%------------------------------------------------------------------------------
% File : Vampire-SAT---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 SAT
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 10:17:36 AM UTC 2026
% Result : Unsatisfiable 0.12s 0.44s
% Output : Refutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 51
% Number of leaves : 66
% Syntax : Number of formulae : 482 ( 30 unt; 18 def)
% Number of atoms : 2090 ( 533 equ)
% Maximal formula atoms : 15 ( 4 avg)
% Number of connectives : 3108 (1500 ~;1590 |; 0 &)
% ( 18 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 20 ( 18 usr; 19 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 11 con; 0-2 aty)
% Number of variables : 139 ( 0 sgn 139 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_identity) ).
fof(f2,axiom,
! [X0] : multiply(inverse(X0),X0) = identity,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_inverse) ).
fof(f3,plain,
! [X0] : identity = multiply(inverse(X0),X0),
inference(reorient_equations,[],[f2]) ).
fof(f4,axiom,
! [X2,X0,X1] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',associativity) ).
fof(f7,negated_conjecture,
( multiply(sk_c9,sk_c8) = sk_c10
| multiply(sk_c10,sk_c4) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_2) ).
fof(f8,plain,
( multiply(sk_c9,sk_c8) = sk_c10
| sk_c9 = multiply(sk_c10,sk_c4) ),
inference(reorient_equations,[],[f7]) ).
fof(f9,negated_conjecture,
( multiply(sk_c9,sk_c8) = sk_c10
| multiply(sk_c3,sk_c10) = sk_c4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_3) ).
fof(f10,plain,
( multiply(sk_c9,sk_c8) = sk_c10
| sk_c4 = multiply(sk_c3,sk_c10) ),
inference(reorient_equations,[],[f9]) ).
fof(f11,negated_conjecture,
( multiply(sk_c9,sk_c8) = sk_c10
| inverse(sk_c3) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_4) ).
fof(f12,plain,
( multiply(sk_c9,sk_c8) = sk_c10
| sk_c10 = inverse(sk_c3) ),
inference(reorient_equations,[],[f11]) ).
fof(f13,negated_conjecture,
( multiply(sk_c9,sk_c8) = sk_c10
| multiply(sk_c5,sk_c6) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_5) ).
fof(f14,plain,
( multiply(sk_c9,sk_c8) = sk_c10
| sk_c8 = multiply(sk_c5,sk_c6) ),
inference(reorient_equations,[],[f13]) ).
fof(f15,negated_conjecture,
( multiply(sk_c9,sk_c8) = sk_c10
| inverse(sk_c5) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_6) ).
fof(f16,plain,
( multiply(sk_c9,sk_c8) = sk_c10
| sk_c6 = inverse(sk_c5) ),
inference(reorient_equations,[],[f15]) ).
fof(f17,negated_conjecture,
( multiply(sk_c9,sk_c8) = sk_c10
| multiply(sk_c6,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_7) ).
fof(f18,plain,
( multiply(sk_c9,sk_c8) = sk_c10
| sk_c8 = multiply(sk_c6,sk_c9) ),
inference(reorient_equations,[],[f17]) ).
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(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(f53,negated_conjecture,
( multiply(sk_c10,sk_c8) = sk_c9
| multiply(sk_c6,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_25) ).
fof(f54,plain,
( sk_c9 = multiply(sk_c10,sk_c8)
| sk_c8 = multiply(sk_c6,sk_c9) ),
inference(reorient_equations,[],[f53]) ).
fof(f55,negated_conjecture,
( multiply(sk_c10,sk_c8) = sk_c9
| inverse(sk_c7) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_26) ).
fof(f56,plain,
( sk_c9 = multiply(sk_c10,sk_c8)
| sk_c10 = inverse(sk_c7) ),
inference(reorient_equations,[],[f55]) ).
fof(f57,negated_conjecture,
( multiply(sk_c10,sk_c8) = sk_c9
| multiply(sk_c7,sk_c8) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_27) ).
fof(f58,plain,
( sk_c9 = multiply(sk_c10,sk_c8)
| sk_c10 = multiply(sk_c7,sk_c8) ),
inference(reorient_equations,[],[f57]) ).
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(f71,negated_conjecture,
( multiply(sk_c10,sk_c2) = sk_c9
| multiply(sk_c6,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_34) ).
fof(f72,plain,
( sk_c9 = multiply(sk_c10,sk_c2)
| sk_c8 = multiply(sk_c6,sk_c9) ),
inference(reorient_equations,[],[f71]) ).
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(f89,negated_conjecture,
( multiply(sk_c1,sk_c10) = sk_c2
| multiply(sk_c6,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_43) ).
fof(f90,plain,
( sk_c2 = multiply(sk_c1,sk_c10)
| sk_c8 = multiply(sk_c6,sk_c9) ),
inference(reorient_equations,[],[f89]) ).
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(f103,negated_conjecture,
( inverse(sk_c1) = sk_c10
| multiply(sk_c5,sk_c6) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_50) ).
fof(f104,plain,
( sk_c10 = inverse(sk_c1)
| sk_c8 = multiply(sk_c5,sk_c6) ),
inference(reorient_equations,[],[f103]) ).
fof(f105,negated_conjecture,
( inverse(sk_c1) = sk_c10
| inverse(sk_c5) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_51) ).
fof(f106,plain,
( sk_c10 = inverse(sk_c1)
| sk_c6 = inverse(sk_c5) ),
inference(reorient_equations,[],[f105]) ).
fof(f107,negated_conjecture,
( inverse(sk_c1) = sk_c10
| multiply(sk_c6,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_52) ).
fof(f108,plain,
( sk_c10 = inverse(sk_c1)
| sk_c8 = multiply(sk_c6,sk_c9) ),
inference(reorient_equations,[],[f107]) ).
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(f116,definition,
( spl0_1
<=> ! [X6] :
( sk_c10 != inverse(X6)
| sk_c10 != multiply(X6,sk_c8) ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f117,plain,
( ! [X6] :
( sk_c10 != inverse(X6)
| sk_c10 != multiply(X6,sk_c8) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f116]) ).
fof(f119,definition,
( spl0_2
<=> ! [X4,X5] :
( sk_c8 != multiply(X4,X5)
| sk_c8 != multiply(X5,sk_c9)
| inverse(X4) != X5 ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f120,plain,
( ! [X4,X5] :
( sk_c8 != multiply(X4,X5)
| sk_c8 != multiply(X5,sk_c9)
| inverse(X4) != X5 )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f119]) ).
fof(f122,definition,
( spl0_3
<=> ! [X2,X3] :
( sk_c9 != multiply(sk_c10,X2)
| sk_c10 != inverse(X3)
| multiply(X3,sk_c10) != X2 ) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f123,plain,
( ! [X2,X3] :
( sk_c9 != multiply(sk_c10,X2)
| sk_c10 != inverse(X3)
| multiply(X3,sk_c10) != X2 )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f122]) ).
fof(f125,definition,
( spl0_4
<=> sk_c9 = inverse(sk_c10) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f126,plain,
( sk_c9 = inverse(sk_c10)
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f125]) ).
fof(f127,plain,
( sk_c9 != inverse(sk_c10)
| spl0_4 ),
inference(avatar_component_clause,[],[f125]) ).
fof(f129,definition,
( spl0_5
<=> sk_c9 = multiply(sk_c10,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f130,plain,
( sk_c9 = multiply(sk_c10,sk_c8)
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f129]) ).
fof(f131,plain,
( sk_c9 != multiply(sk_c10,sk_c8)
| spl0_5 ),
inference(avatar_component_clause,[],[f129]) ).
fof(f133,definition,
( spl0_6
<=> sk_c10 = inverse(sk_c9) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f134,plain,
( sk_c10 = inverse(sk_c9)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f133]) ).
fof(f135,plain,
( sk_c10 != inverse(sk_c9)
| spl0_6 ),
inference(avatar_component_clause,[],[f133]) ).
fof(f137,definition,
( spl0_7
<=> multiply(sk_c9,sk_c8) = sk_c10 ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f138,plain,
( multiply(sk_c9,sk_c8) = sk_c10
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f137]) ).
fof(f139,plain,
( multiply(sk_c9,sk_c8) != sk_c10
| spl0_7 ),
inference(avatar_component_clause,[],[f137]) ).
fof(f140,plain,
( spl0_1
| spl0_2
| spl0_3
| ~ spl0_4
| spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7 ),
inference(avatar_split_clause,[],[f114,f137,f133,f129,f122,f125,f122,f119,f116]) ).
fof(f142,definition,
( spl0_8
<=> sk_c10 = multiply(sk_c7,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f144,plain,
( sk_c10 = multiply(sk_c7,sk_c8)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f142]) ).
fof(f146,definition,
( spl0_9
<=> sk_c10 = inverse(sk_c1) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f148,plain,
( sk_c10 = inverse(sk_c1)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f146]) ).
fof(f149,plain,
( spl0_8
| spl0_9 ),
inference(avatar_split_clause,[],[f112,f146,f142]) ).
