%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GRP318-1 : 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 10:17:28 AM UTC 2026
% Result : Unsatisfiable 0.18s 0.47s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 38
% Number of leaves : 60
% Syntax : Number of formulae : 486 ( 24 unt; 22 def)
% Number of atoms : 1941 ( 570 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 2905 (1450 ~;1433 |; 0 &)
% ( 22 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 26 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 24 ( 22 usr; 23 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 11 con; 0-2 aty)
% Number of variables : 133 ( 0 sgn 133 !; 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_c11,sk_c12) = sk_c10
| multiply(sk_c4,sk_c12) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,plain,
( multiply(sk_c11,sk_c12) = sk_c10
| sk_c11 = multiply(sk_c4,sk_c12) ),
inference(reorient_equations,[],[f5]) ).
fof(f7,negated_conjecture,
( multiply(sk_c11,sk_c12) = sk_c10
| inverse(sk_c4) = sk_c12 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_2) ).
fof(f8,plain,
( multiply(sk_c11,sk_c12) = sk_c10
| sk_c12 = inverse(sk_c4) ),
inference(reorient_equations,[],[f7]) ).
fof(f9,negated_conjecture,
( multiply(sk_c11,sk_c12) = sk_c10
| multiply(sk_c5,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_3) ).
fof(f10,plain,
( multiply(sk_c11,sk_c12) = sk_c10
| sk_c10 = multiply(sk_c5,sk_c11) ),
inference(reorient_equations,[],[f9]) ).
fof(f11,negated_conjecture,
( multiply(sk_c11,sk_c12) = sk_c10
| inverse(sk_c5) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_4) ).
fof(f12,plain,
( multiply(sk_c11,sk_c12) = sk_c10
| sk_c11 = inverse(sk_c5) ),
inference(reorient_equations,[],[f11]) ).
fof(f13,negated_conjecture,
( multiply(sk_c11,sk_c12) = sk_c10
| multiply(sk_c6,sk_c9) = sk_c12 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_5) ).
fof(f14,plain,
( multiply(sk_c11,sk_c12) = sk_c10
| sk_c12 = multiply(sk_c6,sk_c9) ),
inference(reorient_equations,[],[f13]) ).
fof(f15,negated_conjecture,
( multiply(sk_c11,sk_c12) = sk_c10
| inverse(sk_c6) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_6) ).
fof(f16,plain,
( multiply(sk_c11,sk_c12) = sk_c10
| sk_c9 = inverse(sk_c6) ),
inference(reorient_equations,[],[f15]) ).
fof(f24,negated_conjecture,
( multiply(sk_c1,sk_c11) = sk_c12
| multiply(sk_c4,sk_c12) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_11) ).
fof(f25,plain,
( sk_c12 = multiply(sk_c1,sk_c11)
| sk_c11 = multiply(sk_c4,sk_c12) ),
inference(reorient_equations,[],[f24]) ).
fof(f26,negated_conjecture,
( multiply(sk_c1,sk_c11) = sk_c12
| inverse(sk_c4) = sk_c12 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_12) ).
fof(f27,plain,
( sk_c12 = multiply(sk_c1,sk_c11)
| sk_c12 = inverse(sk_c4) ),
inference(reorient_equations,[],[f26]) ).
fof(f28,negated_conjecture,
( multiply(sk_c1,sk_c11) = sk_c12
| multiply(sk_c5,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_13) ).
fof(f29,plain,
( sk_c12 = multiply(sk_c1,sk_c11)
| sk_c10 = multiply(sk_c5,sk_c11) ),
inference(reorient_equations,[],[f28]) ).
fof(f30,negated_conjecture,
( multiply(sk_c1,sk_c11) = sk_c12
| inverse(sk_c5) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_14) ).
fof(f31,plain,
( sk_c12 = multiply(sk_c1,sk_c11)
| sk_c11 = inverse(sk_c5) ),
inference(reorient_equations,[],[f30]) ).
fof(f44,negated_conjecture,
( inverse(sk_c1) = sk_c11
| multiply(sk_c4,sk_c12) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_21) ).
fof(f45,plain,
( sk_c11 = inverse(sk_c1)
| sk_c11 = multiply(sk_c4,sk_c12) ),
inference(reorient_equations,[],[f44]) ).
fof(f46,negated_conjecture,
( inverse(sk_c1) = sk_c11
| inverse(sk_c4) = sk_c12 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_22) ).
fof(f47,plain,
( sk_c11 = inverse(sk_c1)
| sk_c12 = inverse(sk_c4) ),
inference(reorient_equations,[],[f46]) ).
fof(f48,negated_conjecture,
( inverse(sk_c1) = sk_c11
| multiply(sk_c5,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_23) ).
fof(f49,plain,
( sk_c11 = inverse(sk_c1)
| sk_c10 = multiply(sk_c5,sk_c11) ),
inference(reorient_equations,[],[f48]) ).
fof(f50,negated_conjecture,
( inverse(sk_c1) = sk_c11
| inverse(sk_c5) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_24) ).
fof(f51,plain,
( sk_c11 = inverse(sk_c1)
| sk_c11 = inverse(sk_c5) ),
inference(reorient_equations,[],[f50]) ).
fof(f52,negated_conjecture,
( inverse(sk_c1) = sk_c11
| multiply(sk_c6,sk_c9) = sk_c12 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_25) ).
fof(f53,plain,
( sk_c11 = inverse(sk_c1)
| sk_c12 = multiply(sk_c6,sk_c9) ),
inference(reorient_equations,[],[f52]) ).
fof(f54,negated_conjecture,
( inverse(sk_c1) = sk_c11
| inverse(sk_c6) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_26) ).
fof(f55,plain,
( sk_c11 = inverse(sk_c1)
| sk_c9 = inverse(sk_c6) ),
inference(reorient_equations,[],[f54]) ).
fof(f64,negated_conjecture,
( multiply(sk_c12,sk_c3) = sk_c11
| multiply(sk_c4,sk_c12) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_31) ).
fof(f65,plain,
( sk_c11 = multiply(sk_c12,sk_c3)
| sk_c11 = multiply(sk_c4,sk_c12) ),
inference(reorient_equations,[],[f64]) ).
fof(f66,negated_conjecture,
( multiply(sk_c12,sk_c3) = sk_c11
| inverse(sk_c4) = sk_c12 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_32) ).
fof(f67,plain,
( sk_c11 = multiply(sk_c12,sk_c3)
| sk_c12 = inverse(sk_c4) ),
inference(reorient_equations,[],[f66]) ).
fof(f68,negated_conjecture,
( multiply(sk_c12,sk_c3) = sk_c11
| multiply(sk_c5,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_33) ).
fof(f69,plain,
( sk_c11 = multiply(sk_c12,sk_c3)
| sk_c10 = multiply(sk_c5,sk_c11) ),
inference(reorient_equations,[],[f68]) ).
fof(f70,negated_conjecture,
( multiply(sk_c12,sk_c3) = sk_c11
| inverse(sk_c5) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_34) ).
fof(f71,plain,
( sk_c11 = multiply(sk_c12,sk_c3)
| sk_c11 = inverse(sk_c5) ),
inference(reorient_equations,[],[f70]) ).
fof(f72,negated_conjecture,
( multiply(sk_c12,sk_c3) = sk_c11
| multiply(sk_c6,sk_c9) = sk_c12 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_35) ).
fof(f73,plain,
( sk_c11 = multiply(sk_c12,sk_c3)
| sk_c12 = multiply(sk_c6,sk_c9) ),
inference(reorient_equations,[],[f72]) ).
fof(f74,negated_conjecture,
( multiply(sk_c12,sk_c3) = sk_c11
| inverse(sk_c6) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_36) ).
fof(f75,plain,
( sk_c11 = multiply(sk_c12,sk_c3)
| sk_c9 = inverse(sk_c6) ),
inference(reorient_equations,[],[f74]) ).
fof(f84,negated_conjecture,
( multiply(sk_c2,sk_c12) = sk_c3
| multiply(sk_c4,sk_c12) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_41) ).
fof(f85,plain,
( sk_c3 = multiply(sk_c2,sk_c12)
| sk_c11 = multiply(sk_c4,sk_c12) ),
inference(reorient_equations,[],[f84]) ).
fof(f86,negated_conjecture,
( multiply(sk_c2,sk_c12) = sk_c3
| inverse(sk_c4) = sk_c12 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_42) ).
fof(f87,plain,
( sk_c3 = multiply(sk_c2,sk_c12)
| sk_c12 = inverse(sk_c4) ),
inference(reorient_equations,[],[f86]) ).
fof(f88,negated_conjecture,
( multiply(sk_c2,sk_c12) = sk_c3
| multiply(sk_c5,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_43) ).
fof(f89,plain,
( sk_c3 = multiply(sk_c2,sk_c12)
| sk_c10 = multiply(sk_c5,sk_c11) ),
inference(reorient_equations,[],[f88]) ).
fof(f90,negated_conjecture,
( multiply(sk_c2,sk_c12) = sk_c3
| inverse(sk_c5) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_44) ).
fof(f91,plain,
( sk_c3 = multiply(sk_c2,sk_c12)
| sk_c11 = inverse(sk_c5) ),
inference(reorient_equations,[],[f90]) ).
fof(f92,negated_conjecture,
( multiply(sk_c2,sk_c12) = sk_c3
| multiply(sk_c6,sk_c9) = sk_c12 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_45) ).
fof(f93,plain,
( sk_c3 = multiply(sk_c2,sk_c12)
| sk_c12 = multiply(sk_c6,sk_c9) ),
inference(reorient_equations,[],[f92]) ).
fof(f94,negated_conjecture,
( multiply(sk_c2,sk_c12) = sk_c3
| inverse(sk_c6) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_46) ).
fof(f95,plain,
( sk_c3 = multiply(sk_c2,sk_c12)
| sk_c9 = inverse(sk_c6) ),
inference(reorient_equations,[],[f94]) ).
fof(f104,negated_conjecture,
( inverse(sk_c2) = sk_c12
| multiply(sk_c4,sk_c12) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_51) ).
fof(f105,plain,
( sk_c12 = inverse(sk_c2)
| sk_c11 = multiply(sk_c4,sk_c12) ),
inference(reorient_equations,[],[f104]) ).
fof(f106,negated_conjecture,
( inverse(sk_c2) = sk_c12
| inverse(sk_c4) = sk_c12 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_52) ).
fof(f107,plain,
( sk_c12 = inverse(sk_c2)
| sk_c12 = inverse(sk_c4) ),
inference(reorient_equations,[],[f106]) ).
fof(f108,negated_conjecture,
( inverse(sk_c2) = sk_c12
| multiply(sk_c5,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_53) ).
fof(f109,plain,
( sk_c12 = inverse(sk_c2)
| sk_c10 = multiply(sk_c5,sk_c11) ),
inference(reorient_equations,[],[f108]) ).
fof(f110,negated_conjecture,
( inverse(sk_c2) = sk_c12
| inverse(sk_c5) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_54) ).
fof(f111,plain,
( sk_c12 = inverse(sk_c2)
| sk_c11 = inverse(sk_c5) ),
inference(reorient_equations,[],[f110]) ).
fof(f112,negated_conjecture,
( inverse(sk_c2) = sk_c12
| multiply(sk_c6,sk_c9) = sk_c12 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_55) ).
fof(f113,plain,
( sk_c12 = inverse(sk_c2)
| sk_c12 = multiply(sk_c6,sk_c9) ),
inference(reorient_equations,[],[f112]) ).
fof(f114,negated_conjecture,
( inverse(sk_c2) = sk_c12
| inverse(sk_c6) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_56) ).
fof(f115,plain,
( sk_c12 = inverse(sk_c2)
| sk_c9 = inverse(sk_c6) ),
inference(reorient_equations,[],[f114]) ).
