(sk_c11),identity)
| ~ spl0_16 ),
inference(superposition,[],[f293,f269]) ).
fof(f437,plain,
( sk_c11 = multiply(inverse(sk_c4),sk_c10)
| ~ spl0_15 ),
inference(superposition,[],[f293,f178]) ).
fof(f439,plain,
( sk_c10 = multiply(inverse(sk_c5),sk_c9)
| ~ spl0_13 ),
inference(superposition,[],[f293,f168]) ).
fof(f442,plain,
( sk_c8 = multiply(inverse(sk_c7),sk_c10)
| ~ spl0_9 ),
inference(superposition,[],[f293,f148]) ).
fof(f447,plain,
( sk_c10 = multiply(inverse(sk_c2),sk_c9)
| ~ spl0_18 ),
inference(superposition,[],[f293,f209]) ).
fof(f457,plain,
( sk_c10 = multiply(sk_c10,sk_c9)
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f447,f196]) ).
fof(f459,plain,
( sk_c8 = multiply(sk_c8,sk_c10)
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f442,f143]) ).
fof(f462,plain,
( sk_c10 = multiply(sk_c10,sk_c9)
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f439,f163]) ).
fof(f464,plain,
( sk_c11 = multiply(sk_c11,sk_c10)
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f437,f173]) ).
fof(f466,plain,
( identity = sk_c10
| ~ spl0_19
| ~ spl0_20 ),
inference(forward_demodulation,[],[f430,f3]) ).
fof(f477,plain,
( sk_c9 = multiply(inverse(sk_c10),sk_c10)
| ~ spl0_17
| ~ spl0_18 ),
inference(superposition,[],[f293,f457]) ).
fof(f479,plain,
( identity = sk_c9
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f477,f3]) ).
fof(f482,plain,
( sk_c10 = sk_c9
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19
| ~ spl0_20 ),
inference(forward_demodulation,[],[f479,f466]) ).
fof(f493,plain,
( sk_c10 = multiply(inverse(sk_c8),sk_c8)
| ~ spl0_8
| ~ spl0_9 ),
inference(superposition,[],[f293,f459]) ).
fof(f495,plain,
( identity = sk_c10
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f493,f3]) ).
fof(f506,plain,
( sk_c1 = multiply(inverse(sk_c11),sk_c10)
| ~ spl0_19
| ~ spl0_20 ),
inference(forward_demodulation,[],[f429,f466]) ).
fof(f519,plain,
( sk_c3 = multiply(inverse(sk_c11),sk_c10)
| ~ spl0_16
| ~ spl0_19
| ~ spl0_20 ),
inference(forward_demodulation,[],[f433,f466]) ).
fof(f594,plain,
( sk_c1 = sk_c3
| ~ spl0_16
| ~ spl0_19
| ~ spl0_20 ),
inference(forward_demodulation,[],[f519,f506]) ).
fof(f597,plain,
( sk_c11 = multiply(sk_c1,sk_c9)
| ~ spl0_7
| ~ spl0_16
| ~ spl0_19
| ~ spl0_20 ),
inference(superposition,[],[f138,f594]) ).
fof(f599,plain,
( sk_c11 = multiply(sk_c1,sk_c10)
| ~ spl0_7
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19
| ~ spl0_20 ),
inference(forward_demodulation,[],[f597,f482]) ).
fof(f613,plain,
( sk_c11 != sk_c11
| sk_c11 != inverse(sk_c1)
| ~ spl0_2
| ~ spl0_7
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19
| ~ spl0_20 ),
inference(superposition,[],[f120,f599]) ).
fof(f616,plain,
( sk_c11 != inverse(sk_c1)
| ~ spl0_2
| ~ spl0_7
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19
| ~ spl0_20 ),
inference(trivial_inequality_removal,[],[f613]) ).
fof(f618,plain,
( $false
| ~ spl0_2
| ~ spl0_7
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19
| ~ spl0_20 ),
inference(forward_subsumption_resolution,[],[f616,f222]) ).
fof(f619,plain,
( ~ spl0_2
| ~ spl0_7
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19
| ~ spl0_20 ),
inference(avatar_contradiction_clause,[],[f618]) ).