fof(f151,definition,
( spl0_10
<=> sk_c10 = inverse(sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f153,plain,
( sk_c10 = inverse(sk_c7)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f151]) ).
fof(f154,plain,
( spl0_10
| spl0_9 ),
inference(avatar_split_clause,[],[f110,f146,f151]) ).
fof(f156,definition,
( spl0_11
<=> sk_c8 = multiply(sk_c6,sk_c9) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f158,plain,
( sk_c8 = multiply(sk_c6,sk_c9)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f156]) ).
fof(f159,plain,
( spl0_11
| spl0_9 ),
inference(avatar_split_clause,[],[f108,f146,f156]) ).
fof(f161,definition,
( spl0_12
<=> sk_c6 = inverse(sk_c5) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f163,plain,
( sk_c6 = inverse(sk_c5)
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f161]) ).
fof(f164,plain,
( spl0_12
| spl0_9 ),
inference(avatar_split_clause,[],[f106,f146,f161]) ).
fof(f166,definition,
( spl0_13
<=> sk_c8 = multiply(sk_c5,sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f168,plain,
( sk_c8 = multiply(sk_c5,sk_c6)
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f166]) ).
fof(f169,plain,
( spl0_13
| spl0_9 ),
inference(avatar_split_clause,[],[f104,f146,f166]) ).
fof(f171,definition,
( spl0_14
<=> sk_c10 = inverse(sk_c3) ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
fof(f173,plain,
( sk_c10 = inverse(sk_c3)
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f171]) ).
fof(f174,plain,
( spl0_14
| spl0_9 ),
inference(avatar_split_clause,[],[f102,f146,f171]) ).
fof(f176,definition,
( spl0_15
<=> sk_c4 = multiply(sk_c3,sk_c10) ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
fof(f178,plain,
( sk_c4 = multiply(sk_c3,sk_c10)
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f176]) ).
fof(f179,plain,
( spl0_15
| spl0_9 ),
inference(avatar_split_clause,[],[f100,f146,f176]) ).
fof(f181,definition,
( spl0_16
<=> sk_c9 = multiply(sk_c10,sk_c4) ),
introduced(definition,[new_symbols(definition,[spl0_16])],[avatar_definition]) ).
fof(f183,plain,
( sk_c9 = multiply(sk_c10,sk_c4)
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f181]) ).
fof(f184,plain,
( spl0_16
| spl0_9 ),
inference(avatar_split_clause,[],[f98,f146,f181]) ).
fof(f185,plain,
( spl0_4
| spl0_9 ),
inference(avatar_split_clause,[],[f96,f146,f125]) ).
fof(f187,definition,
( spl0_17
<=> sk_c2 = multiply(sk_c1,sk_c10) ),
introduced(definition,[new_symbols(definition,[spl0_17])],[avatar_definition]) ).
fof(f188,plain,
( sk_c2 != multiply(sk_c1,sk_c10)
| spl0_17 ),
inference(avatar_component_clause,[],[f187]) ).
fof(f189,plain,
( sk_c2 = multiply(sk_c1,sk_c10)
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f187]) ).
fof(f190,plain,
( spl0_8
| spl0_17 ),
inference(avatar_split_clause,[],[f94,f187,f142]) ).
fof(f191,plain,
( spl0_10
| spl0_17 ),
inference(avatar_split_clause,[],[f92,f187,f151]) ).
fof(f192,plain,
( spl0_11
| spl0_17 ),
inference(avatar_split_clause,[],[f90,f187,f156]) ).
fof(f193,plain,
( spl0_12
| spl0_17 ),
inference(avatar_split_clause,[],[f88,f187,f161]) ).
fof(f194,plain,
( spl0_13
| spl0_17 ),
inference(avatar_split_clause,[],[f86,f187,f166]) ).
fof(f195,plain,
( spl0_14
| spl0_17 ),
inference(avatar_split_clause,[],[f84,f187,f171]) ).
fof(f196,plain,
( spl0_15
| spl0_17 ),
inference(avatar_split_clause,[],[f82,f187,f176]) ).
fof(f197,plain,
( spl0_16
| spl0_17 ),
inference(avatar_split_clause,[],[f80,f187,f181]) ).
fof(f198,plain,
( spl0_4
| spl0_17 ),
inference(avatar_split_clause,[],[f78,f187,f125]) ).
fof(f200,definition,
( spl0_18
<=> sk_c9 = multiply(sk_c10,sk_c2) ),
introduced(definition,[new_symbols(definition,[spl0_18])],[avatar_definition]) ).
fof(f202,plain,
( sk_c9 = multiply(sk_c10,sk_c2)
| ~ spl0_18 ),
inference(avatar_component_clause,[],[f200]) ).
fof(f203,plain,
( spl0_8
| spl0_18 ),
inference(avatar_split_clause,[],[f76,f200,f142]) ).
fof(f204,plain,
( spl0_10
| spl0_18 ),
inference(avatar_split_clause,[],[f74,f200,f151]) ).
fof(f205,plain,
( spl0_11
| spl0_18 ),
inference(avatar_split_clause,[],[f72,f200,f156]) ).
fof(f206,plain,
( spl0_12
| spl0_18 ),
inference(avatar_split_clause,[],[f70,f200,f161]) ).
fof(f207,plain,
( spl0_13
| spl0_18 ),
inference(avatar_split_clause,[],[f68,f200,f166]) ).
fof(f208,plain,
( spl0_14
| spl0_18 ),
inference(avatar_split_clause,[],[f66,f200,f171]) ).
fof(f209,plain,
( spl0_15
| spl0_18 ),
inference(avatar_split_clause,[],[f64,f200,f176]) ).
fof(f210,plain,
( spl0_16
| spl0_18 ),
inference(avatar_split_clause,[],[f62,f200,f181]) ).
fof(f211,plain,
( spl0_4
| spl0_18 ),
inference(avatar_split_clause,[],[f60,f200,f125]) ).
fof(f212,plain,
( spl0_8
| spl0_5 ),
inference(avatar_split_clause,[],[f58,f129,f142]) ).
fof(f213,plain,
( spl0_10
| spl0_5 ),
inference(avatar_split_clause,[],[f56,f129,f151]) ).
fof(f214,plain,
( spl0_11
| spl0_5 ),
inference(avatar_split_clause,[],[f54,f129,f156]) ).
fof(f215,plain,
( spl0_12
| spl0_5 ),
inference(avatar_split_clause,[],[f52,f129,f161]) ).
fof(f216,plain,
( spl0_13
| spl0_5 ),
inference(avatar_split_clause,[],[f50,f129,f166]) ).
fof(f217,plain,
( spl0_14
| spl0_5 ),
inference(avatar_split_clause,[],[f48,f129,f171]) ).
fof(f218,plain,
( spl0_15
| spl0_5 ),
inference(avatar_split_clause,[],[f46,f129,f176]) ).
fof(f219,plain,
( spl0_16
| spl0_5 ),
inference(avatar_split_clause,[],[f44,f129,f181]) ).
fof(f229,plain,
( spl0_4
| spl0_6 ),
inference(avatar_split_clause,[],[f24,f133,f125]) ).
fof(f230,plain,
( spl0_8
| spl0_7 ),
inference(avatar_split_clause,[],[f22,f137,f142]) ).
fof(f231,plain,
( spl0_10
| spl0_7 ),
inference(avatar_split_clause,[],[f20,f137,f151]) ).
fof(f232,plain,
( spl0_11
| spl0_7 ),
inference(avatar_split_clause,[],[f18,f137,f156]) ).
fof(f233,plain,
( spl0_12
| spl0_7 ),
inference(avatar_split_clause,[],[f16,f137,f161]) ).
fof(f234,plain,
( spl0_13
| spl0_7 ),
inference(avatar_split_clause,[],[f14,f137,f166]) ).
fof(f235,plain,
( spl0_14
| spl0_7 ),
inference(avatar_split_clause,[],[f12,f137,f171]) ).
fof(f236,plain,
( spl0_15
| spl0_7 ),
inference(avatar_split_clause,[],[f10,f137,f176]) ).
fof(f237,plain,
( spl0_16
| spl0_7 ),
inference(avatar_split_clause,[],[f8,f137,f181]) ).
fof(f239,plain,
( sk_c8 = multiply(sk_c5,inverse(sk_c5))
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f168,f163]) ).
fof(f240,plain,
( sk_c8 = multiply(inverse(sk_c5),sk_c9)
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f158,f163]) ).
fof(f241,plain,
! [X0,X1] : multiply(inverse(X0),X0) = multiply(inverse(X1),X1),
inference(superposition,[],[f3,f3]) ).
fof(f242,plain,
( identity = multiply(sk_c9,sk_c10)
| ~ spl0_4 ),
inference(superposition,[],[f3,f126]) ).
fof(f243,plain,
( identity = multiply(sk_c10,sk_c7)
| ~ spl0_10 ),
inference(superposition,[],[f3,f153]) ).
fof(f244,plain,
( identity = multiply(sk_c10,sk_c3)
| ~ spl0_14 ),
inference(superposition,[],[f3,f173]) ).
