%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP362-1 : 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 : n004.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 10:13:45 AM UTC 2026
% Result : Unsatisfiable 2.66s 1.27s
% Output : Refutation 3.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 56
% Syntax : Number of formulae : 302 ( 15 unt; 19 def)
% Number of atoms : 963 ( 331 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 1210 ( 549 ~; 642 |; 0 &)
% ( 19 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 21 ( 19 usr; 20 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 11 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(f19,negated_conjecture,
( multiply(sk_c9,sk_c8) = sk_c10
| inverse(sk_c7) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_8) ).
fof(f20,plain,
( multiply(sk_c9,sk_c8) = sk_c10
| sk_c10 = inverse(sk_c7) ),
inference(reorient_equations,[],[f19]) ).
fof(f21,negated_conjecture,
( multiply(sk_c9,sk_c8) = sk_c10
| multiply(sk_c7,sk_c8) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_9) ).
fof(f22,plain,
( multiply(sk_c9,sk_c8) = sk_c10
| sk_c10 = multiply(sk_c7,sk_c8) ),
inference(reorient_equations,[],[f21]) ).
fof(f23,negated_conjecture,
( inverse(sk_c9) = sk_c10
| inverse(sk_c10) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_10) ).
fof(f24,plain,
( sk_c10 = inverse(sk_c9)
| sk_c9 = inverse(sk_c10) ),
inference(reorient_equations,[],[f23]) ).
fof(f25,negated_conjecture,
( inverse(sk_c9) = sk_c10
| multiply(sk_c10,sk_c4) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_11) ).
fof(f26,plain,
( sk_c10 = inverse(sk_c9)
| sk_c9 = multiply(sk_c10,sk_c4) ),
inference(reorient_equations,[],[f25]) ).
fof(f27,negated_conjecture,
( inverse(sk_c9) = sk_c10
| multiply(sk_c3,sk_c10) = sk_c4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_12) ).
fof(f28,plain,
( sk_c10 = inverse(sk_c9)
| sk_c4 = multiply(sk_c3,sk_c10) ),
inference(reorient_equations,[],[f27]) ).
fof(f29,negated_conjecture,
( inverse(sk_c9) = sk_c10
| inverse(sk_c3) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_13) ).
fof(f30,plain,
( sk_c10 = inverse(sk_c9)
| sk_c10 = inverse(sk_c3) ),
inference(reorient_equations,[],[f29]) ).
fof(f43,negated_conjecture,
( multiply(sk_c10,sk_c8) = sk_c9
| multiply(sk_c10,sk_c4) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_20) ).
fof(f44,plain,
( sk_c9 = multiply(sk_c10,sk_c8)
| sk_c9 = multiply(sk_c10,sk_c4) ),
inference(reorient_equations,[],[f43]) ).
fof(f45,negated_conjecture,
( multiply(sk_c10,sk_c8) = sk_c9
| multiply(sk_c3,sk_c10) = sk_c4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_21) ).
fof(f46,plain,
( sk_c9 = multiply(sk_c10,sk_c8)
| sk_c4 = multiply(sk_c3,sk_c10) ),
inference(reorient_equations,[],[f45]) ).
fof(f47,negated_conjecture,
( multiply(sk_c10,sk_c8) = sk_c9
| inverse(sk_c3) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_22) ).
fof(f48,plain,
( sk_c9 = multiply(sk_c10,sk_c8)
| sk_c10 = inverse(sk_c3) ),
inference(reorient_equations,[],[f47]) ).
fof(f49,negated_conjecture,
( multiply(sk_c10,sk_c8) = sk_c9
| multiply(sk_c5,sk_c6) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_23) ).
fof(f50,plain,
( sk_c9 = multiply(sk_c10,sk_c8)
| sk_c8 = multiply(sk_c5,sk_c6) ),
inference(reorient_equations,[],[f49]) ).
fof(f51,negated_conjecture,
( multiply(sk_c10,sk_c8) = sk_c9
| inverse(sk_c5) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_24) ).
fof(f52,plain,
( sk_c9 = multiply(sk_c10,sk_c8)
| sk_c6 = inverse(sk_c5) ),
inference(reorient_equations,[],[f51]) ).
fof(f59,negated_conjecture,
( multiply(sk_c10,sk_c2) = sk_c9
| inverse(sk_c10) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_28) ).
fof(f60,plain,
( sk_c9 = multiply(sk_c10,sk_c2)
| sk_c9 = inverse(sk_c10) ),
inference(reorient_equations,[],[f59]) ).
fof(f61,negated_conjecture,
( multiply(sk_c10,sk_c2) = sk_c9
| multiply(sk_c10,sk_c4) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_29) ).
fof(f62,plain,
( sk_c9 = multiply(sk_c10,sk_c2)
| sk_c9 = multiply(sk_c10,sk_c4) ),
inference(reorient_equations,[],[f61]) ).
fof(f63,negated_conjecture,
( multiply(sk_c10,sk_c2) = sk_c9
| multiply(sk_c3,sk_c10) = sk_c4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_30) ).
fof(f64,plain,
( sk_c9 = multiply(sk_c10,sk_c2)
| sk_c4 = multiply(sk_c3,sk_c10) ),
inference(reorient_equations,[],[f63]) ).
fof(f65,negated_conjecture,
( multiply(sk_c10,sk_c2) = sk_c9
| inverse(sk_c3) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_31) ).
fof(f66,plain,
( sk_c9 = multiply(sk_c10,sk_c2)
| sk_c10 = inverse(sk_c3) ),
inference(reorient_equations,[],[f65]) ).
fof(f67,negated_conjecture,
( multiply(sk_c10,sk_c2) = sk_c9
| multiply(sk_c5,sk_c6) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_32) ).
fof(f68,plain,
( sk_c9 = multiply(sk_c10,sk_c2)
| sk_c8 = multiply(sk_c5,sk_c6) ),
inference(reorient_equations,[],[f67]) ).
fof(f69,negated_conjecture,
( multiply(sk_c10,sk_c2) = sk_c9
| inverse(sk_c5) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_33) ).
fof(f70,plain,
( sk_c9 = multiply(sk_c10,sk_c2)
| sk_c6 = inverse(sk_c5) ),
inference(reorient_equations,[],[f69]) ).
fof(f73,negated_conjecture,
( multiply(sk_c10,sk_c2) = sk_c9
| inverse(sk_c7) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_35) ).
fof(f74,plain,
( sk_c9 = multiply(sk_c10,sk_c2)
| sk_c10 = inverse(sk_c7) ),
inference(reorient_equations,[],[f73]) ).
fof(f75,negated_conjecture,
( multiply(sk_c10,sk_c2) = sk_c9
| multiply(sk_c7,sk_c8) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_36) ).
fof(f76,plain,
( sk_c9 = multiply(sk_c10,sk_c2)
| sk_c10 = multiply(sk_c7,sk_c8) ),
inference(reorient_equations,[],[f75]) ).