fof(f124,negated_conjecture,
! [X2,X3,X0,X1,X8,X6,X7,X4,X5] :
( multiply(sk_c11,sk_c12) != sk_c10
| multiply(X0,sk_c11) != sk_c12
| inverse(X0) != sk_c11
| multiply(sk_c12,X1) != sk_c11
| multiply(X2,sk_c12) != X1
| inverse(X2) != sk_c12
| multiply(X3,sk_c12) != sk_c11
| inverse(X3) != sk_c12
| multiply(X4,sk_c11) != sk_c10
| inverse(X4) != sk_c11
| multiply(X5,X6) != sk_c12
| inverse(X5) != X6
| multiply(X6,sk_c11) != sk_c12
| inverse(X7) != X8
| inverse(X8) != X6
| multiply(X7,X6) != X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_61) ).
fof(f125,plain,
! [X2,X3,X0,X1,X8,X6,X7,X4,X5] :
( multiply(sk_c11,sk_c12) != sk_c10
| sk_c12 != multiply(X0,sk_c11)
| inverse(X0) != sk_c11
| sk_c11 != multiply(sk_c12,X1)
| multiply(X2,sk_c12) != X1
| sk_c12 != inverse(X2)
| sk_c11 != multiply(X3,sk_c12)
| sk_c12 != inverse(X3)
| sk_c10 != multiply(X4,sk_c11)
| sk_c11 != inverse(X4)
| sk_c12 != multiply(X5,X6)
| inverse(X5) != X6
| sk_c12 != multiply(X6,sk_c11)
| inverse(X7) != X8
| inverse(X8) != X6
| multiply(X7,X6) != X8 ),
inference(reorient_equations,[],[f124]) ).
fof(f126,plain,
! [X2,X3,X0,X8,X6,X7,X4,X5] :
( multiply(sk_c11,sk_c12) != sk_c10
| sk_c12 != multiply(X0,sk_c11)
| inverse(X0) != sk_c11
| sk_c11 != multiply(sk_c12,multiply(X2,sk_c12))
| sk_c12 != inverse(X2)
| sk_c11 != multiply(X3,sk_c12)
| sk_c12 != inverse(X3)
| sk_c10 != multiply(X4,sk_c11)
| sk_c11 != inverse(X4)
| sk_c12 != multiply(X5,X6)
| inverse(X5) != X6
| sk_c12 != multiply(X6,sk_c11)
| inverse(X7) != X8
| inverse(X8) != X6
| multiply(X7,X6) != X8 ),
inference(equality_resolution,[],[f125]) ).
fof(f127,plain,
! [X2,X3,X0,X8,X7,X4,X5] :
( multiply(sk_c11,sk_c12) != sk_c10
| sk_c12 != multiply(X0,sk_c11)
| inverse(X0) != sk_c11
| sk_c11 != multiply(sk_c12,multiply(X2,sk_c12))
| sk_c12 != inverse(X2)
| sk_c11 != multiply(X3,sk_c12)
| sk_c12 != inverse(X3)
| sk_c10 != multiply(X4,sk_c11)
| sk_c11 != inverse(X4)
| sk_c12 != multiply(X5,inverse(X5))
| sk_c12 != multiply(inverse(X5),sk_c11)
| inverse(X7) != X8
| inverse(X5) != inverse(X8)
| multiply(X7,inverse(X5)) != X8 ),
inference(equality_resolution,[],[f126]) ).
fof(f128,plain,
! [X2,X3,X0,X7,X4,X5] :
( multiply(sk_c11,sk_c12) != sk_c10
| sk_c12 != multiply(X0,sk_c11)
| inverse(X0) != sk_c11
| sk_c11 != multiply(sk_c12,multiply(X2,sk_c12))
| sk_c12 != inverse(X2)
| sk_c11 != multiply(X3,sk_c12)
| sk_c12 != inverse(X3)
| sk_c10 != multiply(X4,sk_c11)
| sk_c11 != inverse(X4)
| sk_c12 != multiply(X5,inverse(X5))
| sk_c12 != multiply(inverse(X5),sk_c11)
| inverse(X5) != inverse(inverse(X7))
| inverse(X7) != multiply(X7,inverse(X5)) ),
inference(equality_resolution,[],[f127]) ).
fof(f130,definition,
( spl0_1
<=> ! [X5,X7] :
( sk_c12 != multiply(X5,inverse(X5))
| inverse(X7) != multiply(X7,inverse(X5))
| inverse(X5) != inverse(inverse(X7))
| sk_c12 != multiply(inverse(X5),sk_c11) ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f131,plain,
( ! [X7,X5] :
( sk_c12 != multiply(X5,inverse(X5))
| inverse(X7) != multiply(X7,inverse(X5))
| inverse(X5) != inverse(inverse(X7))
| sk_c12 != multiply(inverse(X5),sk_c11) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f130]) ).
fof(f133,definition,
( spl0_2
<=> ! [X4] :
( sk_c10 != multiply(X4,sk_c11)
| sk_c11 != inverse(X4) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f134,plain,
( ! [X4] :
( sk_c10 != multiply(X4,sk_c11)
| sk_c11 != inverse(X4) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f133]) ).
fof(f136,definition,
( spl0_3
<=> ! [X3] :
( sk_c11 != multiply(X3,sk_c12)
| sk_c12 != inverse(X3) ) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f137,plain,
( ! [X3] :
( sk_c11 != multiply(X3,sk_c12)
| sk_c12 != inverse(X3) )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f136]) ).
fof(f139,definition,
( spl0_4
<=> ! [X2] :
( sk_c11 != multiply(sk_c12,multiply(X2,sk_c12))
| sk_c12 != inverse(X2) ) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f140,plain,
( ! [X2] :
( sk_c11 != multiply(sk_c12,multiply(X2,sk_c12))
| sk_c12 != inverse(X2) )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f139]) ).
fof(f142,definition,
( spl0_5
<=> ! [X0] :
( sk_c12 != multiply(X0,sk_c11)
| inverse(X0) != sk_c11 ) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f143,plain,
( ! [X0] :
( sk_c12 != multiply(X0,sk_c11)
| inverse(X0) != sk_c11 )
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f142]) ).
fof(f145,definition,
( spl0_6
<=> multiply(sk_c11,sk_c12) = sk_c10 ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f146,plain,
( multiply(sk_c11,sk_c12) = sk_c10
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f145]) ).
fof(f147,plain,
( multiply(sk_c11,sk_c12) != sk_c10
| spl0_6 ),
inference(avatar_component_clause,[],[f145]) ).
fof(f148,plain,
( spl0_1
| spl0_2
| spl0_3
| spl0_4
| spl0_5
| ~ spl0_6 ),
inference(avatar_split_clause,[],[f128,f145,f142,f139,f136,f133,f130]) ).
fof(f154,definition,
( spl0_8
<=> sk_c12 = inverse(sk_c2) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f156,plain,
( sk_c12 = inverse(sk_c2)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f154]) ).
fof(f174,definition,
( spl0_12
<=> sk_c9 = inverse(sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f176,plain,
( sk_c9 = inverse(sk_c6)
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f174]) ).
fof(f177,plain,
( spl0_12
| spl0_8 ),
inference(avatar_split_clause,[],[f115,f154,f174]) ).
fof(f179,definition,
( spl0_13
<=> sk_c12 = multiply(sk_c6,sk_c9) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f181,plain,
( sk_c12 = multiply(sk_c6,sk_c9)
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f179]) ).
fof(f182,plain,
( spl0_13
| spl0_8 ),
inference(avatar_split_clause,[],[f113,f154,f179]) ).
fof(f184,definition,
( spl0_14
<=> sk_c11 = inverse(sk_c5) ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
fof(f186,plain,
( sk_c11 = inverse(sk_c5)
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f184]) ).
fof(f187,plain,
( spl0_14
| spl0_8 ),
inference(avatar_split_clause,[],[f111,f154,f184]) ).
fof(f189,definition,
( spl0_15
<=> sk_c10 = multiply(sk_c5,sk_c11) ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
fof(f190,plain,
( sk_c10 != multiply(sk_c5,sk_c11)
| spl0_15 ),
inference(avatar_component_clause,[],[f189]) ).
fof(f191,plain,
( sk_c10 = multiply(sk_c5,sk_c11)
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f189]) ).
fof(f192,plain,
( spl0_15
| spl0_8 ),
inference(avatar_split_clause,[],[f109,f154,f189]) ).
fof(f194,definition,
( spl0_16
<=> sk_c12 = inverse(sk_c4) ),
introduced(definition,[new_symbols(definition,[spl0_16])],[avatar_definition]) ).
fof(f196,plain,
( sk_c12 = inverse(sk_c4)
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f194]) ).
fof(f197,plain,
( spl0_16
| spl0_8 ),
inference(avatar_split_clause,[],[f107,f154,f194]) ).
fof(f199,definition,
( spl0_17
<=> sk_c11 = multiply(sk_c4,sk_c12) ),
introduced(definition,[new_symbols(definition,[spl0_17])],[avatar_definition]) ).
fof(f200,plain,
( sk_c11 != multiply(sk_c4,sk_c12)
| spl0_17 ),
inference(avatar_component_clause,[],[f199]) ).
fof(f201,plain,
( sk_c11 = multiply(sk_c4,sk_c12)
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f199]) ).
fof(f202,plain,
( spl0_17
| spl0_8 ),
inference(avatar_split_clause,[],[f105,f154,f199]) ).
fof(f204,definition,
( spl0_18
<=> sk_c3 = multiply(sk_c2,sk_c12) ),
introduced(definition,[new_symbols(definition,[spl0_18])],[avatar_definition]) ).
fof(f206,plain,
( sk_c3 = multiply(sk_c2,sk_c12)
| ~ spl0_18 ),
inference(avatar_component_clause,[],[f204]) ).
fof(f211,plain,
( spl0_12
| spl0_18 ),
inference(avatar_split_clause,[],[f95,f204,f174]) ).
fof(f212,plain,
( spl0_13
| spl0_18 ),
inference(avatar_split_clause,[],[f93,f204,f179]) ).
fof(f213,plain,
( spl0_14
| spl0_18 ),
inference(avatar_split_clause,[],[f91,f204,f184]) ).
fof(f214,plain,
( spl0_15
| spl0_18 ),
inference(avatar_split_clause,[],[f89,f204,f189]) ).
fof(f215,plain,
( spl0_16
| spl0_18 ),
inference(avatar_split_clause,[],[f87,f204,f194]) ).
fof(f216,plain,
( spl0_17
| spl0_18 ),
inference(avatar_split_clause,[],[f85,f204,f199]) ).
fof(f218,definition,
( spl0_19
<=> sk_c11 = multiply(sk_c12,sk_c3) ),
introduced(definition,[new_symbols(definition,[spl0_19])],[avatar_definition]) ).
fof(f220,plain,
( sk_c11 = multiply(sk_c12,sk_c3)
| ~ spl0_19 ),
inference(avatar_component_clause,[],[f218]) ).
fof(f225,plain,
( spl0_12
| spl0_19 ),
inference(avatar_split_clause,[],[f75,f218,f174]) ).
fof(f226,plain,
( spl0_13
| spl0_19 ),
inference(avatar_split_clause,[],[f73,f218,f179]) ).
fof(f227,plain,
( spl0_14
| spl0_19 ),
inference(avatar_split_clause,[],[f71,f218,f184]) ).
fof(f228,plain,
( spl0_15
| spl0_19 ),
inference(avatar_split_clause,[],[f69,f218,f189]) ).
fof(f229,plain,
( spl0_16
| spl0_19 ),
inference(avatar_split_clause,[],[f67,f218,f194]) ).
fof(f230,plain,
( spl0_17
| spl0_19 ),
inference(avatar_split_clause,[],[f65,f218,f199]) ).
