%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GRP366-1 : 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 : n017.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 0.15s 5.71s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 67
% Syntax : Number of formulae : 429 ( 18 unt; 25 def)
% Number of atoms : 1566 ( 449 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 2170 (1033 ~;1112 |; 0 &)
% ( 25 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 27 ( 25 usr; 26 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 10 con; 0-2 aty)
% Number of variables : 79 ( 0 sgn 79 !; 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(f5,negated_conjecture,
( multiply(sk_c8,sk_c10) = sk_c9
| multiply(sk_c9,sk_c10) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,plain,
( multiply(sk_c8,sk_c10) = sk_c9
| sk_c8 = multiply(sk_c9,sk_c10) ),
inference(reorient_equations,[],[f5]) ).
fof(f7,negated_conjecture,
( multiply(sk_c8,sk_c10) = sk_c9
| multiply(sk_c4,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_2) ).
fof(f8,plain,
( multiply(sk_c8,sk_c10) = sk_c9
| sk_c9 = multiply(sk_c4,sk_c10) ),
inference(reorient_equations,[],[f7]) ).
fof(f9,negated_conjecture,
( multiply(sk_c8,sk_c10) = sk_c9
| inverse(sk_c4) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_3) ).
fof(f10,plain,
( multiply(sk_c8,sk_c10) = sk_c9
| sk_c10 = inverse(sk_c4) ),
inference(reorient_equations,[],[f9]) ).
fof(f11,negated_conjecture,
( multiply(sk_c8,sk_c10) = sk_c9
| inverse(sk_c9) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_4) ).
fof(f12,plain,
( multiply(sk_c8,sk_c10) = sk_c9
| sk_c8 = inverse(sk_c9) ),
inference(reorient_equations,[],[f11]) ).
fof(f13,negated_conjecture,
( multiply(sk_c8,sk_c10) = sk_c9
| multiply(sk_c10,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_5) ).
fof(f14,plain,
( multiply(sk_c8,sk_c10) = sk_c9
| sk_c9 = multiply(sk_c10,sk_c8) ),
inference(reorient_equations,[],[f13]) ).
fof(f15,negated_conjecture,
( multiply(sk_c8,sk_c10) = sk_c9
| inverse(sk_c5) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_6) ).
fof(f16,plain,
( multiply(sk_c8,sk_c10) = sk_c9
| sk_c9 = inverse(sk_c5) ),
inference(reorient_equations,[],[f15]) ).
fof(f17,negated_conjecture,
( multiply(sk_c8,sk_c10) = sk_c9
| multiply(sk_c5,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_7) ).
fof(f18,plain,
( multiply(sk_c8,sk_c10) = sk_c9
| sk_c9 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f17]) ).
fof(f24,negated_conjecture,
( multiply(sk_c10,sk_c2) = sk_c9
| multiply(sk_c9,sk_c10) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_11) ).
fof(f25,plain,
( sk_c9 = multiply(sk_c10,sk_c2)
| sk_c8 = multiply(sk_c9,sk_c10) ),
inference(reorient_equations,[],[f24]) ).
fof(f30,negated_conjecture,
( multiply(sk_c10,sk_c2) = sk_c9
| inverse(sk_c9) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_14) ).
fof(f31,plain,
( sk_c9 = multiply(sk_c10,sk_c2)
| sk_c8 = inverse(sk_c9) ),
inference(reorient_equations,[],[f30]) ).
fof(f34,negated_conjecture,
( multiply(sk_c10,sk_c2) = sk_c9
| inverse(sk_c5) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_16) ).
fof(f35,plain,
( sk_c9 = multiply(sk_c10,sk_c2)
| sk_c9 = inverse(sk_c5) ),
inference(reorient_equations,[],[f34]) ).
fof(f36,negated_conjecture,
( multiply(sk_c10,sk_c2) = sk_c9
| multiply(sk_c5,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_17) ).
fof(f37,plain,
( sk_c9 = multiply(sk_c10,sk_c2)
| sk_c9 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f36]) ).
fof(f44,negated_conjecture,
( multiply(sk_c1,sk_c10) = sk_c2
| multiply(sk_c9,sk_c10) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_21) ).
fof(f45,plain,
( sk_c2 = multiply(sk_c1,sk_c10)
| sk_c8 = multiply(sk_c9,sk_c10) ),
inference(reorient_equations,[],[f44]) ).
fof(f46,negated_conjecture,
( multiply(sk_c1,sk_c10) = sk_c2
| multiply(sk_c4,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_22) ).
fof(f47,plain,
( sk_c2 = multiply(sk_c1,sk_c10)
| sk_c9 = multiply(sk_c4,sk_c10) ),
inference(reorient_equations,[],[f46]) ).
fof(f48,negated_conjecture,
( multiply(sk_c1,sk_c10) = sk_c2
| inverse(sk_c4) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_23) ).
fof(f49,plain,
( sk_c2 = multiply(sk_c1,sk_c10)
| sk_c10 = inverse(sk_c4) ),
inference(reorient_equations,[],[f48]) ).
fof(f50,negated_conjecture,
( multiply(sk_c1,sk_c10) = sk_c2
| inverse(sk_c9) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_24) ).
fof(f51,plain,
( sk_c2 = multiply(sk_c1,sk_c10)
| sk_c8 = inverse(sk_c9) ),
inference(reorient_equations,[],[f50]) ).
fof(f54,negated_conjecture,
( multiply(sk_c1,sk_c10) = sk_c2
| inverse(sk_c5) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_26) ).
fof(f55,plain,
( sk_c2 = multiply(sk_c1,sk_c10)
| sk_c9 = inverse(sk_c5) ),
inference(reorient_equations,[],[f54]) ).
fof(f56,negated_conjecture,
( multiply(sk_c1,sk_c10) = sk_c2
| multiply(sk_c5,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_27) ).
fof(f57,plain,
( sk_c2 = multiply(sk_c1,sk_c10)
| sk_c9 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f56]) ).
fof(f64,negated_conjecture,
( inverse(sk_c1) = sk_c10
| multiply(sk_c9,sk_c10) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_31) ).
fof(f65,plain,
( sk_c10 = inverse(sk_c1)
| sk_c8 = multiply(sk_c9,sk_c10) ),
inference(reorient_equations,[],[f64]) ).
fof(f66,negated_conjecture,
( inverse(sk_c1) = sk_c10
| multiply(sk_c4,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_32) ).
fof(f67,plain,
( sk_c10 = inverse(sk_c1)
| sk_c9 = multiply(sk_c4,sk_c10) ),
inference(reorient_equations,[],[f66]) ).
fof(f68,negated_conjecture,
( inverse(sk_c1) = sk_c10
| inverse(sk_c4) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_33) ).
fof(f69,plain,
( sk_c10 = inverse(sk_c1)
| sk_c10 = inverse(sk_c4) ),
inference(reorient_equations,[],[f68]) ).
fof(f70,negated_conjecture,
( inverse(sk_c1) = sk_c10
| inverse(sk_c9) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_34) ).
fof(f71,plain,
( sk_c10 = inverse(sk_c1)
| sk_c8 = inverse(sk_c9) ),
inference(reorient_equations,[],[f70]) ).
fof(f74,negated_conjecture,
( inverse(sk_c1) = sk_c10
| inverse(sk_c5) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_36) ).
fof(f75,plain,
( sk_c10 = inverse(sk_c1)
| sk_c9 = inverse(sk_c5) ),
inference(reorient_equations,[],[f74]) ).
fof(f76,negated_conjecture,
( inverse(sk_c1) = sk_c10
| multiply(sk_c5,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_37) ).
fof(f77,plain,
( sk_c10 = inverse(sk_c1)
| sk_c9 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f76]) ).
fof(f80,negated_conjecture,
( inverse(sk_c1) = sk_c10
| inverse(sk_c6) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_39) ).
fof(f81,plain,
( sk_c10 = inverse(sk_c1)
| sk_c10 = inverse(sk_c6) ),
inference(reorient_equations,[],[f80]) ).
fof(f84,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c10
| multiply(sk_c9,sk_c10) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_41) ).
fof(f85,plain,
( sk_c10 = multiply(sk_c3,sk_c8)
| sk_c8 = multiply(sk_c9,sk_c10) ),
inference(reorient_equations,[],[f84]) ).
fof(f86,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c10
| multiply(sk_c4,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_42) ).
fof(f87,plain,
( sk_c10 = multiply(sk_c3,sk_c8)
| sk_c9 = multiply(sk_c4,sk_c10) ),
inference(reorient_equations,[],[f86]) ).
fof(f88,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c10
| inverse(sk_c4) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_43) ).
fof(f89,plain,
( sk_c10 = multiply(sk_c3,sk_c8)
| sk_c10 = inverse(sk_c4) ),
inference(reorient_equations,[],[f88]) ).
fof(f90,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c10
| inverse(sk_c9) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_44) ).
fof(f91,plain,
( sk_c10 = multiply(sk_c3,sk_c8)
| sk_c8 = inverse(sk_c9) ),
inference(reorient_equations,[],[f90]) ).
fof(f92,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c10
| multiply(sk_c10,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_45) ).
fof(f93,plain,
( sk_c10 = multiply(sk_c3,sk_c8)
| sk_c9 = multiply(sk_c10,sk_c8) ),
inference(reorient_equations,[],[f92]) ).
fof(f94,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c10
| inverse(sk_c5) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_46) ).
fof(f95,plain,
( sk_c10 = multiply(sk_c3,sk_c8)
| sk_c9 = inverse(sk_c5) ),
inference(reorient_equations,[],[f94]) ).