fof(f77,negated_conjecture,
( multiply(sk_c1,sk_c10) = sk_c2
| inverse(sk_c10) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_37) ).
fof(f78,plain,
( sk_c2 = multiply(sk_c1,sk_c10)
| sk_c9 = inverse(sk_c10) ),
inference(reorient_equations,[],[f77]) ).
fof(f79,negated_conjecture,
( multiply(sk_c1,sk_c10) = sk_c2
| multiply(sk_c10,sk_c4) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_38) ).
fof(f80,plain,
( sk_c2 = multiply(sk_c1,sk_c10)
| sk_c9 = multiply(sk_c10,sk_c4) ),
inference(reorient_equations,[],[f79]) ).
fof(f81,negated_conjecture,
( multiply(sk_c1,sk_c10) = sk_c2
| multiply(sk_c3,sk_c10) = sk_c4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_39) ).
fof(f82,plain,
( sk_c2 = multiply(sk_c1,sk_c10)
| sk_c4 = multiply(sk_c3,sk_c10) ),
inference(reorient_equations,[],[f81]) ).
fof(f83,negated_conjecture,
( multiply(sk_c1,sk_c10) = sk_c2
| inverse(sk_c3) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_40) ).
fof(f84,plain,
( sk_c2 = multiply(sk_c1,sk_c10)
| sk_c10 = inverse(sk_c3) ),
inference(reorient_equations,[],[f83]) ).
fof(f85,negated_conjecture,
( multiply(sk_c1,sk_c10) = sk_c2
| multiply(sk_c5,sk_c6) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_41) ).
fof(f86,plain,
( sk_c2 = multiply(sk_c1,sk_c10)
| sk_c8 = multiply(sk_c5,sk_c6) ),
inference(reorient_equations,[],[f85]) ).
fof(f87,negated_conjecture,
( multiply(sk_c1,sk_c10) = sk_c2
| inverse(sk_c5) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_42) ).
fof(f88,plain,
( sk_c2 = multiply(sk_c1,sk_c10)
| sk_c6 = inverse(sk_c5) ),
inference(reorient_equations,[],[f87]) ).
fof(f91,negated_conjecture,
( multiply(sk_c1,sk_c10) = sk_c2
| inverse(sk_c7) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_44) ).
fof(f92,plain,
( sk_c2 = multiply(sk_c1,sk_c10)
| sk_c10 = inverse(sk_c7) ),
inference(reorient_equations,[],[f91]) ).
fof(f93,negated_conjecture,
( multiply(sk_c1,sk_c10) = sk_c2
| multiply(sk_c7,sk_c8) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_45) ).
fof(f94,plain,
( sk_c2 = multiply(sk_c1,sk_c10)
| sk_c10 = multiply(sk_c7,sk_c8) ),
inference(reorient_equations,[],[f93]) ).
fof(f95,negated_conjecture,
( inverse(sk_c1) = sk_c10
| inverse(sk_c10) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_46) ).
fof(f96,plain,
( sk_c10 = inverse(sk_c1)
| sk_c9 = inverse(sk_c10) ),
inference(reorient_equations,[],[f95]) ).
fof(f97,negated_conjecture,
( inverse(sk_c1) = sk_c10
| multiply(sk_c10,sk_c4) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_47) ).
fof(f98,plain,
( sk_c10 = inverse(sk_c1)
| sk_c9 = multiply(sk_c10,sk_c4) ),
inference(reorient_equations,[],[f97]) ).
fof(f99,negated_conjecture,
( inverse(sk_c1) = sk_c10
| multiply(sk_c3,sk_c10) = sk_c4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_48) ).
fof(f100,plain,
( sk_c10 = inverse(sk_c1)
| sk_c4 = multiply(sk_c3,sk_c10) ),
inference(reorient_equations,[],[f99]) ).
fof(f101,negated_conjecture,
( inverse(sk_c1) = sk_c10
| inverse(sk_c3) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_49) ).
fof(f102,plain,
( sk_c10 = inverse(sk_c1)
| sk_c10 = inverse(sk_c3) ),
inference(reorient_equations,[],[f101]) ).
fof(f109,negated_conjecture,
( inverse(sk_c1) = sk_c10
| inverse(sk_c7) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_53) ).
fof(f110,plain,
( sk_c10 = inverse(sk_c1)
| sk_c10 = inverse(sk_c7) ),
inference(reorient_equations,[],[f109]) ).
fof(f111,negated_conjecture,
( inverse(sk_c1) = sk_c10
| multiply(sk_c7,sk_c8) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_54) ).
fof(f112,plain,
( sk_c10 = inverse(sk_c1)
| sk_c10 = multiply(sk_c7,sk_c8) ),
inference(reorient_equations,[],[f111]) ).
fof(f113,negated_conjecture,
! [X2,X3,X0,X1,X6,X4,X5] :
( multiply(sk_c9,sk_c8) != sk_c10
| inverse(sk_c9) != sk_c10
| multiply(sk_c10,sk_c8) != sk_c9
| multiply(sk_c10,X0) != sk_c9
| multiply(X1,sk_c10) != X0
| inverse(X1) != sk_c10
| inverse(sk_c10) != sk_c9
| multiply(sk_c10,X2) != sk_c9
| multiply(X3,sk_c10) != X2
| inverse(X3) != sk_c10
| multiply(X4,X5) != sk_c8
| inverse(X4) != X5
| multiply(X5,sk_c9) != sk_c8
| inverse(X6) != sk_c10
| multiply(X6,sk_c8) != sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_55) ).
fof(f114,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( multiply(sk_c9,sk_c8) != sk_c10
| sk_c10 != inverse(sk_c9)
| sk_c9 != multiply(sk_c10,sk_c8)
| sk_c9 != multiply(sk_c10,X0)
| multiply(X1,sk_c10) != X0
| sk_c10 != inverse(X1)
| sk_c9 != inverse(sk_c10)
| sk_c9 != multiply(sk_c10,X2)
| multiply(X3,sk_c10) != X2
| sk_c10 != inverse(X3)
| sk_c8 != multiply(X4,X5)
| inverse(X4) != X5
| sk_c8 != multiply(X5,sk_c9)
| sk_c10 != inverse(X6)
| sk_c10 != multiply(X6,sk_c8) ),
inference(reorient_equations,[],[f113]) ).
fof(f115,plain,
! [X2,X3,X1,X6,X4,X5] :
( multiply(sk_c9,sk_c8) != sk_c10
| sk_c10 != inverse(sk_c9)
| sk_c9 != multiply(sk_c10,sk_c8)
| sk_c9 != multiply(sk_c10,multiply(X1,sk_c10))
| sk_c10 != inverse(X1)
| sk_c9 != inverse(sk_c10)
| sk_c9 != multiply(sk_c10,X2)
| multiply(X3,sk_c10) != X2
| sk_c10 != inverse(X3)
| sk_c8 != multiply(X4,X5)
| inverse(X4) != X5
| sk_c8 != multiply(X5,sk_c9)
| sk_c10 != inverse(X6)
| sk_c10 != multiply(X6,sk_c8) ),
inference(equality_resolution,[],[f114]) ).