fof(f623,plain,
( sk_c10 != sk_c10
| sk_c11 != inverse(sk_c1)
| ~ spl0_4
| ~ spl0_20 ),
inference(superposition,[],[f126,f235]) ).
fof(f625,plain,
( sk_c10 != sk_c10
| sk_c11 != inverse(sk_c4)
| ~ spl0_4
| ~ spl0_15 ),
inference(superposition,[],[f126,f178]) ).
fof(f626,plain,
( sk_c11 != inverse(sk_c4)
| ~ spl0_4
| ~ spl0_15 ),
inference(trivial_inequality_removal,[],[f625]) ).
fof(f627,plain,
( sk_c11 != inverse(sk_c1)
| ~ spl0_4
| ~ spl0_20 ),
inference(trivial_inequality_removal,[],[f623]) ).
fof(f628,plain,
( $false
| ~ spl0_4
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f626,f173]) ).
fof(f629,plain,
( ~ spl0_4
| ~ spl0_14
| ~ spl0_15 ),
inference(avatar_contradiction_clause,[],[f628]) ).
fof(f631,plain,
( $false
| ~ spl0_4
| ~ spl0_19
| ~ spl0_20 ),
inference(forward_subsumption_resolution,[],[f627,f222]) ).
fof(f632,plain,
( ~ spl0_4
| ~ spl0_19
| ~ spl0_20 ),
inference(avatar_contradiction_clause,[],[f631]) ).
fof(f633,plain,
( ! [X4] :
( sk_c10 != inverse(X4)
| sk_c10 != multiply(X4,sk_c10) )
| ~ spl0_3
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19
| ~ spl0_20 ),
inference(forward_demodulation,[],[f123,f482]) ).
fof(f640,plain,
( sk_c10 != sk_c10
| sk_c10 != multiply(sk_c2,sk_c10)
| ~ spl0_3
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19
| ~ spl0_20 ),
inference(superposition,[],[f633,f196]) ).
fof(f642,plain,
( sk_c10 != multiply(sk_c2,sk_c10)
| ~ spl0_3
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19
| ~ spl0_20 ),
inference(trivial_inequality_removal,[],[f640]) ).
fof(f645,plain,
( sk_c10 != sk_c9
| ~ spl0_3
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19
| ~ spl0_20 ),
inference(forward_demodulation,[],[f642,f209]) ).
fof(f650,plain,
( $false
| ~ spl0_3
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19
| ~ spl0_20 ),
inference(forward_subsumption_resolution,[],[f645,f482]) ).
fof(f651,plain,
( ~ spl0_3
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19
| ~ spl0_20 ),
inference(avatar_contradiction_clause,[],[f650]) ).
fof(f657,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,f482]) ).
fof(f672,plain,
( sk_c10 != multiply(sk_c10,sk_c10)
| sk_c10 != multiply(sk_c2,sk_c10)
| ~ spl0_1
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19
| ~ spl0_20 ),
inference(superposition,[],[f657,f196]) ).
fof(f688,plain,
( sk_c10 != multiply(sk_c2,sk_c10)
| ~ spl0_1
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19
| ~ spl0_20 ),
inference(forward_subsumption_resolution,[],[f672,f333]) ).
fof(f696,plain,
( sk_c10 != sk_c9
| ~ spl0_1
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19
| ~ spl0_20 ),
inference(forward_demodulation,[],[f688,f209]) ).
fof(f704,plain,
( $false
| ~ spl0_1
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19
| ~ spl0_20 ),
inference(forward_subsumption_resolution,[],[f696,f482]) ).
fof(f705,plain,
( ~ spl0_1
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19
| ~ spl0_20 ),
inference(avatar_contradiction_clause,[],[f704]) ).
fof(f708,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,f482]) ).
fof(f709,plain,
( spl0_2
| ~ spl0_5
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19
| ~ spl0_20 ),
inference(avatar_split_clause,[],[f708,f233,f220,f207,f194,f128,f119]) ).
fof(f716,plain,
( sk_c10 = sk_c9
| ~ spl0_8
| ~ spl0_9
| ~ spl0_17
| ~ spl0_18 ),
inference(superposition,[],[f495,f479]) ).