fof(f232,definition,
( spl0_20
<=> sk_c11 = inverse(sk_c1) ),
introduced(definition,[new_symbols(definition,[spl0_20])],[avatar_definition]) ).
fof(f234,plain,
( sk_c11 = inverse(sk_c1)
| ~ spl0_20 ),
inference(avatar_component_clause,[],[f232]) ).
fof(f239,plain,
( spl0_12
| spl0_20 ),
inference(avatar_split_clause,[],[f55,f232,f174]) ).
fof(f240,plain,
( spl0_13
| spl0_20 ),
inference(avatar_split_clause,[],[f53,f232,f179]) ).
fof(f241,plain,
( spl0_14
| spl0_20 ),
inference(avatar_split_clause,[],[f51,f232,f184]) ).
fof(f242,plain,
( spl0_15
| spl0_20 ),
inference(avatar_split_clause,[],[f49,f232,f189]) ).
fof(f243,plain,
( spl0_16
| spl0_20 ),
inference(avatar_split_clause,[],[f47,f232,f194]) ).
fof(f244,plain,
( spl0_17
| spl0_20 ),
inference(avatar_split_clause,[],[f45,f232,f199]) ).
fof(f246,definition,
( spl0_21
<=> sk_c12 = multiply(sk_c1,sk_c11) ),
introduced(definition,[new_symbols(definition,[spl0_21])],[avatar_definition]) ).
fof(f248,plain,
( sk_c12 = multiply(sk_c1,sk_c11)
| ~ spl0_21 ),
inference(avatar_component_clause,[],[f246]) ).
fof(f255,plain,
( spl0_14
| spl0_21 ),
inference(avatar_split_clause,[],[f31,f246,f184]) ).
fof(f256,plain,
( spl0_15
| spl0_21 ),
inference(avatar_split_clause,[],[f29,f246,f189]) ).
fof(f257,plain,
( spl0_16
| spl0_21 ),
inference(avatar_split_clause,[],[f27,f246,f194]) ).
fof(f258,plain,
( spl0_17
| spl0_21 ),
inference(avatar_split_clause,[],[f25,f246,f199]) ).
fof(f263,plain,
( spl0_12
| spl0_6 ),
inference(avatar_split_clause,[],[f16,f145,f174]) ).
fof(f264,plain,
( spl0_13
| spl0_6 ),
inference(avatar_split_clause,[],[f14,f145,f179]) ).
fof(f265,plain,
( spl0_14
| spl0_6 ),
inference(avatar_split_clause,[],[f12,f145,f184]) ).
fof(f266,plain,
( spl0_15
| spl0_6 ),
inference(avatar_split_clause,[],[f10,f145,f189]) ).
fof(f267,plain,
( spl0_16
| spl0_6 ),
inference(avatar_split_clause,[],[f8,f145,f194]) ).
fof(f268,plain,
( spl0_17
| spl0_6 ),
inference(avatar_split_clause,[],[f6,f145,f199]) ).
fof(f269,plain,
( identity = multiply(sk_c12,sk_c4)
| ~ spl0_16 ),
inference(superposition,[],[f3,f196]) ).
fof(f270,plain,
( identity = multiply(sk_c11,sk_c5)
| ~ spl0_14 ),
inference(superposition,[],[f3,f186]) ).
fof(f276,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[],[f4,f3]) ).
fof(f282,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f276,f1]) ).
fof(f285,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c12,multiply(sk_c4,X0))
| ~ spl0_16 ),
inference(superposition,[],[f4,f269]) ).
fof(f286,plain,
( ! [X0] : multiply(sk_c12,multiply(sk_c4,X0)) = X0
| ~ spl0_16 ),
inference(forward_demodulation,[],[f285,f1]) ).
fof(f299,plain,
( sk_c12 = multiply(sk_c12,sk_c11)
| ~ spl0_16
| ~ spl0_17 ),
inference(superposition,[],[f286,f201]) ).
fof(f350,plain,
( sk_c11 = multiply(inverse(sk_c12),sk_c12)
| ~ spl0_16
| ~ spl0_17 ),
inference(superposition,[],[f282,f299]) ).
fof(f354,plain,
( sk_c11 = multiply(inverse(sk_c5),sk_c10)
| ~ spl0_15 ),
inference(superposition,[],[f282,f191]) ).
fof(f356,plain,
( sk_c9 = multiply(inverse(sk_c6),sk_c12)
| ~ spl0_13 ),
inference(superposition,[],[f282,f181]) ).
fof(f373,plain,
( sk_c9 = multiply(sk_c9,sk_c12)
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f356,f176]) ).
fof(f375,plain,
( sk_c11 = multiply(sk_c11,sk_c10)
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f354,f186]) ).
fof(f379,plain,
( identity = sk_c11
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f350,f3]) ).
fof(f384,plain,
( identity = multiply(identity,sk_c5)
| ~ spl0_14
| ~ spl0_16
| ~ spl0_17 ),
inference(superposition,[],[f270,f379]) ).
fof(f392,plain,
( identity = sk_c5
| ~ spl0_14
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f384,f1]) ).
fof(f415,plain,
( sk_c12 = multiply(inverse(sk_c9),sk_c9)
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f282,f373]) ).
fof(f417,plain,
( identity = sk_c12
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f415,f3]) ).
fof(f420,plain,
( sk_c10 != multiply(sk_c11,identity)
| spl0_6
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f147,f417]) ).
fof(f422,plain,
( identity = multiply(identity,sk_c4)
| ~ spl0_12
| ~ spl0_13
| ~ spl0_16 ),
inference(superposition,[],[f269,f417]) ).
fof(f431,plain,
( identity = sk_c4
| ~ spl0_12
| ~ spl0_13
| ~ spl0_16 ),
inference(forward_demodulation,[],[f422,f1]) ).
fof(f433,plain,
( sk_c10 != multiply(identity,identity)
| spl0_6
| ~ spl0_12
| ~ spl0_13
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f420,f379]) ).
fof(f435,plain,
( identity != sk_c10
| spl0_6
| ~ spl0_12
| ~ spl0_13
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f433,f1]) ).
fof(f437,plain,
( identity = multiply(identity,sk_c10)
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f375,f379]) ).
fof(f438,plain,
( identity = sk_c10
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f437,f1]) ).
fof(f447,plain,
( sk_c12 = inverse(identity)
| ~ spl0_12
| ~ spl0_13
| ~ spl0_16 ),
inference(superposition,[],[f196,f431]) ).
fof(f448,plain,
( identity = inverse(identity)
| ~ spl0_12
| ~ spl0_13
| ~ spl0_16 ),
inference(forward_demodulation,[],[f447,f417]) ).
fof(f458,plain,
( $false
| spl0_6
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f435,f438]) ).
fof(f459,plain,
( spl0_6
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(avatar_contradiction_clause,[],[f458]) ).
fof(f460,plain,
( ! [X3] :
( sk_c11 != multiply(X3,identity)
| sk_c12 != inverse(X3) )
| ~ spl0_3
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f137,f417]) ).
fof(f461,plain,
( identity = multiply(sk_c11,sk_c12)
| ~ spl0_6
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f146,f438]) ).
fof(f462,plain,
( ! [X3] :
( identity != multiply(X3,identity)
| sk_c12 != inverse(X3) )
| ~ spl0_3
| ~ spl0_12
| ~ spl0_13
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f460,f379]) ).
fof(f464,plain,
( ! [X3] :
( identity != multiply(X3,identity)
| identity != inverse(X3) )
| ~ spl0_3
| ~ spl0_12
| ~ spl0_13
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f462,f417]) ).
fof(f466,plain,
( identity != identity
| identity != inverse(identity)
| ~ spl0_3
| ~ spl0_12
| ~ spl0_13
| ~ spl0_16
| ~ spl0_17 ),
inference(superposition,[],[f464,f1]) ).
fof(f471,plain,
( identity != inverse(identity)
| ~ spl0_3
| ~ spl0_12
| ~ spl0_13
| ~ spl0_16
| ~ spl0_17 ),
inference(trivial_inequality_removal,[],[f466]) ).
fof(f519,plain,
( $false
| ~ spl0_3
| ~ spl0_12
| ~ spl0_13
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f448,f471]) ).
fof(f520,plain,
( ~ spl0_3
| ~ spl0_12
| ~ spl0_13
| ~ spl0_16
| ~ spl0_17 ),
inference(avatar_contradiction_clause,[],[f519]) ).
fof(f522,plain,
( identity = inverse(sk_c1)
| ~ spl0_16
| ~ spl0_17
| ~ spl0_20 ),
inference(forward_demodulation,[],[f234,f379]) ).
fof(f523,plain,
( sk_c12 = multiply(sk_c1,identity)
| ~ spl0_16
| ~ spl0_17
| ~ spl0_21 ),
inference(forward_demodulation,[],[f248,f379]) ).
fof(f525,plain,
( identity = multiply(identity,sk_c12)
| ~ spl0_6
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f461,f379]) ).
fof(f526,plain,
( identity = sk_c12
| ~ spl0_6
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f525,f1]) ).
fof(f555,plain,
( identity = multiply(identity,sk_c1)
| ~ spl0_16
| ~ spl0_17
| ~ spl0_20 ),
inference(superposition,[],[f3,f522]) ).
fof(f556,plain,
( identity = sk_c1
| ~ spl0_16
| ~ spl0_17
| ~ spl0_20 ),
inference(forward_demodulation,[],[f555,f1]) ).
fof(f572,plain,
( sk_c12 = multiply(identity,identity)
| ~ spl0_16
| ~ spl0_17
| ~ spl0_20
| ~ spl0_21 ),
inference(forward_demodulation,[],[f523,f556]) ).
fof(f573,plain,
( identity = sk_c12
| ~ spl0_16
| ~ spl0_17
| ~ spl0_20
| ~ spl0_21 ),
inference(forward_demodulation,[],[f572,f1]) ).
fof(f587,plain,
( sk_c10 != multiply(sk_c5,identity)
| spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f190,f379]) ).
fof(f588,plain,
( sk_c10 = multiply(identity,sk_c12)
| ~ spl0_6
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f146,f379]) ).
fof(f589,plain,
( sk_c10 != multiply(identity,identity)
| ~ spl0_14
| spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f587,f392]) ).
fof(f590,plain,
( sk_c12 = sk_c10
| ~ spl0_6
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f588,f1]) ).
fof(f591,plain,
( identity != sk_c10
| ~ spl0_14
| spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f589,f1]) ).
fof(f605,plain,
( identity = sk_c10
| ~ spl0_6
| ~ spl0_16
| ~ spl0_17
| ~ spl0_20
| ~ spl0_21 ),
inference(forward_demodulation,[],[f590,f573]) ).
fof(f606,plain,
( $false
| ~ spl0_6
| ~ spl0_14
| spl0_15
| ~ spl0_16
| ~ spl0_17
| ~ spl0_20
| ~ spl0_21 ),
inference(forward_subsumption_resolution,[],[f605,f591]) ).
fof(f607,plain,
( ~ spl0_6
| ~ spl0_14
| spl0_15
| ~ spl0_16
| ~ spl0_17
| ~ spl0_20
| ~ spl0_21 ),
inference(avatar_contradiction_clause,[],[f606]) ).
fof(f609,plain,
( identity = inverse(sk_c2)
| ~ spl0_8
| ~ spl0_16
| ~ spl0_17
| ~ spl0_20
| ~ spl0_21 ),
inference(forward_demodulation,[],[f156,f573]) ).
fof(f624,plain,
( identity = multiply(identity,sk_c2)
| ~ spl0_8
| ~ spl0_16
| ~ spl0_17
| ~ spl0_20
| ~ spl0_21 ),
inference(superposition,[],[f3,f609]) ).
fof(f625,plain,
( identity = sk_c2
| ~ spl0_8
| ~ spl0_16
| ~ spl0_17
| ~ spl0_20
| ~ spl0_21 ),
inference(forward_demodulation,[],[f624,f1]) ).