fof(f116,plain,
! [X3,X1,X6,X4,X5] :
( multiply(sk_c9,sk_c8) != sk_c10
| sk_c10 != inverse(sk_c9)
| sk_c9 != multiply(sk_c10,sk_c8)
| sk_c9 != multiply(sk_c10,multiply(X1,sk_c10))
| sk_c10 != inverse(X1)
| sk_c9 != inverse(sk_c10)
| sk_c9 != multiply(sk_c10,multiply(X3,sk_c10))
| sk_c10 != inverse(X3)
| sk_c8 != multiply(X4,X5)
| inverse(X4) != X5
| sk_c8 != multiply(X5,sk_c9)
| sk_c10 != inverse(X6)
| sk_c10 != multiply(X6,sk_c8) ),
inference(equality_resolution,[],[f115]) ).
fof(f117,plain,
! [X3,X1,X6,X4] :
( multiply(sk_c9,sk_c8) != sk_c10
| sk_c10 != inverse(sk_c9)
| sk_c9 != multiply(sk_c10,sk_c8)
| sk_c9 != multiply(sk_c10,multiply(X1,sk_c10))
| sk_c10 != inverse(X1)
| sk_c9 != inverse(sk_c10)
| sk_c9 != multiply(sk_c10,multiply(X3,sk_c10))
| sk_c10 != inverse(X3)
| sk_c8 != multiply(X4,inverse(X4))
| sk_c8 != multiply(inverse(X4),sk_c9)
| sk_c10 != inverse(X6)
| sk_c10 != multiply(X6,sk_c8) ),
inference(equality_resolution,[],[f116]) ).
fof(f119,definition,
( spl0_1
<=> ! [X6] :
( sk_c10 != inverse(X6)
| sk_c10 != multiply(X6,sk_c8) ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f120,plain,
( ! [X6] :
( sk_c10 != inverse(X6)
| sk_c10 != multiply(X6,sk_c8) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f119]) ).
fof(f122,definition,
( spl0_2
<=> ! [X4] :
( sk_c8 != multiply(X4,inverse(X4))
| sk_c8 != multiply(inverse(X4),sk_c9) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f123,plain,
( ! [X4] :
( sk_c8 != multiply(X4,inverse(X4))
| sk_c8 != multiply(inverse(X4),sk_c9) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f122]) ).
fof(f125,definition,
( spl0_3
<=> ! [X3] :
( sk_c9 != multiply(sk_c10,multiply(X3,sk_c10))
| sk_c10 != inverse(X3) ) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f126,plain,
( ! [X3] :
( sk_c10 != inverse(X3)
| sk_c9 != multiply(sk_c10,multiply(X3,sk_c10)) )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f125]) ).
fof(f128,definition,
( spl0_4
<=> sk_c9 = inverse(sk_c10) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f129,plain,
( sk_c9 = inverse(sk_c10)
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f128]) ).
fof(f130,plain,
( sk_c9 != inverse(sk_c10)
| spl0_4 ),
inference(avatar_component_clause,[],[f128]) ).
fof(f132,definition,
( spl0_5
<=> sk_c9 = multiply(sk_c10,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f133,plain,
( sk_c9 = multiply(sk_c10,sk_c8)
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f132]) ).
fof(f134,plain,
( sk_c9 != multiply(sk_c10,sk_c8)
| spl0_5 ),
inference(avatar_component_clause,[],[f132]) ).
fof(f136,definition,
( spl0_6
<=> sk_c10 = inverse(sk_c9) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f137,plain,
( sk_c10 = inverse(sk_c9)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f136]) ).
fof(f138,plain,
( sk_c10 != inverse(sk_c9)
| spl0_6 ),
inference(avatar_component_clause,[],[f136]) ).
fof(f140,definition,
( spl0_7
<=> multiply(sk_c9,sk_c8) = sk_c10 ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f141,plain,
( multiply(sk_c9,sk_c8) = sk_c10
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f140]) ).
fof(f143,plain,
( spl0_1
| spl0_2
| spl0_3
| ~ spl0_4
| spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7 ),
inference(avatar_split_clause,[],[f117,f140,f136,f132,f125,f128,f125,f122,f119]) ).
fof(f145,definition,
( spl0_8
<=> sk_c10 = multiply(sk_c7,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f147,plain,
( sk_c10 = multiply(sk_c7,sk_c8)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f145]) ).
fof(f149,definition,
( spl0_9
<=> sk_c10 = inverse(sk_c1) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f151,plain,
( sk_c10 = inverse(sk_c1)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f149]) ).
fof(f152,plain,
( spl0_8
| spl0_9 ),
inference(avatar_split_clause,[],[f112,f149,f145]) ).
fof(f154,definition,
( spl0_10
<=> sk_c10 = inverse(sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f156,plain,
( sk_c10 = inverse(sk_c7)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f154]) ).
fof(f157,plain,
( spl0_10
| spl0_9 ),
inference(avatar_split_clause,[],[f110,f149,f154]) ).
fof(f164,definition,
( spl0_12
<=> sk_c6 = inverse(sk_c5) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f166,plain,
( sk_c6 = inverse(sk_c5)
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f164]) ).
fof(f169,definition,
( spl0_13
<=> sk_c8 = multiply(sk_c5,sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f171,plain,
( sk_c8 = multiply(sk_c5,sk_c6)
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f169]) ).
fof(f174,definition,
( spl0_14
<=> sk_c10 = inverse(sk_c3) ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
fof(f176,plain,
( sk_c10 = inverse(sk_c3)
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f174]) ).
fof(f177,plain,
( spl0_14
| spl0_9 ),
inference(avatar_split_clause,[],[f102,f149,f174]) ).
fof(f179,definition,
( spl0_15
<=> sk_c4 = multiply(sk_c3,sk_c10) ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
fof(f181,plain,
( sk_c4 = multiply(sk_c3,sk_c10)
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f179]) ).
fof(f182,plain,
( spl0_15
| spl0_9 ),
inference(avatar_split_clause,[],[f100,f149,f179]) ).
fof(f184,definition,
( spl0_16
<=> sk_c9 = multiply(sk_c10,sk_c4) ),
introduced(definition,[new_symbols(definition,[spl0_16])],[avatar_definition]) ).
fof(f186,plain,
( sk_c9 = multiply(sk_c10,sk_c4)
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f184]) ).
fof(f187,plain,
( spl0_16
| spl0_9 ),
inference(avatar_split_clause,[],[f98,f149,f184]) ).
fof(f188,plain,
( spl0_4
| spl0_9 ),
inference(avatar_split_clause,[],[f96,f149,f128]) ).