fof(f96,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c10
| multiply(sk_c5,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_47) ).
fof(f97,plain,
( sk_c10 = multiply(sk_c3,sk_c8)
| sk_c9 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f96]) ).
fof(f104,negated_conjecture,
( inverse(sk_c3) = sk_c8
| multiply(sk_c9,sk_c10) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_51) ).
fof(f105,plain,
( sk_c8 = inverse(sk_c3)
| sk_c8 = multiply(sk_c9,sk_c10) ),
inference(reorient_equations,[],[f104]) ).
fof(f106,negated_conjecture,
( inverse(sk_c3) = sk_c8
| multiply(sk_c4,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_52) ).
fof(f107,plain,
( sk_c8 = inverse(sk_c3)
| sk_c9 = multiply(sk_c4,sk_c10) ),
inference(reorient_equations,[],[f106]) ).
fof(f108,negated_conjecture,
( inverse(sk_c3) = sk_c8
| inverse(sk_c4) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_53) ).
fof(f109,plain,
( sk_c8 = inverse(sk_c3)
| sk_c10 = inverse(sk_c4) ),
inference(reorient_equations,[],[f108]) ).
fof(f110,negated_conjecture,
( inverse(sk_c3) = sk_c8
| inverse(sk_c9) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_54) ).
fof(f111,plain,
( sk_c8 = inverse(sk_c3)
| sk_c8 = inverse(sk_c9) ),
inference(reorient_equations,[],[f110]) ).
fof(f112,negated_conjecture,
( inverse(sk_c3) = sk_c8
| multiply(sk_c10,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_55) ).
fof(f113,plain,
( sk_c8 = inverse(sk_c3)
| sk_c9 = multiply(sk_c10,sk_c8) ),
inference(reorient_equations,[],[f112]) ).
fof(f114,negated_conjecture,
( inverse(sk_c3) = sk_c8
| inverse(sk_c5) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_56) ).
fof(f115,plain,
( sk_c8 = inverse(sk_c3)
| sk_c9 = inverse(sk_c5) ),
inference(reorient_equations,[],[f114]) ).
fof(f116,negated_conjecture,
( inverse(sk_c3) = sk_c8
| multiply(sk_c5,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_57) ).
fof(f117,plain,
( sk_c8 = inverse(sk_c3)
| sk_c9 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f116]) ).
fof(f124,negated_conjecture,
! [X2,X3,X0,X1,X6,X4,X5] :
( multiply(sk_c8,sk_c10) != sk_c9
| multiply(sk_c10,X0) != sk_c9
| multiply(X1,sk_c10) != X0
| inverse(X1) != sk_c10
| multiply(X2,sk_c8) != sk_c10
| inverse(X2) != sk_c8
| multiply(sk_c9,sk_c10) != sk_c8
| multiply(X3,sk_c10) != sk_c9
| inverse(X3) != sk_c10
| inverse(sk_c9) != sk_c8
| multiply(sk_c10,sk_c8) != sk_c9
| inverse(X4) != sk_c9
| multiply(X4,sk_c8) != sk_c9
| inverse(X5) != X6
| inverse(X6) != sk_c10
| multiply(X5,sk_c10) != X6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_61) ).
fof(f125,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( multiply(sk_c8,sk_c10) != sk_c9
| sk_c9 != multiply(sk_c10,X0)
| multiply(X1,sk_c10) != X0
| sk_c10 != inverse(X1)
| sk_c10 != multiply(X2,sk_c8)
| sk_c8 != inverse(X2)
| sk_c8 != multiply(sk_c9,sk_c10)
| sk_c9 != multiply(X3,sk_c10)
| sk_c10 != inverse(X3)
| sk_c8 != inverse(sk_c9)
| sk_c9 != multiply(sk_c10,sk_c8)
| sk_c9 != inverse(X4)
| sk_c9 != multiply(X4,sk_c8)
| inverse(X5) != X6
| sk_c10 != inverse(X6)
| multiply(X5,sk_c10) != X6 ),
inference(reorient_equations,[],[f124]) ).
fof(f126,plain,
! [X2,X3,X1,X6,X4,X5] :
( multiply(sk_c8,sk_c10) != sk_c9
| sk_c9 != multiply(sk_c10,multiply(X1,sk_c10))
| sk_c10 != inverse(X1)
| sk_c10 != multiply(X2,sk_c8)
| sk_c8 != inverse(X2)
| sk_c8 != multiply(sk_c9,sk_c10)
| sk_c9 != multiply(X3,sk_c10)
| sk_c10 != inverse(X3)
| sk_c8 != inverse(sk_c9)
| sk_c9 != multiply(sk_c10,sk_c8)
| sk_c9 != inverse(X4)
| sk_c9 != multiply(X4,sk_c8)
| inverse(X5) != X6
| sk_c10 != inverse(X6)
| multiply(X5,sk_c10) != X6 ),
inference(equality_resolution,[],[f125]) ).
fof(f127,plain,
! [X2,X3,X1,X4,X5] :
( multiply(sk_c8,sk_c10) != sk_c9
| sk_c9 != multiply(sk_c10,multiply(X1,sk_c10))
| sk_c10 != inverse(X1)
| sk_c10 != multiply(X2,sk_c8)
| sk_c8 != inverse(X2)
| sk_c8 != multiply(sk_c9,sk_c10)
| sk_c9 != multiply(X3,sk_c10)
| sk_c10 != inverse(X3)
| sk_c8 != inverse(sk_c9)
| sk_c9 != multiply(sk_c10,sk_c8)
| sk_c9 != inverse(X4)
| sk_c9 != multiply(X4,sk_c8)
| sk_c10 != inverse(inverse(X5))
| inverse(X5) != multiply(X5,sk_c10) ),
inference(equality_resolution,[],[f126]) ).
fof(f129,definition,
( spl0_1
<=> ! [X5] :
( sk_c10 != inverse(inverse(X5))
| inverse(X5) != multiply(X5,sk_c10) ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f130,plain,
( ! [X5] :
( inverse(X5) != multiply(X5,sk_c10)
| sk_c10 != inverse(inverse(X5)) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f129]) ).
fof(f132,definition,
( spl0_2
<=> ! [X4] :
( sk_c9 != inverse(X4)
| sk_c9 != multiply(X4,sk_c8) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f133,plain,
( ! [X4] :
( sk_c9 != inverse(X4)
| sk_c9 != multiply(X4,sk_c8) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f132]) ).
fof(f135,definition,
( spl0_3
<=> sk_c9 = multiply(sk_c10,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f136,plain,
( sk_c9 = multiply(sk_c10,sk_c8)
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f135]) ).
fof(f137,plain,
( sk_c9 != multiply(sk_c10,sk_c8)
| spl0_3 ),
inference(avatar_component_clause,[],[f135]) ).
fof(f139,definition,
( spl0_4
<=> sk_c8 = inverse(sk_c9) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f140,plain,
( sk_c8 = inverse(sk_c9)
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f139]) ).
fof(f141,plain,
( sk_c8 != inverse(sk_c9)
| spl0_4 ),
inference(avatar_component_clause,[],[f139]) ).
fof(f143,definition,
( spl0_5
<=> ! [X3] :
( sk_c9 != multiply(X3,sk_c10)
| sk_c10 != inverse(X3) ) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f144,plain,
( ! [X3] :
( sk_c9 != multiply(X3,sk_c10)
| sk_c10 != inverse(X3) )
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f143]) ).
fof(f146,definition,
( spl0_6
<=> sk_c8 = multiply(sk_c9,sk_c10) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f147,plain,
( sk_c8 = multiply(sk_c9,sk_c10)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f146]) ).
fof(f148,plain,
( sk_c8 != multiply(sk_c9,sk_c10)
| spl0_6 ),
inference(avatar_component_clause,[],[f146]) ).
fof(f150,definition,
( spl0_7
<=> ! [X2] :
( sk_c10 != multiply(X2,sk_c8)
| sk_c8 != inverse(X2) ) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f151,plain,
( ! [X2] :
( sk_c10 != multiply(X2,sk_c8)
| sk_c8 != inverse(X2) )
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f150]) ).
fof(f153,definition,
( spl0_8
<=> ! [X1] :
( sk_c9 != multiply(sk_c10,multiply(X1,sk_c10))
| sk_c10 != inverse(X1) ) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f154,plain,
( ! [X1] :
( sk_c9 != multiply(sk_c10,multiply(X1,sk_c10))
| sk_c10 != inverse(X1) )
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f153]) ).
fof(f156,definition,
( spl0_9
<=> multiply(sk_c8,sk_c10) = sk_c9 ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f157,plain,
( multiply(sk_c8,sk_c10) = sk_c9
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f156]) ).
fof(f158,plain,
( multiply(sk_c8,sk_c10) != sk_c9
| spl0_9 ),
inference(avatar_component_clause,[],[f156]) ).
fof(f159,plain,
( spl0_1
| spl0_2
| ~ spl0_3
| ~ spl0_4
| spl0_5
| ~ spl0_6
| spl0_7
| spl0_8
| ~ spl0_9 ),
inference(avatar_split_clause,[],[f127,f156,f153,f150,f146,f143,f139,f135,f132,f129]) ).
fof(f165,definition,
( spl0_11
<=> sk_c8 = inverse(sk_c3) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f167,plain,
( sk_c8 = inverse(sk_c3)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f165]) ).
fof(f170,definition,
( spl0_12
<=> sk_c10 = inverse(sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f172,plain,
( sk_c10 = inverse(sk_c6)
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f170]) ).