fof(f754,plain,
( ! [X6] :
( sk_c10 != multiply(inverse(X6),sk_c10)
| sk_c10 != multiply(X6,inverse(X6)) )
| ~ spl0_1
| ~ spl0_8
| ~ spl0_9
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f117,f716]) ).
fof(f763,plain,
( sk_c10 != multiply(sk_c10,sk_c10)
| sk_c10 != multiply(sk_c2,sk_c10)
| ~ spl0_1
| ~ spl0_8
| ~ spl0_9
| ~ spl0_17
| ~ spl0_18 ),
inference(superposition,[],[f754,f196]) ).
fof(f776,plain,
( sk_c10 != sk_c9
| sk_c10 != multiply(sk_c10,sk_c10)
| ~ spl0_1
| ~ spl0_8
| ~ spl0_9
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f763,f209]) ).
fof(f785,plain,
( sk_c10 != multiply(sk_c10,sk_c10)
| ~ spl0_1
| ~ spl0_8
| ~ spl0_9
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[],[f776,f716]) ).
fof(f791,plain,
( multiply(sk_c4,sk_c11) = multiply(sk_c10,sk_c10)
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f285,f464]) ).
fof(f797,plain,
( sk_c10 = multiply(sk_c10,sk_c10)
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f791,f178]) ).
fof(f800,plain,
( $false
| ~ spl0_1
| ~ spl0_8
| ~ spl0_9
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[],[f797,f785]) ).
fof(f801,plain,
( ~ spl0_1
| ~ spl0_8
| ~ spl0_9
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17
| ~ spl0_18 ),
inference(avatar_contradiction_clause,[],[f800]) ).
fof(f810,plain,
( sk_c10 != sk_c10
| multiply(sk_c5,sk_c10) != sk_c9
| ~ spl0_3
| ~ spl0_12 ),
inference(superposition,[],[f123,f163]) ).
fof(f814,plain,
( multiply(sk_c5,sk_c10) != sk_c9
| ~ spl0_3
| ~ spl0_12 ),
inference(trivial_inequality_removal,[],[f810]) ).
fof(f815,plain,
( $false
| ~ spl0_3
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f814,f168]) ).
fof(f816,plain,
( ~ spl0_3
| ~ spl0_12
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[],[f815]) ).
fof(f819,plain,
( sk_c9 = multiply(inverse(sk_c10),sk_c10)
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f293,f462]) ).
fof(f821,plain,
( identity = sk_c9
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f819,f3]) ).
fof(f824,plain,
( sk_c10 = sk_c9
| ~ spl0_8
| ~ spl0_9
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f821,f495]) ).
fof(f828,plain,
( sk_c10 != multiply(sk_c8,sk_c9)
| sk_c10 != multiply(sk_c7,sk_c8)
| ~ spl0_1
| ~ spl0_8 ),
inference(superposition,[],[f117,f143]) ).
fof(f837,plain,
( sk_c10 != multiply(sk_c7,sk_c8)
| ~ spl0_1
| ~ spl0_6
| ~ spl0_8 ),
inference(forward_subsumption_resolution,[],[f828,f134]) ).
fof(f841,plain,
( $false
| ~ spl0_1
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_subsumption_resolution,[],[f837,f148]) ).
fof(f842,plain,
( ~ spl0_1
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(avatar_contradiction_clause,[],[f841]) ).
fof(f851,plain,
( ! [X2] :
( sk_c11 != multiply(X2,sk_c10)
| sk_c11 != inverse(X2) )
| ~ spl0_5
| ~ spl0_8
| ~ spl0_9
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f129,f824]) ).
fof(f852,plain,
( spl0_2
| ~ spl0_5
| ~ spl0_8
| ~ spl0_9
| ~ spl0_12
| ~ spl0_13 ),
inference(avatar_split_clause,[],[f851,f166,f161,f146,f141,f128,f119]) ).