fof(f649,plain,
( ! [X4] :
( sk_c10 != multiply(X4,identity)
| sk_c11 != inverse(X4) )
| ~ spl0_2
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f134,f379]) ).
fof(f651,plain,
( identity = inverse(sk_c5)
| ~ spl0_14
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f186,f379]) ).
fof(f655,plain,
( ! [X4] :
( identity != inverse(X4)
| sk_c10 != multiply(X4,identity) )
| ~ spl0_2
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f649,f379]) ).
fof(f670,plain,
( identity = sk_c10
| ~ spl0_6
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f590,f526]) ).
fof(f690,plain,
( identity = multiply(identity,sk_c5)
| ~ spl0_14
| ~ spl0_16
| ~ spl0_17 ),
inference(superposition,[],[f3,f651]) ).
fof(f691,plain,
( identity = sk_c5
| ~ spl0_14
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f690,f1]) ).
fof(f693,plain,
( identity = inverse(identity)
| ~ spl0_14
| ~ spl0_16
| ~ spl0_17 ),
inference(superposition,[],[f651,f691]) ).
fof(f710,plain,
( ! [X4] :
( identity != multiply(X4,identity)
| identity != inverse(X4) )
| ~ spl0_2
| ~ spl0_6
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f655,f670]) ).
fof(f713,plain,
( identity != identity
| identity != inverse(inverse(identity))
| ~ spl0_2
| ~ spl0_6
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(superposition,[],[f710,f3]) ).
fof(f717,plain,
( identity != inverse(inverse(identity))
| ~ spl0_2
| ~ spl0_6
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(trivial_inequality_removal,[],[f713]) ).
fof(f724,plain,
( ! [X2] :
( sk_c11 != multiply(identity,multiply(X2,identity))
| sk_c12 != inverse(X2) )
| ~ spl0_4
| ~ spl0_6
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f140,f526]) ).
fof(f725,plain,
( ! [X2] :
( sk_c11 != multiply(X2,identity)
| sk_c12 != inverse(X2) )
| ~ spl0_4
| ~ spl0_6
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f724,f1]) ).
fof(f726,plain,
( ! [X2] :
( identity != multiply(X2,identity)
| sk_c12 != inverse(X2) )
| ~ spl0_4
| ~ spl0_6
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f725,f379]) ).
fof(f727,plain,
( ! [X2] :
( identity != multiply(X2,identity)
| identity != inverse(X2) )
| ~ spl0_4
| ~ spl0_6
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f726,f526]) ).
fof(f728,plain,
( identity != identity
| identity != inverse(identity)
| ~ spl0_4
| ~ spl0_6
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(superposition,[],[f727,f1]) ).
fof(f735,plain,
( identity != inverse(identity)
| ~ spl0_4
| ~ spl0_6
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(trivial_inequality_removal,[],[f728]) ).
fof(f746,plain,
( $false
| ~ spl0_4
| ~ spl0_6
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f693,f735]) ).
fof(f747,plain,
( ~ spl0_4
| ~ spl0_6
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(avatar_contradiction_clause,[],[f746]) ).
fof(f748,plain,
( ! [X0] :
( sk_c12 != multiply(X0,identity)
| inverse(X0) != sk_c11 )
| ~ spl0_5
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f143,f379]) ).
fof(f749,plain,
( ! [X0] :
( identity != multiply(X0,identity)
| inverse(X0) != sk_c11 )
| ~ spl0_5
| ~ spl0_6
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f748,f526]) ).
fof(f750,plain,
( ! [X0] :
( identity != multiply(X0,identity)
| identity != inverse(X0) )
| ~ spl0_5
| ~ spl0_6
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f749,f379]) ).
fof(f759,plain,
( identity != identity
| identity != inverse(inverse(identity))
| ~ spl0_5
| ~ spl0_6
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(superposition,[],[f750,f3]) ).
fof(f765,plain,
( identity != inverse(inverse(identity))
| ~ spl0_5
| ~ spl0_6
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(trivial_inequality_removal,[],[f759]) ).
fof(f767,plain,
( identity != inverse(identity)
| ~ spl0_5
| ~ spl0_6
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f765,f693]) ).
fof(f770,plain,
( $false
| ~ spl0_5
| ~ spl0_6
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f767,f693]) ).
fof(f771,plain,
( ~ spl0_5
| ~ spl0_6
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(avatar_contradiction_clause,[],[f770]) ).
fof(f772,plain,
( ! [X7,X5] :
( identity != multiply(X5,inverse(X5))
| inverse(X7) != multiply(X7,inverse(X5))
| inverse(X5) != inverse(inverse(X7))
| sk_c12 != multiply(inverse(X5),sk_c11) )
| ~ spl0_1
| ~ spl0_6
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f131,f526]) ).
fof(f773,plain,
( ! [X7,X5] :
( sk_c12 != multiply(inverse(X5),identity)
| identity != multiply(X5,inverse(X5))
| inverse(X7) != multiply(X7,inverse(X5))
| inverse(X5) != inverse(inverse(X7)) )
| ~ spl0_1
| ~ spl0_6
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f772,f379]) ).
fof(f774,plain,
( ! [X7,X5] :
( inverse(X7) != multiply(X7,inverse(X5))
| identity != multiply(X5,inverse(X5))
| identity != multiply(inverse(X5),identity)
| inverse(X5) != inverse(inverse(X7)) )
| ~ spl0_1
| ~ spl0_6
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f773,f526]) ).
fof(f777,plain,
( ! [X0] :
( inverse(X0) != multiply(X0,identity)
| identity != multiply(sk_c5,identity)
| identity != multiply(identity,identity)
| identity != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_6
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(superposition,[],[f774,f651]) ).
fof(f800,plain,
( ! [X0] :
( inverse(X0) != multiply(X0,identity)
| identity != multiply(sk_c5,identity)
| identity != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_6
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f777,f1]) ).
fof(f813,plain,
( ! [X0] :
( identity != multiply(identity,identity)
| inverse(X0) != multiply(X0,identity)
| identity != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_6
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f800,f691]) ).
fof(f818,plain,
( ! [X0] :
( inverse(X0) != multiply(X0,identity)
| identity != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_6
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f813,f1]) ).
fof(f841,plain,
( identity != inverse(inverse(identity))
| identity != inverse(inverse(inverse(identity)))
| ~ spl0_1
| ~ spl0_6
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(superposition,[],[f818,f3]) ).
fof(f852,definition,
( spl0_30
<=> identity = inverse(sk_c1) ),
introduced(definition,[new_symbols(definition,[spl0_30])],[avatar_definition]) ).
fof(f853,plain,
( identity = inverse(sk_c1)
| ~ spl0_30 ),
inference(avatar_component_clause,[],[f852]) ).
fof(f854,plain,
( identity != inverse(sk_c1)
| spl0_30 ),
inference(avatar_component_clause,[],[f852]) ).
fof(f866,plain,
( identity != inverse(identity)
| identity != inverse(inverse(inverse(identity)))
| ~ spl0_1
| ~ spl0_6
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f841,f693]) ).
fof(f868,plain,
( identity != inverse(inverse(inverse(identity)))
| ~ spl0_1
| ~ spl0_6
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f866,f693]) ).
fof(f870,plain,
( identity != inverse(inverse(identity))
| ~ spl0_1
| ~ spl0_6
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f868,f693]) ).
fof(f873,plain,
( identity != inverse(identity)
| ~ spl0_1
| ~ spl0_6
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f870,f693]) ).
fof(f874,plain,
( $false
| ~ spl0_1
| ~ spl0_6
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f873,f693]) ).
fof(f875,plain,
( ~ spl0_1
| ~ spl0_6
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(avatar_contradiction_clause,[],[f874]) ).
fof(f885,plain,
( identity != inverse(identity)
| ~ spl0_2
| ~ spl0_6
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f717,f693]) ).
fof(f891,plain,
( $false
| ~ spl0_2
| ~ spl0_6
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f885,f693]) ).
fof(f892,plain,
( ~ spl0_2
| ~ spl0_6
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(avatar_contradiction_clause,[],[f891]) ).
fof(f896,plain,
( spl0_30
| ~ spl0_16
| ~ spl0_17
| ~ spl0_20 ),
inference(avatar_split_clause,[],[f522,f232,f199,f194,f852]) ).
fof(f926,plain,
( identity = inverse(identity)
| ~ spl0_8
| ~ spl0_16
| ~ spl0_17
| ~ spl0_20
| ~ spl0_21 ),
inference(forward_demodulation,[],[f609,f625]) ).
fof(f945,plain,
( ! [X4] :
( identity != multiply(X4,identity)
| identity != inverse(X4) )
| ~ spl0_2
| ~ spl0_6
| ~ spl0_16
| ~ spl0_17
| ~ spl0_20
| ~ spl0_21 ),
inference(forward_demodulation,[],[f655,f605]) ).
fof(f952,plain,
( identity != identity
| identity != inverse(inverse(identity))
| ~ spl0_2
| ~ spl0_6
| ~ spl0_16
| ~ spl0_17
| ~ spl0_20
| ~ spl0_21 ),
inference(superposition,[],[f945,f3]) ).
fof(f958,plain,
( identity != inverse(inverse(identity))
| ~ spl0_2
| ~ spl0_6
| ~ spl0_16
| ~ spl0_17
| ~ spl0_20
| ~ spl0_21 ),
inference(trivial_inequality_removal,[],[f952]) ).
fof(f960,plain,
( identity != inverse(identity)
| ~ spl0_2
| ~ spl0_6
| ~ spl0_8
| ~ spl0_16
| ~ spl0_17
| ~ spl0_20
| ~ spl0_21 ),
inference(forward_demodulation,[],[f958,f926]) ).
fof(f963,plain,
( $false
| ~ spl0_2
| ~ spl0_6
| ~ spl0_8
| ~ spl0_16
| ~ spl0_17
| ~ spl0_20
| ~ spl0_21 ),
inference(forward_subsumption_resolution,[],[f960,f926]) ).
fof(f964,plain,
( ~ spl0_2
| ~ spl0_6
| ~ spl0_8
| ~ spl0_16
| ~ spl0_17
| ~ spl0_20
| ~ spl0_21 ),
inference(avatar_contradiction_clause,[],[f963]) ).
fof(f966,plain,
( ! [X0] :
( identity != multiply(X0,identity)
| inverse(X0) != sk_c11 )
| ~ spl0_5
| ~ spl0_16
| ~ spl0_17
| ~ spl0_20
| ~ spl0_21 ),
inference(forward_demodulation,[],[f748,f573]) ).
fof(f968,plain,
( ! [X0] :
( identity != multiply(X0,identity)
| identity != inverse(X0) )
| ~ spl0_5
| ~ spl0_16
| ~ spl0_17
| ~ spl0_20
| ~ spl0_21 ),
inference(forward_demodulation,[],[f966,f379]) ).
fof(f973,plain,
( identity != identity
| identity != inverse(inverse(identity))
| ~ spl0_5
| ~ spl0_16
| ~ spl0_17
| ~ spl0_20
| ~ spl0_21 ),
inference(superposition,[],[f968,f3]) ).
fof(f979,plain,
( identity != inverse(inverse(identity))
| ~ spl0_5
| ~ spl0_16
| ~ spl0_17
| ~ spl0_20
| ~ spl0_21 ),
inference(trivial_inequality_removal,[],[f973]) ).
fof(f981,plain,
( identity != inverse(identity)
| ~ spl0_5
| ~ spl0_8
| ~ spl0_16
| ~ spl0_17
| ~ spl0_20
| ~ spl0_21 ),
inference(forward_demodulation,[],[f979,f926]) ).
fof(f984,plain,
( $false
| ~ spl0_5
| ~ spl0_8
| ~ spl0_16
| ~ spl0_17
| ~ spl0_20
| ~ spl0_21 ),
inference(forward_subsumption_resolution,[],[f981,f926]) ).