fof(f180,definition,
( spl0_14
<=> sk_c9 = multiply(sk_c5,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
fof(f182,plain,
( sk_c9 = multiply(sk_c5,sk_c8)
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f180]) ).
fof(f183,plain,
( spl0_14
| spl0_11 ),
inference(avatar_split_clause,[],[f117,f165,f180]) ).
fof(f185,definition,
( spl0_15
<=> sk_c9 = inverse(sk_c5) ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
fof(f187,plain,
( sk_c9 = inverse(sk_c5)
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f185]) ).
fof(f188,plain,
( spl0_15
| spl0_11 ),
inference(avatar_split_clause,[],[f115,f165,f185]) ).
fof(f189,plain,
( spl0_3
| spl0_11 ),
inference(avatar_split_clause,[],[f113,f165,f135]) ).
fof(f190,plain,
( spl0_4
| spl0_11 ),
inference(avatar_split_clause,[],[f111,f165,f139]) ).
fof(f192,definition,
( spl0_16
<=> sk_c10 = inverse(sk_c4) ),
introduced(definition,[new_symbols(definition,[spl0_16])],[avatar_definition]) ).
fof(f194,plain,
( sk_c10 = inverse(sk_c4)
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f192]) ).
fof(f195,plain,
( spl0_16
| spl0_11 ),
inference(avatar_split_clause,[],[f109,f165,f192]) ).
fof(f197,definition,
( spl0_17
<=> sk_c9 = multiply(sk_c4,sk_c10) ),
introduced(definition,[new_symbols(definition,[spl0_17])],[avatar_definition]) ).
fof(f199,plain,
( sk_c9 = multiply(sk_c4,sk_c10)
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f197]) ).
fof(f200,plain,
( spl0_17
| spl0_11 ),
inference(avatar_split_clause,[],[f107,f165,f197]) ).
fof(f201,plain,
( spl0_6
| spl0_11 ),
inference(avatar_split_clause,[],[f105,f165,f146]) ).
fof(f203,definition,
( spl0_18
<=> sk_c10 = multiply(sk_c3,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_18])],[avatar_definition]) ).
fof(f205,plain,
( sk_c10 = multiply(sk_c3,sk_c8)
| ~ spl0_18 ),
inference(avatar_component_clause,[],[f203]) ).
fof(f209,plain,
( spl0_14
| spl0_18 ),
inference(avatar_split_clause,[],[f97,f203,f180]) ).
fof(f210,plain,
( spl0_15
| spl0_18 ),
inference(avatar_split_clause,[],[f95,f203,f185]) ).
fof(f211,plain,
( spl0_3
| spl0_18 ),
inference(avatar_split_clause,[],[f93,f203,f135]) ).
fof(f212,plain,
( spl0_4
| spl0_18 ),
inference(avatar_split_clause,[],[f91,f203,f139]) ).
fof(f213,plain,
( spl0_16
| spl0_18 ),
inference(avatar_split_clause,[],[f89,f203,f192]) ).
fof(f214,plain,
( spl0_17
| spl0_18 ),
inference(avatar_split_clause,[],[f87,f203,f197]) ).
fof(f215,plain,
( spl0_6
| spl0_18 ),
inference(avatar_split_clause,[],[f85,f203,f146]) ).
fof(f217,definition,
( spl0_19
<=> sk_c10 = inverse(sk_c1) ),
introduced(definition,[new_symbols(definition,[spl0_19])],[avatar_definition]) ).
fof(f219,plain,
( sk_c10 = inverse(sk_c1)
| ~ spl0_19 ),
inference(avatar_component_clause,[],[f217]) ).
fof(f221,plain,
( spl0_12
| spl0_19 ),
inference(avatar_split_clause,[],[f81,f217,f170]) ).
fof(f223,plain,
( spl0_14
| spl0_19 ),
inference(avatar_split_clause,[],[f77,f217,f180]) ).
fof(f224,plain,
( spl0_15
| spl0_19 ),
inference(avatar_split_clause,[],[f75,f217,f185]) ).
fof(f226,plain,
( spl0_4
| spl0_19 ),
inference(avatar_split_clause,[],[f71,f217,f139]) ).
fof(f227,plain,
( spl0_16
| spl0_19 ),
inference(avatar_split_clause,[],[f69,f217,f192]) ).
fof(f228,plain,
( spl0_17
| spl0_19 ),
inference(avatar_split_clause,[],[f67,f217,f197]) ).
fof(f229,plain,
( spl0_6
| spl0_19 ),
inference(avatar_split_clause,[],[f65,f217,f146]) ).
fof(f231,definition,
( spl0_20
<=> sk_c2 = multiply(sk_c1,sk_c10) ),
introduced(definition,[new_symbols(definition,[spl0_20])],[avatar_definition]) ).
fof(f233,plain,
( sk_c2 = multiply(sk_c1,sk_c10)
| ~ spl0_20 ),
inference(avatar_component_clause,[],[f231]) ).
fof(f237,plain,
( spl0_14
| spl0_20 ),
inference(avatar_split_clause,[],[f57,f231,f180]) ).
fof(f238,plain,
( spl0_15
| spl0_20 ),
inference(avatar_split_clause,[],[f55,f231,f185]) ).
fof(f240,plain,
( spl0_4
| spl0_20 ),
inference(avatar_split_clause,[],[f51,f231,f139]) ).
fof(f241,plain,
( spl0_16
| spl0_20 ),
inference(avatar_split_clause,[],[f49,f231,f192]) ).
fof(f242,plain,
( spl0_17
| spl0_20 ),
inference(avatar_split_clause,[],[f47,f231,f197]) ).
fof(f243,plain,
( spl0_6
| spl0_20 ),
inference(avatar_split_clause,[],[f45,f231,f146]) ).
fof(f245,definition,
( spl0_21
<=> sk_c9 = multiply(sk_c10,sk_c2) ),
introduced(definition,[new_symbols(definition,[spl0_21])],[avatar_definition]) ).
fof(f247,plain,
( sk_c9 = multiply(sk_c10,sk_c2)
| ~ spl0_21 ),
inference(avatar_component_clause,[],[f245]) ).
fof(f251,plain,
( spl0_14
| spl0_21 ),
inference(avatar_split_clause,[],[f37,f245,f180]) ).
fof(f252,plain,
( spl0_15
| spl0_21 ),
inference(avatar_split_clause,[],[f35,f245,f185]) ).
fof(f254,plain,
( spl0_4
| spl0_21 ),
inference(avatar_split_clause,[],[f31,f245,f139]) ).
fof(f257,plain,
( spl0_6
| spl0_21 ),
inference(avatar_split_clause,[],[f25,f245,f146]) ).
fof(f261,plain,
( spl0_14
| spl0_9 ),
inference(avatar_split_clause,[],[f18,f156,f180]) ).
fof(f262,plain,
( spl0_15
| spl0_9 ),
inference(avatar_split_clause,[],[f16,f156,f185]) ).
fof(f263,plain,
( spl0_3
| spl0_9 ),
inference(avatar_split_clause,[],[f14,f156,f135]) ).
fof(f264,plain,
( spl0_4
| spl0_9 ),
inference(avatar_split_clause,[],[f12,f156,f139]) ).
fof(f265,plain,
( spl0_16
| spl0_9 ),
inference(avatar_split_clause,[],[f10,f156,f192]) ).
fof(f266,plain,
( spl0_17
| spl0_9 ),
inference(avatar_split_clause,[],[f8,f156,f197]) ).
fof(f267,plain,
( spl0_6
| spl0_9 ),
inference(avatar_split_clause,[],[f6,f156,f146]) ).
fof(f268,plain,
( identity = multiply(sk_c8,sk_c9)
| ~ spl0_4 ),
inference(superposition,[],[f3,f140]) ).
fof(f269,plain,
( identity = multiply(sk_c10,sk_c4)
| ~ spl0_16 ),
inference(superposition,[],[f3,f194]) ).
fof(f272,plain,
( identity = multiply(sk_c10,sk_c6)
| ~ spl0_12 ),
inference(superposition,[],[f3,f172]) ).
fof(f275,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[],[f4,f3]) ).
fof(f276,plain,
( ! [X0] : multiply(sk_c10,multiply(sk_c8,X0)) = multiply(sk_c9,X0)
| ~ spl0_3 ),
inference(superposition,[],[f4,f136]) ).
fof(f281,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f275,f1]) ).
fof(f284,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c8,multiply(sk_c9,X0))
| ~ spl0_4 ),
inference(superposition,[],[f4,f268]) ).
fof(f285,plain,
( ! [X0] : multiply(sk_c8,multiply(sk_c9,X0)) = X0
| ~ spl0_4 ),
inference(forward_demodulation,[],[f284,f1]) ).
fof(f286,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c10,multiply(sk_c4,X0))
| ~ spl0_16 ),
inference(superposition,[],[f4,f269]) ).
fof(f287,plain,
( ! [X0] : multiply(sk_c10,multiply(sk_c4,X0)) = X0
| ~ spl0_16 ),
inference(forward_demodulation,[],[f286,f1]) ).
fof(f298,plain,
( sk_c10 = multiply(sk_c8,sk_c8)
| ~ spl0_4
| ~ spl0_6 ),
inference(superposition,[],[f285,f147]) ).
fof(f330,plain,
( sk_c10 = multiply(sk_c10,sk_c9)
| ~ spl0_16
| ~ spl0_17 ),
inference(superposition,[],[f287,f199]) ).
fof(f367,plain,
( sk_c9 = multiply(inverse(sk_c10),sk_c10)
| ~ spl0_16
| ~ spl0_17 ),
inference(superposition,[],[f281,f330]) ).