fof(f190,definition,
( spl0_17
<=> sk_c2 = multiply(sk_c1,sk_c10) ),
introduced(definition,[new_symbols(definition,[spl0_17])],[avatar_definition]) ).
fof(f192,plain,
( sk_c2 = multiply(sk_c1,sk_c10)
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f190]) ).
fof(f193,plain,
( spl0_8
| spl0_17 ),
inference(avatar_split_clause,[],[f94,f190,f145]) ).
fof(f194,plain,
( spl0_10
| spl0_17 ),
inference(avatar_split_clause,[],[f92,f190,f154]) ).
fof(f196,plain,
( spl0_12
| spl0_17 ),
inference(avatar_split_clause,[],[f88,f190,f164]) ).
fof(f197,plain,
( spl0_13
| spl0_17 ),
inference(avatar_split_clause,[],[f86,f190,f169]) ).
fof(f198,plain,
( spl0_14
| spl0_17 ),
inference(avatar_split_clause,[],[f84,f190,f174]) ).
fof(f199,plain,
( spl0_15
| spl0_17 ),
inference(avatar_split_clause,[],[f82,f190,f179]) ).
fof(f200,plain,
( spl0_16
| spl0_17 ),
inference(avatar_split_clause,[],[f80,f190,f184]) ).
fof(f201,plain,
( spl0_4
| spl0_17 ),
inference(avatar_split_clause,[],[f78,f190,f128]) ).
fof(f203,definition,
( spl0_18
<=> sk_c9 = multiply(sk_c10,sk_c2) ),
introduced(definition,[new_symbols(definition,[spl0_18])],[avatar_definition]) ).
fof(f205,plain,
( sk_c9 = multiply(sk_c10,sk_c2)
| ~ spl0_18 ),
inference(avatar_component_clause,[],[f203]) ).
fof(f206,plain,
( spl0_8
| spl0_18 ),
inference(avatar_split_clause,[],[f76,f203,f145]) ).
fof(f207,plain,
( spl0_10
| spl0_18 ),
inference(avatar_split_clause,[],[f74,f203,f154]) ).
fof(f209,plain,
( spl0_12
| spl0_18 ),
inference(avatar_split_clause,[],[f70,f203,f164]) ).
fof(f210,plain,
( spl0_13
| spl0_18 ),
inference(avatar_split_clause,[],[f68,f203,f169]) ).
fof(f211,plain,
( spl0_14
| spl0_18 ),
inference(avatar_split_clause,[],[f66,f203,f174]) ).
fof(f212,plain,
( spl0_15
| spl0_18 ),
inference(avatar_split_clause,[],[f64,f203,f179]) ).
fof(f213,plain,
( spl0_16
| spl0_18 ),
inference(avatar_split_clause,[],[f62,f203,f184]) ).
fof(f214,plain,
( spl0_4
| spl0_18 ),
inference(avatar_split_clause,[],[f60,f203,f128]) ).
fof(f218,plain,
( spl0_12
| spl0_5 ),
inference(avatar_split_clause,[],[f52,f132,f164]) ).
fof(f219,plain,
( spl0_13
| spl0_5 ),
inference(avatar_split_clause,[],[f50,f132,f169]) ).
fof(f220,plain,
( spl0_14
| spl0_5 ),
inference(avatar_split_clause,[],[f48,f132,f174]) ).
fof(f221,plain,
( spl0_15
| spl0_5 ),
inference(avatar_split_clause,[],[f46,f132,f179]) ).
fof(f222,plain,
( spl0_16
| spl0_5 ),
inference(avatar_split_clause,[],[f44,f132,f184]) ).
fof(f229,plain,
( spl0_14
| spl0_6 ),
inference(avatar_split_clause,[],[f30,f136,f174]) ).
fof(f230,plain,
( spl0_15
| spl0_6 ),
inference(avatar_split_clause,[],[f28,f136,f179]) ).
fof(f231,plain,
( spl0_16
| spl0_6 ),
inference(avatar_split_clause,[],[f26,f136,f184]) ).
fof(f232,plain,
( spl0_4
| spl0_6 ),
inference(avatar_split_clause,[],[f24,f136,f128]) ).
fof(f233,plain,
( spl0_8
| spl0_7 ),
inference(avatar_split_clause,[],[f22,f140,f145]) ).
fof(f234,plain,
( spl0_10
| spl0_7 ),
inference(avatar_split_clause,[],[f20,f140,f154]) ).
fof(f242,plain,
( identity = multiply(sk_c9,sk_c10)
| ~ spl0_4 ),
inference(superposition,[],[f3,f129]) ).
fof(f245,plain,
( identity = multiply(sk_c10,sk_c7)
| ~ spl0_10 ),
inference(superposition,[],[f3,f156]) ).
fof(f248,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[],[f4,f3]) ).
fof(f249,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c9,multiply(sk_c10,X0))
| ~ spl0_4 ),
inference(superposition,[],[f4,f242]) ).
fof(f255,plain,
( ! [X0] : multiply(sk_c9,multiply(sk_c10,X0)) = X0
| ~ spl0_4 ),
inference(forward_demodulation,[],[f249,f1]) ).
fof(f256,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f248,f1]) ).
fof(f320,plain,
( sk_c7 = multiply(inverse(sk_c10),identity)
| ~ spl0_10 ),
inference(superposition,[],[f256,f245]) ).
fof(f321,plain,
( sk_c10 = multiply(inverse(sk_c3),sk_c4)
| ~ spl0_15 ),
inference(superposition,[],[f256,f181]) ).
fof(f323,plain,
( sk_c6 = multiply(inverse(sk_c5),sk_c8)
| ~ spl0_13 ),
inference(superposition,[],[f256,f171]) ).
fof(f328,plain,
( sk_c8 = multiply(inverse(sk_c7),sk_c10)
| ~ spl0_8 ),
inference(superposition,[],[f256,f147]) ).
fof(f333,plain,
( sk_c8 = multiply(sk_c10,sk_c10)
| ~ spl0_8
| ~ spl0_10 ),
inference(forward_demodulation,[],[f328,f156]) ).
fof(f335,plain,
( sk_c6 = multiply(sk_c6,sk_c8)
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f323,f166]) ).
fof(f337,plain,
( sk_c10 = multiply(sk_c10,sk_c4)
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f321,f176]) ).
fof(f338,plain,
( sk_c7 = multiply(sk_c9,identity)
| ~ spl0_4
| ~ spl0_10 ),
inference(forward_demodulation,[],[f320,f129]) ).
fof(f345,plain,
( multiply(sk_c9,sk_c8) = sk_c10
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10 ),
inference(superposition,[],[f255,f333]) ).
fof(f349,plain,
( spl0_7
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10 ),
inference(avatar_split_clause,[],[f345,f154,f145,f128,f140]) ).
fof(f354,plain,
( sk_c8 = multiply(inverse(sk_c6),sk_c6)
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f256,f335]) ).
