%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GRP350-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n003.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 10:17:34 AM UTC 2026
% Result : Unsatisfiable 0.10s 0.48s
% Output : Refutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 66
% Syntax : Number of formulae : 494 ( 22 unt; 24 def)
% Number of atoms : 1951 ( 568 equ)
% Maximal formula atoms : 17 ( 3 avg)
% Number of connectives : 2862 (1405 ~;1433 |; 0 &)
% ( 24 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 26 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 26 ( 24 usr; 25 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 10 con; 0-2 aty)
% Number of variables : 80 ( 0 sgn 80 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',left_identity) ).
fof(f2,axiom,
! [X0] : multiply(inverse(X0),X0) = identity,
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/GRP004-0.ax',associativity) ).
fof(f5,negated_conjecture,
( multiply(sk_c10,sk_c11) = sk_c9
| multiply(sk_c3,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,plain,
( multiply(sk_c10,sk_c11) = sk_c9
| sk_c10 = multiply(sk_c3,sk_c11) ),
inference(reorient_equations,[],[f5]) ).
fof(f7,negated_conjecture,
( multiply(sk_c10,sk_c11) = sk_c9
| inverse(sk_c3) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_2) ).
fof(f8,plain,
( multiply(sk_c10,sk_c11) = sk_c9
| sk_c11 = inverse(sk_c3) ),
inference(reorient_equations,[],[f7]) ).
fof(f9,negated_conjecture,
( multiply(sk_c10,sk_c11) = sk_c9
| multiply(sk_c4,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_3) ).
fof(f10,plain,
( multiply(sk_c10,sk_c11) = sk_c9
| sk_c9 = multiply(sk_c4,sk_c10) ),
inference(reorient_equations,[],[f9]) ).
fof(f11,negated_conjecture,
( multiply(sk_c10,sk_c11) = sk_c9
| inverse(sk_c4) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_4) ).
fof(f12,plain,
( multiply(sk_c10,sk_c11) = sk_c9
| sk_c10 = inverse(sk_c4) ),
inference(reorient_equations,[],[f11]) ).
fof(f13,negated_conjecture,
( multiply(sk_c10,sk_c11) = sk_c9
| multiply(sk_c5,sk_c8) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_5) ).
fof(f14,plain,
( multiply(sk_c10,sk_c11) = sk_c9
| sk_c11 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f13]) ).
fof(f15,negated_conjecture,
( multiply(sk_c10,sk_c11) = sk_c9
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_6) ).
fof(f16,plain,
( multiply(sk_c10,sk_c11) = sk_c9
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f15]) ).
fof(f24,negated_conjecture,
( inverse(sk_c10) = sk_c9
| multiply(sk_c3,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_11) ).
fof(f25,plain,
( sk_c9 = inverse(sk_c10)
| sk_c10 = multiply(sk_c3,sk_c11) ),
inference(reorient_equations,[],[f24]) ).
fof(f26,negated_conjecture,
( inverse(sk_c10) = sk_c9
| inverse(sk_c3) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_12) ).
fof(f27,plain,
( sk_c9 = inverse(sk_c10)
| sk_c11 = inverse(sk_c3) ),
inference(reorient_equations,[],[f26]) ).
fof(f28,negated_conjecture,
( inverse(sk_c10) = sk_c9
| multiply(sk_c4,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_13) ).
fof(f29,plain,
( sk_c9 = inverse(sk_c10)
| sk_c9 = multiply(sk_c4,sk_c10) ),
inference(reorient_equations,[],[f28]) ).
fof(f30,negated_conjecture,
( inverse(sk_c10) = sk_c9
| inverse(sk_c4) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_14) ).
fof(f31,plain,
( sk_c9 = inverse(sk_c10)
| sk_c10 = inverse(sk_c4) ),
inference(reorient_equations,[],[f30]) ).
fof(f32,negated_conjecture,
( inverse(sk_c10) = sk_c9
| multiply(sk_c5,sk_c8) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_15) ).
fof(f33,plain,
( sk_c9 = inverse(sk_c10)
| sk_c11 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f32]) ).
fof(f34,negated_conjecture,
( inverse(sk_c10) = sk_c9
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_16) ).
fof(f35,plain,
( sk_c9 = inverse(sk_c10)
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f34]) ).
fof(f44,negated_conjecture,
( multiply(sk_c9,sk_c11) = sk_c10
| multiply(sk_c3,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_21) ).
fof(f45,plain,
( sk_c10 = multiply(sk_c9,sk_c11)
| sk_c10 = multiply(sk_c3,sk_c11) ),
inference(reorient_equations,[],[f44]) ).
fof(f46,negated_conjecture,
( multiply(sk_c9,sk_c11) = sk_c10
| inverse(sk_c3) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_22) ).
fof(f47,plain,
( sk_c10 = multiply(sk_c9,sk_c11)
| sk_c11 = inverse(sk_c3) ),
inference(reorient_equations,[],[f46]) ).
fof(f48,negated_conjecture,
( multiply(sk_c9,sk_c11) = sk_c10
| multiply(sk_c4,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_23) ).
fof(f49,plain,
( sk_c10 = multiply(sk_c9,sk_c11)
| sk_c9 = multiply(sk_c4,sk_c10) ),
inference(reorient_equations,[],[f48]) ).
fof(f50,negated_conjecture,
( multiply(sk_c9,sk_c11) = sk_c10
| inverse(sk_c4) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_24) ).
fof(f51,plain,
( sk_c10 = multiply(sk_c9,sk_c11)
| sk_c10 = inverse(sk_c4) ),
inference(reorient_equations,[],[f50]) ).