fof(f375,plain,
( sk_c8 = multiply(inverse(sk_c5),sk_c9)
| ~ spl0_14 ),
inference(superposition,[],[f281,f182]) ).
fof(f386,plain,
( sk_c8 = multiply(sk_c9,sk_c9)
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f375,f187]) ).
fof(f392,plain,
( identity = sk_c9
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f367,f3]) ).
fof(f430,plain,
( sk_c8 = multiply(identity,identity)
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f386,f392]) ).
fof(f431,plain,
( identity = sk_c8
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f430,f1]) ).
fof(f433,plain,
( sk_c9 != multiply(identity,sk_c10)
| spl0_9
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(superposition,[],[f158,f431]) ).
fof(f439,plain,
( sk_c10 = multiply(identity,identity)
| ~ spl0_4
| ~ spl0_6
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(superposition,[],[f298,f431]) ).
fof(f442,plain,
( identity = sk_c10
| ~ spl0_4
| ~ spl0_6
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f439,f1]) ).
fof(f448,plain,
( sk_c10 != sk_c9
| spl0_9
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f433,f1]) ).
fof(f453,plain,
( identity != sk_c10
| spl0_9
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f448,f392]) ).
fof(f473,plain,
( $false
| ~ spl0_4
| ~ spl0_6
| spl0_9
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f442,f453]) ).
fof(f474,plain,
( ~ spl0_4
| ~ spl0_6
| spl0_9
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(avatar_contradiction_clause,[],[f473]) ).
fof(f475,plain,
( ! [X3] :
( identity != multiply(X3,sk_c10)
| sk_c10 != inverse(X3) )
| ~ spl0_5
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f144,f392]) ).
fof(f476,plain,
( identity = multiply(sk_c8,sk_c10)
| ~ spl0_9
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f157,f392]) ).
fof(f477,plain,
( identity = multiply(identity,sk_c10)
| ~ spl0_9
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f476,f431]) ).
fof(f478,plain,
( identity = sk_c10
| ~ spl0_9
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f477,f1]) ).
fof(f483,plain,
( identity = multiply(identity,sk_c4)
| ~ spl0_9
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(superposition,[],[f269,f478]) ).
fof(f502,plain,
( identity = sk_c4
| ~ spl0_9
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f483,f1]) ).
fof(f521,plain,
( sk_c10 = inverse(identity)
| ~ spl0_9
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(superposition,[],[f194,f502]) ).
fof(f522,plain,
( identity = inverse(identity)
| ~ spl0_9
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f521,f478]) ).
fof(f530,plain,
( ! [X3] :
( identity != multiply(X3,identity)
| sk_c10 != inverse(X3) )
| ~ spl0_5
| ~ spl0_9
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f475,f478]) ).
fof(f531,plain,
( ! [X3] :
( identity != multiply(X3,identity)
| identity != inverse(X3) )
| ~ spl0_5
| ~ spl0_9
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f530,f478]) ).
fof(f533,plain,
( ! [X0,X1] :
( identity != multiply(X0,multiply(X1,identity))
| identity != inverse(multiply(X0,X1)) )
| ~ spl0_5
| ~ spl0_9
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(superposition,[],[f531,f4]) ).
fof(f560,plain,
( identity != multiply(sk_c9,identity)
| identity != inverse(multiply(sk_c10,sk_c8))
| ~ spl0_3
| ~ spl0_5
| ~ spl0_9
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(superposition,[],[f533,f276]) ).
fof(f575,plain,
( identity != multiply(identity,identity)
| identity != inverse(multiply(sk_c10,sk_c8))
| ~ spl0_3
| ~ spl0_5
| ~ spl0_9
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f560,f392]) ).
fof(f587,plain,
( identity != inverse(multiply(sk_c10,sk_c8))
| ~ spl0_3
| ~ spl0_5
| ~ spl0_9
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f575,f1]) ).
fof(f595,plain,
( identity != inverse(sk_c9)
| ~ spl0_3
| ~ spl0_5
| ~ spl0_9
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f587,f136]) ).
fof(f601,plain,
( identity != sk_c8
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_9
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f595,f140]) ).
fof(f608,plain,
( $false
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_9
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f601,f431]) ).
fof(f609,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_9
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(avatar_contradiction_clause,[],[f608]) ).
fof(f610,plain,
( ! [X2] :
( sk_c10 != multiply(X2,identity)
| sk_c8 != inverse(X2) )
| ~ spl0_7
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f151,f431]) ).
fof(f611,plain,
( ! [X2] :
( identity != multiply(X2,identity)
| sk_c8 != inverse(X2) )
| ~ spl0_7
| ~ spl0_9
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f610,f478]) ).
fof(f612,plain,
( ! [X2] :
( identity != multiply(X2,identity)
| identity != inverse(X2) )
| ~ spl0_7
| ~ spl0_9
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f611,f431]) ).
fof(f625,plain,
( identity != identity
| identity != inverse(identity)
| ~ spl0_7
| ~ spl0_9
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(superposition,[],[f612,f1]) ).
fof(f632,plain,
( identity != inverse(identity)
| ~ spl0_7
| ~ spl0_9
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(trivial_inequality_removal,[],[f625]) ).
fof(f639,plain,
( $false
| ~ spl0_7
| ~ spl0_9
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f522,f632]) ).
fof(f640,plain,
( ~ spl0_7
| ~ spl0_9
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(avatar_contradiction_clause,[],[f639]) ).
fof(f641,plain,
( ! [X1] :
( sk_c9 != multiply(identity,multiply(X1,identity))
| sk_c10 != inverse(X1) )
| ~ spl0_8
| ~ spl0_9
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f154,f478]) ).
fof(f642,plain,
( ! [X1] :
( sk_c9 != multiply(X1,identity)
| sk_c10 != inverse(X1) )
| ~ spl0_8
| ~ spl0_9
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f641,f1]) ).
fof(f643,plain,
( ! [X1] :
( identity != multiply(X1,identity)
| sk_c10 != inverse(X1) )
| ~ spl0_8
| ~ spl0_9
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f642,f392]) ).
fof(f644,plain,
( ! [X1] :
( identity != multiply(X1,identity)
| identity != inverse(X1) )
| ~ spl0_8
| ~ spl0_9
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f643,f478]) ).
fof(f645,plain,
( identity != identity
| identity != inverse(identity)
| ~ spl0_8
| ~ spl0_9
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(superposition,[],[f644,f1]) ).
fof(f652,plain,
( identity != inverse(identity)
| ~ spl0_8
| ~ spl0_9
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(trivial_inequality_removal,[],[f645]) ).
fof(f659,plain,
( $false
| ~ spl0_8
| ~ spl0_9
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f522,f652]) ).
fof(f660,plain,
( ~ spl0_8
| ~ spl0_9
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(avatar_contradiction_clause,[],[f659]) ).
fof(f661,plain,
( ! [X4] :
( identity != inverse(X4)
| sk_c9 != multiply(X4,sk_c8) )
| ~ spl0_2
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f133,f392]) ).
fof(f662,plain,
( ! [X4] :
( sk_c9 != multiply(X4,identity)
| identity != inverse(X4) )
| ~ spl0_2
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f661,f431]) ).
fof(f663,plain,
( ! [X4] :
( identity != multiply(X4,identity)
| identity != inverse(X4) )
| ~ spl0_2
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f662,f392]) ).
fof(f664,plain,
( identity != identity
| identity != inverse(identity)
| ~ spl0_2
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(superposition,[],[f663,f1]) ).
fof(f671,plain,
( identity != inverse(identity)
| ~ spl0_2
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(trivial_inequality_removal,[],[f664]) ).
fof(f678,plain,
( $false
| ~ spl0_2
| ~ spl0_9
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f522,f671]) ).
fof(f679,plain,
( ~ spl0_2
| ~ spl0_9
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(avatar_contradiction_clause,[],[f678]) ).
fof(f680,plain,
( ! [X5] :
( identity != inverse(inverse(X5))
| inverse(X5) != multiply(X5,sk_c10) )
| ~ spl0_1
| ~ spl0_9
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f130,f478]) ).
fof(f681,plain,
( ! [X5] :
( inverse(X5) != multiply(X5,identity)
| identity != inverse(inverse(X5)) )
| ~ spl0_1
| ~ spl0_9
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f680,f478]) ).
fof(f682,plain,
( identity != inverse(identity)
| identity != inverse(inverse(identity))
| ~ spl0_1
| ~ spl0_9
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(superposition,[],[f681,f1]) ).
fof(f696,definition,
( spl0_23
<=> identity = inverse(inverse(identity)) ),
introduced(definition,[new_symbols(definition,[spl0_23])],[avatar_definition]) ).
fof(f698,plain,
( identity != inverse(inverse(identity))
| spl0_23 ),
inference(avatar_component_clause,[],[f696]) ).
fof(f701,definition,
( spl0_24
<=> identity = inverse(identity) ),
introduced(definition,[new_symbols(definition,[spl0_24])],[avatar_definition]) ).
fof(f702,plain,
( identity = inverse(identity)
| ~ spl0_24 ),
inference(avatar_component_clause,[],[f701]) ).
fof(f704,plain,
( ~ spl0_23
| ~ spl0_24
| ~ spl0_1
| ~ spl0_9
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(avatar_split_clause,[],[f682,f197,f192,f185,f180,f156,f129,f701,f696]) ).
fof(f715,plain,
( spl0_24
| ~ spl0_9
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(avatar_split_clause,[],[f522,f197,f192,f185,f180,f156,f701]) ).