fof(f985,plain,
( ~ spl0_5
| ~ spl0_8
| ~ spl0_16
| ~ spl0_17
| ~ spl0_20
| ~ spl0_21 ),
inference(avatar_contradiction_clause,[],[f984]) ).
fof(f986,plain,
( ! [X7,X5] :
( identity != multiply(X5,inverse(X5))
| inverse(X7) != multiply(X7,inverse(X5))
| inverse(X5) != inverse(inverse(X7))
| sk_c12 != multiply(inverse(X5),sk_c11) )
| ~ spl0_1
| ~ spl0_16
| ~ spl0_17
| ~ spl0_20
| ~ spl0_21 ),
inference(forward_demodulation,[],[f131,f573]) ).
fof(f987,plain,
( ! [X7,X5] :
( sk_c12 != multiply(inverse(X5),identity)
| identity != multiply(X5,inverse(X5))
| inverse(X7) != multiply(X7,inverse(X5))
| inverse(X5) != inverse(inverse(X7)) )
| ~ spl0_1
| ~ spl0_16
| ~ spl0_17
| ~ spl0_20
| ~ spl0_21 ),
inference(forward_demodulation,[],[f986,f379]) ).
fof(f988,plain,
( ! [X7,X5] :
( inverse(X7) != multiply(X7,inverse(X5))
| identity != multiply(X5,inverse(X5))
| identity != multiply(inverse(X5),identity)
| inverse(X5) != inverse(inverse(X7)) )
| ~ spl0_1
| ~ spl0_16
| ~ spl0_17
| ~ spl0_20
| ~ spl0_21 ),
inference(forward_demodulation,[],[f987,f573]) ).
fof(f990,plain,
( ! [X0] :
( inverse(X0) != multiply(X0,identity)
| identity != multiply(identity,identity)
| identity != multiply(identity,identity)
| identity != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_8
| ~ spl0_16
| ~ spl0_17
| ~ spl0_20
| ~ spl0_21 ),
inference(superposition,[],[f988,f926]) ).
fof(f999,plain,
( ! [X0] :
( inverse(X0) != multiply(X0,identity)
| identity != multiply(identity,identity)
| identity != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_8
| ~ spl0_16
| ~ spl0_17
| ~ spl0_20
| ~ spl0_21 ),
inference(duplicate_literal_removal,[],[f990]) ).
fof(f1004,plain,
( ! [X0] :
( inverse(X0) != multiply(X0,identity)
| identity != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_8
| ~ spl0_16
| ~ spl0_17
| ~ spl0_20
| ~ spl0_21 ),
inference(forward_subsumption_resolution,[],[f999,f1]) ).
fof(f1018,plain,
( identity != inverse(inverse(identity))
| identity != inverse(inverse(inverse(identity)))
| ~ spl0_1
| ~ spl0_8
| ~ spl0_16
| ~ spl0_17
| ~ spl0_20
| ~ spl0_21 ),
inference(superposition,[],[f1004,f3]) ).
fof(f1023,plain,
( identity != inverse(identity)
| identity != inverse(inverse(inverse(identity)))
| ~ spl0_1
| ~ spl0_8
| ~ spl0_16
| ~ spl0_17
| ~ spl0_20
| ~ spl0_21 ),
inference(forward_demodulation,[],[f1018,f926]) ).
fof(f1025,plain,
( identity != inverse(inverse(inverse(identity)))
| ~ spl0_1
| ~ spl0_8
| ~ spl0_16
| ~ spl0_17
| ~ spl0_20
| ~ spl0_21 ),
inference(forward_subsumption_resolution,[],[f1023,f926]) ).
fof(f1027,plain,
( identity != inverse(inverse(identity))
| ~ spl0_1
| ~ spl0_8
| ~ spl0_16
| ~ spl0_17
| ~ spl0_20
| ~ spl0_21 ),
inference(forward_demodulation,[],[f1025,f926]) ).
fof(f1030,plain,
( identity != inverse(identity)
| ~ spl0_1
| ~ spl0_8
| ~ spl0_16
| ~ spl0_17
| ~ spl0_20
| ~ spl0_21 ),
inference(forward_demodulation,[],[f1027,f926]) ).
fof(f1031,plain,
( $false
| ~ spl0_1
| ~ spl0_8
| ~ spl0_16
| ~ spl0_17
| ~ spl0_20
| ~ spl0_21 ),
inference(forward_subsumption_resolution,[],[f1030,f926]) ).
fof(f1032,plain,
( ~ spl0_1
| ~ spl0_8
| ~ spl0_16
| ~ spl0_17
| ~ spl0_20
| ~ spl0_21 ),
inference(avatar_contradiction_clause,[],[f1031]) ).
fof(f1033,plain,
( ! [X2] :
( sk_c11 != multiply(identity,multiply(X2,identity))
| sk_c12 != inverse(X2) )
| ~ spl0_4
| ~ spl0_16
| ~ spl0_17
| ~ spl0_20
| ~ spl0_21 ),
inference(forward_demodulation,[],[f140,f573]) ).
fof(f1034,plain,
( ! [X2] :
( sk_c11 != multiply(X2,identity)
| sk_c12 != inverse(X2) )
| ~ spl0_4
| ~ spl0_16
| ~ spl0_17
| ~ spl0_20
| ~ spl0_21 ),
inference(forward_demodulation,[],[f1033,f1]) ).
fof(f1035,plain,
( ! [X2] :
( identity != multiply(X2,identity)
| sk_c12 != inverse(X2) )
| ~ spl0_4
| ~ spl0_16
| ~ spl0_17
| ~ spl0_20
| ~ spl0_21 ),
inference(forward_demodulation,[],[f1034,f379]) ).
fof(f1036,plain,
( ! [X2] :
( identity != multiply(X2,identity)
| identity != inverse(X2) )
| ~ spl0_4
| ~ spl0_16
| ~ spl0_17
| ~ spl0_20
| ~ spl0_21 ),
inference(forward_demodulation,[],[f1035,f573]) ).
fof(f1040,plain,
( identity != identity
| identity != inverse(inverse(identity))
| ~ spl0_4
| ~ spl0_16
| ~ spl0_17
| ~ spl0_20
| ~ spl0_21 ),
inference(superposition,[],[f1036,f3]) ).
fof(f1046,plain,
( identity != inverse(inverse(identity))
| ~ spl0_4
| ~ spl0_16
| ~ spl0_17
| ~ spl0_20
| ~ spl0_21 ),
inference(trivial_inequality_removal,[],[f1040]) ).
fof(f1048,plain,
( identity != inverse(identity)
| ~ spl0_4
| ~ spl0_8
| ~ spl0_16
| ~ spl0_17
| ~ spl0_20
| ~ spl0_21 ),
inference(forward_demodulation,[],[f1046,f926]) ).
fof(f1051,plain,
( $false
| ~ spl0_4
| ~ spl0_8
| ~ spl0_16
| ~ spl0_17
| ~ spl0_20
| ~ spl0_21 ),
inference(forward_subsumption_resolution,[],[f1048,f926]) ).
fof(f1052,plain,
( ~ spl0_4
| ~ spl0_8
| ~ spl0_16
| ~ spl0_17
| ~ spl0_20
| ~ spl0_21 ),
inference(avatar_contradiction_clause,[],[f1051]) ).
fof(f1066,plain,
( identity = multiply(sk_c11,sk_c1)
| ~ spl0_20 ),
inference(superposition,[],[f3,f234]) ).
fof(f1073,plain,
( identity = sk_c11
| ~ spl0_20
| ~ spl0_30 ),
inference(superposition,[],[f853,f234]) ).
fof(f1093,plain,
( identity != sk_c11
| ~ spl0_20
| spl0_30 ),
inference(forward_demodulation,[],[f854,f234]) ).
fof(f1107,plain,
( sk_c12 = multiply(inverse(sk_c2),sk_c3)
| ~ spl0_18 ),
inference(superposition,[],[f282,f206]) ).
fof(f1109,plain,
( sk_c12 = multiply(sk_c12,sk_c3)
| ~ spl0_8
| ~ spl0_18 ),
inference(forward_demodulation,[],[f1107,f156]) ).
fof(f1112,plain,
( sk_c11 = multiply(inverse(sk_c1),sk_c12)
| ~ spl0_21 ),
inference(superposition,[],[f282,f248]) ).
fof(f1114,plain,
( sk_c11 = multiply(sk_c11,sk_c12)
| ~ spl0_20
| ~ spl0_21 ),
inference(forward_demodulation,[],[f1112,f234]) ).
fof(f1120,plain,
( sk_c11 != sk_c12
| sk_c12 != inverse(identity)
| ~ spl0_3 ),
inference(superposition,[],[f137,f1]) ).
fof(f1131,definition,
( spl0_34
<=> sk_c11 = sk_c10 ),
introduced(definition,[new_symbols(definition,[spl0_34])],[avatar_definition]) ).
fof(f1132,plain,
( sk_c11 = sk_c10
| ~ spl0_34 ),
inference(avatar_component_clause,[],[f1131]) ).
fof(f1136,definition,
( spl0_35
<=> sk_c12 = inverse(identity) ),
introduced(definition,[new_symbols(definition,[spl0_35])],[avatar_definition]) ).
fof(f1137,plain,
( sk_c12 = inverse(identity)
| ~ spl0_35 ),
inference(avatar_component_clause,[],[f1136]) ).
fof(f1138,plain,
( sk_c12 != inverse(identity)
| spl0_35 ),
inference(avatar_component_clause,[],[f1136]) ).
fof(f1140,definition,
( spl0_36
<=> sk_c11 = sk_c12 ),
introduced(definition,[new_symbols(definition,[spl0_36])],[avatar_definition]) ).
fof(f1141,plain,
( sk_c11 = sk_c12
| ~ spl0_36 ),
inference(avatar_component_clause,[],[f1140]) ).
fof(f1143,plain,
( ~ spl0_35
| ~ spl0_36
| ~ spl0_3 ),
inference(avatar_split_clause,[],[f1120,f136,f1140,f1136]) ).
fof(f1147,plain,
( sk_c11 = sk_c12
| ~ spl0_8
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_demodulation,[],[f1109,f220]) ).
fof(f1150,plain,
( spl0_36
| ~ spl0_8
| ~ spl0_18
| ~ spl0_19 ),
inference(avatar_split_clause,[],[f1147,f218,f204,f154,f1140]) ).
fof(f1152,plain,
( sk_c10 = multiply(sk_c11,sk_c11)
| ~ spl0_6
| ~ spl0_36 ),
inference(superposition,[],[f146,f1141]) ).
fof(f1153,plain,
( sk_c11 != multiply(sk_c4,sk_c11)
| spl0_17
| ~ spl0_36 ),
inference(superposition,[],[f200,f1141]) ).
fof(f1156,plain,
( identity = multiply(sk_c11,sk_c4)
| ~ spl0_16
| ~ spl0_36 ),
inference(superposition,[],[f269,f1141]) ).
fof(f1159,plain,
( sk_c11 != inverse(identity)
| spl0_35
| ~ spl0_36 ),
inference(forward_demodulation,[],[f1138,f1141]) ).
fof(f1160,plain,
( sk_c11 = multiply(sk_c11,sk_c11)
| ~ spl0_20
| ~ spl0_21
| ~ spl0_36 ),
inference(forward_demodulation,[],[f1114,f1141]) ).
fof(f1243,plain,
( sk_c11 = sk_c10
| ~ spl0_6
| ~ spl0_20
| ~ spl0_21
| ~ spl0_36 ),
inference(superposition,[],[f1152,f1160]) ).
fof(f1248,plain,
( sk_c11 = multiply(inverse(sk_c11),sk_c11)
| ~ spl0_20
| ~ spl0_21
| ~ spl0_36 ),
inference(superposition,[],[f282,f1160]) ).