fof(f52,negated_conjecture,
( multiply(sk_c9,sk_c11) = sk_c10
| multiply(sk_c5,sk_c8) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_25) ).
fof(f53,plain,
( sk_c10 = multiply(sk_c9,sk_c11)
| sk_c11 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f52]) ).
fof(f54,negated_conjecture,
( multiply(sk_c9,sk_c11) = sk_c10
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_26) ).
fof(f55,plain,
( sk_c10 = multiply(sk_c9,sk_c11)
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f54]) ).
fof(f64,negated_conjecture,
( inverse(sk_c1) = sk_c11
| multiply(sk_c3,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_31) ).
fof(f65,plain,
( sk_c11 = inverse(sk_c1)
| sk_c10 = multiply(sk_c3,sk_c11) ),
inference(reorient_equations,[],[f64]) ).
fof(f66,negated_conjecture,
( inverse(sk_c1) = sk_c11
| inverse(sk_c3) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_32) ).
fof(f67,plain,
( sk_c11 = inverse(sk_c1)
| sk_c11 = inverse(sk_c3) ),
inference(reorient_equations,[],[f66]) ).
fof(f68,negated_conjecture,
( inverse(sk_c1) = sk_c11
| multiply(sk_c4,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_33) ).
fof(f69,plain,
( sk_c11 = inverse(sk_c1)
| sk_c9 = multiply(sk_c4,sk_c10) ),
inference(reorient_equations,[],[f68]) ).
fof(f70,negated_conjecture,
( inverse(sk_c1) = sk_c11
| inverse(sk_c4) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_34) ).
fof(f71,plain,
( sk_c11 = inverse(sk_c1)
| sk_c10 = inverse(sk_c4) ),
inference(reorient_equations,[],[f70]) ).
fof(f84,negated_conjecture,
( multiply(sk_c1,sk_c10) = sk_c11
| multiply(sk_c3,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_41) ).
fof(f85,plain,
( sk_c11 = multiply(sk_c1,sk_c10)
| sk_c10 = multiply(sk_c3,sk_c11) ),
inference(reorient_equations,[],[f84]) ).
fof(f86,negated_conjecture,
( multiply(sk_c1,sk_c10) = sk_c11
| inverse(sk_c3) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_42) ).
fof(f87,plain,
( sk_c11 = multiply(sk_c1,sk_c10)
| sk_c11 = inverse(sk_c3) ),
inference(reorient_equations,[],[f86]) ).
fof(f88,negated_conjecture,
( multiply(sk_c1,sk_c10) = sk_c11
| multiply(sk_c4,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_43) ).
fof(f89,plain,
( sk_c11 = multiply(sk_c1,sk_c10)
| sk_c9 = multiply(sk_c4,sk_c10) ),
inference(reorient_equations,[],[f88]) ).
fof(f90,negated_conjecture,
( multiply(sk_c1,sk_c10) = sk_c11
| inverse(sk_c4) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_44) ).
fof(f91,plain,
( sk_c11 = multiply(sk_c1,sk_c10)
| sk_c10 = inverse(sk_c4) ),
inference(reorient_equations,[],[f90]) ).
fof(f104,negated_conjecture,
( inverse(sk_c2) = sk_c10
| multiply(sk_c3,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_51) ).
fof(f105,plain,
( sk_c10 = inverse(sk_c2)
| sk_c10 = multiply(sk_c3,sk_c11) ),
inference(reorient_equations,[],[f104]) ).
fof(f106,negated_conjecture,
( inverse(sk_c2) = sk_c10
| inverse(sk_c3) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_52) ).
fof(f107,plain,
( sk_c10 = inverse(sk_c2)
| sk_c11 = inverse(sk_c3) ),
inference(reorient_equations,[],[f106]) ).
fof(f108,negated_conjecture,
( inverse(sk_c2) = sk_c10
| multiply(sk_c4,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_53) ).
fof(f109,plain,
( sk_c10 = inverse(sk_c2)
| sk_c9 = multiply(sk_c4,sk_c10) ),
inference(reorient_equations,[],[f108]) ).
fof(f110,negated_conjecture,
( inverse(sk_c2) = sk_c10
| inverse(sk_c4) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_54) ).
fof(f111,plain,
( sk_c10 = inverse(sk_c2)
| sk_c10 = inverse(sk_c4) ),
inference(reorient_equations,[],[f110]) ).
fof(f112,negated_conjecture,
( inverse(sk_c2) = sk_c10
| multiply(sk_c5,sk_c8) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_55) ).
fof(f113,plain,
( sk_c10 = inverse(sk_c2)
| sk_c11 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f112]) ).
fof(f114,negated_conjecture,
( inverse(sk_c2) = sk_c10
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_56) ).
fof(f115,plain,
( sk_c10 = inverse(sk_c2)
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f114]) ).
fof(f124,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c10
| multiply(sk_c3,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_61) ).
fof(f125,plain,
( sk_c10 = multiply(sk_c2,sk_c9)
| sk_c10 = multiply(sk_c3,sk_c11) ),
inference(reorient_equations,[],[f124]) ).
fof(f126,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c10
| inverse(sk_c3) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_62) ).
fof(f127,plain,
( sk_c10 = multiply(sk_c2,sk_c9)
| sk_c11 = inverse(sk_c3) ),
inference(reorient_equations,[],[f126]) ).
fof(f128,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c10
| multiply(sk_c4,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_63) ).
fof(f129,plain,
( sk_c10 = multiply(sk_c2,sk_c9)
| sk_c9 = multiply(sk_c4,sk_c10) ),
inference(reorient_equations,[],[f128]) ).