fof(f720,plain,
( identity != inverse(identity)
| spl0_23
| ~ spl0_24 ),
inference(forward_demodulation,[],[f698,f702]) ).
fof(f721,plain,
( $false
| spl0_23
| ~ spl0_24 ),
inference(forward_subsumption_resolution,[],[f720,f702]) ).
fof(f722,plain,
( spl0_23
| ~ spl0_24 ),
inference(avatar_contradiction_clause,[],[f721]) ).
fof(f748,plain,
( identity = multiply(sk_c10,sk_c1)
| ~ spl0_19 ),
inference(superposition,[],[f3,f219]) ).
fof(f753,plain,
( sk_c8 = multiply(inverse(sk_c3),sk_c10)
| ~ spl0_18 ),
inference(superposition,[],[f281,f205]) ).
fof(f755,plain,
( sk_c8 = multiply(sk_c8,sk_c10)
| ~ spl0_11
| ~ spl0_18 ),
inference(forward_demodulation,[],[f753,f167]) ).
fof(f756,plain,
( sk_c10 = multiply(inverse(sk_c1),sk_c2)
| ~ spl0_20 ),
inference(superposition,[],[f281,f233]) ).
fof(f758,plain,
( sk_c10 = multiply(sk_c10,sk_c2)
| ~ spl0_19
| ~ spl0_20 ),
inference(forward_demodulation,[],[f756,f219]) ).
fof(f767,plain,
( sk_c10 != inverse(identity)
| sk_c10 != inverse(inverse(identity))
| ~ spl0_1 ),
inference(superposition,[],[f130,f1]) ).
fof(f794,plain,
( identity != sk_c10
| sk_c10 != inverse(inverse(identity))
| ~ spl0_1
| ~ spl0_24 ),
inference(forward_demodulation,[],[f767,f702]) ).
fof(f797,plain,
( sk_c10 != inverse(identity)
| identity != sk_c10
| ~ spl0_1
| ~ spl0_24 ),
inference(forward_demodulation,[],[f794,f702]) ).
fof(f803,definition,
( spl0_30
<=> sk_c10 = inverse(sk_c10) ),
introduced(definition,[new_symbols(definition,[spl0_30])],[avatar_definition]) ).
fof(f804,plain,
( sk_c10 = inverse(sk_c10)
| ~ spl0_30 ),
inference(avatar_component_clause,[],[f803]) ).
fof(f805,plain,
( sk_c10 != inverse(sk_c10)
| spl0_30 ),
inference(avatar_component_clause,[],[f803]) ).
fof(f807,plain,
( identity != sk_c10
| identity != sk_c10
| ~ spl0_1
| ~ spl0_24 ),
inference(forward_demodulation,[],[f797,f702]) ).
fof(f808,plain,
( identity != sk_c10
| ~ spl0_1
| ~ spl0_24 ),
inference(duplicate_literal_removal,[],[f807]) ).
fof(f834,plain,
( sk_c9 = multiply(sk_c8,sk_c8)
| ~ spl0_4
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f285,f386]) ).
fof(f838,plain,
( sk_c10 = sk_c9
| ~ spl0_4
| ~ spl0_6
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f834,f298]) ).
fof(f852,plain,
( sk_c8 = inverse(sk_c10)
| ~ spl0_4
| ~ spl0_6
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f140,f838]) ).
fof(f862,plain,
( sk_c8 != sk_c10
| ~ spl0_4
| ~ spl0_6
| ~ spl0_14
| ~ spl0_15
| spl0_30 ),
inference(superposition,[],[f805,f852]) ).
fof(f965,plain,
( sk_c8 = sk_c9
| ~ spl0_9
| ~ spl0_11
| ~ spl0_18 ),
inference(superposition,[],[f755,f157]) ).
fof(f971,plain,
( sk_c10 = multiply(inverse(sk_c8),sk_c8)
| ~ spl0_11
| ~ spl0_18 ),
inference(superposition,[],[f281,f755]) ).
fof(f973,plain,
( identity = sk_c10
| ~ spl0_11
| ~ spl0_18 ),
inference(forward_demodulation,[],[f971,f3]) ).
fof(f976,plain,
( $false
| ~ spl0_1
| ~ spl0_11
| ~ spl0_18
| ~ spl0_24 ),
inference(forward_subsumption_resolution,[],[f973,f808]) ).
fof(f977,plain,
( ~ spl0_1
| ~ spl0_11
| ~ spl0_18
| ~ spl0_24 ),
inference(avatar_contradiction_clause,[],[f976]) ).
fof(f980,plain,
( sk_c8 = sk_c10
| ~ spl0_4
| ~ spl0_6
| ~ spl0_9
| ~ spl0_11
| ~ spl0_14
| ~ spl0_15
| ~ spl0_18 ),
inference(superposition,[],[f965,f838]) ).
fof(f991,plain,
( $false
| ~ spl0_4
| ~ spl0_6
| ~ spl0_9
| ~ spl0_11
| ~ spl0_14
| ~ spl0_15
| ~ spl0_18
| spl0_30 ),
inference(forward_subsumption_resolution,[],[f980,f862]) ).
fof(f992,plain,
( ~ spl0_4
| ~ spl0_6
| ~ spl0_9
| ~ spl0_11
| ~ spl0_14
| ~ spl0_15
| ~ spl0_18
| spl0_30 ),
inference(avatar_contradiction_clause,[],[f991]) ).
fof(f993,plain,
( sk_c8 = sk_c10
| ~ spl0_4
| ~ spl0_6
| ~ spl0_14
| ~ spl0_15
| ~ spl0_30 ),
inference(forward_demodulation,[],[f804,f852]) ).
fof(f1037,definition,
( spl0_38
<=> identity = sk_c10 ),
introduced(definition,[new_symbols(definition,[spl0_38])],[avatar_definition]) ).
fof(f1038,plain,
( identity = sk_c10
| ~ spl0_38 ),
inference(avatar_component_clause,[],[f1037]) ).
fof(f1042,definition,
( spl0_39
<=> sk_c8 = sk_c10 ),
introduced(definition,[new_symbols(definition,[spl0_39])],[avatar_definition]) ).
fof(f1043,plain,
( sk_c8 = sk_c10
| ~ spl0_39 ),
inference(avatar_component_clause,[],[f1042]) ).
fof(f1057,plain,
( spl0_39
| ~ spl0_4
| ~ spl0_6
| ~ spl0_14
| ~ spl0_15
| ~ spl0_30 ),
inference(avatar_split_clause,[],[f993,f803,f185,f180,f146,f139,f1042]) ).
fof(f1091,plain,
( spl0_38
| ~ spl0_11
| ~ spl0_18 ),
inference(avatar_split_clause,[],[f973,f203,f165,f1037]) ).
fof(f1092,plain,
( identity = sk_c8
| ~ spl0_38
| ~ spl0_39 ),
inference(superposition,[],[f1038,f1043]) ).
fof(f1098,plain,
( sk_c9 = multiply(identity,sk_c2)
| ~ spl0_21
| ~ spl0_38 ),
inference(superposition,[],[f247,f1038]) ).
fof(f1100,plain,
( identity = multiply(identity,sk_c6)
| ~ spl0_12
| ~ spl0_38 ),
inference(superposition,[],[f272,f1038]) ).
fof(f1105,plain,
( identity = multiply(identity,sk_c1)
| ~ spl0_19
| ~ spl0_38 ),
inference(superposition,[],[f748,f1038]) ).
fof(f1118,plain,
( identity = sk_c1
| ~ spl0_19
| ~ spl0_38 ),
inference(forward_demodulation,[],[f1105,f1]) ).
fof(f1123,plain,
( identity = sk_c6
| ~ spl0_12
| ~ spl0_38 ),
inference(forward_demodulation,[],[f1100,f1]) ).
fof(f1125,plain,
( sk_c9 = sk_c2
| ~ spl0_21
| ~ spl0_38 ),
inference(forward_demodulation,[],[f1098,f1]) ).
fof(f1141,plain,
( sk_c9 = multiply(identity,sk_c10)
| ~ spl0_9
| ~ spl0_38
| ~ spl0_39 ),
inference(superposition,[],[f157,f1092]) ).
fof(f1166,plain,
( sk_c10 = sk_c9
| ~ spl0_9
| ~ spl0_38
| ~ spl0_39 ),
inference(forward_demodulation,[],[f1141,f1]) ).
fof(f1191,plain,
( sk_c10 = inverse(identity)
| ~ spl0_19
| ~ spl0_38 ),
inference(superposition,[],[f219,f1118]) ).
fof(f1199,plain,
( sk_c10 = inverse(identity)
| ~ spl0_12
| ~ spl0_38 ),
inference(superposition,[],[f172,f1123]) ).
fof(f1241,plain,
( sk_c8 = sk_c2
| ~ spl0_9
| ~ spl0_11
| ~ spl0_18
| ~ spl0_21
| ~ spl0_38 ),
inference(forward_demodulation,[],[f1125,f965]) ).
fof(f1302,plain,
( identity = multiply(identity,sk_c2)
| ~ spl0_19
| ~ spl0_20
| ~ spl0_38 ),
inference(forward_demodulation,[],[f758,f1038]) ).
fof(f1312,plain,
( sk_c9 != multiply(identity,sk_c8)
| spl0_3
| ~ spl0_38 ),
inference(forward_demodulation,[],[f137,f1038]) ).
fof(f1317,plain,
( identity = sk_c2
| ~ spl0_19
| ~ spl0_20
| ~ spl0_38 ),
inference(forward_demodulation,[],[f1302,f1]) ).