fof(f245,plain,
! [X0,X1] : multiply(multiply(inverse(X0),X0),X1) = X1,
inference(superposition,[],[f1,f3]) ).
fof(f246,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f245,f4]) ).
fof(f251,plain,
( ! [X0] : multiply(sk_c9,X0) = multiply(sk_c10,multiply(sk_c4,X0))
| ~ spl0_16 ),
inference(superposition,[],[f4,f183]) ).
fof(f252,plain,
( ! [X0] : multiply(sk_c4,X0) = multiply(sk_c3,multiply(sk_c10,X0))
| ~ spl0_15 ),
inference(superposition,[],[f4,f178]) ).
fof(f253,plain,
( ! [X0] : multiply(sk_c8,X0) = multiply(sk_c5,multiply(inverse(sk_c5),X0))
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f4,f239]) ).
fof(f260,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c9,multiply(sk_c10,X0))
| ~ spl0_4 ),
inference(superposition,[],[f4,f242]) ).
fof(f261,plain,
( ! [X0] : multiply(sk_c9,multiply(sk_c10,X0)) = X0
| ~ spl0_4 ),
inference(forward_demodulation,[],[f260,f1]) ).
fof(f270,plain,
( sk_c4 = multiply(sk_c9,sk_c9)
| ~ spl0_4
| ~ spl0_16 ),
inference(superposition,[],[f261,f183]) ).
fof(f271,plain,
( sk_c3 = multiply(sk_c9,identity)
| ~ spl0_4
| ~ spl0_14 ),
inference(superposition,[],[f261,f244]) ).
fof(f272,plain,
( sk_c7 = multiply(sk_c9,identity)
| ~ spl0_4
| ~ spl0_10 ),
inference(superposition,[],[f261,f243]) ).
fof(f306,plain,
( sk_c9 = multiply(sk_c10,multiply(sk_c9,sk_c9))
| ~ spl0_4
| ~ spl0_16 ),
inference(superposition,[],[f183,f270]) ).
fof(f311,plain,
( ! [X0] : multiply(sk_c4,X0) = multiply(multiply(sk_c9,identity),multiply(sk_c10,X0))
| ~ spl0_4
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f252,f271]) ).
fof(f313,plain,
( sk_c4 = multiply(multiply(sk_c9,identity),sk_c10)
| ~ spl0_4
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f178,f271]) ).
fof(f314,plain,
( sk_c10 = inverse(multiply(sk_c9,identity))
| ~ spl0_4
| ~ spl0_14 ),
inference(superposition,[],[f173,f271]) ).
fof(f315,plain,
( sk_c4 = multiply(sk_c9,multiply(identity,sk_c10))
| ~ spl0_4
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f313,f4]) ).
fof(f317,plain,
( ! [X0] : multiply(sk_c4,X0) = multiply(sk_c9,multiply(identity,multiply(sk_c10,X0)))
| ~ spl0_4
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f311,f4]) ).
fof(f318,plain,
( sk_c4 = multiply(sk_c9,sk_c10)
| ~ spl0_4
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f315,f1]) ).
fof(f319,plain,
( ! [X0] : multiply(sk_c4,X0) = multiply(sk_c9,multiply(sk_c10,X0))
| ~ spl0_4
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f317,f1]) ).
fof(f320,plain,
( identity = sk_c4
| ~ spl0_4
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f318,f242]) ).
fof(f321,plain,
( ! [X0] : multiply(sk_c4,X0) = X0
| ~ spl0_4
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f319,f261]) ).
fof(f322,plain,
( ! [X0] : multiply(multiply(sk_c9,sk_c9),X0) = X0
| ~ spl0_4
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f321,f270]) ).
fof(f323,plain,
( ! [X0] : multiply(sk_c9,multiply(sk_c9,X0)) = X0
| ~ spl0_4
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f322,f4]) ).
fof(f330,plain,
( identity = multiply(sk_c9,sk_c9)
| ~ spl0_4
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(superposition,[],[f270,f320]) ).
fof(f331,plain,
( ! [X0] : multiply(sk_c9,X0) = multiply(sk_c10,multiply(identity,X0))
| ~ spl0_4
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(superposition,[],[f251,f320]) ).
fof(f334,plain,
( ! [X0] : multiply(sk_c10,X0) = multiply(sk_c9,X0)
| ~ spl0_4
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f331,f1]) ).
fof(f335,plain,
( ! [X0] : multiply(sk_c9,X0) = multiply(inverse(multiply(sk_c9,identity)),X0)
| ~ spl0_4
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f334,f314]) ).
fof(f341,plain,
( sk_c9 = multiply(inverse(inverse(sk_c5)),sk_c8)
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f246,f240]) ).
fof(f342,plain,
! [X0] : multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[],[f246,f3]) ).
fof(f343,plain,
! [X0,X1] : multiply(X1,X0) = multiply(inverse(inverse(X1)),X0),
inference(superposition,[],[f246,f246]) ).
fof(f344,plain,
( sk_c10 = multiply(inverse(sk_c9),identity)
| ~ spl0_4 ),
inference(superposition,[],[f246,f242]) ).
fof(f345,plain,
( ! [X0] : multiply(sk_c10,X0) = multiply(inverse(sk_c9),X0)
| ~ spl0_4 ),
inference(superposition,[],[f246,f261]) ).
fof(f355,plain,
( sk_c8 = multiply(inverse(sk_c7),sk_c10)
| ~ spl0_8 ),
inference(superposition,[],[f246,f144]) ).
fof(f361,plain,
( sk_c8 = multiply(inverse(sk_c7),inverse(multiply(sk_c9,identity)))
| ~ spl0_4
| ~ spl0_8
| ~ spl0_14 ),
inference(forward_demodulation,[],[f355,f314]) ).
fof(f369,plain,
( ! [X0] : multiply(inverse(multiply(sk_c9,identity)),X0) = multiply(inverse(sk_c9),X0)
| ~ spl0_4
| ~ spl0_14 ),
inference(forward_demodulation,[],[f345,f314]) ).
fof(f370,plain,
! [X0] : multiply(X0,identity) = X0,
inference(forward_demodulation,[],[f342,f343]) ).
fof(f371,plain,
( sk_c9 = multiply(sk_c5,sk_c8)
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f341,f343]) ).
fof(f373,plain,
( sk_c8 = multiply(sk_c10,inverse(multiply(sk_c9,identity)))
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_14 ),
inference(forward_demodulation,[],[f361,f153]) ).
fof(f378,plain,
( ! [X0] : multiply(sk_c9,X0) = multiply(inverse(sk_c9),X0)
| ~ spl0_4
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f369,f335]) ).
fof(f380,plain,
( sk_c8 = multiply(sk_c10,inverse(sk_c9))
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_14 ),
inference(forward_demodulation,[],[f373,f370]) ).
fof(f385,plain,
( sk_c8 = multiply(inverse(multiply(sk_c9,identity)),inverse(sk_c9))
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_14 ),
inference(forward_demodulation,[],[f380,f314]) ).
fof(f388,plain,
( sk_c8 = multiply(sk_c9,inverse(sk_c9))
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f385,f335]) ).
fof(f394,plain,
( ! [X0] : multiply(sk_c9,X0) = multiply(sk_c5,multiply(sk_c8,X0))
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f4,f371]) ).
fof(f395,plain,
( ! [X0] : multiply(sk_c9,X0) = multiply(sk_c5,multiply(multiply(sk_c9,inverse(sk_c9)),X0))
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f394,f388]) ).
fof(f396,plain,
( ! [X0] : multiply(sk_c9,X0) = multiply(sk_c5,multiply(sk_c9,multiply(inverse(sk_c9),X0)))
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f395,f4]) ).
fof(f397,plain,
( ! [X0] : multiply(sk_c9,X0) = multiply(sk_c5,multiply(sk_c9,multiply(sk_c9,X0)))
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f396,f378]) ).
fof(f398,plain,
( ! [X0] : multiply(sk_c9,X0) = multiply(sk_c5,X0)
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f397,f323]) ).
fof(f416,plain,
( ! [X0] : multiply(sk_c8,sk_c5) = multiply(sk_c5,multiply(inverse(X0),X0))
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f253,f241]) ).
fof(f417,plain,
! [X0,X1] : multiply(inverse(inverse(X1)),multiply(inverse(X0),X0)) = X1,
inference(superposition,[],[f246,f241]) ).
fof(f420,plain,
! [X0,X1] : multiply(X1,multiply(inverse(X0),X0)) = X1,
inference(forward_demodulation,[],[f417,f343]) ).
fof(f421,plain,
( ! [X0] : multiply(sk_c8,sk_c5) = multiply(sk_c9,multiply(inverse(X0),X0))
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f416,f398]) ).
fof(f432,plain,
( sk_c9 = multiply(sk_c8,sk_c5)
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f421,f420]) ).
fof(f441,plain,
( sk_c9 = multiply(multiply(sk_c9,inverse(sk_c9)),sk_c5)
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f432,f388]) ).
fof(f447,plain,
( sk_c9 = multiply(sk_c9,multiply(inverse(sk_c9),sk_c5))
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f441,f4]) ).