fof(f356,plain,
( identity = sk_c8
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f354,f3]) ).
fof(f366,plain,
( sk_c9 = sk_c10
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(superposition,[],[f337,f186]) ).
fof(f370,plain,
( sk_c4 = multiply(inverse(sk_c10),sk_c10)
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f256,f337]) ).
fof(f372,plain,
( identity = sk_c4
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f370,f3]) ).
fof(f374,plain,
( sk_c8 = sk_c4
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f372,f356]) ).
fof(f375,plain,
( sk_c10 != inverse(sk_c10)
| spl0_6
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(superposition,[],[f138,f366]) ).
fof(f387,plain,
( sk_c9 != sk_c10
| ~ spl0_4
| spl0_6
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f375,f129]) ).
fof(f388,plain,
( $false
| ~ spl0_4
| spl0_6
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_subsumption_resolution,[],[f387,f366]) ).
fof(f389,plain,
( ~ spl0_4
| spl0_6
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(avatar_contradiction_clause,[],[f388]) ).
fof(f390,plain,
( sk_c10 != multiply(sk_c10,sk_c8)
| spl0_5
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f134,f366]) ).
fof(f391,plain,
( sk_c10 = inverse(sk_c10)
| ~ spl0_6
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f137,f366]) ).
fof(f399,plain,
( sk_c9 = multiply(sk_c10,sk_c8)
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(superposition,[],[f186,f374]) ).
fof(f400,plain,
( sk_c10 = multiply(sk_c10,sk_c8)
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f399,f366]) ).
fof(f404,plain,
( $false
| spl0_5
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_subsumption_resolution,[],[f400,f390]) ).
fof(f405,plain,
( spl0_5
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(avatar_contradiction_clause,[],[f404]) ).
fof(f450,plain,
( ! [X4] :
( sk_c8 != multiply(inverse(X4),sk_c10)
| sk_c8 != multiply(X4,inverse(X4)) )
| ~ spl0_2
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f123,f366]) ).
fof(f451,plain,
( sk_c8 != multiply(sk_c10,sk_c10)
| sk_c8 != multiply(sk_c10,sk_c10)
| ~ spl0_2
| ~ spl0_6
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(superposition,[],[f450,f391]) ).
fof(f457,plain,
( sk_c8 != multiply(sk_c10,sk_c10)
| ~ spl0_2
| ~ spl0_6
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(duplicate_literal_removal,[],[f451]) ).
fof(f463,plain,
( $false
| ~ spl0_2
| ~ spl0_6
| ~ spl0_8
| ~ spl0_10
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_subsumption_resolution,[],[f457,f333]) ).
fof(f464,plain,
( ~ spl0_2
| ~ spl0_6
| ~ spl0_8
| ~ spl0_10
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(avatar_contradiction_clause,[],[f463]) ).
fof(f480,plain,
( ! [X3] :
( sk_c10 != inverse(X3)
| sk_c10 != multiply(sk_c10,multiply(X3,sk_c10)) )
| ~ spl0_3
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f126,f366]) ).
fof(f490,plain,
( sk_c10 != sk_c10
| sk_c10 != multiply(sk_c10,multiply(sk_c3,sk_c10))
| ~ spl0_3
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(superposition,[],[f480,f176]) ).
fof(f494,plain,
( sk_c10 != multiply(sk_c10,multiply(sk_c3,sk_c10))
| ~ spl0_3
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(trivial_inequality_removal,[],[f490]) ).
fof(f502,plain,
( sk_c10 != multiply(sk_c10,sk_c4)
| ~ spl0_3
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f494,f181]) ).
fof(f506,plain,
( $false
| ~ spl0_3
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_subsumption_resolution,[],[f502,f337]) ).
fof(f507,plain,
( ~ spl0_3
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(avatar_contradiction_clause,[],[f506]) ).
fof(f516,plain,
( multiply(sk_c9,sk_c8) = sk_c7
| ~ spl0_4
| ~ spl0_10
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f338,f356]) ).
fof(f518,plain,
( sk_c10 = sk_c7
| ~ spl0_4
| ~ spl0_7
| ~ spl0_10
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f516,f141]) ).
fof(f522,plain,
( sk_c10 = inverse(sk_c10)
| ~ spl0_4
| ~ spl0_7
| ~ spl0_10
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f156,f518]) ).
fof(f532,plain,
( sk_c8 = multiply(inverse(sk_c10),sk_c9)
| ~ spl0_5 ),
inference(superposition,[],[f256,f133]) ).
fof(f534,plain,
( sk_c8 = multiply(sk_c9,sk_c9)
| ~ spl0_4
| ~ spl0_5 ),
inference(forward_demodulation,[],[f532,f129]) ).
fof(f535,plain,
( sk_c9 = sk_c10
| ~ spl0_4
| ~ spl0_7
| ~ spl0_10
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f522,f129]) ).
fof(f540,plain,
( sk_c10 = multiply(inverse(sk_c1),sk_c2)
| ~ spl0_17 ),
inference(superposition,[],[f256,f192]) ).
fof(f541,plain,
( ! [X0] : multiply(sk_c1,multiply(sk_c10,X0)) = multiply(sk_c2,X0)
| ~ spl0_17 ),
inference(superposition,[],[f4,f192]) ).
fof(f542,plain,
( sk_c10 = multiply(sk_c10,sk_c2)
| ~ spl0_9
| ~ spl0_17 ),
inference(forward_demodulation,[],[f540,f151]) ).
fof(f564,plain,
( ! [X3] :
( sk_c10 != inverse(X3)
| sk_c10 != multiply(sk_c10,multiply(X3,sk_c10)) )
| ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_10
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f126,f535]) ).
fof(f565,plain,
( sk_c10 != sk_c10
| sk_c10 != multiply(sk_c10,multiply(sk_c9,sk_c10))
| ~ spl0_3
| ~ spl0_4
| ~ spl0_6
| ~ spl0_7
| ~ spl0_10
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f564,f137]) ).
fof(f574,plain,
( sk_c10 != multiply(sk_c10,multiply(sk_c9,sk_c10))
| ~ spl0_3
| ~ spl0_4
| ~ spl0_6
| ~ spl0_7
| ~ spl0_10
| ~ spl0_12
| ~ spl0_13 ),
inference(trivial_inequality_removal,[],[f565]) ).
fof(f580,plain,
( sk_c10 != multiply(sk_c10,identity)
| ~ spl0_3
| ~ spl0_4
| ~ spl0_6
| ~ spl0_7
| ~ spl0_10
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f574,f242]) ).
fof(f586,plain,
( sk_c10 != multiply(sk_c10,sk_c8)
| ~ spl0_3
| ~ spl0_4
| ~ spl0_6
| ~ spl0_7
| ~ spl0_10
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f580,f356]) ).
fof(f591,plain,
( sk_c9 != sk_c10
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_10
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f586,f133]) ).
fof(f596,plain,
( $false
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_10
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f591,f535]) ).