fof(f1320,plain,
( sk_c8 != sk_c9
| spl0_3
| ~ spl0_38 ),
inference(forward_demodulation,[],[f1312,f1]) ).
fof(f1324,plain,
( $false
| spl0_3
| ~ spl0_9
| ~ spl0_11
| ~ spl0_18
| ~ spl0_38 ),
inference(forward_subsumption_resolution,[],[f1320,f965]) ).
fof(f1325,plain,
( spl0_3
| ~ spl0_9
| ~ spl0_11
| ~ spl0_18
| ~ spl0_38 ),
inference(avatar_contradiction_clause,[],[f1324]) ).
fof(f1327,plain,
( ! [X2] :
( identity != multiply(X2,sk_c8)
| sk_c8 != inverse(X2) )
| ~ spl0_7
| ~ spl0_38 ),
inference(forward_demodulation,[],[f151,f1038]) ).
fof(f1337,plain,
( identity != sk_c10
| sk_c8 != inverse(sk_c3)
| ~ spl0_7
| ~ spl0_18
| ~ spl0_38 ),
inference(superposition,[],[f1327,f205]) ).
fof(f1339,plain,
( sk_c8 != inverse(sk_c3)
| ~ spl0_7
| ~ spl0_18
| ~ spl0_38 ),
inference(forward_subsumption_resolution,[],[f1337,f1038]) ).
fof(f1341,plain,
( $false
| ~ spl0_7
| ~ spl0_11
| ~ spl0_18
| ~ spl0_38 ),
inference(forward_subsumption_resolution,[],[f1339,f167]) ).
fof(f1342,plain,
( ~ spl0_7
| ~ spl0_11
| ~ spl0_18
| ~ spl0_38 ),
inference(avatar_contradiction_clause,[],[f1341]) ).
fof(f1343,plain,
( ! [X4] :
( sk_c8 != inverse(X4)
| sk_c9 != multiply(X4,sk_c8) )
| ~ spl0_2
| ~ spl0_9
| ~ spl0_11
| ~ spl0_18 ),
inference(forward_demodulation,[],[f133,f965]) ).
fof(f1344,plain,
( ! [X4] :
( sk_c8 != multiply(X4,sk_c8)
| sk_c8 != inverse(X4) )
| ~ spl0_2
| ~ spl0_9
| ~ spl0_11
| ~ spl0_18 ),
inference(forward_demodulation,[],[f1343,f965]) ).
fof(f1350,plain,
( sk_c8 != sk_c10
| sk_c8 != inverse(sk_c3)
| ~ spl0_2
| ~ spl0_9
| ~ spl0_11
| ~ spl0_18 ),
inference(superposition,[],[f1344,f205]) ).
fof(f1352,plain,
( sk_c8 != sk_c10
| ~ spl0_2
| ~ spl0_9
| ~ spl0_11
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[],[f1350,f167]) ).
fof(f1355,plain,
( identity != sk_c8
| ~ spl0_2
| ~ spl0_9
| ~ spl0_11
| ~ spl0_18
| ~ spl0_38 ),
inference(forward_demodulation,[],[f1352,f1038]) ).
fof(f1357,plain,
( identity = sk_c8
| ~ spl0_9
| ~ spl0_11
| ~ spl0_18
| ~ spl0_19
| ~ spl0_20
| ~ spl0_21
| ~ spl0_38 ),
inference(superposition,[],[f1241,f1317]) ).
fof(f1373,plain,
( sk_c8 = sk_c10
| ~ spl0_9
| ~ spl0_11
| ~ spl0_18
| ~ spl0_38
| ~ spl0_39 ),
inference(forward_demodulation,[],[f1166,f965]) ).
fof(f1389,definition,
( spl0_42
<=> identity = sk_c8 ),
introduced(definition,[new_symbols(definition,[spl0_42])],[avatar_definition]) ).
fof(f1390,plain,
( identity = sk_c8
| ~ spl0_42 ),
inference(avatar_component_clause,[],[f1389]) ).
fof(f1399,plain,
( ~ spl0_42
| ~ spl0_2
| ~ spl0_9
| ~ spl0_11
| ~ spl0_18
| ~ spl0_38 ),
inference(avatar_split_clause,[],[f1355,f1037,f203,f165,f156,f132,f1389]) ).
fof(f1400,plain,
( spl0_42
| ~ spl0_9
| ~ spl0_11
| ~ spl0_18
| ~ spl0_19
| ~ spl0_20
| ~ spl0_21
| ~ spl0_38 ),
inference(avatar_split_clause,[],[f1357,f1037,f245,f231,f217,f203,f165,f156,f1389]) ).
fof(f1410,plain,
( identity = sk_c8
| ~ spl0_9
| ~ spl0_11
| ~ spl0_18
| ~ spl0_38
| ~ spl0_39 ),
inference(forward_demodulation,[],[f1373,f1038]) ).
fof(f1418,plain,
( spl0_42
| ~ spl0_9
| ~ spl0_11
| ~ spl0_18
| ~ spl0_38
| ~ spl0_39 ),
inference(avatar_split_clause,[],[f1410,f1042,f1037,f203,f165,f156,f1389]) ).
fof(f1440,plain,
( identity = inverse(identity)
| ~ spl0_19
| ~ spl0_38 ),
inference(forward_demodulation,[],[f1191,f1038]) ).
fof(f1441,plain,
( identity = inverse(identity)
| ~ spl0_12
| ~ spl0_38 ),
inference(forward_demodulation,[],[f1199,f1038]) ).
fof(f1465,plain,
( spl0_24
| ~ spl0_19
| ~ spl0_38 ),
inference(avatar_split_clause,[],[f1440,f1037,f217,f701]) ).
fof(f1466,plain,
( spl0_24
| ~ spl0_12
| ~ spl0_38 ),
inference(avatar_split_clause,[],[f1441,f1037,f170,f701]) ).
fof(f1486,plain,
( ! [X1] :
( sk_c9 != multiply(identity,multiply(X1,identity))
| sk_c10 != inverse(X1) )
| ~ spl0_8
| ~ spl0_38 ),
inference(forward_demodulation,[],[f154,f1038]) ).
fof(f1488,plain,
( ! [X1] :
( sk_c9 != multiply(X1,identity)
| sk_c10 != inverse(X1) )
| ~ spl0_8
| ~ spl0_38 ),
inference(forward_demodulation,[],[f1486,f1]) ).
fof(f1490,plain,
( ! [X1] :
( sk_c8 != multiply(X1,identity)
| sk_c10 != inverse(X1) )
| ~ spl0_8
| ~ spl0_9
| ~ spl0_11
| ~ spl0_18
| ~ spl0_38 ),
inference(forward_demodulation,[],[f1488,f965]) ).
fof(f1492,plain,
( ! [X1] :
( identity != inverse(X1)
| sk_c8 != multiply(X1,identity) )
| ~ spl0_8
| ~ spl0_9
| ~ spl0_11
| ~ spl0_18
| ~ spl0_38 ),
inference(forward_demodulation,[],[f1490,f1038]) ).
fof(f1527,plain,
( ! [X1] :
( identity != multiply(X1,identity)
| identity != inverse(X1) )
| ~ spl0_8
| ~ spl0_9
| ~ spl0_11
| ~ spl0_18
| ~ spl0_38
| ~ spl0_42 ),
inference(forward_demodulation,[],[f1492,f1390]) ).
fof(f1544,plain,
( identity != identity
| identity != inverse(identity)
| ~ spl0_8
| ~ spl0_9
| ~ spl0_11
| ~ spl0_18
| ~ spl0_38
| ~ spl0_42 ),
inference(superposition,[],[f1527,f1]) ).
fof(f1548,plain,
( identity != inverse(identity)
| ~ spl0_8
| ~ spl0_9
| ~ spl0_11
| ~ spl0_18
| ~ spl0_38
| ~ spl0_42 ),
inference(trivial_inequality_removal,[],[f1544]) ).
fof(f1550,plain,
( ~ spl0_24
| ~ spl0_8
| ~ spl0_9
| ~ spl0_11
| ~ spl0_18
| ~ spl0_38
| ~ spl0_42 ),
inference(avatar_split_clause,[],[f1548,f1389,f1037,f203,f165,f156,f153,f701]) ).
fof(f1551,plain,
( ! [X3] :
( sk_c9 != multiply(X3,identity)
| sk_c10 != inverse(X3) )
| ~ spl0_5
| ~ spl0_38 ),
inference(forward_demodulation,[],[f144,f1038]) ).
fof(f1552,plain,
( ! [X3] :
( sk_c8 != multiply(X3,identity)
| sk_c10 != inverse(X3) )
| ~ spl0_5
| ~ spl0_9
| ~ spl0_11
| ~ spl0_18
| ~ spl0_38 ),
inference(forward_demodulation,[],[f1551,f965]) ).
fof(f1553,plain,
( ! [X3] :
( identity != multiply(X3,identity)
| sk_c10 != inverse(X3) )
| ~ spl0_5
| ~ spl0_9
| ~ spl0_11
| ~ spl0_18
| ~ spl0_38
| ~ spl0_42 ),
inference(forward_demodulation,[],[f1552,f1390]) ).
fof(f1554,plain,
( ! [X3] :
( identity != multiply(X3,identity)
| identity != inverse(X3) )
| ~ spl0_5
| ~ spl0_9
| ~ spl0_11
| ~ spl0_18
| ~ spl0_38
| ~ spl0_42 ),
inference(forward_demodulation,[],[f1553,f1038]) ).