fof(f130,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c10
| inverse(sk_c4) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_64) ).
fof(f131,plain,
( sk_c10 = multiply(sk_c2,sk_c9)
| sk_c10 = inverse(sk_c4) ),
inference(reorient_equations,[],[f130]) ).
fof(f132,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c10
| multiply(sk_c5,sk_c8) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_65) ).
fof(f133,plain,
( sk_c10 = multiply(sk_c2,sk_c9)
| sk_c11 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f132]) ).
fof(f134,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c10
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_66) ).
fof(f135,plain,
( sk_c10 = multiply(sk_c2,sk_c9)
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f134]) ).
fof(f144,negated_conjecture,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( multiply(sk_c10,sk_c11) != sk_c9
| inverse(sk_c10) != sk_c9
| multiply(sk_c9,sk_c11) != sk_c10
| inverse(X0) != sk_c11
| multiply(X0,sk_c10) != sk_c11
| inverse(X1) != sk_c10
| multiply(X1,sk_c9) != sk_c10
| multiply(X2,sk_c11) != sk_c10
| inverse(X2) != sk_c11
| multiply(X3,sk_c10) != sk_c9
| inverse(X3) != sk_c10
| multiply(X4,X5) != sk_c11
| inverse(X4) != X5
| multiply(X5,sk_c10) != sk_c11
| inverse(X6) != X7
| inverse(X7) != X5
| multiply(X6,X5) != X7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_71) ).
fof(f145,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( multiply(sk_c10,sk_c11) != sk_c9
| sk_c9 != inverse(sk_c10)
| sk_c10 != multiply(sk_c9,sk_c11)
| inverse(X0) != sk_c11
| sk_c11 != multiply(X0,sk_c10)
| sk_c10 != inverse(X1)
| sk_c10 != multiply(X1,sk_c9)
| sk_c10 != multiply(X2,sk_c11)
| sk_c11 != inverse(X2)
| sk_c9 != multiply(X3,sk_c10)
| sk_c10 != inverse(X3)
| sk_c11 != multiply(X4,X5)
| inverse(X4) != X5
| sk_c11 != multiply(X5,sk_c10)
| inverse(X6) != X7
| inverse(X7) != X5
| multiply(X6,X5) != X7 ),
inference(reorient_equations,[],[f144]) ).
fof(f146,plain,
! [X2,X3,X0,X1,X6,X7,X4] :
( multiply(sk_c10,sk_c11) != sk_c9
| sk_c9 != inverse(sk_c10)
| sk_c10 != multiply(sk_c9,sk_c11)
| inverse(X0) != sk_c11
| sk_c11 != multiply(X0,sk_c10)
| sk_c10 != inverse(X1)
| sk_c10 != multiply(X1,sk_c9)
| sk_c10 != multiply(X2,sk_c11)
| sk_c11 != inverse(X2)
| sk_c9 != multiply(X3,sk_c10)
| sk_c10 != inverse(X3)
| sk_c11 != multiply(X4,inverse(X4))
| sk_c11 != multiply(inverse(X4),sk_c10)
| inverse(X6) != X7
| inverse(X4) != inverse(X7)
| multiply(X6,inverse(X4)) != X7 ),
inference(equality_resolution,[],[f145]) ).
fof(f147,plain,
! [X2,X3,X0,X1,X6,X4] :
( multiply(sk_c10,sk_c11) != sk_c9
| sk_c9 != inverse(sk_c10)
| sk_c10 != multiply(sk_c9,sk_c11)
| inverse(X0) != sk_c11
| sk_c11 != multiply(X0,sk_c10)
| sk_c10 != inverse(X1)
| sk_c10 != multiply(X1,sk_c9)
| sk_c10 != multiply(X2,sk_c11)
| sk_c11 != inverse(X2)
| sk_c9 != multiply(X3,sk_c10)
| sk_c10 != inverse(X3)
| sk_c11 != multiply(X4,inverse(X4))
| sk_c11 != multiply(inverse(X4),sk_c10)
| inverse(X4) != inverse(inverse(X6))
| inverse(X6) != multiply(X6,inverse(X4)) ),
inference(equality_resolution,[],[f146]) ).
fof(f149,definition,
( spl0_1
<=> ! [X6,X4] :
( sk_c11 != multiply(X4,inverse(X4))
| inverse(X6) != multiply(X6,inverse(X4))
| inverse(X4) != inverse(inverse(X6))
| sk_c11 != multiply(inverse(X4),sk_c10) ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f150,plain,
( ! [X6,X4] :
( inverse(X6) != multiply(X6,inverse(X4))
| sk_c11 != multiply(X4,inverse(X4))
| inverse(X4) != inverse(inverse(X6))
| sk_c11 != multiply(inverse(X4),sk_c10) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f149]) ).
fof(f152,definition,
( spl0_2
<=> ! [X3] :
( sk_c9 != multiply(X3,sk_c10)
| sk_c10 != inverse(X3) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f153,plain,
( ! [X3] :
( sk_c9 != multiply(X3,sk_c10)
| sk_c10 != inverse(X3) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f152]) ).
fof(f155,definition,
( spl0_3
<=> ! [X2] :
( sk_c10 != multiply(X2,sk_c11)
| sk_c11 != inverse(X2) ) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f156,plain,
( ! [X2] :
( sk_c10 != multiply(X2,sk_c11)
| sk_c11 != inverse(X2) )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f155]) ).