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(s15,plain,
( spl0_10
| spl0_16 ),
inference(sat_conversion,[],[f187]) ).
cnf(s16,plain,
( spl0_11
| spl0_16 ),
inference(sat_conversion,[],[f188]) ).
cnf(s21,plain,
( spl0_6
| spl0_17 ),
inference(sat_conversion,[],[f197]) ).
cnf(s22,plain,
( spl0_8
| spl0_17 ),
inference(sat_conversion,[],[f198]) ).
cnf(s23,plain,
( spl0_9
| spl0_17 ),
inference(sat_conversion,[],[f199]) ).
cnf(s24,plain,
( spl0_10
| spl0_17 ),
inference(sat_conversion,[],[f200]) ).
cnf(s25,plain,
( spl0_11
| spl0_17 ),
inference(sat_conversion,[],[f201]) ).
cnf(s26,plain,
( spl0_12
| spl0_17 ),
inference(sat_conversion,[],[f202]) ).
cnf(s27,plain,
( spl0_13
| spl0_17 ),
inference(sat_conversion,[],[f203]) ).
cnf(s30,plain,
( spl0_6
| spl0_18 ),
inference(sat_conversion,[],[f210]) ).
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(s42,plain,
( spl0_10
| spl0_19 ),
inference(sat_conversion,[],[f226]) ).
cnf(s43,plain,
( spl0_11
| spl0_19 ),
inference(sat_conversion,[],[f227]) ).
cnf(s44,plain,
( spl0_12
| spl0_19 ),
inference(sat_conversion,[],[f228]) ).
cnf(s45,plain,
( spl0_13
| spl0_19 ),
inference(sat_conversion,[],[f229]) ).
cnf(s46,plain,
( spl0_14
| spl0_19 ),
inference(sat_conversion,[],[f230]) ).
cnf(s47,plain,
( spl0_15
| spl0_19 ),
inference(sat_conversion,[],[f231]) ).
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(s65,plain,
( ~ spl0_2
| ~ spl0_7
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19
| ~ spl0_20 ),
inference(sat_conversion,[],[f619]) ).
cnf(s66,plain,
( ~ spl0_4
| ~ spl0_14
| ~ spl0_15 ),
inference(sat_conversion,[],[f629]) ).
cnf(s67,plain,
( ~ spl0_4
| ~ spl0_19
| ~ spl0_20 ),
inference(sat_conversion,[],[f632]) ).
cnf(s69,plain,
( ~ spl0_3
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19
| ~ spl0_20 ),
inference(sat_conversion,[],[f651]) ).
cnf(s76,plain,
( ~ spl0_1
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19
| ~ spl0_20 ),
inference(sat_conversion,[],[f705]) ).
cnf(s78,plain,
( spl0_2
| ~ spl0_5
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19
| ~ spl0_20 ),
inference(sat_conversion,[],[f709]) ).
cnf(s87,plain,
( ~ spl0_1
| ~ spl0_8
| ~ spl0_9
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17
| ~ spl0_18 ),
inference(sat_conversion,[],[f801]) ).
cnf(s89,plain,
( ~ spl0_3
| ~ spl0_12
| ~ spl0_13 ),
inference(sat_conversion,[],[f816]) ).
cnf(s92,plain,
( ~ spl0_1
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(sat_conversion,[],[f842]) ).
cnf(s94,plain,
( spl0_2
| ~ spl0_5
| ~ spl0_8
| ~ spl0_9
| ~ spl0_12
| ~ spl0_13 ),
inference(sat_conversion,[],[f852]) ).
cnf(s96,plain,
( spl0_20
| ~ spl0_5
| spl0_2 ),
inference(rat,[],[s94,s49,s50,s53,s54]) ).
cnf(s97,plain,
( spl0_19
| ~ spl0_5
| spl0_2 ),
inference(rat,[],[s94,s40,s41,s44,s45]) ).
cnf(s98,plain,
( spl0_18
| ~ spl0_5
| spl0_2 ),
inference(rat,[],[s94,s31,s32,s35,s36]) ).
cnf(s99,plain,
( ~ spl0_18
| ~ spl0_20
| spl0_2
| ~ spl0_5
| ~ spl0_19 ),
inference(rat,[],[s94,s22,s23,s26,s27,s78]) ).
cnf(s100,plain,
( ~ spl0_5
| spl0_2 ),
inference(rat,[],[s99,s98,s97,s96]) ).
cnf(s101,plain,
( spl0_20
| ~ spl0_4 ),
inference(rat,[],[s66,s55,s56]) ).