fof(f453,plain,
( sk_c9 = multiply(sk_c9,multiply(sk_c9,sk_c5))
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f447,f378]) ).
fof(f455,plain,
( sk_c9 = sk_c5
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f453,f323]) ).
fof(f457,plain,
( sk_c9 = multiply(sk_c9,sk_c8)
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(superposition,[],[f371,f455]) ).
fof(f459,plain,
( sk_c8 = multiply(inverse(sk_c9),sk_c9)
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(superposition,[],[f240,f455]) ).
fof(f461,plain,
( identity = sk_c8
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f459,f3]) ).
fof(f463,plain,
( sk_c9 = multiply(sk_c9,multiply(sk_c9,inverse(sk_c9)))
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f457,f388]) ).
fof(f465,plain,
( sk_c9 = inverse(sk_c9)
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f463,f323]) ).
fof(f469,plain,
( sk_c9 = inverse(multiply(inverse(sk_c9),identity))
| ~ spl0_4 ),
inference(superposition,[],[f126,f344]) ).
fof(f470,plain,
( inverse(sk_c9) != multiply(inverse(sk_c9),identity)
| ~ spl0_4
| spl0_6 ),
inference(superposition,[],[f135,f344]) ).
fof(f487,plain,
( $false
| ~ spl0_4
| spl0_6 ),
inference(forward_subsumption_resolution,[],[f470,f370]) ).
fof(f488,plain,
( ~ spl0_4
| spl0_6 ),
inference(avatar_contradiction_clause,[],[f487]) ).
fof(f518,plain,
( sk_c9 != multiply(sk_c10,multiply(sk_c9,inverse(sk_c9)))
| ~ spl0_4
| spl0_5
| ~ spl0_8
| ~ spl0_10
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f131,f388]) ).
fof(f519,plain,
( sk_c9 = sk_c10
| ~ spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f134,f465]) ).
fof(f520,plain,
( sk_c9 != multiply(sk_c10,multiply(sk_c9,sk_c9))
| ~ spl0_4
| spl0_5
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f518,f465]) ).
fof(f521,plain,
( $false
| ~ spl0_4
| spl0_5
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_subsumption_resolution,[],[f520,f306]) ).
fof(f522,plain,
( ~ spl0_4
| spl0_5
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(avatar_contradiction_clause,[],[f521]) ).
fof(f524,plain,
( multiply(sk_c9,sk_c8) != inverse(multiply(sk_c9,identity))
| ~ spl0_4
| spl0_7
| ~ spl0_14 ),
inference(forward_demodulation,[],[f139,f314]) ).
fof(f526,plain,
( multiply(sk_c9,sk_c8) != inverse(sk_c9)
| ~ spl0_4
| spl0_7
| ~ spl0_14 ),
inference(forward_demodulation,[],[f524,f370]) ).
fof(f527,plain,
( sk_c9 != multiply(sk_c9,sk_c8)
| ~ spl0_4
| spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f526,f465]) ).
fof(f528,plain,
( sk_c9 != multiply(sk_c9,multiply(sk_c9,inverse(sk_c9)))
| ~ spl0_4
| spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f527,f388]) ).
fof(f529,plain,
( sk_c9 != inverse(sk_c9)
| ~ spl0_4
| spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f528,f323]) ).
fof(f530,plain,
( $false
| ~ spl0_4
| spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_subsumption_resolution,[],[f529,f465]) ).
fof(f531,plain,
( ~ spl0_4
| spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(avatar_contradiction_clause,[],[f530]) ).
fof(f532,plain,
( ! [X6] :
( inverse(X6) != inverse(multiply(sk_c9,identity))
| sk_c10 != multiply(X6,sk_c8) )
| ~ spl0_1
| ~ spl0_4
| ~ spl0_14 ),
inference(forward_demodulation,[],[f117,f314]) ).
fof(f534,plain,
( ! [X6] :
( inverse(sk_c9) != inverse(X6)
| sk_c10 != multiply(X6,sk_c8) )
| ~ spl0_1
| ~ spl0_4
| ~ spl0_14 ),
inference(forward_demodulation,[],[f532,f370]) ).
fof(f536,plain,
( ! [X6] :
( sk_c9 != inverse(X6)
| sk_c10 != multiply(X6,sk_c8) )
| ~ spl0_1
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f534,f465]) ).
fof(f538,plain,
( ! [X6] :
( sk_c10 != multiply(X6,multiply(sk_c9,inverse(sk_c9)))
| sk_c9 != inverse(X6) )
| ~ spl0_1
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f536,f388]) ).
fof(f540,plain,
( ! [X6] :
( sk_c10 != multiply(X6,multiply(sk_c9,sk_c9))
| sk_c9 != inverse(X6) )
| ~ spl0_1
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f538,f465]) ).
fof(f542,plain,
( ! [X6] :
( sk_c10 != multiply(X6,identity)
| sk_c9 != inverse(X6) )
| ~ spl0_1
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f540,f330]) ).
fof(f543,plain,
( ! [X6] :
( sk_c10 != X6
| sk_c9 != inverse(X6) )
| ~ spl0_1
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f542,f370]) ).
fof(f544,plain,
( ! [X6] :
( inverse(multiply(sk_c9,identity)) != X6
| sk_c9 != inverse(X6) )
| ~ spl0_1
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f543,f314]) ).
fof(f545,plain,
( ! [X6] :
( inverse(sk_c9) != X6
| sk_c9 != inverse(X6) )
| ~ spl0_1
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f544,f370]) ).
fof(f546,plain,
( ! [X6] :
( sk_c9 != inverse(X6)
| sk_c9 != X6 )
| ~ spl0_1
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f545,f465]) ).
fof(f575,plain,
( sk_c9 != sk_c10
| sk_c9 != sk_c7
| ~ spl0_1
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(superposition,[],[f546,f153]) ).
fof(f579,plain,
( sk_c9 != sk_c7
| ~ spl0_1
| ~ spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_subsumption_resolution,[],[f575,f519]) ).
fof(f583,plain,
( sk_c9 != multiply(sk_c9,identity)
| ~ spl0_1
| ~ spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f579,f272]) ).
fof(f586,plain,
( $false
| ~ spl0_1
| ~ spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_subsumption_resolution,[],[f583,f370]) ).
fof(f587,plain,
( ~ spl0_1
| ~ spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(avatar_contradiction_clause,[],[f586]) ).
fof(f588,plain,
( ! [X4,X5] :
( multiply(X4,X5) != multiply(sk_c9,inverse(sk_c9))
| sk_c8 != multiply(X5,sk_c9)
| inverse(X4) != X5 )
| ~ spl0_2
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f120,f388]) ).
fof(f589,plain,
( ! [X4,X5] :
( multiply(X4,X5) != multiply(sk_c9,sk_c9)
| sk_c8 != multiply(X5,sk_c9)
| inverse(X4) != X5 )
| ~ spl0_2
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f588,f465]) ).
fof(f590,plain,
( ! [X4,X5] :
( identity != multiply(X4,X5)
| sk_c8 != multiply(X5,sk_c9)
| inverse(X4) != X5 )
| ~ spl0_2
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f589,f330]) ).
fof(f591,plain,
( ! [X4,X5] :
( multiply(X5,sk_c9) != multiply(sk_c9,inverse(sk_c9))
| identity != multiply(X4,X5)
| inverse(X4) != X5 )
| ~ spl0_2
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f590,f388]) ).
fof(f592,plain,
( ! [X4,X5] :
( multiply(X5,sk_c9) != multiply(sk_c9,sk_c9)
| identity != multiply(X4,X5)
| inverse(X4) != X5 )
| ~ spl0_2
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f591,f465]) ).
fof(f593,plain,
( ! [X4,X5] :
( identity != multiply(X5,sk_c9)
| identity != multiply(X4,X5)
| inverse(X4) != X5 )
| ~ spl0_2
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f592,f330]) ).
fof(f611,plain,
( ! [X0] :
( identity != identity
| identity != multiply(X0,inverse(sk_c9))
| inverse(X0) != inverse(sk_c9) )
| ~ spl0_2
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(superposition,[],[f593,f3]) ).
fof(f613,plain,
( ! [X0] :
( identity != multiply(X0,inverse(sk_c9))
| inverse(X0) != inverse(sk_c9) )
| ~ spl0_2
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(trivial_inequality_removal,[],[f611]) ).
fof(f615,plain,
( ! [X0] :
( identity != multiply(X0,sk_c9)
| inverse(X0) != inverse(sk_c9) )
| ~ spl0_2
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f613,f465]) ).
fof(f621,plain,
( ! [X0] :
( inverse(X0) != sk_c9
| identity != multiply(X0,sk_c9) )
| ~ spl0_2
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f615,f465]) ).
fof(f643,plain,
( sk_c9 != sk_c9
| identity != multiply(sk_c10,sk_c9)
| ~ spl0_2
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(superposition,[],[f621,f126]) ).
fof(f646,plain,
( identity != multiply(sk_c10,sk_c9)
| ~ spl0_2
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(trivial_inequality_removal,[],[f643]) ).