fof(f158,definition,
( spl0_4
<=> ! [X1] :
( sk_c10 != inverse(X1)
| sk_c10 != multiply(X1,sk_c9) ) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f159,plain,
( ! [X1] :
( sk_c10 != inverse(X1)
| sk_c10 != multiply(X1,sk_c9) )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f158]) ).
fof(f161,definition,
( spl0_5
<=> ! [X0] :
( inverse(X0) != sk_c11
| sk_c11 != multiply(X0,sk_c10) ) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f162,plain,
( ! [X0] :
( sk_c11 != multiply(X0,sk_c10)
| inverse(X0) != sk_c11 )
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f161]) ).
fof(f164,definition,
( spl0_6
<=> sk_c10 = multiply(sk_c9,sk_c11) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f165,plain,
( sk_c10 = multiply(sk_c9,sk_c11)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f164]) ).
fof(f166,plain,
( sk_c10 != multiply(sk_c9,sk_c11)
| spl0_6 ),
inference(avatar_component_clause,[],[f164]) ).
fof(f168,definition,
( spl0_7
<=> sk_c9 = inverse(sk_c10) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f169,plain,
( sk_c9 = inverse(sk_c10)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f168]) ).
fof(f170,plain,
( sk_c9 != inverse(sk_c10)
| spl0_7 ),
inference(avatar_component_clause,[],[f168]) ).
fof(f172,definition,
( spl0_8
<=> multiply(sk_c10,sk_c11) = sk_c9 ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f173,plain,
( multiply(sk_c10,sk_c11) = sk_c9
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f172]) ).
fof(f174,plain,
( multiply(sk_c10,sk_c11) != sk_c9
| spl0_8 ),
inference(avatar_component_clause,[],[f172]) ).
fof(f175,plain,
( spl0_1
| spl0_2
| spl0_3
| spl0_4
| spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8 ),
inference(avatar_split_clause,[],[f147,f172,f168,f164,f161,f158,f155,f152,f149]) ).
fof(f181,definition,
( spl0_10
<=> sk_c10 = multiply(sk_c2,sk_c9) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f183,plain,
( sk_c10 = multiply(sk_c2,sk_c9)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f181]) ).
fof(f201,definition,
( spl0_14
<=> sk_c8 = inverse(sk_c5) ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
fof(f203,plain,
( sk_c8 = inverse(sk_c5)
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f201]) ).
fof(f204,plain,
( spl0_14
| spl0_10 ),
inference(avatar_split_clause,[],[f135,f181,f201]) ).
fof(f206,definition,
( spl0_15
<=> sk_c11 = multiply(sk_c5,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
fof(f208,plain,
( sk_c11 = multiply(sk_c5,sk_c8)
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f206]) ).
fof(f209,plain,
( spl0_15
| spl0_10 ),
inference(avatar_split_clause,[],[f133,f181,f206]) ).
fof(f211,definition,
( spl0_16
<=> sk_c10 = inverse(sk_c4) ),
introduced(definition,[new_symbols(definition,[spl0_16])],[avatar_definition]) ).
fof(f213,plain,
( sk_c10 = inverse(sk_c4)
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f211]) ).
fof(f214,plain,
( spl0_16
| spl0_10 ),
inference(avatar_split_clause,[],[f131,f181,f211]) ).
fof(f216,definition,
( spl0_17
<=> sk_c9 = multiply(sk_c4,sk_c10) ),
introduced(definition,[new_symbols(definition,[spl0_17])],[avatar_definition]) ).
fof(f218,plain,
( sk_c9 = multiply(sk_c4,sk_c10)
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f216]) ).
fof(f219,plain,
( spl0_17
| spl0_10 ),
inference(avatar_split_clause,[],[f129,f181,f216]) ).
fof(f221,definition,
( spl0_18
<=> sk_c11 = inverse(sk_c3) ),
introduced(definition,[new_symbols(definition,[spl0_18])],[avatar_definition]) ).
fof(f223,plain,
( sk_c11 = inverse(sk_c3)
| ~ spl0_18 ),
inference(avatar_component_clause,[],[f221]) ).
fof(f224,plain,
( spl0_18
| spl0_10 ),
inference(avatar_split_clause,[],[f127,f181,f221]) ).
fof(f226,definition,
( spl0_19
<=> sk_c10 = multiply(sk_c3,sk_c11) ),
introduced(definition,[new_symbols(definition,[spl0_19])],[avatar_definition]) ).
fof(f228,plain,
( sk_c10 = multiply(sk_c3,sk_c11)
| ~ spl0_19 ),
inference(avatar_component_clause,[],[f226]) ).
fof(f229,plain,
( spl0_19
| spl0_10 ),
inference(avatar_split_clause,[],[f125,f181,f226]) ).
fof(f231,definition,
( spl0_20
<=> sk_c10 = inverse(sk_c2) ),
introduced(definition,[new_symbols(definition,[spl0_20])],[avatar_definition]) ).
fof(f233,plain,
( sk_c10 = inverse(sk_c2)
| ~ spl0_20 ),
inference(avatar_component_clause,[],[f231]) ).
fof(f238,plain,
( spl0_14
| spl0_20 ),
inference(avatar_split_clause,[],[f115,f231,f201]) ).
fof(f239,plain,
( spl0_15
| spl0_20 ),
inference(avatar_split_clause,[],[f113,f231,f206]) ).
fof(f240,plain,
( spl0_16
| spl0_20 ),
inference(avatar_split_clause,[],[f111,f231,f211]) ).
fof(f241,plain,
( spl0_17
| spl0_20 ),
inference(avatar_split_clause,[],[f109,f231,f216]) ).
fof(f242,plain,
( spl0_18
| spl0_20 ),
inference(avatar_split_clause,[],[f107,f231,f221]) ).