cnf(s102,plain,
( ~ spl0_20
| ~ spl0_4 ),
inference(rat,[],[s66,s46,s47,s67]) ).
cnf(s103,plain,
~ spl0_4,
inference(rat,[],[s102,s101]) ).
cnf(s104,plain,
( spl0_20
| ~ spl0_3 ),
inference(rat,[],[s89,s53,s54]) ).
cnf(s105,plain,
( spl0_17
| ~ spl0_3 ),
inference(rat,[],[s89,s26,s27]) ).
cnf(s106,plain,
( spl0_18
| ~ spl0_3 ),
inference(rat,[],[s89,s35,s36]) ).
cnf(s107,plain,
( ~ spl0_18
| ~ spl0_20
| ~ spl0_3
| ~ spl0_17 ),
inference(rat,[],[s89,s44,s45,s69]) ).
cnf(s108,plain,
~ spl0_3,
inference(rat,[],[s107,s106,s105,s104]) ).
cnf(s109,plain,
( spl0_20
| spl0_1 ),
inference(rat,[],[s2,s94,s57,s49,s50,s51,s52,s53,s54,s108,s103]) ).
cnf(s110,plain,
( spl0_2
| spl0_1 ),
inference(rat,[],[s2,s100,s108,s103]) ).
cnf(s111,plain,
( spl0_11
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19
| spl0_1 ),
inference(rat,[],[s65,s7,s16,s109,s110]) ).
cnf(s112,plain,
( ~ spl0_17
| ~ spl0_18
| ~ spl0_19
| spl0_1 ),
inference(rat,[],[s65,s6,s15,s57,s111,s109,s110]) ).
cnf(s113,plain,
( spl0_17
| ~ spl0_2 ),
inference(rat,[],[s57,s24,s25]) ).
cnf(s114,plain,
( spl0_18
| ~ spl0_2 ),
inference(rat,[],[s57,s33,s34]) ).
cnf(s115,plain,
spl0_1,
inference(rat,[],[s57,s42,s43,s112,s114,s113,s110]) ).
cnf(s119,plain,
spl0_17,
inference(rat,[],[s92,s21,s22,s23,s115]) ).
cnf(s120,plain,
spl0_18,
inference(rat,[],[s92,s30,s31,s32,s115]) ).
cnf(s121,plain,
spl0_20,
inference(rat,[],[s87,s49,s50,s55,s56,s115,s119,s120]) ).
cnf(s122,plain,
~ spl0_19,
inference(rat,[],[s76,s120,s119,s115,s121]) ).
cnf(s123,plain,
spl0_15,
inference(rat,[],[s47,s122]) ).
cnf(s124,plain,
spl0_14,
inference(rat,[],[s46,s122]) ).
cnf(s129,plain,
spl0_9,
inference(rat,[],[s41,s122]) ).
cnf(s130,plain,
spl0_8,
inference(rat,[],[s40,s122]) ).
cnf(s133,plain,
$false,
inference(rat,[],[s87,s120,s124,s123,s119,s115,s130,s129]) ).
fof(f853,plain,
$false,
inference(avatar_sat_refutation,[],[s133]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP246-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.41 % Computer : n008.cluster.edu
% 0.12/0.41 % Model : x86_64 x86_64
% 0.12/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.41 % Memory : 8046.5625MB
% 0.12/0.41 % OS : Linux 6.8.0-71-generic
% 0.12/0.41 % CPULimit : 300
% 0.12/0.41 % WCLimit : 300
% 0.12/0.41 % DateTime : Sun Sep 27 09:39:39 UTC 2026
% 0.12/0.41 % CPUTime :
% 0.12/0.41 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.45 Running first-order theorem proving
% 0.12/0.45 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.09/1.35 % (984569)Input is clausal, will run a generic CNF schedule.
% 3.09/1.35 % (984577)lrs+10_1_sil=8000:sp=occurrence:random_seed=4019974352:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.09/1.35 % (984577)Instruction limit reached!