fof(f649,plain,
( identity != multiply(inverse(multiply(sk_c9,identity)),sk_c9)
| ~ spl0_2
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f646,f314]) ).
fof(f652,plain,
( identity != multiply(sk_c9,sk_c9)
| ~ spl0_2
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f649,f335]) ).
fof(f655,plain,
( $false
| ~ spl0_2
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_subsumption_resolution,[],[f652,f330]) ).
fof(f656,plain,
( ~ spl0_2
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(avatar_contradiction_clause,[],[f655]) ).
fof(f663,plain,
( inverse(sk_c1) = multiply(inverse(sk_c9),identity)
| ~ spl0_4
| ~ spl0_9 ),
inference(forward_demodulation,[],[f148,f344]) ).
fof(f665,plain,
( sk_c2 = multiply(sk_c1,multiply(inverse(sk_c9),identity))
| ~ spl0_4
| ~ spl0_17 ),
inference(forward_demodulation,[],[f189,f344]) ).
fof(f666,plain,
( sk_c9 = multiply(multiply(inverse(sk_c9),identity),sk_c2)
| ~ spl0_4
| ~ spl0_18 ),
inference(forward_demodulation,[],[f202,f344]) ).
fof(f684,plain,
( sk_c9 = inverse(inverse(sk_c9))
| ~ spl0_4 ),
inference(forward_demodulation,[],[f469,f370]) ).
fof(f690,plain,
( sk_c9 = multiply(multiply(inverse(sk_c9),identity),sk_c8)
| ~ spl0_4
| ~ spl0_5 ),
inference(forward_demodulation,[],[f130,f344]) ).
fof(f691,plain,
( multiply(sk_c9,sk_c8) = multiply(inverse(sk_c9),identity)
| ~ spl0_4
| ~ spl0_7 ),
inference(forward_demodulation,[],[f138,f344]) ).
fof(f692,plain,
( inverse(sk_c9) = inverse(sk_c1)
| ~ spl0_4
| ~ spl0_9 ),
inference(forward_demodulation,[],[f663,f370]) ).
fof(f694,plain,
( sk_c2 = multiply(sk_c1,inverse(sk_c9))
| ~ spl0_4
| ~ spl0_17 ),
inference(forward_demodulation,[],[f665,f370]) ).
fof(f695,plain,
( sk_c9 = multiply(inverse(sk_c9),multiply(identity,sk_c2))
| ~ spl0_4
| ~ spl0_18 ),
inference(forward_demodulation,[],[f666,f4]) ).
fof(f713,plain,
( sk_c9 = multiply(inverse(sk_c9),multiply(identity,sk_c8))
| ~ spl0_4
| ~ spl0_5 ),
inference(forward_demodulation,[],[f690,f4]) ).
fof(f714,plain,
( multiply(sk_c9,sk_c8) = inverse(sk_c9)
| ~ spl0_4
| ~ spl0_7 ),
inference(forward_demodulation,[],[f691,f370]) ).
fof(f715,plain,
( sk_c9 = multiply(inverse(sk_c9),sk_c2)
| ~ spl0_4
| ~ spl0_18 ),
inference(forward_demodulation,[],[f695,f1]) ).
fof(f726,plain,
( sk_c9 = multiply(inverse(sk_c9),sk_c8)
| ~ spl0_4
| ~ spl0_5 ),
inference(forward_demodulation,[],[f713,f1]) ).
fof(f771,plain,
( identity = multiply(inverse(sk_c9),sk_c1)
| ~ spl0_4
| ~ spl0_9 ),
inference(superposition,[],[f3,f692]) ).
fof(f772,plain,
( inverse(sk_c9) = multiply(inverse(sk_c1),sk_c2)
| ~ spl0_4
| ~ spl0_17 ),
inference(superposition,[],[f246,f694]) ).
fof(f774,plain,
( inverse(sk_c9) = multiply(inverse(sk_c9),sk_c2)
| ~ spl0_4
| ~ spl0_9
| ~ spl0_17 ),
inference(forward_demodulation,[],[f772,f692]) ).
fof(f775,plain,
( sk_c9 = inverse(sk_c9)
| ~ spl0_4
| ~ spl0_9
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f774,f715]) ).
fof(f780,plain,
( identity = multiply(sk_c9,sk_c9)
| ~ spl0_4
| ~ spl0_9
| ~ spl0_17
| ~ spl0_18 ),
inference(superposition,[],[f3,f775]) ).
fof(f798,plain,
( sk_c2 = multiply(inverse(inverse(sk_c9)),sk_c9)
| ~ spl0_4
| ~ spl0_18 ),
inference(superposition,[],[f246,f715]) ).
fof(f801,plain,
( sk_c2 = multiply(sk_c9,sk_c9)
| ~ spl0_4
| ~ spl0_18 ),
inference(forward_demodulation,[],[f798,f343]) ).
fof(f802,plain,
( identity = sk_c2
| ~ spl0_4
| ~ spl0_9
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f801,f780]) ).
fof(f806,plain,
( sk_c8 = multiply(inverse(inverse(sk_c9)),sk_c9)
| ~ spl0_4
| ~ spl0_5 ),
inference(superposition,[],[f246,f726]) ).
fof(f809,plain,
( sk_c8 = multiply(sk_c9,sk_c9)
| ~ spl0_4
| ~ spl0_5 ),
inference(forward_demodulation,[],[f806,f343]) ).
fof(f812,plain,
( identity = sk_c8
| ~ spl0_4
| ~ spl0_5
| ~ spl0_9
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f809,f780]) ).
fof(f853,plain,
( sk_c8 != sk_c8
| sk_c8 != multiply(inverse(sk_c5),sk_c9)
| inverse(sk_c5) != inverse(sk_c5)
| ~ spl0_2
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f120,f239]) ).
fof(f859,plain,
( sk_c8 != sk_c2
| sk_c8 != multiply(inverse(sk_c9),sk_c9)
| inverse(sk_c9) != inverse(sk_c1)
| ~ spl0_2
| ~ spl0_4
| ~ spl0_17 ),
inference(superposition,[],[f120,f694]) ).
fof(f861,plain,
( sk_c8 != multiply(inverse(sk_c5),sk_c9)
| ~ spl0_2
| ~ spl0_12
| ~ spl0_13 ),
inference(trivial_inequality_removal,[],[f853]) ).
fof(f864,plain,
( sk_c8 != sk_c2
| sk_c8 != multiply(inverse(sk_c9),sk_c9)
| ~ spl0_2
| ~ spl0_4
| ~ spl0_9
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f859,f692]) ).
fof(f870,plain,
( $false
| ~ spl0_2
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f861,f240]) ).
fof(f871,plain,
( ~ spl0_2
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[],[f870]) ).
fof(f890,plain,
( identity != sk_c8
| sk_c8 != multiply(inverse(sk_c9),sk_c9)
| ~ spl0_2
| ~ spl0_4
| ~ spl0_9
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f864,f802]) ).
fof(f914,plain,
( sk_c8 != multiply(inverse(sk_c9),sk_c9)
| ~ spl0_2
| ~ spl0_4
| ~ spl0_5
| ~ spl0_9
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[],[f890,f812]) ).
fof(f938,plain,
( identity != sk_c8
| ~ spl0_2
| ~ spl0_4
| ~ spl0_5
| ~ spl0_9
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f914,f3]) ).
fof(f959,plain,
( $false
| ~ spl0_2
| ~ spl0_4
| ~ spl0_5
| ~ spl0_9
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[],[f938,f812]) ).
fof(f960,plain,
( ~ spl0_2
| ~ spl0_4
| ~ spl0_5
| ~ spl0_9
| ~ spl0_17
| ~ spl0_18 ),
inference(avatar_contradiction_clause,[],[f959]) ).
fof(f1057,plain,
( ! [X6] :
( inverse(X6) != multiply(inverse(sk_c9),identity)
| sk_c10 != multiply(X6,sk_c8) )
| ~ spl0_1
| ~ spl0_4 ),
inference(forward_demodulation,[],[f117,f344]) ).
fof(f1058,plain,
( ! [X6] :
( inverse(sk_c9) != inverse(X6)
| sk_c10 != multiply(X6,sk_c8) )
| ~ spl0_1
| ~ spl0_4 ),
inference(forward_demodulation,[],[f1057,f370]) ).
fof(f1059,plain,
( ! [X6] :
( sk_c9 != inverse(X6)
| sk_c10 != multiply(X6,sk_c8) )
| ~ spl0_1
| ~ spl0_4
| ~ spl0_9
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f1058,f775]) ).
fof(f1098,plain,
( ! [X2,X3] :
( sk_c9 != multiply(multiply(inverse(sk_c9),identity),X2)
| sk_c10 != inverse(X3)
| multiply(X3,sk_c10) != X2 )
| ~ spl0_3
| ~ spl0_4 ),
inference(forward_demodulation,[],[f123,f344]) ).