fof(f243,plain,
( spl0_19
| spl0_20 ),
inference(avatar_split_clause,[],[f105,f231,f226]) ).
fof(f245,definition,
( spl0_21
<=> sk_c11 = multiply(sk_c1,sk_c10) ),
introduced(definition,[new_symbols(definition,[spl0_21])],[avatar_definition]) ).
fof(f247,plain,
( sk_c11 = multiply(sk_c1,sk_c10)
| ~ spl0_21 ),
inference(avatar_component_clause,[],[f245]) ).
fof(f254,plain,
( spl0_16
| spl0_21 ),
inference(avatar_split_clause,[],[f91,f245,f211]) ).
fof(f255,plain,
( spl0_17
| spl0_21 ),
inference(avatar_split_clause,[],[f89,f245,f216]) ).
fof(f256,plain,
( spl0_18
| spl0_21 ),
inference(avatar_split_clause,[],[f87,f245,f221]) ).
fof(f257,plain,
( spl0_19
| spl0_21 ),
inference(avatar_split_clause,[],[f85,f245,f226]) ).
fof(f259,definition,
( spl0_22
<=> sk_c11 = inverse(sk_c1) ),
introduced(definition,[new_symbols(definition,[spl0_22])],[avatar_definition]) ).
fof(f261,plain,
( sk_c11 = inverse(sk_c1)
| ~ spl0_22 ),
inference(avatar_component_clause,[],[f259]) ).
fof(f268,plain,
( spl0_16
| spl0_22 ),
inference(avatar_split_clause,[],[f71,f259,f211]) ).
fof(f269,plain,
( spl0_17
| spl0_22 ),
inference(avatar_split_clause,[],[f69,f259,f216]) ).
fof(f270,plain,
( spl0_18
| spl0_22 ),
inference(avatar_split_clause,[],[f67,f259,f221]) ).
fof(f271,plain,
( spl0_19
| spl0_22 ),
inference(avatar_split_clause,[],[f65,f259,f226]) ).
fof(f276,plain,
( spl0_14
| spl0_6 ),
inference(avatar_split_clause,[],[f55,f164,f201]) ).
fof(f277,plain,
( spl0_15
| spl0_6 ),
inference(avatar_split_clause,[],[f53,f164,f206]) ).
fof(f278,plain,
( spl0_16
| spl0_6 ),
inference(avatar_split_clause,[],[f51,f164,f211]) ).
fof(f279,plain,
( spl0_17
| spl0_6 ),
inference(avatar_split_clause,[],[f49,f164,f216]) ).
fof(f280,plain,
( spl0_18
| spl0_6 ),
inference(avatar_split_clause,[],[f47,f164,f221]) ).
fof(f281,plain,
( spl0_19
| spl0_6 ),
inference(avatar_split_clause,[],[f45,f164,f226]) ).
fof(f286,plain,
( spl0_14
| spl0_7 ),
inference(avatar_split_clause,[],[f35,f168,f201]) ).
fof(f287,plain,
( spl0_15
| spl0_7 ),
inference(avatar_split_clause,[],[f33,f168,f206]) ).
fof(f288,plain,
( spl0_16
| spl0_7 ),
inference(avatar_split_clause,[],[f31,f168,f211]) ).
fof(f289,plain,
( spl0_17
| spl0_7 ),
inference(avatar_split_clause,[],[f29,f168,f216]) ).
fof(f290,plain,
( spl0_18
| spl0_7 ),
inference(avatar_split_clause,[],[f27,f168,f221]) ).
fof(f291,plain,
( spl0_19
| spl0_7 ),
inference(avatar_split_clause,[],[f25,f168,f226]) ).
fof(f296,plain,
( spl0_14
| spl0_8 ),
inference(avatar_split_clause,[],[f16,f172,f201]) ).
fof(f297,plain,
( spl0_15
| spl0_8 ),
inference(avatar_split_clause,[],[f14,f172,f206]) ).
fof(f298,plain,
( spl0_16
| spl0_8 ),
inference(avatar_split_clause,[],[f12,f172,f211]) ).
fof(f299,plain,
( spl0_17
| spl0_8 ),
inference(avatar_split_clause,[],[f10,f172,f216]) ).
fof(f300,plain,
( spl0_18
| spl0_8 ),
inference(avatar_split_clause,[],[f8,f172,f221]) ).
fof(f301,plain,
( spl0_19
| spl0_8 ),
inference(avatar_split_clause,[],[f6,f172,f226]) ).
fof(f302,plain,
( identity = multiply(sk_c11,sk_c3)
| ~ spl0_18 ),
inference(superposition,[],[f3,f223]) ).
fof(f309,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[],[f4,f3]) ).
fof(f311,plain,
( ! [X0] : multiply(sk_c4,multiply(sk_c10,X0)) = multiply(sk_c9,X0)
| ~ spl0_17 ),
inference(superposition,[],[f4,f218]) ).
fof(f315,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f309,f1]) ).
fof(f318,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c11,multiply(sk_c3,X0))
| ~ spl0_18 ),
inference(superposition,[],[f4,f302]) ).
fof(f319,plain,
( ! [X0] : multiply(sk_c11,multiply(sk_c3,X0)) = X0
| ~ spl0_18 ),
inference(forward_demodulation,[],[f318,f1]) ).
fof(f332,plain,
( sk_c11 = multiply(sk_c11,sk_c10)
| ~ spl0_18
| ~ spl0_19 ),
inference(superposition,[],[f319,f228]) ).