fof(f1566,plain,
( identity != identity
| identity != inverse(identity)
| ~ spl0_5
| ~ spl0_9
| ~ spl0_11
| ~ spl0_18
| ~ spl0_38
| ~ spl0_42 ),
inference(superposition,[],[f1554,f1]) ).
fof(f1570,plain,
( identity != inverse(identity)
| ~ spl0_5
| ~ spl0_9
| ~ spl0_11
| ~ spl0_18
| ~ spl0_38
| ~ spl0_42 ),
inference(trivial_inequality_removal,[],[f1566]) ).
fof(f1572,plain,
( ~ spl0_24
| ~ spl0_5
| ~ spl0_9
| ~ spl0_11
| ~ spl0_18
| ~ spl0_38
| ~ spl0_42 ),
inference(avatar_split_clause,[],[f1570,f1389,f1037,f203,f165,f156,f143,f701]) ).
fof(f1573,plain,
( sk_c8 != inverse(sk_c8)
| spl0_4
| ~ spl0_9
| ~ spl0_11
| ~ spl0_18 ),
inference(forward_demodulation,[],[f141,f965]) ).
fof(f1579,plain,
( identity != inverse(identity)
| spl0_4
| ~ spl0_9
| ~ spl0_11
| ~ spl0_18
| ~ spl0_42 ),
inference(forward_demodulation,[],[f1573,f1390]) ).
fof(f1585,plain,
( ~ spl0_24
| spl0_4
| ~ spl0_9
| ~ spl0_11
| ~ spl0_18
| ~ spl0_42 ),
inference(avatar_split_clause,[],[f1579,f1389,f203,f165,f156,f139,f701]) ).
fof(f1602,plain,
( sk_c8 != multiply(sk_c9,identity)
| spl0_6
| ~ spl0_38 ),
inference(forward_demodulation,[],[f148,f1038]) ).
fof(f1609,plain,
( sk_c8 != multiply(sk_c8,identity)
| spl0_6
| ~ spl0_9
| ~ spl0_11
| ~ spl0_18
| ~ spl0_38 ),
inference(forward_demodulation,[],[f1602,f965]) ).
fof(f1614,plain,
( identity != multiply(identity,identity)
| spl0_6
| ~ spl0_9
| ~ spl0_11
| ~ spl0_18
| ~ spl0_38
| ~ spl0_42 ),
inference(forward_demodulation,[],[f1609,f1390]) ).
fof(f1617,plain,
( $false
| spl0_6
| ~ spl0_9
| ~ spl0_11
| ~ spl0_18
| ~ spl0_38
| ~ spl0_42 ),
inference(forward_subsumption_resolution,[],[f1614,f1]) ).
fof(f1618,plain,
( spl0_6
| ~ spl0_9
| ~ spl0_11
| ~ spl0_18
| ~ spl0_38
| ~ spl0_42 ),
inference(avatar_contradiction_clause,[],[f1617]) ).
cnf(s1,plain,
( spl0_1
| spl0_2
| ~ spl0_3
| ~ spl0_4
| spl0_5
| ~ spl0_6
| spl0_7
| spl0_8
| ~ spl0_9 ),
inference(sat_conversion,[],[f159]) ).
cnf(s5,plain,
( spl0_11
| spl0_14 ),
inference(sat_conversion,[],[f183]) ).
cnf(s6,plain,
( spl0_11
| spl0_15 ),
inference(sat_conversion,[],[f188]) ).
cnf(s7,plain,
( spl0_3
| spl0_11 ),
inference(sat_conversion,[],[f189]) ).
cnf(s8,plain,
( spl0_4
| spl0_11 ),
inference(sat_conversion,[],[f190]) ).
cnf(s9,plain,
( spl0_11
| spl0_16 ),
inference(sat_conversion,[],[f195]) ).
cnf(s10,plain,
( spl0_11
| spl0_17 ),
inference(sat_conversion,[],[f200]) ).
cnf(s11,plain,
( spl0_6
| spl0_11 ),
inference(sat_conversion,[],[f201]) ).
cnf(s15,plain,
( spl0_14
| spl0_18 ),
inference(sat_conversion,[],[f209]) ).
cnf(s16,plain,
( spl0_15
| spl0_18 ),
inference(sat_conversion,[],[f210]) ).
cnf(s17,plain,
( spl0_3
| spl0_18 ),
inference(sat_conversion,[],[f211]) ).
cnf(s18,plain,
( spl0_4
| spl0_18 ),
inference(sat_conversion,[],[f212]) ).
cnf(s19,plain,
( spl0_16
| spl0_18 ),
inference(sat_conversion,[],[f213]) ).
cnf(s20,plain,
( spl0_17
| spl0_18 ),
inference(sat_conversion,[],[f214]) ).
cnf(s21,plain,
( spl0_6
| spl0_18 ),
inference(sat_conversion,[],[f215]) ).
cnf(s23,plain,
( spl0_12
| spl0_19 ),
inference(sat_conversion,[],[f221]) ).
cnf(s25,plain,
( spl0_14
| spl0_19 ),
inference(sat_conversion,[],[f223]) ).
cnf(s26,plain,
( spl0_15
| spl0_19 ),
inference(sat_conversion,[],[f224]) ).
cnf(s28,plain,
( spl0_4
| spl0_19 ),
inference(sat_conversion,[],[f226]) ).
cnf(s29,plain,
( spl0_16
| spl0_19 ),
inference(sat_conversion,[],[f227]) ).
cnf(s30,plain,
( spl0_17
| spl0_19 ),
inference(sat_conversion,[],[f228]) ).
cnf(s31,plain,
( spl0_6
| spl0_19 ),
inference(sat_conversion,[],[f229]) ).
cnf(s35,plain,
( spl0_14
| spl0_20 ),
inference(sat_conversion,[],[f237]) ).
cnf(s36,plain,
( spl0_15
| spl0_20 ),
inference(sat_conversion,[],[f238]) ).
cnf(s38,plain,
( spl0_4
| spl0_20 ),
inference(sat_conversion,[],[f240]) ).
cnf(s39,plain,
( spl0_16
| spl0_20 ),
inference(sat_conversion,[],[f241]) ).
cnf(s40,plain,
( spl0_17
| spl0_20 ),
inference(sat_conversion,[],[f242]) ).
cnf(s41,plain,
( spl0_6
| spl0_20 ),
inference(sat_conversion,[],[f243]) ).
cnf(s45,plain,
( spl0_14
| spl0_21 ),
inference(sat_conversion,[],[f251]) ).
cnf(s46,plain,
( spl0_15
| spl0_21 ),
inference(sat_conversion,[],[f252]) ).
cnf(s48,plain,
( spl0_4
| spl0_21 ),
inference(sat_conversion,[],[f254]) ).
cnf(s51,plain,
( spl0_6
| spl0_21 ),
inference(sat_conversion,[],[f257]) ).
cnf(s55,plain,
( spl0_9
| spl0_14 ),
inference(sat_conversion,[],[f261]) ).
cnf(s56,plain,
( spl0_9
| spl0_15 ),
inference(sat_conversion,[],[f262]) ).
cnf(s57,plain,
( spl0_3
| spl0_9 ),
inference(sat_conversion,[],[f263]) ).
cnf(s58,plain,
( spl0_4
| spl0_9 ),
inference(sat_conversion,[],[f264]) ).
cnf(s59,plain,
( spl0_9
| spl0_16 ),
inference(sat_conversion,[],[f265]) ).
cnf(s60,plain,
( spl0_9
| spl0_17 ),
inference(sat_conversion,[],[f266]) ).
cnf(s61,plain,
( spl0_6
| spl0_9 ),
inference(sat_conversion,[],[f267]) ).
cnf(s62,plain,
( ~ spl0_4
| ~ spl0_6
| spl0_9
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(sat_conversion,[],[f474]) ).
cnf(s66,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_9
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(sat_conversion,[],[f609]) ).
cnf(s67,plain,
( ~ spl0_7
| ~ spl0_9
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(sat_conversion,[],[f640]) ).
cnf(s68,plain,
( ~ spl0_8
| ~ spl0_9
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(sat_conversion,[],[f660]) ).
cnf(s69,plain,
( ~ spl0_2
| ~ spl0_9
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(sat_conversion,[],[f679]) ).
cnf(s71,plain,
( ~ spl0_1
| ~ spl0_9
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17
| ~ spl0_23
| ~ spl0_24 ),
inference(sat_conversion,[],[f704]) ).
cnf(s75,plain,
( ~ spl0_9
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17
| spl0_24 ),
inference(sat_conversion,[],[f715]) ).
cnf(s76,plain,
( spl0_23
| ~ spl0_24 ),
inference(sat_conversion,[],[f722]) ).
cnf(s83,plain,
( ~ spl0_1
| ~ spl0_11
| ~ spl0_18
| ~ spl0_24 ),
inference(sat_conversion,[],[f977]) ).
cnf(s85,plain,
( ~ spl0_4
| ~ spl0_6
| ~ spl0_9
| ~ spl0_11
| ~ spl0_14
| ~ spl0_15
| ~ spl0_18
| spl0_30 ),
inference(sat_conversion,[],[f992]) ).
cnf(s96,plain,
( ~ spl0_4
| ~ spl0_6
| ~ spl0_14
| ~ spl0_15
| ~ spl0_30
| spl0_39 ),
inference(sat_conversion,[],[f1057]) ).
cnf(s97,plain,
( ~ spl0_11
| ~ spl0_18
| spl0_38 ),
inference(sat_conversion,[],[f1091]) ).
cnf(s105,plain,
( spl0_3
| ~ spl0_9
| ~ spl0_11
| ~ spl0_18
| ~ spl0_38 ),
inference(sat_conversion,[],[f1325]) ).