fof(f1099,plain,
( ! [X2,X3] :
( sk_c9 != multiply(inverse(sk_c9),multiply(identity,X2))
| sk_c10 != inverse(X3)
| multiply(X3,sk_c10) != X2 )
| ~ spl0_3
| ~ spl0_4 ),
inference(forward_demodulation,[],[f1098,f4]) ).
fof(f1100,plain,
( ! [X2,X3] :
( sk_c9 != multiply(inverse(sk_c9),X2)
| sk_c10 != inverse(X3)
| multiply(X3,sk_c10) != X2 )
| ~ spl0_3
| ~ spl0_4 ),
inference(forward_demodulation,[],[f1099,f1]) ).
fof(f1101,plain,
( ! [X2,X3] :
( sk_c9 != multiply(sk_c9,X2)
| sk_c10 != inverse(X3)
| multiply(X3,sk_c10) != X2 )
| ~ spl0_3
| ~ spl0_4
| ~ spl0_9
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f1100,f775]) ).
fof(f1102,plain,
( ! [X2,X3] :
( inverse(X3) != multiply(inverse(sk_c9),identity)
| sk_c9 != multiply(sk_c9,X2)
| multiply(X3,sk_c10) != X2 )
| ~ spl0_3
| ~ spl0_4
| ~ spl0_9
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f1101,f344]) ).
fof(f1103,plain,
( ! [X2,X3] :
( inverse(sk_c9) != inverse(X3)
| sk_c9 != multiply(sk_c9,X2)
| multiply(X3,sk_c10) != X2 )
| ~ spl0_3
| ~ spl0_4
| ~ spl0_9
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f1102,f370]) ).
fof(f1104,plain,
( ! [X2,X3] :
( sk_c9 != inverse(X3)
| sk_c9 != multiply(sk_c9,X2)
| multiply(X3,sk_c10) != X2 )
| ~ spl0_3
| ~ spl0_4
| ~ spl0_9
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f1103,f775]) ).
fof(f1105,plain,
( ! [X2,X3] :
( multiply(X3,multiply(inverse(sk_c9),identity)) != X2
| sk_c9 != inverse(X3)
| sk_c9 != multiply(sk_c9,X2) )
| ~ spl0_3
| ~ spl0_4
| ~ spl0_9
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f1104,f344]) ).
fof(f1106,plain,
( ! [X2,X3] :
( multiply(X3,inverse(sk_c9)) != X2
| sk_c9 != inverse(X3)
| sk_c9 != multiply(sk_c9,X2) )
| ~ spl0_3
| ~ spl0_4
| ~ spl0_9
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f1105,f370]) ).
fof(f1107,plain,
( ! [X2,X3] :
( multiply(X3,sk_c9) != X2
| sk_c9 != inverse(X3)
| sk_c9 != multiply(sk_c9,X2) )
| ~ spl0_3
| ~ spl0_4
| ~ spl0_9
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f1106,f775]) ).
fof(f1140,plain,
( ! [X0] :
( identity != X0
| sk_c9 != inverse(inverse(sk_c9))
| sk_c9 != multiply(sk_c9,X0) )
| ~ spl0_3
| ~ spl0_4
| ~ spl0_9
| ~ spl0_17
| ~ spl0_18 ),
inference(superposition,[],[f1107,f3]) ).
fof(f1144,plain,
( ! [X0] :
( sk_c9 != multiply(sk_c9,X0)
| identity != X0 )
| ~ spl0_3
| ~ spl0_4
| ~ spl0_9
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[],[f1140,f684]) ).
fof(f1161,plain,
( sk_c1 = multiply(inverse(inverse(sk_c9)),identity)
| ~ spl0_4
| ~ spl0_9 ),
inference(superposition,[],[f246,f771]) ).
fof(f1164,plain,
( sk_c1 = multiply(sk_c9,identity)
| ~ spl0_4
| ~ spl0_9 ),
inference(forward_demodulation,[],[f1161,f343]) ).
fof(f1165,plain,
( sk_c9 = sk_c1
| ~ spl0_4
| ~ spl0_9 ),
inference(forward_demodulation,[],[f1164,f370]) ).
fof(f1171,plain,
( sk_c9 != inverse(sk_c9)
| identity != sk_c8
| ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_17
| ~ spl0_18 ),
inference(superposition,[],[f1144,f714]) ).
fof(f1172,plain,
( identity != sk_c8
| ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[],[f1171,f775]) ).
fof(f1174,plain,
( $false
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[],[f1172,f812]) ).
fof(f1175,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_17
| ~ spl0_18 ),
inference(avatar_contradiction_clause,[],[f1174]) ).
fof(f1180,plain,
( ! [X6] :
( sk_c10 != multiply(X6,identity)
| sk_c9 != inverse(X6) )
| ~ spl0_1
| ~ spl0_4
| ~ spl0_5
| ~ spl0_9
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f1059,f812]) ).
fof(f1191,plain,
( ! [X6] :
( sk_c10 != X6
| sk_c9 != inverse(X6) )
| ~ spl0_1
| ~ spl0_4
| ~ spl0_5
| ~ spl0_9
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f1180,f370]) ).
fof(f1198,plain,
( ! [X6] :
( multiply(inverse(sk_c9),identity) != X6
| sk_c9 != inverse(X6) )
| ~ spl0_1
| ~ spl0_4
| ~ spl0_5
| ~ spl0_9
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f1191,f344]) ).
fof(f1201,plain,
( ! [X6] :
( inverse(sk_c9) != X6
| sk_c9 != inverse(X6) )
| ~ spl0_1
| ~ spl0_4
| ~ spl0_5
| ~ spl0_9
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f1198,f370]) ).
fof(f1204,plain,
( ! [X6] :
( sk_c9 != inverse(X6)
| sk_c9 != X6 )
| ~ spl0_1
| ~ spl0_4
| ~ spl0_5
| ~ spl0_9
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f1201,f775]) ).
fof(f1212,plain,
( sk_c9 != inverse(inverse(sk_c9))
| spl0_4
| ~ spl0_6 ),
inference(forward_demodulation,[],[f127,f134]) ).
fof(f1221,plain,
( inverse(sk_c9) = inverse(sk_c1)
| ~ spl0_6
| ~ spl0_9 ),
inference(forward_demodulation,[],[f148,f134]) ).
fof(f1223,plain,
( sk_c2 = multiply(sk_c1,inverse(sk_c9))
| ~ spl0_6
| ~ spl0_17 ),
inference(forward_demodulation,[],[f189,f134]) ).
fof(f1224,plain,
( sk_c9 = multiply(inverse(sk_c9),sk_c2)
| ~ spl0_6
| ~ spl0_18 ),
inference(forward_demodulation,[],[f202,f134]) ).
fof(f1226,plain,
( multiply(sk_c9,sk_c8) = inverse(sk_c9)
| ~ spl0_6
| ~ spl0_7 ),
inference(forward_demodulation,[],[f138,f134]) ).
fof(f1238,plain,
( inverse(sk_c9) = multiply(inverse(sk_c1),sk_c2)
| ~ spl0_6
| ~ spl0_17 ),
inference(superposition,[],[f246,f1223]) ).
fof(f1240,plain,
( inverse(sk_c9) = multiply(inverse(sk_c9),sk_c2)
| ~ spl0_6
| ~ spl0_9
| ~ spl0_17 ),
inference(forward_demodulation,[],[f1238,f1221]) ).
fof(f1241,plain,
( sk_c9 = inverse(sk_c9)
| ~ spl0_6
| ~ spl0_9
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f1240,f1224]) ).
fof(f1243,plain,
( sk_c9 != inverse(sk_c9)
| spl0_4
| ~ spl0_6
| ~ spl0_9
| ~ spl0_17
| ~ spl0_18 ),
inference(superposition,[],[f1212,f1241]) ).
fof(f1248,plain,
( $false
| spl0_4
| ~ spl0_6
| ~ spl0_9
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[],[f1243,f1241]) ).
fof(f1249,plain,
( spl0_4
| ~ spl0_6
| ~ spl0_9
| ~ spl0_17
| ~ spl0_18 ),
inference(avatar_contradiction_clause,[],[f1248]) ).
fof(f1338,plain,
( sk_c9 != inverse(sk_c9)
| sk_c9 != sk_c1
| ~ spl0_1
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_9
| ~ spl0_17
| ~ spl0_18 ),
inference(superposition,[],[f1204,f1221]) ).
fof(f1342,plain,
( sk_c9 != sk_c1
| ~ spl0_1
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_9
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[],[f1338,f1241]) ).
fof(f1343,plain,
( $false
| ~ spl0_1
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_9
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[],[f1342,f1165]) ).
fof(f1344,plain,
( ~ spl0_1
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_9
| ~ spl0_17
| ~ spl0_18 ),
inference(avatar_contradiction_clause,[],[f1343]) ).
fof(f1345,plain,
( ! [X2,X3] :
( sk_c9 != multiply(inverse(sk_c9),X2)
| sk_c10 != inverse(X3)
| multiply(X3,sk_c10) != X2 )
| ~ spl0_3
| ~ spl0_6 ),
inference(forward_demodulation,[],[f123,f134]) ).