fof(f383,plain,
( sk_c10 = multiply(inverse(sk_c11),sk_c11)
| ~ spl0_18
| ~ spl0_19 ),
inference(superposition,[],[f315,f332]) ).
fof(f387,plain,
( sk_c10 = multiply(inverse(sk_c4),sk_c9)
| ~ spl0_17 ),
inference(superposition,[],[f315,f218]) ).
fof(f389,plain,
( sk_c8 = multiply(inverse(sk_c5),sk_c11)
| ~ spl0_15 ),
inference(superposition,[],[f315,f208]) ).
fof(f406,plain,
( sk_c8 = multiply(sk_c8,sk_c11)
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f389,f203]) ).
fof(f408,plain,
( sk_c10 = multiply(sk_c10,sk_c9)
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f387,f213]) ).
fof(f412,plain,
( identity = sk_c10
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_demodulation,[],[f383,f3]) ).
fof(f448,plain,
( sk_c11 = multiply(inverse(sk_c8),sk_c8)
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f315,f406]) ).
fof(f450,plain,
( identity = sk_c11
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f448,f3]) ).
fof(f453,plain,
( sk_c9 != multiply(sk_c10,identity)
| spl0_8
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f174,f450]) ).
fof(f455,plain,
( identity = multiply(identity,sk_c3)
| ~ spl0_14
| ~ spl0_15
| ~ spl0_18 ),
inference(superposition,[],[f302,f450]) ).
fof(f464,plain,
( identity = sk_c3
| ~ spl0_14
| ~ spl0_15
| ~ spl0_18 ),
inference(forward_demodulation,[],[f455,f1]) ).
fof(f466,plain,
( sk_c9 != multiply(identity,identity)
| spl0_8
| ~ spl0_14
| ~ spl0_15
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_demodulation,[],[f453,f412]) ).
fof(f468,plain,
( identity != sk_c9
| spl0_8
| ~ spl0_14
| ~ spl0_15
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_demodulation,[],[f466,f1]) ).
fof(f470,plain,
( identity = multiply(identity,sk_c9)
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_demodulation,[],[f408,f412]) ).
fof(f471,plain,
( identity = sk_c9
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_demodulation,[],[f470,f1]) ).
fof(f480,plain,
( sk_c11 = inverse(identity)
| ~ spl0_14
| ~ spl0_15
| ~ spl0_18 ),
inference(superposition,[],[f223,f464]) ).
fof(f481,plain,
( identity = inverse(identity)
| ~ spl0_14
| ~ spl0_15
| ~ spl0_18 ),
inference(forward_demodulation,[],[f480,f450]) ).
fof(f491,plain,
( $false
| spl0_8
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_subsumption_resolution,[],[f468,f471]) ).
fof(f492,plain,
( spl0_8
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19 ),
inference(avatar_contradiction_clause,[],[f491]) ).
fof(f493,plain,
( sk_c10 != multiply(sk_c9,identity)
| spl0_6
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f166,f450]) ).
fof(f494,plain,
( identity = multiply(sk_c10,sk_c11)
| ~ spl0_8
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_demodulation,[],[f173,f471]) ).
fof(f495,plain,
( sk_c10 != multiply(identity,identity)
| spl0_6
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_demodulation,[],[f493,f471]) ).
fof(f497,plain,
( identity != sk_c10
| spl0_6
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_demodulation,[],[f495,f1]) ).
fof(f499,plain,
( $false
| spl0_6
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_subsumption_resolution,[],[f497,f412]) ).
fof(f500,plain,
( spl0_6
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19 ),
inference(avatar_contradiction_clause,[],[f499]) ).
fof(f502,plain,
( sk_c9 != inverse(identity)
| spl0_7
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_demodulation,[],[f170,f412]) ).
fof(f504,plain,
( identity != inverse(identity)
| spl0_7
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_demodulation,[],[f502,f471]) ).
fof(f511,plain,
( $false
| spl0_7
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_subsumption_resolution,[],[f481,f504]) ).
fof(f512,plain,
( spl0_7
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19 ),
inference(avatar_contradiction_clause,[],[f511]) ).
fof(f513,plain,
( ! [X0] :
( identity != inverse(X0)
| sk_c11 != multiply(X0,sk_c10) )
| ~ spl0_5
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f162,f450]) ).
fof(f514,plain,
( sk_c9 = inverse(identity)
| ~ spl0_7
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_demodulation,[],[f169,f412]) ).
fof(f515,plain,
( ! [X0] :
( sk_c11 != multiply(X0,identity)
| identity != inverse(X0) )
| ~ spl0_5
| ~ spl0_14
| ~ spl0_15
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_demodulation,[],[f513,f412]) ).
fof(f516,plain,
( identity = inverse(identity)
| ~ spl0_7
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_demodulation,[],[f514,f471]) ).
fof(f517,plain,
( ! [X0] :
( identity != multiply(X0,identity)
| identity != inverse(X0) )
| ~ spl0_5
| ~ spl0_14
| ~ spl0_15
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_demodulation,[],[f515,f450]) ).
fof(f523,plain,
( identity != identity
| identity != inverse(inverse(identity))
| ~ spl0_5
| ~ spl0_14
| ~ spl0_15
| ~ spl0_18
| ~ spl0_19 ),
inference(superposition,[],[f517,f3]) ).
fof(f526,plain,
( identity != inverse(inverse(identity))
| ~ spl0_5
| ~ spl0_14
| ~ spl0_15
| ~ spl0_18
| ~ spl0_19 ),
inference(trivial_inequality_removal,[],[f523]) ).