fof(f1250,plain,
( identity = sk_c11
| ~ spl0_20
| ~ spl0_21
| ~ spl0_36 ),
inference(forward_demodulation,[],[f1248,f3]) ).
fof(f1254,plain,
( spl0_34
| ~ spl0_6
| ~ spl0_20
| ~ spl0_21
| ~ spl0_36 ),
inference(avatar_split_clause,[],[f1243,f1140,f246,f232,f145,f1131]) ).
fof(f1255,plain,
( $false
| ~ spl0_20
| ~ spl0_21
| spl0_30
| ~ spl0_36 ),
inference(forward_subsumption_resolution,[],[f1250,f1093]) ).
fof(f1256,plain,
( ~ spl0_20
| ~ spl0_21
| spl0_30
| ~ spl0_36 ),
inference(avatar_contradiction_clause,[],[f1255]) ).
fof(f1264,definition,
( spl0_37
<=> identity = sk_c11 ),
introduced(definition,[new_symbols(definition,[spl0_37])],[avatar_definition]) ).
fof(f1265,plain,
( identity = sk_c11
| ~ spl0_37 ),
inference(avatar_component_clause,[],[f1264]) ).
fof(f1275,plain,
( spl0_37
| ~ spl0_20
| ~ spl0_30 ),
inference(avatar_split_clause,[],[f1073,f852,f232,f1264]) ).
fof(f1281,plain,
( identity = multiply(identity,sk_c1)
| ~ spl0_20
| ~ spl0_37 ),
inference(superposition,[],[f1066,f1265]) ).
fof(f1288,plain,
( identity = multiply(identity,sk_c4)
| ~ spl0_16
| ~ spl0_36
| ~ spl0_37 ),
inference(superposition,[],[f1156,f1265]) ).
fof(f1296,plain,
( identity = sk_c4
| ~ spl0_16
| ~ spl0_36
| ~ spl0_37 ),
inference(forward_demodulation,[],[f1288,f1]) ).
fof(f1302,plain,
( identity = sk_c1
| ~ spl0_20
| ~ spl0_37 ),
inference(forward_demodulation,[],[f1281,f1]) ).
fof(f1321,plain,
( sk_c11 = inverse(identity)
| ~ spl0_20
| ~ spl0_37 ),
inference(superposition,[],[f234,f1302]) ).
fof(f1322,plain,
( $false
| ~ spl0_20
| spl0_35
| ~ spl0_36
| ~ spl0_37 ),
inference(forward_subsumption_resolution,[],[f1321,f1159]) ).
fof(f1323,plain,
( ~ spl0_20
| spl0_35
| ~ spl0_36
| ~ spl0_37 ),
inference(avatar_contradiction_clause,[],[f1322]) ).
fof(f1326,plain,
( ! [X4] :
( sk_c10 != multiply(X4,identity)
| sk_c11 != inverse(X4) )
| ~ spl0_2
| ~ spl0_37 ),
inference(forward_demodulation,[],[f134,f1265]) ).
fof(f1327,plain,
( sk_c11 = inverse(identity)
| ~ spl0_35
| ~ spl0_36 ),
inference(forward_demodulation,[],[f1137,f1141]) ).
fof(f1330,plain,
( ! [X4] :
( sk_c11 != multiply(X4,identity)
| sk_c11 != inverse(X4) )
| ~ spl0_2
| ~ spl0_34
| ~ spl0_37 ),
inference(forward_demodulation,[],[f1326,f1132]) ).
fof(f1331,plain,
( identity = inverse(identity)
| ~ spl0_35
| ~ spl0_36
| ~ spl0_37 ),
inference(forward_demodulation,[],[f1327,f1265]) ).
fof(f1332,plain,
( ! [X4] :
( identity != multiply(X4,identity)
| sk_c11 != inverse(X4) )
| ~ spl0_2
| ~ spl0_34
| ~ spl0_37 ),
inference(forward_demodulation,[],[f1330,f1265]) ).
fof(f1333,plain,
( ! [X4] :
( identity != multiply(X4,identity)
| identity != inverse(X4) )
| ~ spl0_2
| ~ spl0_34
| ~ spl0_37 ),
inference(forward_demodulation,[],[f1332,f1265]) ).
fof(f1334,plain,
( identity != identity
| identity != inverse(identity)
| ~ spl0_2
| ~ spl0_34
| ~ spl0_37 ),
inference(superposition,[],[f1333,f1]) ).
fof(f1338,plain,
( identity != inverse(identity)
| ~ spl0_2
| ~ spl0_34
| ~ spl0_37 ),
inference(trivial_inequality_removal,[],[f1334]) ).
fof(f1342,plain,
( $false
| ~ spl0_2
| ~ spl0_34
| ~ spl0_35
| ~ spl0_36
| ~ spl0_37 ),
inference(forward_subsumption_resolution,[],[f1338,f1331]) ).
fof(f1343,plain,
( ~ spl0_2
| ~ spl0_34
| ~ spl0_35
| ~ spl0_36
| ~ spl0_37 ),
inference(avatar_contradiction_clause,[],[f1342]) ).
fof(f1344,plain,
( ! [X0] :
( sk_c12 != multiply(X0,identity)
| inverse(X0) != sk_c11 )
| ~ spl0_5
| ~ spl0_37 ),
inference(forward_demodulation,[],[f143,f1265]) ).
fof(f1345,plain,
( ! [X0] :
( sk_c11 != multiply(X0,identity)
| inverse(X0) != sk_c11 )
| ~ spl0_5
| ~ spl0_36
| ~ spl0_37 ),
inference(forward_demodulation,[],[f1344,f1141]) ).
fof(f1346,plain,
( ! [X0] :
( identity != multiply(X0,identity)
| inverse(X0) != sk_c11 )
| ~ spl0_5
| ~ spl0_36
| ~ spl0_37 ),
inference(forward_demodulation,[],[f1345,f1265]) ).
fof(f1347,plain,
( ! [X0] :
( identity != multiply(X0,identity)
| identity != inverse(X0) )
| ~ spl0_5
| ~ spl0_36
| ~ spl0_37 ),
inference(forward_demodulation,[],[f1346,f1265]) ).
fof(f1350,plain,
( identity != identity
| identity != inverse(inverse(identity))
| ~ spl0_5
| ~ spl0_36
| ~ spl0_37 ),
inference(superposition,[],[f1347,f3]) ).
fof(f1351,plain,
( identity != inverse(inverse(identity))
| ~ spl0_5
| ~ spl0_36
| ~ spl0_37 ),
inference(trivial_inequality_removal,[],[f1350]) ).
fof(f1353,plain,
( identity != inverse(identity)
| ~ spl0_5
| ~ spl0_35
| ~ spl0_36
| ~ spl0_37 ),
inference(forward_demodulation,[],[f1351,f1331]) ).
fof(f1356,plain,
( $false
| ~ spl0_5
| ~ spl0_35
| ~ spl0_36
| ~ spl0_37 ),
inference(forward_subsumption_resolution,[],[f1353,f1331]) ).
fof(f1357,plain,
( ~ spl0_5
| ~ spl0_35
| ~ spl0_36
| ~ spl0_37 ),
inference(avatar_contradiction_clause,[],[f1356]) ).
fof(f1358,plain,
( ! [X2] :
( sk_c11 != multiply(sk_c11,multiply(X2,sk_c11))
| sk_c12 != inverse(X2) )
| ~ spl0_4
| ~ spl0_36 ),
inference(forward_demodulation,[],[f140,f1141]) ).
fof(f1359,plain,
( ! [X2] :
( identity != multiply(identity,multiply(X2,identity))
| sk_c12 != inverse(X2) )
| ~ spl0_4
| ~ spl0_36
| ~ spl0_37 ),
inference(forward_demodulation,[],[f1358,f1265]) ).
fof(f1360,plain,
( ! [X2] :
( identity != multiply(X2,identity)
| sk_c12 != inverse(X2) )
| ~ spl0_4
| ~ spl0_36
| ~ spl0_37 ),
inference(forward_demodulation,[],[f1359,f1]) ).
fof(f1361,plain,
( ! [X2] :
( sk_c11 != inverse(X2)
| identity != multiply(X2,identity) )
| ~ spl0_4
| ~ spl0_36
| ~ spl0_37 ),
inference(forward_demodulation,[],[f1360,f1141]) ).
fof(f1362,plain,
( ! [X2] :
( identity != multiply(X2,identity)
| identity != inverse(X2) )
| ~ spl0_4
| ~ spl0_36
| ~ spl0_37 ),
inference(forward_demodulation,[],[f1361,f1265]) ).
fof(f1381,plain,
( identity != identity
| identity != inverse(inverse(identity))
| ~ spl0_4
| ~ spl0_36
| ~ spl0_37 ),
inference(superposition,[],[f1362,f3]) ).
fof(f1382,plain,
( identity != inverse(inverse(identity))
| ~ spl0_4
| ~ spl0_36
| ~ spl0_37 ),
inference(trivial_inequality_removal,[],[f1381]) ).
fof(f1384,plain,
( identity != inverse(identity)
| ~ spl0_4
| ~ spl0_35
| ~ spl0_36
| ~ spl0_37 ),
inference(forward_demodulation,[],[f1382,f1331]) ).
fof(f1387,plain,
( $false
| ~ spl0_4
| ~ spl0_35
| ~ spl0_36
| ~ spl0_37 ),
inference(forward_subsumption_resolution,[],[f1384,f1331]) ).
fof(f1388,plain,
( ~ spl0_4
| ~ spl0_35
| ~ spl0_36
| ~ spl0_37 ),
inference(avatar_contradiction_clause,[],[f1387]) ).
fof(f1389,plain,
( ! [X7,X5] :
( sk_c11 != multiply(X5,inverse(X5))
| inverse(X7) != multiply(X7,inverse(X5))
| inverse(X5) != inverse(inverse(X7))
| sk_c12 != multiply(inverse(X5),sk_c11) )
| ~ spl0_1
| ~ spl0_36 ),
inference(forward_demodulation,[],[f131,f1141]) ).
fof(f1390,plain,
( ! [X7,X5] :
( identity != multiply(X5,inverse(X5))
| inverse(X7) != multiply(X7,inverse(X5))
| inverse(X5) != inverse(inverse(X7))
| sk_c12 != multiply(inverse(X5),sk_c11) )
| ~ spl0_1
| ~ spl0_36
| ~ spl0_37 ),
inference(forward_demodulation,[],[f1389,f1265]) ).
fof(f1391,plain,
( ! [X7,X5] :
( sk_c12 != multiply(inverse(X5),identity)
| identity != multiply(X5,inverse(X5))
| inverse(X7) != multiply(X7,inverse(X5))
| inverse(X5) != inverse(inverse(X7)) )
| ~ spl0_1
| ~ spl0_36
| ~ spl0_37 ),
inference(forward_demodulation,[],[f1390,f1265]) ).
fof(f1392,plain,
( ! [X7,X5] :
( sk_c11 != multiply(inverse(X5),identity)
| identity != multiply(X5,inverse(X5))
| inverse(X7) != multiply(X7,inverse(X5))
| inverse(X5) != inverse(inverse(X7)) )
| ~ spl0_1
| ~ spl0_36
| ~ spl0_37 ),
inference(forward_demodulation,[],[f1391,f1141]) ).
fof(f1393,plain,
( ! [X7,X5] :
( inverse(X7) != multiply(X7,inverse(X5))
| identity != multiply(X5,inverse(X5))
| identity != multiply(inverse(X5),identity)
| inverse(X5) != inverse(inverse(X7)) )
| ~ spl0_1
| ~ spl0_36
| ~ spl0_37 ),
inference(forward_demodulation,[],[f1392,f1265]) ).