fof(f1352,plain,
( sk_c2 != multiply(sk_c1,inverse(sk_c9))
| ~ spl0_6
| spl0_17 ),
inference(forward_demodulation,[],[f188,f134]) ).
fof(f1353,plain,
( identity = sk_c2
| ~ spl0_4
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_18 ),
inference(forward_demodulation,[],[f801,f330]) ).
fof(f1364,plain,
( ! [X2,X3] :
( sk_c9 != multiply(sk_c9,X2)
| sk_c10 != inverse(X3)
| multiply(X3,sk_c10) != X2 )
| ~ spl0_3
| ~ spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f1345,f465]) ).
fof(f1371,plain,
( sk_c2 != multiply(sk_c1,sk_c9)
| ~ spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| spl0_17 ),
inference(forward_demodulation,[],[f1352,f465]) ).
fof(f1377,plain,
( ! [X2,X3] :
( inverse(sk_c9) != inverse(X3)
| sk_c9 != multiply(sk_c9,X2)
| multiply(X3,sk_c10) != X2 )
| ~ spl0_3
| ~ spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f1364,f134]) ).
fof(f1380,plain,
( sk_c2 != multiply(sk_c9,sk_c9)
| ~ spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| spl0_17 ),
inference(forward_demodulation,[],[f1371,f1165]) ).
fof(f1381,plain,
( ! [X2,X3] :
( sk_c9 != inverse(X3)
| sk_c9 != multiply(sk_c9,X2)
| multiply(X3,sk_c10) != X2 )
| ~ spl0_3
| ~ spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f1377,f465]) ).
fof(f1383,plain,
( identity != sk_c2
| ~ spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| spl0_17 ),
inference(forward_demodulation,[],[f1380,f330]) ).
fof(f1384,plain,
( ! [X2,X3] :
( multiply(X3,inverse(sk_c9)) != X2
| sk_c9 != inverse(X3)
| sk_c9 != multiply(sk_c9,X2) )
| ~ spl0_3
| ~ spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f1381,f134]) ).
fof(f1385,plain,
( $false
| ~ spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| spl0_17
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[],[f1383,f1353]) ).
fof(f1386,plain,
( ~ spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| spl0_17
| ~ spl0_18 ),
inference(avatar_contradiction_clause,[],[f1385]) ).
fof(f1387,plain,
( ! [X2,X3] :
( multiply(X3,sk_c9) != X2
| sk_c9 != inverse(X3)
| sk_c9 != multiply(sk_c9,X2) )
| ~ spl0_3
| ~ spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f1384,f465]) ).
fof(f1438,plain,
( ! [X0] :
( identity != X0
| sk_c9 != inverse(inverse(sk_c9))
| sk_c9 != multiply(sk_c9,X0) )
| ~ spl0_3
| ~ spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(superposition,[],[f1387,f3]) ).
fof(f1442,plain,
( ! [X0] :
( sk_c9 != inverse(sk_c9)
| identity != X0
| sk_c9 != multiply(sk_c9,X0) )
| ~ spl0_3
| ~ spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f1438,f465]) ).
fof(f1447,plain,
( ! [X0] :
( sk_c9 != multiply(sk_c9,X0)
| identity != X0 )
| ~ spl0_3
| ~ spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_subsumption_resolution,[],[f1442,f465]) ).
fof(f1509,plain,
( sk_c9 != inverse(sk_c9)
| identity != sk_c8
| ~ spl0_3
| ~ spl0_4
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(superposition,[],[f1447,f1226]) ).
fof(f1513,plain,
( identity != sk_c8
| ~ spl0_3
| ~ spl0_4
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_subsumption_resolution,[],[f1509,f465]) ).
fof(f1514,plain,
( $false
| ~ spl0_3
| ~ spl0_4
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_subsumption_resolution,[],[f1513,f461]) ).
fof(f1515,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(avatar_contradiction_clause,[],[f1514]) ).
cnf(s1,plain,
( spl0_3
| spl0_2
| spl0_1
| spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7 ),
inference(sat_conversion,[],[f140]) ).
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,[],[f149]) ).
cnf(s4,plain,
( spl0_9
| spl0_10 ),
inference(sat_conversion,[],[f154]) ).
cnf(s5,plain,
( spl0_9
| spl0_11 ),
inference(sat_conversion,[],[f159]) ).
cnf(s6,plain,
( spl0_9
| spl0_12 ),
inference(sat_conversion,[],[f164]) ).
cnf(s7,plain,
( spl0_9
| spl0_13 ),
inference(sat_conversion,[],[f169]) ).
cnf(s8,plain,
( spl0_9
| spl0_14 ),
inference(sat_conversion,[],[f174]) ).
cnf(s9,plain,
( spl0_9
| spl0_15 ),
inference(sat_conversion,[],[f179]) ).
cnf(s10,plain,
( spl0_9
| spl0_16 ),
inference(sat_conversion,[],[f184]) ).
cnf(s11,plain,
( spl0_4
| spl0_9 ),
inference(sat_conversion,[],[f185]) ).
cnf(s12,plain,
( spl0_8
| spl0_17 ),
inference(sat_conversion,[],[f190]) ).
cnf(s13,plain,
( spl0_10
| spl0_17 ),
inference(sat_conversion,[],[f191]) ).
cnf(s14,plain,
( spl0_11
| spl0_17 ),
inference(sat_conversion,[],[f192]) ).
cnf(s15,plain,
( spl0_12
| spl0_17 ),
inference(sat_conversion,[],[f193]) ).
cnf(s16,plain,
( spl0_13
| spl0_17 ),
inference(sat_conversion,[],[f194]) ).
cnf(s17,plain,
( spl0_14
| spl0_17 ),
inference(sat_conversion,[],[f195]) ).
cnf(s18,plain,
( spl0_15
| spl0_17 ),
inference(sat_conversion,[],[f196]) ).
cnf(s19,plain,
( spl0_16
| spl0_17 ),
inference(sat_conversion,[],[f197]) ).
cnf(s20,plain,
( spl0_4
| spl0_17 ),
inference(sat_conversion,[],[f198]) ).
cnf(s21,plain,
( spl0_8
| spl0_18 ),
inference(sat_conversion,[],[f203]) ).
cnf(s22,plain,
( spl0_10
| spl0_18 ),
inference(sat_conversion,[],[f204]) ).
cnf(s23,plain,
( spl0_11
| spl0_18 ),
inference(sat_conversion,[],[f205]) ).
cnf(s24,plain,
( spl0_12
| spl0_18 ),
inference(sat_conversion,[],[f206]) ).
cnf(s25,plain,
( spl0_13
| spl0_18 ),
inference(sat_conversion,[],[f207]) ).
cnf(s26,plain,
( spl0_14
| spl0_18 ),
inference(sat_conversion,[],[f208]) ).
cnf(s27,plain,
( spl0_15
| spl0_18 ),
inference(sat_conversion,[],[f209]) ).
cnf(s28,plain,
( spl0_16
| spl0_18 ),
inference(sat_conversion,[],[f210]) ).
cnf(s29,plain,
( spl0_4
| spl0_18 ),
inference(sat_conversion,[],[f211]) ).
cnf(s30,plain,
( spl0_5
| spl0_8 ),
inference(sat_conversion,[],[f212]) ).
cnf(s31,plain,
( spl0_5
| spl0_10 ),
inference(sat_conversion,[],[f213]) ).
cnf(s32,plain,
( spl0_5
| spl0_11 ),
inference(sat_conversion,[],[f214]) ).
cnf(s33,plain,
( spl0_5
| spl0_12 ),
inference(sat_conversion,[],[f215]) ).
cnf(s34,plain,
( spl0_5
| spl0_13 ),
inference(sat_conversion,[],[f216]) ).
cnf(s35,plain,
( spl0_5
| spl0_14 ),
inference(sat_conversion,[],[f217]) ).
cnf(s36,plain,
( spl0_5
| spl0_15 ),
inference(sat_conversion,[],[f218]) ).
cnf(s37,plain,
( spl0_5
| spl0_16 ),
inference(sat_conversion,[],[f219]) ).
cnf(s47,plain,
( spl0_4
| spl0_6 ),
inference(sat_conversion,[],[f229]) ).
cnf(s48,plain,
( spl0_7
| spl0_8 ),
inference(sat_conversion,[],[f230]) ).
cnf(s49,plain,
( spl0_7
| spl0_10 ),
inference(sat_conversion,[],[f231]) ).
cnf(s50,plain,
( spl0_7
| spl0_11 ),
inference(sat_conversion,[],[f232]) ).
cnf(s51,plain,
( spl0_7
| spl0_12 ),
inference(sat_conversion,[],[f233]) ).
cnf(s52,plain,
( spl0_7
| spl0_13 ),
inference(sat_conversion,[],[f234]) ).
cnf(s53,plain,
( spl0_7
| spl0_14 ),
inference(sat_conversion,[],[f235]) ).
cnf(s54,plain,
( spl0_7
| spl0_15 ),
inference(sat_conversion,[],[f236]) ).