fof(f546,plain,
( identity != inverse(identity)
| ~ spl0_5
| ~ spl0_7
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_demodulation,[],[f526,f516]) ).
fof(f549,plain,
( $false
| ~ spl0_5
| ~ spl0_7
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_subsumption_resolution,[],[f546,f516]) ).
fof(f550,plain,
( ~ spl0_5
| ~ spl0_7
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19 ),
inference(avatar_contradiction_clause,[],[f549]) ).
fof(f551,plain,
( ! [X6,X4] :
( identity != multiply(X4,inverse(X4))
| inverse(X6) != multiply(X6,inverse(X4))
| inverse(X4) != inverse(inverse(X6))
| sk_c11 != multiply(inverse(X4),sk_c10) )
| ~ spl0_1
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f150,f450]) ).
fof(f552,plain,
( ! [X6,X4] :
( sk_c11 != multiply(inverse(X4),identity)
| identity != multiply(X4,inverse(X4))
| inverse(X6) != multiply(X6,inverse(X4))
| inverse(X4) != inverse(inverse(X6)) )
| ~ spl0_1
| ~ spl0_14
| ~ spl0_15
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_demodulation,[],[f551,f412]) ).
fof(f553,plain,
( ! [X6,X4] :
( inverse(X6) != multiply(X6,inverse(X4))
| identity != multiply(X4,inverse(X4))
| identity != multiply(inverse(X4),identity)
| inverse(X4) != inverse(inverse(X6)) )
| ~ spl0_1
| ~ spl0_14
| ~ spl0_15
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_demodulation,[],[f552,f450]) ).
fof(f554,plain,
( ! [X0] :
( inverse(X0) != multiply(X0,identity)
| identity != multiply(identity,identity)
| identity != multiply(identity,identity)
| identity != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19 ),
inference(superposition,[],[f553,f516]) ).
fof(f563,plain,
( ! [X0] :
( inverse(X0) != multiply(X0,identity)
| identity != multiply(identity,identity)
| identity != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19 ),
inference(duplicate_literal_removal,[],[f554]) ).
fof(f581,plain,
( ! [X0] :
( inverse(X0) != multiply(X0,identity)
| identity != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_subsumption_resolution,[],[f563,f1]) ).
fof(f609,plain,
( identity != inverse(inverse(identity))
| identity != inverse(inverse(inverse(identity)))
| ~ spl0_1
| ~ spl0_7
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19 ),
inference(superposition,[],[f581,f3]) ).
fof(f626,plain,
( identity != inverse(identity)
| identity != inverse(inverse(inverse(identity)))
| ~ spl0_1
| ~ spl0_7
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_demodulation,[],[f609,f516]) ).
fof(f628,plain,
( identity != inverse(inverse(inverse(identity)))
| ~ spl0_1
| ~ spl0_7
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_subsumption_resolution,[],[f626,f516]) ).
fof(f630,plain,
( identity != inverse(inverse(identity))
| ~ spl0_1
| ~ spl0_7
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_demodulation,[],[f628,f516]) ).
fof(f633,plain,
( identity != inverse(identity)
| ~ spl0_1
| ~ spl0_7
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_demodulation,[],[f630,f516]) ).
fof(f634,plain,
( $false
| ~ spl0_1
| ~ spl0_7
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_subsumption_resolution,[],[f633,f516]) ).
fof(f635,plain,
( ~ spl0_1
| ~ spl0_7
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19 ),
inference(avatar_contradiction_clause,[],[f634]) ).
fof(f636,plain,
( ! [X3] :
( sk_c9 != multiply(X3,identity)
| sk_c10 != inverse(X3) )
| ~ spl0_2
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_demodulation,[],[f153,f412]) ).
fof(f637,plain,
( ! [X3] :
( identity != multiply(X3,identity)
| sk_c10 != inverse(X3) )
| ~ spl0_2
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_demodulation,[],[f636,f471]) ).
fof(f638,plain,
( ! [X3] :
( identity != multiply(X3,identity)
| identity != inverse(X3) )
| ~ spl0_2
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_demodulation,[],[f637,f412]) ).
fof(f647,plain,
( identity != identity
| identity != inverse(inverse(identity))
| ~ spl0_2
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19 ),
inference(superposition,[],[f638,f3]) ).
fof(f650,plain,
( identity != inverse(inverse(identity))
| ~ spl0_2
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19 ),
inference(trivial_inequality_removal,[],[f647]) ).
fof(f653,plain,
( identity != inverse(identity)
| ~ spl0_2
| ~ spl0_7
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_demodulation,[],[f650,f516]) ).
fof(f656,plain,
( $false
| ~ spl0_2
| ~ spl0_7
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_subsumption_resolution,[],[f653,f516]) ).
fof(f657,plain,
( ~ spl0_2
| ~ spl0_7
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19 ),
inference(avatar_contradiction_clause,[],[f656]) ).
fof(f676,plain,
( identity = inverse(sk_c2)
| ~ spl0_18
| ~ spl0_19
| ~ spl0_20 ),
inference(forward_demodulation,[],[f233,f412]) ).
fof(f678,plain,
( identity = multiply(identity,sk_c11)
| ~ spl0_8
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_demodulation,[],[f494,f412]) ).
fof(f681,plain,
( ! [X2] :
( identity != multiply(X2,sk_c11)
| sk_c11 != inverse(X2) )
| ~ spl0_3
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_demodulation,[],[f156,f412]) ).
fof(f683,plain,
( identity = sk_c11
| ~ spl0_8
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_demodulation,[],[f678,f1]) ).