fof(f597,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_10
| ~ spl0_12
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[],[f596]) ).
fof(f613,plain,
( sk_c10 != sk_c10
| sk_c9 != multiply(sk_c10,multiply(sk_c1,sk_c10))
| ~ spl0_3
| ~ spl0_9 ),
inference(superposition,[],[f126,f151]) ).
fof(f614,plain,
( sk_c9 != multiply(sk_c10,multiply(sk_c1,sk_c10))
| ~ spl0_3
| ~ spl0_9 ),
inference(trivial_inequality_removal,[],[f613]) ).
fof(f617,plain,
( sk_c9 != multiply(sk_c10,sk_c2)
| ~ spl0_3
| ~ spl0_9
| ~ spl0_17 ),
inference(forward_demodulation,[],[f614,f192]) ).
fof(f625,plain,
( $false
| ~ spl0_3
| ~ spl0_9
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[],[f617,f205]) ).
fof(f626,plain,
( ~ spl0_3
| ~ spl0_9
| ~ spl0_17
| ~ spl0_18 ),
inference(avatar_contradiction_clause,[],[f625]) ).
fof(f631,plain,
( sk_c10 != sk_c10
| multiply(sk_c9,sk_c8) != sk_c10
| ~ spl0_1
| ~ spl0_6 ),
inference(superposition,[],[f120,f137]) ).
fof(f636,plain,
( multiply(sk_c9,sk_c8) != sk_c10
| ~ spl0_1
| ~ spl0_6 ),
inference(trivial_inequality_removal,[],[f631]) ).
fof(f637,plain,
( $false
| ~ spl0_1
| ~ spl0_6
| ~ spl0_7 ),
inference(forward_subsumption_resolution,[],[f636,f141]) ).
fof(f638,plain,
( ~ spl0_1
| ~ spl0_6
| ~ spl0_7 ),
inference(avatar_contradiction_clause,[],[f637]) ).
fof(f643,plain,
( sk_c9 = sk_c10
| ~ spl0_9
| ~ spl0_17
| ~ spl0_18 ),
inference(superposition,[],[f542,f205]) ).
fof(f646,plain,
( sk_c2 = multiply(inverse(sk_c10),sk_c10)
| ~ spl0_9
| ~ spl0_17 ),
inference(superposition,[],[f256,f542]) ).
fof(f648,plain,
( identity = sk_c2
| ~ spl0_9
| ~ spl0_17 ),
inference(forward_demodulation,[],[f646,f3]) ).
fof(f655,plain,
( sk_c10 = inverse(sk_c10)
| ~ spl0_6
| ~ spl0_9
| ~ spl0_17
| ~ spl0_18 ),
inference(superposition,[],[f137,f643]) ).
fof(f664,plain,
( multiply(sk_c2,sk_c8) = multiply(sk_c1,sk_c9)
| ~ spl0_5
| ~ spl0_17 ),
inference(superposition,[],[f541,f133]) ).
fof(f676,plain,
( multiply(sk_c1,sk_c10) = multiply(sk_c2,sk_c8)
| ~ spl0_5
| ~ spl0_9
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f664,f643]) ).
fof(f683,plain,
( sk_c2 = multiply(sk_c2,sk_c8)
| ~ spl0_5
| ~ spl0_9
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f676,f192]) ).
fof(f697,plain,
( sk_c9 != sk_c10
| spl0_4
| ~ spl0_6
| ~ spl0_9
| ~ spl0_17
| ~ spl0_18 ),
inference(superposition,[],[f130,f655]) ).
fof(f701,plain,
( $false
| spl0_4
| ~ spl0_6
| ~ spl0_9
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[],[f697,f643]) ).
fof(f702,plain,
( spl0_4
| ~ spl0_6
| ~ spl0_9
| ~ spl0_17
| ~ spl0_18 ),
inference(avatar_contradiction_clause,[],[f701]) ).
fof(f703,plain,
( ! [X4] :
( sk_c8 != multiply(inverse(X4),sk_c10)
| sk_c8 != multiply(X4,inverse(X4)) )
| ~ spl0_2
| ~ spl0_9
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f123,f643]) ).
fof(f707,plain,
( sk_c8 = multiply(sk_c10,sk_c10)
| ~ spl0_4
| ~ spl0_5
| ~ spl0_9
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f534,f643]) ).
fof(f713,plain,
( sk_c8 != multiply(sk_c10,sk_c10)
| sk_c8 != multiply(sk_c1,sk_c10)
| ~ spl0_2
| ~ spl0_9
| ~ spl0_17
| ~ spl0_18 ),
inference(superposition,[],[f703,f151]) ).
fof(f717,plain,
( sk_c8 != sk_c2
| sk_c8 != multiply(sk_c10,sk_c10)
| ~ spl0_2
| ~ spl0_9
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f713,f192]) ).
fof(f727,definition,
( spl0_24
<=> sk_c8 = multiply(sk_c10,sk_c10) ),
introduced(definition,[new_symbols(definition,[spl0_24])],[avatar_definition]) ).
fof(f729,plain,
( sk_c8 != multiply(sk_c10,sk_c10)
| spl0_24 ),
inference(avatar_component_clause,[],[f727]) ).
fof(f731,definition,
( spl0_25
<=> sk_c8 = sk_c2 ),
introduced(definition,[new_symbols(definition,[spl0_25])],[avatar_definition]) ).
fof(f734,plain,
( ~ spl0_24
| ~ spl0_25
| ~ spl0_2
| ~ spl0_9
| ~ spl0_17
| ~ spl0_18 ),
inference(avatar_split_clause,[],[f717,f203,f190,f149,f122,f731,f727]) ).
fof(f751,plain,
( sk_c8 = multiply(inverse(sk_c2),sk_c2)
| ~ spl0_5
| ~ spl0_9
| ~ spl0_17
| ~ spl0_18 ),
inference(superposition,[],[f256,f683]) ).
fof(f753,plain,
( identity = sk_c8
| ~ spl0_5
| ~ spl0_9
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f751,f3]) ).
fof(f756,plain,
( sk_c8 = sk_c2
| ~ spl0_5
| ~ spl0_9
| ~ spl0_17
| ~ spl0_18 ),
inference(superposition,[],[f648,f753]) ).
fof(f758,plain,
( spl0_25
| ~ spl0_5
| ~ spl0_9
| ~ spl0_17
| ~ spl0_18 ),
inference(avatar_split_clause,[],[f756,f203,f190,f149,f132,f731]) ).
fof(f768,plain,
( $false
| ~ spl0_4
| ~ spl0_5
| ~ spl0_9
| ~ spl0_17
| ~ spl0_18
| spl0_24 ),
inference(forward_subsumption_resolution,[],[f707,f729]) ).
fof(f769,plain,
( ~ spl0_4
| ~ spl0_5
| ~ spl0_9
| ~ spl0_17
| ~ spl0_18
| spl0_24 ),
inference(avatar_contradiction_clause,[],[f768]) ).