cnf(s106,plain,
( ~ spl0_7
| ~ spl0_11
| ~ spl0_18
| ~ spl0_38 ),
inference(sat_conversion,[],[f1342]) ).
cnf(s112,plain,
( ~ spl0_2
| ~ spl0_9
| ~ spl0_11
| ~ spl0_18
| ~ spl0_38
| ~ spl0_42 ),
inference(sat_conversion,[],[f1399]) ).
cnf(s113,plain,
( ~ spl0_9
| ~ spl0_11
| ~ spl0_18
| ~ spl0_19
| ~ spl0_20
| ~ spl0_21
| ~ spl0_38
| spl0_42 ),
inference(sat_conversion,[],[f1400]) ).
cnf(s116,plain,
( ~ spl0_9
| ~ spl0_11
| ~ spl0_18
| ~ spl0_38
| ~ spl0_39
| spl0_42 ),
inference(sat_conversion,[],[f1418]) ).
cnf(s127,plain,
( ~ spl0_19
| spl0_24
| ~ spl0_38 ),
inference(sat_conversion,[],[f1465]) ).
cnf(s128,plain,
( ~ spl0_12
| spl0_24
| ~ spl0_38 ),
inference(sat_conversion,[],[f1466]) ).
cnf(s142,plain,
( ~ spl0_8
| ~ spl0_9
| ~ spl0_11
| ~ spl0_18
| ~ spl0_24
| ~ spl0_38
| ~ spl0_42 ),
inference(sat_conversion,[],[f1550]) ).
cnf(s145,plain,
( ~ spl0_5
| ~ spl0_9
| ~ spl0_11
| ~ spl0_18
| ~ spl0_24
| ~ spl0_38
| ~ spl0_42 ),
inference(sat_conversion,[],[f1572]) ).
cnf(s146,plain,
( spl0_4
| ~ spl0_9
| ~ spl0_11
| ~ spl0_18
| ~ spl0_24
| ~ spl0_42 ),
inference(sat_conversion,[],[f1585]) ).
cnf(s151,plain,
( spl0_6
| ~ spl0_9
| ~ spl0_11
| ~ spl0_18
| ~ spl0_38
| ~ spl0_42 ),
inference(sat_conversion,[],[f1618]) ).
cnf(s152,plain,
( ~ spl0_9
| spl0_3
| ~ spl0_11
| ~ spl0_18 ),
inference(rat,[],[s97,s105]) ).
cnf(s153,plain,
spl0_3,
inference(rat,[],[s152,s7,s17,s57]) ).
cnf(s154,plain,
( spl0_4
| ~ spl0_18
| ~ spl0_11
| ~ spl0_9 ),
inference(rat,[],[s146,s127,s113,s28,s38,s48,s97]) ).
cnf(s155,plain,
( ~ spl0_42
| ~ spl0_24
| ~ spl0_18
| ~ spl0_11
| ~ spl0_9
| spl0_2
| spl0_1 ),
inference(rat,[],[s1,s142,s145,s151,s106,s97,s154,s153]) ).
cnf(s156,plain,
( spl0_21
| spl0_39
| ~ spl0_18
| ~ spl0_11
| ~ spl0_9 ),
inference(rat,[],[s96,s85,s45,s46,s51,s154]) ).
cnf(s157,plain,
( ~ spl0_19
| ~ spl0_18
| ~ spl0_11
| ~ spl0_9
| spl0_2
| spl0_1 ),
inference(rat,[],[s96,s85,s35,s36,s41,s113,s156,s116,s155,s127,s97,s154]) ).
cnf(s158,plain,
( ~ spl0_18
| ~ spl0_11
| ~ spl0_9
| spl0_2
| spl0_1 ),
inference(rat,[],[s1,s66,s68,s25,s26,s29,s30,s31,s157,s154,s106,s97,s153]) ).
cnf(s159,plain,
( spl0_18
| ~ spl0_9
| spl0_2
| spl0_1 ),
inference(rat,[],[s1,s66,s67,s68,s15,s16,s18,s19,s20,s21,s153]) ).
cnf(s160,plain,
( ~ spl0_18
| ~ spl0_9
| spl0_1
| spl0_2 ),
inference(rat,[],[s1,s66,s67,s68,s5,s6,s8,s9,s10,s11,s158,s153]) ).
cnf(s161,plain,
( ~ spl0_9
| spl0_2
| spl0_1 ),
inference(rat,[],[s160,s159]) ).
cnf(s162,plain,
spl0_9,
inference(rat,[],[s62,s55,s56,s58,s59,s60,s61]) ).
cnf(s163,plain,
( spl0_14
| spl0_42
| ~ spl0_11
| ~ spl0_18 ),
inference(rat,[],[s113,s25,s35,s156,s116,s97,s162]) ).
cnf(s164,plain,
( spl0_20
| ~ spl0_14
| ~ spl0_2 ),
inference(rat,[],[s69,s36,s39,s40,s162]) ).
cnf(s165,plain,
( ~ spl0_11
| ~ spl0_38
| ~ spl0_18
| ~ spl0_2 ),
inference(rat,[],[s69,s26,s29,s30,s113,s164,s163,s156,s116,s112,s162]) ).
cnf(s166,plain,
( ~ spl0_11
| ~ spl0_18
| ~ spl0_2 ),
inference(rat,[],[s165,s97]) ).
cnf(s167,plain,
( spl0_11
| ~ spl0_2 ),
inference(rat,[],[s69,s5,s6,s9,s10,s162]) ).
cnf(s168,plain,
( ~ spl0_11
| ~ spl0_2 ),
inference(rat,[],[s69,s15,s16,s19,s20,s166,s162]) ).
cnf(s169,plain,
~ spl0_2,
inference(rat,[],[s168,s167]) ).
cnf(s170,plain,
spl0_1,
inference(rat,[],[s161,s162,s169]) ).
cnf(s171,plain,
( spl0_24
| ~ spl0_38 ),
inference(rat,[],[s23,s127,s128]) ).
cnf(s172,plain,
( ~ spl0_11
| ~ spl0_18 ),
inference(rat,[],[s171,s97,s83,s170]) ).
cnf(s173,plain,
( ~ spl0_14
| ~ spl0_17
| ~ spl0_16
| ~ spl0_15 ),
inference(rat,[],[s71,s76,s75,s162,s170]) ).
cnf(s174,plain,
spl0_11,
inference(rat,[],[s173,s5,s6,s9,s10]) ).
cnf(s175,plain,
~ spl0_18,
inference(rat,[],[s172,s174]) ).
cnf(s177,plain,
spl0_17,
inference(rat,[],[s20,s175]) ).
cnf(s178,plain,
spl0_16,
inference(rat,[],[s19,s175]) ).
cnf(s180,plain,
spl0_15,
inference(rat,[],[s16,s175]) ).
cnf(s181,plain,
spl0_14,
inference(rat,[],[s15,s175]) ).
cnf(s185,plain,
$false,
inference(rat,[],[s173,s180,s178,s177,s181]) ).
fof(f1619,plain,
$false,
inference(avatar_sat_refutation,[],[s185]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP366-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/5.60 % Computer : n017.cluster.edu
% 0.12/5.60 % Model : x86_64 x86_64
% 0.12/5.60 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/5.60 % Memory : 8046.5625MB
% 0.12/5.60 % OS : Linux 6.8.0-71-generic
% 0.12/5.60 % CPULimit : 300
% 0.12/5.60 % WCLimit : 300
% 0.12/5.60 % DateTime : Sun Sep 27 09:51:59 UTC 2026
% 0.12/5.60 % CPUTime :
% 0.12/5.60 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/5.63 Running first-order model finding
% 0.12/5.64 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
% 0.15/5.71 % (2301214)Will run a generic schedule for satisfiability detection.
% 0.15/5.71 % (2301225)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2394167385:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.15/5.71 % (2301220)% WARNING: option uhcvi not known.
% 0.15/5.71 % (2301219)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2981323192_2999 on theBenchmark for (2999ds/0Mi)
% 0.15/5.71 % (2301220)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=4293854171:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.15/5.71 % (2301221)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1955230177:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.15/5.71 % (2301222)dis+10_1_sil=32000:sp=arity:random_seed=1763173733:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.15/5.71 % (2301223)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2723289006:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.15/5.71 % (2301224)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2401072535:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.15/5.71 % TRYING [1]
% 0.15/5.71 % TRYING [2]
% 0.15/5.71 % TRYING [3]
% 0.15/5.71 % TRYING [4]
% 0.15/5.71 % (2301222) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2301214-2301222"...
% 0.15/5.71 % (2301223) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2301214-2301223"...
% 0.15/5.71 % (2301222)...printing done.
% 0.15/5.71 % (2301222)Refutation found. Thanks to Tanya!
% 0.15/5.71 % SZS status Unsatisfiable for theBenchmark
% 0.15/5.71 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/5.72 % (2301222)------------------------------
% 0.15/5.72 % (2301222)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.15/5.72 % (2301222)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.15/5.72 % (2301222)CaDiCaL version: 2.1.3
% 0.15/5.72 % (2301222)Termination reason: Refutation
% 0.15/5.72 % (2301222)Time elapsed: 0.029 s
% 0.15/5.72 % (2301222)Peak memory usage: 13 MB
% 0.15/5.72 % (2301222)Instructions burned: 49 (million)
% 0.15/5.72 % (2301214)Success in time 0.068 s
% 0.15/5.72 % Vampire exiting
%------------------------------------------------------------------------------