% 3.09/1.35 % (984577)------------------------------
% 3.09/1.35 % (984577)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.09/1.35 % (984577)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.09/1.35 % (984577)CaDiCaL version: 2.1.3
% 3.09/1.35 % (984577)Termination reason: Instruction limit
% 3.09/1.35 % (984577)Termination phase: Saturation
% 3.09/1.35 % (984577)Time elapsed: 0.030 s
% 3.09/1.35 % (984577)Peak memory usage: 89 MB
% 3.09/1.35 % (984577)Instructions burned: 109 (million)
% 3.09/1.35 % (984574)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=883249354:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.09/1.35 % (984580)dis-21_1_sil=8000:lcm=predicate:random_seed=1808893429: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)
% 3.09/1.35 % (984578)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1262365003:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.09/1.35 % (984579)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=130219711:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.09/1.35 % (984576)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=1539637923:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.09/1.35 % (984575)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=1525238594:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.09/1.35 % (984580)Refutation not found, incomplete strategy
% 3.09/1.35 % (984580)------------------------------
% 3.09/1.35 % (984580)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.09/1.35 % (984580)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.09/1.35 % (984580)CaDiCaL version: 2.1.3
% 3.09/1.35 % (984580)Termination reason: Refutation not found, incomplete strategy
% 3.09/1.35 % (984580)Time elapsed: 0.003 s
% 3.09/1.35 % (984580)Peak memory usage: 88 MB
% 3.09/1.35 % (984580)Instructions burned: 3 (million)
% 3.09/1.35 % (984579)First to succeed.
% 3.09/1.35 % (984579)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-984569"
% 3.09/1.35 % (984578)Instruction limit reached!
% 3.09/1.35 % (984578)------------------------------
% 3.09/1.35 % (984578)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.09/1.35 % (984578)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.09/1.35 % (984578)CaDiCaL version: 2.1.3
% 3.09/1.35 % (984578)Termination reason: Instruction limit
% 3.09/1.35 % (984578)Termination phase: Saturation
% 3.09/1.35 % (984578)Time elapsed: 0.065 s
% 3.09/1.35 % (984578)Peak memory usage: 89 MB
% 3.09/1.35 % (984578)Instructions burned: 116 (million)
% 3.09/1.35 % (984582)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=4149249145:i=143:sd=2:aac=none:ss=axioms:sgt=16_2998 on theBenchmark for (2998ds/143Mi)
% 3.09/1.35 % (984582)Instruction limit reached!
% 3.09/1.35 % (984582)------------------------------
% 3.09/1.35 % (984582)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.09/1.35 % (984582)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.09/1.35 % (984582)CaDiCaL version: 2.1.3
% 3.09/1.35 % (984582)Termination reason: Instruction limit
% 3.09/1.35 % (984582)Termination phase: Saturation
% 3.09/1.35 % (984582)Time elapsed: 0.039 s
% 3.09/1.35 % (984582)Peak memory usage: 89 MB
% 3.09/1.35 % (984582)Instructions burned: 144 (million)
% 3.09/1.35 % (984589)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=3784992716:st=3:avsq=on:s2a=on:i=189:s2at=1.2:avsqr=1,16:sd=2:bd=all:nm=64:ss=axioms:sgt=30_2997 on theBenchmark for (2997ds/189Mi)
% 3.09/1.35 % (984580)------------------------------
% 3.09/1.35 % (984580)------------------------------
% 3.09/1.35 % (984579)Refutation found. Thanks to Tanya!
% 3.09/1.35 % SZS status Unsatisfiable for theBenchmark
% 3.09/1.35 % SZS output start Proof for theBenchmark
% See solution above
% 3.84/1.54 % (984579)------------------------------
% 3.84/1.54 % (984579)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.84/1.54 % (984579)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.84/1.54 % (984579)CaDiCaL version: 2.1.3
% 3.84/1.54 % (984579)Termination reason: Refutation
% 3.84/1.54 % (984579)Time elapsed: 0.019 s
% 3.84/1.54 % (984579)Peak memory usage: 89 MB
% 3.84/1.54 % (984579)Instructions burned: 29 (million)
% 3.84/1.54 % (984579)------------------------------
% 3.84/1.54 % (984579)------------------------------
% 3.84/1.54 % (984569)Success in time 0.451 s
% 3.84/1.54 % Vampire exiting
%------------------------------------------------------------------------------