cnf(s1,plain,
( spl0_3
| spl0_2
| spl0_1
| spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7 ),
inference(sat_conversion,[],[f143]) ).
cnf(s2,plain,
( spl0_1
| spl0_2
| spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7 ),
inference(rat,[],[s1]) ).
cnf(s3,plain,
( spl0_8
| spl0_9 ),
inference(sat_conversion,[],[f152]) ).
cnf(s4,plain,
( spl0_9
| spl0_10 ),
inference(sat_conversion,[],[f157]) ).
cnf(s8,plain,
( spl0_9
| spl0_14 ),
inference(sat_conversion,[],[f177]) ).
cnf(s9,plain,
( spl0_9
| spl0_15 ),
inference(sat_conversion,[],[f182]) ).
cnf(s10,plain,
( spl0_9
| spl0_16 ),
inference(sat_conversion,[],[f187]) ).
cnf(s11,plain,
( spl0_4
| spl0_9 ),
inference(sat_conversion,[],[f188]) ).
cnf(s12,plain,
( spl0_8
| spl0_17 ),
inference(sat_conversion,[],[f193]) ).
cnf(s13,plain,
( spl0_10
| spl0_17 ),
inference(sat_conversion,[],[f194]) ).
cnf(s15,plain,
( spl0_12
| spl0_17 ),
inference(sat_conversion,[],[f196]) ).
cnf(s16,plain,
( spl0_13
| spl0_17 ),
inference(sat_conversion,[],[f197]) ).
cnf(s17,plain,
( spl0_14
| spl0_17 ),
inference(sat_conversion,[],[f198]) ).
cnf(s18,plain,
( spl0_15
| spl0_17 ),
inference(sat_conversion,[],[f199]) ).
cnf(s19,plain,
( spl0_16
| spl0_17 ),
inference(sat_conversion,[],[f200]) ).
cnf(s20,plain,
( spl0_4
| spl0_17 ),
inference(sat_conversion,[],[f201]) ).
cnf(s21,plain,
( spl0_8
| spl0_18 ),
inference(sat_conversion,[],[f206]) ).
cnf(s22,plain,
( spl0_10
| spl0_18 ),
inference(sat_conversion,[],[f207]) ).
cnf(s24,plain,
( spl0_12
| spl0_18 ),
inference(sat_conversion,[],[f209]) ).
cnf(s25,plain,
( spl0_13
| spl0_18 ),
inference(sat_conversion,[],[f210]) ).
cnf(s26,plain,
( spl0_14
| spl0_18 ),
inference(sat_conversion,[],[f211]) ).
cnf(s27,plain,
( spl0_15
| spl0_18 ),
inference(sat_conversion,[],[f212]) ).
cnf(s28,plain,
( spl0_16
| spl0_18 ),
inference(sat_conversion,[],[f213]) ).
cnf(s29,plain,
( spl0_4
| spl0_18 ),
inference(sat_conversion,[],[f214]) ).
cnf(s33,plain,
( spl0_5
| spl0_12 ),
inference(sat_conversion,[],[f218]) ).
cnf(s34,plain,
( spl0_5
| spl0_13 ),
inference(sat_conversion,[],[f219]) ).
cnf(s35,plain,
( spl0_5
| spl0_14 ),
inference(sat_conversion,[],[f220]) ).
cnf(s36,plain,
( spl0_5
| spl0_15 ),
inference(sat_conversion,[],[f221]) ).
cnf(s37,plain,
( spl0_5
| spl0_16 ),
inference(sat_conversion,[],[f222]) ).
cnf(s44,plain,
( spl0_6
| spl0_14 ),
inference(sat_conversion,[],[f229]) ).
cnf(s45,plain,
( spl0_6
| spl0_15 ),
inference(sat_conversion,[],[f230]) ).
cnf(s46,plain,
( spl0_6
| spl0_16 ),
inference(sat_conversion,[],[f231]) ).
cnf(s47,plain,
( spl0_4
| spl0_6 ),
inference(sat_conversion,[],[f232]) ).
cnf(s48,plain,
( spl0_7
| spl0_8 ),
inference(sat_conversion,[],[f233]) ).
cnf(s49,plain,
( spl0_7
| spl0_10 ),
inference(sat_conversion,[],[f234]) ).
cnf(s57,plain,
( ~ spl0_4
| spl0_7
| ~ spl0_8
| ~ spl0_10 ),
inference(sat_conversion,[],[f349]) ).
cnf(s59,plain,
( ~ spl0_4
| spl0_6
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(sat_conversion,[],[f389]) ).
cnf(s61,plain,
( spl0_5
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(sat_conversion,[],[f405]) ).
cnf(s67,plain,
( ~ spl0_2
| ~ spl0_6
| ~ spl0_8
| ~ spl0_10
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(sat_conversion,[],[f464]) ).
cnf(s73,plain,
( ~ spl0_3
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(sat_conversion,[],[f507]) ).
cnf(s82,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_10
| ~ spl0_12
| ~ spl0_13 ),
inference(sat_conversion,[],[f597]) ).
cnf(s84,plain,
( ~ spl0_3
| ~ spl0_9
| ~ spl0_17
| ~ spl0_18 ),
inference(sat_conversion,[],[f626]) ).
cnf(s86,plain,
( ~ spl0_1
| ~ spl0_6
| ~ spl0_7 ),
inference(sat_conversion,[],[f638]) ).
cnf(s87,plain,
( spl0_4
| ~ spl0_6
| ~ spl0_9
| ~ spl0_17
| ~ spl0_18 ),
inference(sat_conversion,[],[f702]) ).
cnf(s89,plain,
( ~ spl0_2
| ~ spl0_9
| ~ spl0_17
| ~ spl0_18
| ~ spl0_24
| ~ spl0_25 ),
inference(sat_conversion,[],[f734]) ).
cnf(s92,plain,
( ~ spl0_5
| ~ spl0_9
| ~ spl0_17
| ~ spl0_18
| spl0_25 ),
inference(sat_conversion,[],[f758]) ).
cnf(s94,plain,
( ~ spl0_4
| ~ spl0_5
| ~ spl0_9
| ~ spl0_17
| ~ spl0_18
| spl0_24 ),
inference(sat_conversion,[],[f769]) ).
cnf(s95,plain,
spl0_4,
inference(rat,[],[s87,s11,s20,s29,s47]) ).
cnf(s96,plain,
spl0_7,
inference(rat,[],[s57,s48,s49,s95]) ).
cnf(s97,plain,
spl0_6,
inference(rat,[],[s59,s44,s45,s46,s95]) ).
cnf(s98,plain,
spl0_5,
inference(rat,[],[s61,s33,s34,s35,s36,s37]) ).
cnf(s99,plain,
( spl0_13
| ~ spl0_9
| ~ spl0_3 ),
inference(rat,[],[s84,s16,s25]) ).