fof(f1395,plain,
( sk_c11 != multiply(identity,sk_c12)
| ~ spl0_16
| spl0_17
| ~ spl0_36
| ~ spl0_37 ),
inference(superposition,[],[f200,f1296]) ).
fof(f1398,plain,
( sk_c11 != multiply(identity,sk_c11)
| ~ spl0_16
| spl0_17
| ~ spl0_36
| ~ spl0_37 ),
inference(superposition,[],[f1153,f1296]) ).
fof(f1401,plain,
( $false
| ~ spl0_16
| spl0_17
| ~ spl0_36
| ~ spl0_37 ),
inference(forward_subsumption_resolution,[],[f1398,f1]) ).
fof(f1402,plain,
( ~ spl0_16
| spl0_17
| ~ spl0_36
| ~ spl0_37 ),
inference(avatar_contradiction_clause,[],[f1401]) ).
fof(f1405,plain,
( sk_c11 != sk_c12
| ~ spl0_16
| spl0_17
| ~ spl0_36
| ~ spl0_37 ),
inference(forward_demodulation,[],[f1395,f1]) ).
fof(f1409,plain,
( $false
| ~ spl0_16
| spl0_17
| ~ spl0_36
| ~ spl0_37 ),
inference(forward_subsumption_resolution,[],[f1405,f1141]) ).
fof(f1410,plain,
( ~ spl0_16
| spl0_17
| ~ spl0_36
| ~ spl0_37 ),
inference(avatar_contradiction_clause,[],[f1409]) ).
fof(f1417,plain,
( ! [X0] :
( inverse(X0) != multiply(X0,sk_c11)
| identity != multiply(sk_c1,sk_c11)
| identity != multiply(sk_c11,identity)
| sk_c11 != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_20
| ~ spl0_36
| ~ spl0_37 ),
inference(superposition,[],[f1393,f234]) ).
fof(f1425,plain,
( ! [X0] :
( inverse(X0) != multiply(X0,identity)
| identity != multiply(sk_c1,sk_c11)
| identity != multiply(sk_c11,identity)
| sk_c11 != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_20
| ~ spl0_36
| ~ spl0_37 ),
inference(forward_demodulation,[],[f1417,f1265]) ).
fof(f1438,plain,
( ! [X0] :
( identity != sk_c12
| inverse(X0) != multiply(X0,identity)
| identity != multiply(sk_c11,identity)
| sk_c11 != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_20
| ~ spl0_21
| ~ spl0_36
| ~ spl0_37 ),
inference(forward_demodulation,[],[f1425,f248]) ).
fof(f1442,plain,
( ! [X0] :
( identity != sk_c11
| inverse(X0) != multiply(X0,identity)
| identity != multiply(sk_c11,identity)
| sk_c11 != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_20
| ~ spl0_21
| ~ spl0_36
| ~ spl0_37 ),
inference(forward_demodulation,[],[f1438,f1141]) ).
fof(f1444,plain,
( ! [X0] :
( inverse(X0) != multiply(X0,identity)
| identity != multiply(sk_c11,identity)
| sk_c11 != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_20
| ~ spl0_21
| ~ spl0_36
| ~ spl0_37 ),
inference(forward_subsumption_resolution,[],[f1442,f1265]) ).
fof(f1446,plain,
( ! [X0] :
( identity != multiply(identity,identity)
| inverse(X0) != multiply(X0,identity)
| sk_c11 != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_20
| ~ spl0_21
| ~ spl0_36
| ~ spl0_37 ),
inference(forward_demodulation,[],[f1444,f1265]) ).
fof(f1448,plain,
( ! [X0] :
( inverse(X0) != multiply(X0,identity)
| sk_c11 != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_20
| ~ spl0_21
| ~ spl0_36
| ~ spl0_37 ),
inference(forward_subsumption_resolution,[],[f1446,f1]) ).
fof(f1450,plain,
( ! [X0] :
( inverse(X0) != multiply(X0,identity)
| identity != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_20
| ~ spl0_21
| ~ spl0_36
| ~ spl0_37 ),
inference(forward_demodulation,[],[f1448,f1265]) ).
fof(f1469,plain,
( identity != inverse(inverse(identity))
| identity != inverse(inverse(inverse(identity)))
| ~ spl0_1
| ~ spl0_20
| ~ spl0_21
| ~ spl0_36
| ~ spl0_37 ),
inference(superposition,[],[f1450,f3]) ).
fof(f1470,plain,
( identity != inverse(identity)
| identity != inverse(inverse(inverse(identity)))
| ~ spl0_1
| ~ spl0_20
| ~ spl0_21
| ~ spl0_35
| ~ spl0_36
| ~ spl0_37 ),
inference(forward_demodulation,[],[f1469,f1331]) ).
fof(f1472,plain,
( identity != inverse(inverse(inverse(identity)))
| ~ spl0_1
| ~ spl0_20
| ~ spl0_21
| ~ spl0_35
| ~ spl0_36
| ~ spl0_37 ),
inference(forward_subsumption_resolution,[],[f1470,f1331]) ).
fof(f1474,plain,
( identity != inverse(inverse(identity))
| ~ spl0_1
| ~ spl0_20
| ~ spl0_21
| ~ spl0_35
| ~ spl0_36
| ~ spl0_37 ),
inference(forward_demodulation,[],[f1472,f1331]) ).
fof(f1477,plain,
( identity != inverse(identity)
| ~ spl0_1
| ~ spl0_20
| ~ spl0_21
| ~ spl0_35
| ~ spl0_36
| ~ spl0_37 ),
inference(forward_demodulation,[],[f1474,f1331]) ).
fof(f1478,plain,
( $false
| ~ spl0_1
| ~ spl0_20
| ~ spl0_21
| ~ spl0_35
| ~ spl0_36
| ~ spl0_37 ),
inference(forward_subsumption_resolution,[],[f1477,f1331]) ).
fof(f1479,plain,
( ~ spl0_1
| ~ spl0_20
| ~ spl0_21
| ~ spl0_35
| ~ spl0_36
| ~ spl0_37 ),
inference(avatar_contradiction_clause,[],[f1478]) ).
cnf(s1,plain,
( spl0_1
| spl0_2
| spl0_3
| spl0_4
| spl0_5
| ~ spl0_6 ),
inference(sat_conversion,[],[f148]) ).
cnf(s6,plain,
( spl0_8
| spl0_12 ),
inference(sat_conversion,[],[f177]) ).
cnf(s7,plain,
( spl0_8
| spl0_13 ),
inference(sat_conversion,[],[f182]) ).
cnf(s8,plain,
( spl0_8
| spl0_14 ),
inference(sat_conversion,[],[f187]) ).
cnf(s9,plain,
( spl0_8
| spl0_15 ),
inference(sat_conversion,[],[f192]) ).
cnf(s10,plain,
( spl0_8
| spl0_16 ),
inference(sat_conversion,[],[f197]) ).
cnf(s11,plain,
( spl0_8
| spl0_17 ),
inference(sat_conversion,[],[f202]) ).
cnf(s16,plain,
( spl0_12
| spl0_18 ),
inference(sat_conversion,[],[f211]) ).
cnf(s17,plain,
( spl0_13
| spl0_18 ),
inference(sat_conversion,[],[f212]) ).
cnf(s18,plain,
( spl0_14
| spl0_18 ),
inference(sat_conversion,[],[f213]) ).
cnf(s19,plain,
( spl0_15
| spl0_18 ),
inference(sat_conversion,[],[f214]) ).
cnf(s20,plain,
( spl0_16
| spl0_18 ),
inference(sat_conversion,[],[f215]) ).
cnf(s21,plain,
( spl0_17
| spl0_18 ),
inference(sat_conversion,[],[f216]) ).
cnf(s26,plain,
( spl0_12
| spl0_19 ),
inference(sat_conversion,[],[f225]) ).
cnf(s27,plain,
( spl0_13
| spl0_19 ),
inference(sat_conversion,[],[f226]) ).
cnf(s28,plain,
( spl0_14
| spl0_19 ),
inference(sat_conversion,[],[f227]) ).
cnf(s29,plain,
( spl0_15
| spl0_19 ),
inference(sat_conversion,[],[f228]) ).
cnf(s30,plain,
( spl0_16
| spl0_19 ),
inference(sat_conversion,[],[f229]) ).
cnf(s31,plain,
( spl0_17
| spl0_19 ),
inference(sat_conversion,[],[f230]) ).
cnf(s36,plain,
( spl0_12
| spl0_20 ),
inference(sat_conversion,[],[f239]) ).
cnf(s37,plain,
( spl0_13
| spl0_20 ),
inference(sat_conversion,[],[f240]) ).
cnf(s38,plain,
( spl0_14
| spl0_20 ),
inference(sat_conversion,[],[f241]) ).
cnf(s39,plain,
( spl0_15
| spl0_20 ),
inference(sat_conversion,[],[f242]) ).
cnf(s40,plain,
( spl0_16
| spl0_20 ),
inference(sat_conversion,[],[f243]) ).
cnf(s41,plain,
( spl0_17
| spl0_20 ),
inference(sat_conversion,[],[f244]) ).
cnf(s48,plain,
( spl0_14
| spl0_21 ),
inference(sat_conversion,[],[f255]) ).
cnf(s49,plain,
( spl0_15
| spl0_21 ),
inference(sat_conversion,[],[f256]) ).
cnf(s50,plain,
( spl0_16
| spl0_21 ),
inference(sat_conversion,[],[f257]) ).
cnf(s51,plain,
( spl0_17
| spl0_21 ),
inference(sat_conversion,[],[f258]) ).
cnf(s56,plain,
( spl0_6
| spl0_12 ),
inference(sat_conversion,[],[f263]) ).
cnf(s57,plain,
( spl0_6
| spl0_13 ),
inference(sat_conversion,[],[f264]) ).
cnf(s58,plain,
( spl0_6
| spl0_14 ),
inference(sat_conversion,[],[f265]) ).
cnf(s59,plain,
( spl0_6
| spl0_15 ),
inference(sat_conversion,[],[f266]) ).
cnf(s60,plain,
( spl0_6
| spl0_16 ),
inference(sat_conversion,[],[f267]) ).
cnf(s61,plain,
( spl0_6
| spl0_17 ),
inference(sat_conversion,[],[f268]) ).
cnf(s62,plain,
( spl0_6
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(sat_conversion,[],[f459]) ).
cnf(s64,plain,
( ~ spl0_3
| ~ spl0_12
| ~ spl0_13
| ~ spl0_16
| ~ spl0_17 ),
inference(sat_conversion,[],[f520]) ).
cnf(s67,plain,
( ~ spl0_6
| ~ spl0_14
| spl0_15
| ~ spl0_16
| ~ spl0_17
| ~ spl0_20
| ~ spl0_21 ),
inference(sat_conversion,[],[f607]) ).
cnf(s74,plain,
( ~ spl0_4
| ~ spl0_6
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(sat_conversion,[],[f747]) ).
cnf(s76,plain,
( ~ spl0_5
| ~ spl0_6
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(sat_conversion,[],[f771]) ).
cnf(s84,plain,
( ~ spl0_1
| ~ spl0_6
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(sat_conversion,[],[f875]) ).
cnf(s90,plain,
( ~ spl0_2
| ~ spl0_6
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(sat_conversion,[],[f892]) ).
cnf(s91,plain,
( ~ spl0_16
| ~ spl0_17
| ~ spl0_20
| spl0_30 ),
inference(sat_conversion,[],[f896]) ).
cnf(s94,plain,
( ~ spl0_2
| ~ spl0_6
| ~ spl0_8
| ~ spl0_16
| ~ spl0_17
| ~ spl0_20
| ~ spl0_21 ),
inference(sat_conversion,[],[f964]) ).
cnf(s96,plain,
( ~ spl0_5
| ~ spl0_8
| ~ spl0_16
| ~ spl0_17
| ~ spl0_20
| ~ spl0_21 ),
inference(sat_conversion,[],[f985]) ).