cnf(s55,plain,
( spl0_7
| spl0_16 ),
inference(sat_conversion,[],[f237]) ).
cnf(s57,plain,
( ~ spl0_4
| spl0_6 ),
inference(sat_conversion,[],[f488]) ).
cnf(s58,plain,
( ~ spl0_4
| spl0_5
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(sat_conversion,[],[f522]) ).
cnf(s59,plain,
( ~ spl0_4
| spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(sat_conversion,[],[f531]) ).
cnf(s62,plain,
( ~ spl0_1
| ~ spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(sat_conversion,[],[f587]) ).
cnf(s64,plain,
( ~ spl0_2
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(sat_conversion,[],[f656]) ).
cnf(s67,plain,
( ~ spl0_2
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(sat_conversion,[],[f871]) ).
cnf(s69,plain,
( ~ spl0_2
| ~ spl0_4
| ~ spl0_5
| ~ spl0_9
| ~ spl0_17
| ~ spl0_18 ),
inference(sat_conversion,[],[f960]) ).
cnf(s78,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_17
| ~ spl0_18 ),
inference(sat_conversion,[],[f1175]) ).
cnf(s80,plain,
( spl0_4
| ~ spl0_6
| ~ spl0_9
| ~ spl0_17
| ~ spl0_18 ),
inference(sat_conversion,[],[f1249]) ).
cnf(s82,plain,
( ~ spl0_1
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_9
| ~ spl0_17
| ~ spl0_18 ),
inference(sat_conversion,[],[f1344]) ).
cnf(s83,plain,
( ~ spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| spl0_17
| ~ spl0_18 ),
inference(sat_conversion,[],[f1386]) ).
cnf(s84,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(sat_conversion,[],[f1515]) ).
cnf(s85,plain,
spl0_4,
inference(rat,[],[s80,s11,s20,s29,s47]) ).
cnf(s86,plain,
spl0_6,
inference(rat,[],[s57,s85]) ).
cnf(s87,plain,
spl0_7,
inference(rat,[],[s59,s48,s49,s50,s51,s52,s53,s54,s55,s85]) ).
cnf(s88,plain,
spl0_5,
inference(rat,[],[s58,s30,s31,s32,s33,s34,s35,s36,s37,s85]) ).
cnf(s89,plain,
( spl0_16
| ~ spl0_9
| ~ spl0_3 ),
inference(rat,[],[s78,s19,s28,s85,s87,s88]) ).
cnf(s90,plain,
( spl0_15
| ~ spl0_9
| ~ spl0_3 ),
inference(rat,[],[s78,s18,s27,s85,s87,s88]) ).
cnf(s91,plain,
( spl0_14
| ~ spl0_9
| ~ spl0_3 ),
inference(rat,[],[s78,s17,s26,s85,s87,s88]) ).
cnf(s92,plain,
( spl0_13
| ~ spl0_9
| ~ spl0_3 ),
inference(rat,[],[s78,s16,s25,s85,s87,s88]) ).
cnf(s93,plain,
( spl0_12
| ~ spl0_9
| ~ spl0_3 ),
inference(rat,[],[s78,s15,s24,s85,s87,s88]) ).
cnf(s94,plain,
( spl0_11
| ~ spl0_9
| ~ spl0_3 ),
inference(rat,[],[s78,s14,s23,s85,s87,s88]) ).
cnf(s95,plain,
( ~ spl0_9
| ~ spl0_8
| ~ spl0_3 ),
inference(rat,[],[s78,s13,s22,s84,s94,s93,s92,s91,s90,s89,s85,s87,s88,s86]) ).
cnf(s96,plain,
( ~ spl0_8
| ~ spl0_3 ),
inference(rat,[],[s84,s4,s5,s6,s7,s8,s9,s10,s95,s87,s86,s85]) ).
cnf(s97,plain,
~ spl0_3,
inference(rat,[],[s78,s3,s12,s21,s96,s85,s87,s88]) ).
cnf(s98,plain,
( spl0_13
| ~ spl0_9
| ~ spl0_2 ),
inference(rat,[],[s69,s16,s25,s85,s88]) ).
cnf(s99,plain,
( spl0_12
| ~ spl0_9
| ~ spl0_2 ),
inference(rat,[],[s69,s15,s24,s85,s88]) ).
cnf(s100,plain,
( ~ spl0_9
| ~ spl0_2 ),
inference(rat,[],[s69,s14,s23,s67,s99,s98,s88,s85]) ).
cnf(s101,plain,
~ spl0_2,
inference(rat,[],[s3,s64,s4,s5,s6,s7,s8,s9,s10,s100,s85]) ).
cnf(s102,plain,
spl0_1,
inference(rat,[],[s2,s87,s86,s88,s85,s97,s101]) ).
cnf(s103,plain,
( spl0_18
| ~ spl0_13
| ~ spl0_12
| ~ spl0_11 ),
inference(rat,[],[s62,s21,s22,s26,s27,s28,s85,s86,s102]) ).
cnf(s104,plain,
( ~ spl0_13
| ~ spl0_12
| ~ spl0_11
| ~ spl0_9 ),
inference(rat,[],[s83,s12,s13,s17,s18,s19,s82,s103,s85,s86,s88,s102]) ).
cnf(s105,plain,
( spl0_13
| ~ spl0_9 ),
inference(rat,[],[s82,s16,s25,s85,s86,s88,s102]) ).
cnf(s106,plain,
( spl0_12
| ~ spl0_9 ),
inference(rat,[],[s82,s15,s24,s85,s86,s88,s102]) ).
cnf(s107,plain,
( ~ spl0_12
| ~ spl0_9
| ~ spl0_13 ),
inference(rat,[],[s82,s14,s23,s104,s102,s88,s86,s85]) ).
cnf(s108,plain,
~ spl0_9,
inference(rat,[],[s107,s106,s105]) ).
cnf(s109,plain,
spl0_16,
inference(rat,[],[s10,s108]) ).
cnf(s110,plain,
spl0_15,
inference(rat,[],[s9,s108]) ).
cnf(s111,plain,
spl0_14,
inference(rat,[],[s8,s108]) ).
cnf(s112,plain,
spl0_13,
inference(rat,[],[s7,s108]) ).
cnf(s113,plain,
spl0_12,
inference(rat,[],[s6,s108]) ).
cnf(s114,plain,
spl0_11,
inference(rat,[],[s5,s108]) ).
cnf(s115,plain,
spl0_10,
inference(rat,[],[s4,s108]) ).
cnf(s116,plain,
spl0_8,
inference(rat,[],[s3,s108]) ).
cnf(s118,plain,
$false,
inference(rat,[],[s62,s109,s110,s111,s114,s113,s102,s86,s85,s112,s115,s116]) ).
fof(f1516,plain,
$false,
inference(avatar_sat_refutation,[],[s118]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP362-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.36 % Computer : n005.cluster.edu
% 0.12/0.36 % Model : x86_64 x86_64
% 0.12/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.36 % Memory : 8046.5625MB
% 0.12/0.36 % OS : Linux 6.8.0-71-generic
% 0.12/0.36 % CPULimit : 300
% 0.12/0.36 % WCLimit : 300
% 0.12/0.36 % DateTime : Sun Sep 27 09:55:17 UTC 2026
% 0.12/0.36 % CPUTime :
% 0.12/0.36 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.39 Running first-order model finding
% 0.12/0.39 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.44 % (3749057)Will run a generic schedule for satisfiability detection.
% 0.12/0.44 % (3749067)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2704222718:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.12/0.44 % (3749063)% WARNING: option uhcvi not known.
% 0.12/0.44 % (3749062)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1341227868_2999 on theBenchmark for (2999ds/0Mi)
% 0.12/0.44 % (3749063)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3134572223:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.12/0.44 % (3749064)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=4110831334:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.12/0.44 % (3749065)dis+10_1_sil=32000:sp=arity:random_seed=346187904:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.12/0.44 % (3749066)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3198734008:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.12/0.44 % (3749068)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1774124730:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.12/0.44 % (3749067) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3749057-3749067"...
% 0.12/0.44 % TRYING [1]
% 0.12/0.44 % TRYING [2]
% 0.12/0.44 % TRYING [3]
% 0.12/0.44 % (3749067)...printing done.
% 0.12/0.44 % (3749067)Refutation found. Thanks to Tanya!
% 0.12/0.44 % SZS status Unsatisfiable for theBenchmark
% 0.12/0.44 % SZS output start Proof for theBenchmark
% See solution above
% 0.12/0.44 % (3749067)------------------------------
% 0.12/0.44 % (3749067)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.12/0.44 % (3749067)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.12/0.44 % (3749067)CaDiCaL version: 2.1.3
% 0.12/0.44 % (3749067)Termination reason: Refutation
% 0.12/0.44 % (3749067)Time elapsed: 0.015 s
% 0.12/0.44 % (3749067)Peak memory usage: 12 MB
% 0.12/0.44 % (3749067)Instructions burned: 47 (million)
% 0.12/0.44 % (3749057)Success in time 0.041 s
% 0.12/0.44 % Vampire exiting
%------------------------------------------------------------------------------