cnf(s100,plain,
( spl0_12
| ~ spl0_9
| ~ spl0_3 ),
inference(rat,[],[s84,s15,s24]) ).
cnf(s101,plain,
( ~ spl0_9
| ~ spl0_3 ),
inference(rat,[],[s84,s13,s22,s82,s100,s99,s98,s97,s95,s96]) ).
cnf(s102,plain,
~ spl0_3,
inference(rat,[],[s73,s8,s9,s10,s101]) ).
cnf(s104,plain,
( ~ spl0_18
| ~ spl0_17
| ~ spl0_9
| ~ spl0_2 ),
inference(rat,[],[s89,s94,s92,s95,s98]) ).
cnf(s105,plain,
( spl0_18
| ~ spl0_10
| ~ spl0_2 ),
inference(rat,[],[s67,s21,s26,s27,s28,s97]) ).
cnf(s106,plain,
( ~ spl0_10
| ~ spl0_9
| ~ spl0_2 ),
inference(rat,[],[s67,s12,s17,s18,s19,s104,s105,s97]) ).
cnf(s107,plain,
( ~ spl0_9
| ~ spl0_2 ),
inference(rat,[],[s104,s13,s22,s106]) ).
cnf(s108,plain,
~ spl0_2,
inference(rat,[],[s67,s3,s4,s8,s9,s10,s107,s97]) ).
cnf(s109,plain,
~ spl0_1,
inference(rat,[],[s86,s96,s97]) ).
cnf(s110,plain,
$false,
inference(rat,[],[s2,s96,s95,s98,s97,s109,s108,s102]) ).
fof(f770,plain,
$false,
inference(avatar_sat_refutation,[],[s110]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP362-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n004.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Sun Sep 27 09:55:22 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.41 Running first-order theorem proving
% 0.12/0.41 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
% 2.66/1.27 % (3262600)Input is clausal, will run a generic CNF schedule.
% 2.66/1.27 % (3262611)dis-21_1_sil=8000:lcm=predicate:random_seed=130356637: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)
% 2.66/1.27 % (3262611)Refutation not found, incomplete strategy
% 2.66/1.27 % (3262611)------------------------------
% 2.66/1.27 % (3262611)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.66/1.27 % (3262611)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.66/1.27 % (3262611)CaDiCaL version: 2.1.3
% 2.66/1.27 % (3262611)Termination reason: Refutation not found, incomplete strategy
% 2.66/1.27 % (3262611)Time elapsed: 0.001 s
% 2.66/1.27 % (3262611)Peak memory usage: 88 MB
% 2.66/1.27 % (3262611)Instructions burned: 3 (million)
% 2.66/1.27 % (3262610)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2976396667:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.66/1.27 % (3262605)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=2538939586:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.66/1.27 % (3262606)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=255202449:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.66/1.27 % (3262608)lrs+10_1_sil=8000:sp=occurrence:random_seed=2806604756:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.66/1.27 % (3262607)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=2915408080:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.66/1.27 % (3262608)Refutation not found, incomplete strategy
% 2.66/1.27 % (3262608)------------------------------
% 2.66/1.27 % (3262608)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.66/1.27 % (3262608)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.66/1.27 % (3262608)CaDiCaL version: 2.1.3
% 2.66/1.27 % (3262608)Termination reason: Refutation not found, incomplete strategy
% 2.66/1.27 % (3262608)Time elapsed: 0.004 s
% 2.66/1.27 % (3262608)Peak memory usage: 88 MB
% 2.66/1.27 % (3262608)Instructions burned: 5 (million)
% 2.66/1.27 % (3262609)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=3017843696:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.66/1.27 % (3262610)First to succeed.
% 2.66/1.27 % (3262610)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3262600"
% 2.66/1.27 % (3262609)Instruction limit reached!
% 2.66/1.27 % (3262609)------------------------------
% 2.66/1.27 % (3262609)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.66/1.27 % (3262609)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.66/1.27 % (3262609)CaDiCaL version: 2.1.3
% 2.66/1.27 % (3262609)Termination reason: Instruction limit
% 2.66/1.27 % (3262609)Termination phase: Saturation
% 2.66/1.27 % (3262609)Time elapsed: 0.066 s
% 2.66/1.27 % (3262609)Peak memory usage: 89 MB
% 2.66/1.27 % (3262609)Instructions burned: 114 (million)
% 2.66/1.27 % (3262611)------------------------------
% 2.66/1.27 % (3262611)------------------------------
% 2.66/1.27 % (3262620)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=3860618324: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)
% 2.66/1.27 % (3262620)Refutation not found, incomplete strategy
% 2.66/1.27 % (3262620)------------------------------
% 2.66/1.27 % (3262620)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.66/1.27 % (3262620)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.66/1.27 % (3262620)CaDiCaL version: 2.1.3
% 2.66/1.27 % (3262620)Termination reason: Refutation not found, incomplete strategy
% 2.66/1.27 % (3262620)Time elapsed: 0.002 s
% 2.66/1.27 % (3262620)Peak memory usage: 88 MB
% 2.66/1.27 % (3262620)Instructions burned: 6 (million)
% 2.66/1.27 % (3262619)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=3132502598:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 2.66/1.27 % (3262619)Refutation not found, incomplete strategy
% 2.66/1.27 % (3262619)------------------------------
% 2.66/1.27 % (3262619)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.66/1.27 % (3262619)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.66/1.27 % (3262619)CaDiCaL version: 2.1.3
% 2.66/1.27 % (3262619)Termination reason: Refutation not found, incomplete strategy
% 2.66/1.27 % (3262619)Time elapsed: 0.004 s
% 2.66/1.27 % (3262619)Peak memory usage: 88 MB
% 2.66/1.27 % (3262619)Instructions burned: 5 (million)
% 2.66/1.27 % (3262608)------------------------------
% 2.66/1.27 % (3262608)------------------------------
% 2.66/1.27 % (3262610)Refutation found. Thanks to Tanya!
% 2.66/1.27 % SZS status Unsatisfiable for theBenchmark
% 2.66/1.27 % SZS output start Proof for theBenchmark
% See solution above
% 3.55/1.47 % (3262610)------------------------------
% 3.55/1.47 % (3262610)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.55/1.47 % (3262610)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.55/1.47 % (3262610)CaDiCaL version: 2.1.3
% 3.55/1.47 % (3262610)Termination reason: Refutation
% 3.55/1.47 % (3262610)Time elapsed: 0.020 s
% 3.55/1.47 % (3262610)Peak memory usage: 90 MB
% 3.55/1.47 % (3262610)Instructions burned: 26 (million)
% 3.55/1.47 % (3262610)------------------------------
% 3.55/1.47 % (3262610)------------------------------
% 3.55/1.47 % (3262600)Success in time 0.417 s
% 3.55/1.47 % Vampire exiting
%------------------------------------------------------------------------------