cnf(s99,plain,
( ~ spl0_1
| ~ spl0_8
| ~ spl0_16
| ~ spl0_17
| ~ spl0_20
| ~ spl0_21 ),
inference(sat_conversion,[],[f1032]) ).
cnf(s101,plain,
( ~ spl0_4
| ~ spl0_8
| ~ spl0_16
| ~ spl0_17
| ~ spl0_20
| ~ spl0_21 ),
inference(sat_conversion,[],[f1052]) ).
cnf(s105,plain,
( ~ spl0_3
| ~ spl0_35
| ~ spl0_36 ),
inference(sat_conversion,[],[f1143]) ).
cnf(s107,plain,
( ~ spl0_8
| ~ spl0_18
| ~ spl0_19
| spl0_36 ),
inference(sat_conversion,[],[f1150]) ).
cnf(s109,plain,
( ~ spl0_6
| ~ spl0_20
| ~ spl0_21
| spl0_34
| ~ spl0_36 ),
inference(sat_conversion,[],[f1254]) ).
cnf(s111,plain,
( ~ spl0_20
| ~ spl0_21
| spl0_30
| ~ spl0_36 ),
inference(sat_conversion,[],[f1256]) ).
cnf(s115,plain,
( ~ spl0_20
| ~ spl0_30
| spl0_37 ),
inference(sat_conversion,[],[f1275]) ).
cnf(s116,plain,
( ~ spl0_20
| spl0_35
| ~ spl0_36
| ~ spl0_37 ),
inference(sat_conversion,[],[f1323]) ).
cnf(s117,plain,
( ~ spl0_2
| ~ spl0_34
| ~ spl0_35
| ~ spl0_36
| ~ spl0_37 ),
inference(sat_conversion,[],[f1343]) ).
cnf(s119,plain,
( ~ spl0_5
| ~ spl0_35
| ~ spl0_36
| ~ spl0_37 ),
inference(sat_conversion,[],[f1357]) ).
cnf(s121,plain,
( ~ spl0_4
| ~ spl0_35
| ~ spl0_36
| ~ spl0_37 ),
inference(sat_conversion,[],[f1388]) ).
cnf(s122,plain,
( ~ spl0_16
| spl0_17
| ~ spl0_36
| ~ spl0_37 ),
inference(sat_conversion,[],[f1402]) ).
cnf(s123,plain,
( ~ spl0_16
| spl0_17
| ~ spl0_36
| ~ spl0_37 ),
inference(sat_conversion,[],[f1410]) ).
cnf(s128,plain,
( ~ spl0_1
| ~ spl0_20
| ~ spl0_21
| ~ spl0_35
| ~ spl0_36
| ~ spl0_37 ),
inference(sat_conversion,[],[f1479]) ).
cnf(s129,plain,
spl0_6,
inference(rat,[],[s62,s56,s57,s58,s59,s60,s61]) ).
cnf(s130,plain,
( spl0_8
| ~ spl0_5 ),
inference(rat,[],[s76,s8,s9,s10,s11,s129]) ).
cnf(s131,plain,
( ~ spl0_16
| ~ spl0_15
| ~ spl0_14
| ~ spl0_5 ),
inference(rat,[],[s115,s111,s123,s107,s21,s31,s41,s51,s76,s130,s129]) ).
cnf(s132,plain,
( spl0_16
| ~ spl0_5 ),
inference(rat,[],[s116,s119,s115,s111,s107,s20,s30,s40,s50,s130]) ).
cnf(s133,plain,
( ~ spl0_14
| ~ spl0_5 ),
inference(rat,[],[s115,s111,s122,s107,s67,s19,s29,s39,s49,s131,s130,s132,s129]) ).
cnf(s134,plain,
~ spl0_5,
inference(rat,[],[s115,s111,s122,s107,s96,s18,s28,s38,s48,s133,s132,s130]) ).
cnf(s135,plain,
( ~ spl0_16
| ~ spl0_15
| ~ spl0_14
| ~ spl0_8
| ~ spl0_4 ),
inference(rat,[],[s115,s111,s123,s107,s21,s31,s41,s51,s74,s129]) ).
cnf(s136,plain,
( spl0_16
| ~ spl0_8
| ~ spl0_4 ),
inference(rat,[],[s121,s116,s115,s111,s107,s20,s30,s40,s50]) ).
cnf(s137,plain,
( ~ spl0_16
| ~ spl0_14
| ~ spl0_4
| ~ spl0_8 ),
inference(rat,[],[s115,s111,s123,s107,s67,s19,s29,s39,s49,s135,s129]) ).
cnf(s138,plain,
( ~ spl0_16
| ~ spl0_8
| ~ spl0_4 ),
inference(rat,[],[s115,s111,s123,s107,s101,s18,s28,s38,s48,s137]) ).
cnf(s139,plain,
( ~ spl0_8
| ~ spl0_4 ),
inference(rat,[],[s138,s136]) ).
cnf(s140,plain,
~ spl0_4,
inference(rat,[],[s74,s8,s9,s10,s11,s139,s129]) ).
cnf(s141,plain,
( ~ spl0_20
| spl0_35
| ~ spl0_36
| ~ spl0_16 ),
inference(rat,[],[s51,s111,s91,s115,s116]) ).
cnf(s142,plain,
( spl0_20
| ~ spl0_16
| ~ spl0_3 ),
inference(rat,[],[s64,s36,s37,s41]) ).
cnf(s143,plain,
( ~ spl0_36
| ~ spl0_16
| ~ spl0_3 ),
inference(rat,[],[s141,s105,s142]) ).
cnf(s144,plain,
( spl0_19
| ~ spl0_16
| ~ spl0_3 ),
inference(rat,[],[s64,s26,s27,s31]) ).
cnf(s145,plain,
( ~ spl0_16
| ~ spl0_8
| ~ spl0_3 ),
inference(rat,[],[s64,s16,s17,s21,s107,s144,s143]) ).
cnf(s146,plain,
( ~ spl0_8
| ~ spl0_3 ),
inference(rat,[],[s115,s116,s111,s105,s107,s20,s30,s40,s50,s145]) ).
cnf(s147,plain,
~ spl0_3,
inference(rat,[],[s64,s6,s7,s10,s11,s146]) ).
cnf(s148,plain,
( spl0_17
| ~ spl0_20
| ~ spl0_36
| ~ spl0_16 ),
inference(rat,[],[s115,s111,s123,s51]) ).
cnf(s149,plain,
( ~ spl0_17
| ~ spl0_20
| ~ spl0_2
| ~ spl0_8
| ~ spl0_16 ),
inference(rat,[],[s90,s48,s49,s94,s129]) ).
cnf(s150,plain,
( ~ spl0_20
| ~ spl0_8
| ~ spl0_36
| ~ spl0_16
| ~ spl0_2 ),
inference(rat,[],[s149,s148]) ).
cnf(s151,plain,
( spl0_20
| ~ spl0_16
| ~ spl0_2 ),
inference(rat,[],[s90,s38,s39,s41,s129]) ).
cnf(s152,plain,
( ~ spl0_36
| ~ spl0_16
| ~ spl0_2 ),
inference(rat,[],[s90,s8,s9,s150,s148,s151,s129]) ).
cnf(s153,plain,
( ~ spl0_8
| ~ spl0_16
| ~ spl0_2 ),
inference(rat,[],[s107,s21,s31,s149,s151,s152]) ).
cnf(s154,plain,
( ~ spl0_16
| ~ spl0_2 ),
inference(rat,[],[s90,s8,s9,s11,s153,s129]) ).
cnf(s155,plain,
~ spl0_2,
inference(rat,[],[s117,s116,s115,s109,s111,s107,s10,s20,s30,s40,s50,s154,s129]) ).
cnf(s156,plain,
spl0_1,
inference(rat,[],[s1,s134,s140,s129,s147,s155]) ).
cnf(s157,plain,
( spl0_17
| ~ spl0_36
| ~ spl0_16 ),
inference(rat,[],[s148,s41]) ).
cnf(s158,plain,
( spl0_21
| ~ spl0_17
| ~ spl0_16 ),
inference(rat,[],[s84,s48,s49,s129,s156]) ).
cnf(s159,plain,
( ~ spl0_21
| ~ spl0_17
| ~ spl0_8
| ~ spl0_16 ),
inference(rat,[],[s84,s38,s39,s99,s156,s129]) ).
cnf(s160,plain,
( ~ spl0_17
| ~ spl0_8
| ~ spl0_16 ),
inference(rat,[],[s159,s158]) ).
cnf(s161,plain,
( ~ spl0_8
| ~ spl0_16 ),
inference(rat,[],[s107,s157,s21,s31,s160]) ).
cnf(s162,plain,
~ spl0_16,
inference(rat,[],[s84,s8,s9,s11,s161,s129,s156]) ).
cnf(s163,plain,
spl0_21,
inference(rat,[],[s50,s162]) ).
cnf(s164,plain,
spl0_20,
inference(rat,[],[s40,s162]) ).
cnf(s165,plain,
spl0_19,
inference(rat,[],[s30,s162]) ).
cnf(s166,plain,
spl0_18,
inference(rat,[],[s20,s162]) ).
cnf(s167,plain,
spl0_8,
inference(rat,[],[s10,s162]) ).
cnf(s168,plain,
spl0_36,
inference(rat,[],[s107,s165,s167,s166]) ).
cnf(s169,plain,
spl0_30,
inference(rat,[],[s111,s164,s163,s168]) ).
cnf(s171,plain,
spl0_37,
inference(rat,[],[s115,s164,s169]) ).
cnf(s172,plain,
spl0_35,
inference(rat,[],[s116,s168,s164,s171]) ).
cnf(s175,plain,
$false,
inference(rat,[],[s128,s168,s164,s163,s156,s171,s172]) ).
fof(f1480,plain,
$false,
inference(avatar_sat_refutation,[],[s175]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP318-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.38 % Computer : n005.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Sun Sep 27 09:49:17 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.41 Running first-order model finding
% 0.10/0.41 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
% 0.18/0.47 % (3746558)Will run a generic schedule for satisfiability detection.
% 0.18/0.47 % (3746566)dis+10_1_sil=32000:sp=arity:random_seed=1753495410:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.18/0.47 % (3746564)% WARNING: option uhcvi not known.
% 0.18/0.47 % (3746563)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2555275377_2999 on theBenchmark for (2999ds/0Mi)
% 0.18/0.47 % (3746567)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=385725410:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.18/0.47 % (3746564)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=901391840:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.18/0.47 % (3746565)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=4194026434:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.18/0.47 % (3746568)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3565616061:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.18/0.47 % (3746569)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=686085106:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.18/0.47 % TRYING [1]
% 0.18/0.47 % TRYING [2]
% 0.18/0.47 % (3746566) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3746558-3746566"...
% 0.18/0.47 % TRYING [3]
% 0.18/0.47 % (3746566)...printing done.
% 0.18/0.47 % (3746566)Refutation found. Thanks to Tanya!
% 0.18/0.47 % SZS status Unsatisfiable for theBenchmark
% 0.18/0.47 % SZS output start Proof for theBenchmark
% See solution above
% 0.18/0.47 % (3746566)------------------------------
% 0.18/0.47 % (3746566)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.47 % (3746566)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.47 % (3746566)CaDiCaL version: 2.1.3
% 0.18/0.47 % (3746566)Termination reason: Refutation
% 0.18/0.47 % (3746566)Time elapsed: 0.018 s
% 0.18/0.47 % (3746566)Peak memory usage: 13 MB
% 0.18/0.47 % (3746566)Instructions burned: 53 (million)
% 0.18/0.47 % (3746558)Success in time 0.044 s
% 0.18/0.47 % Vampire exiting
%------------------------------------------------------------------------------