fof(f713,plain,
( identity = multiply(identity,sk_c2)
| ~ spl0_18
| ~ spl0_19
| ~ spl0_20 ),
inference(superposition,[],[f3,f676]) ).
fof(f714,plain,
( identity = sk_c2
| ~ spl0_18
| ~ spl0_19
| ~ spl0_20 ),
inference(forward_demodulation,[],[f713,f1]) ).
fof(f727,plain,
( ! [X2] :
( identity != multiply(X2,identity)
| sk_c11 != inverse(X2) )
| ~ spl0_3
| ~ spl0_8
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_demodulation,[],[f681,f683]) ).
fof(f728,plain,
( ! [X2] :
( identity != multiply(X2,identity)
| identity != inverse(X2) )
| ~ spl0_3
| ~ spl0_8
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_demodulation,[],[f727,f683]) ).
fof(f732,plain,
( identity != identity
| identity != inverse(inverse(identity))
| ~ spl0_3
| ~ spl0_8
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19 ),
inference(superposition,[],[f728,f3]) ).
fof(f735,plain,
( identity != inverse(inverse(identity))
| ~ spl0_3
| ~ spl0_8
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19 ),
inference(trivial_inequality_removal,[],[f732]) ).
fof(f738,plain,
( identity != inverse(identity)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_8
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_demodulation,[],[f735,f516]) ).
fof(f741,plain,
( $false
| ~ spl0_3
| ~ spl0_7
| ~ spl0_8
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_subsumption_resolution,[],[f738,f516]) ).
fof(f742,plain,
( ~ spl0_3
| ~ spl0_7
| ~ spl0_8
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19 ),
inference(avatar_contradiction_clause,[],[f741]) ).
fof(f746,plain,
( sk_c9 = multiply(identity,sk_c11)
| ~ spl0_8
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_demodulation,[],[f173,f412]) ).
fof(f747,plain,
( sk_c10 = multiply(identity,sk_c9)
| ~ spl0_10
| ~ spl0_18
| ~ spl0_19
| ~ spl0_20 ),
inference(forward_demodulation,[],[f183,f714]) ).
fof(f750,plain,
( sk_c11 = sk_c9
| ~ spl0_8
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_demodulation,[],[f746,f1]) ).
fof(f751,plain,
( sk_c10 = sk_c9
| ~ spl0_10
| ~ spl0_18
| ~ spl0_19
| ~ spl0_20 ),
inference(forward_demodulation,[],[f747,f1]) ).
fof(f752,plain,
( identity = sk_c9
| ~ spl0_10
| ~ spl0_18
| ~ spl0_19
| ~ spl0_20 ),
inference(forward_demodulation,[],[f751,f412]) ).
fof(f754,plain,
( identity = sk_c11
| ~ spl0_8
| ~ spl0_10
| ~ spl0_18
| ~ spl0_19
| ~ spl0_20 ),
inference(superposition,[],[f752,f750]) ).
fof(f771,plain,
( sk_c11 = inverse(identity)
| ~ spl0_7
| ~ spl0_8
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_demodulation,[],[f514,f750]) ).
fof(f772,plain,
( identity = inverse(identity)
| ~ spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_18
| ~ spl0_19
| ~ spl0_20 ),
inference(forward_demodulation,[],[f771,f754]) ).
fof(f906,plain,
( ! [X0] :
( identity != inverse(X0)
| sk_c11 != multiply(X0,sk_c10) )
| ~ spl0_5
| ~ spl0_8
| ~ spl0_10
| ~ spl0_18
| ~ spl0_19
| ~ spl0_20 ),
inference(forward_demodulation,[],[f162,f754]) ).
fof(f907,plain,
( ! [X0] :
( sk_c11 != multiply(X0,identity)
| identity != inverse(X0) )
| ~ spl0_5
| ~ spl0_8
| ~ spl0_10
| ~ spl0_18
| ~ spl0_19
| ~ spl0_20 ),
inference(forward_demodulation,[],[f906,f412]) ).
fof(f908,plain,
( ! [X0] :
( identity != multiply(X0,identity)
| identity != inverse(X0) )
| ~ spl0_5
| ~ spl0_8
| ~ spl0_10
| ~ spl0_18
| ~ spl0_19
| ~ spl0_20 ),
inference(forward_demodulation,[],[f907,f754]) ).
fof(f912,plain,
( identity != identity
| identity != inverse(inverse(identity))
| ~ spl0_5
| ~ spl0_8
| ~ spl0_10
| ~ spl0_18
| ~ spl0_19
| ~ spl0_20 ),
inference(superposition,[],[f908,f3]) ).
fof(f915,plain,
( identity != inverse(inverse(identity))
| ~ spl0_5
| ~ spl0_8
| ~ spl0_10
| ~ spl0_18
| ~ spl0_19
| ~ spl0_20 ),
inference(trivial_inequality_removal,[],[f912]) ).
fof(f918,plain,
( identity != inverse(identity)
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_18
| ~ spl0_19
| ~ spl0_20 ),
inference(forward_demodulation,[],[f915,f772]) ).
fof(f921,plain,
( $false
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_18
| ~ spl0_19
| ~ spl0_20 ),
inference(forward_subsumption_resolution,[],[f918,f772]) ).
fof(f922,plain,
( ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_18
| ~ spl0_19
| ~ spl0_20 ),
inference(avatar_contradiction_clause,[],[f921]) ).
fof(f924,plain,
( identity = multiply(sk_c9,sk_c10)
| ~ spl0_7 ),
inference(superposition,[],[f3,f169]) ).
fof(f932,plain,
( multiply(sk_c9,sk_c11) = multiply(sk_c4,sk_c9)
| ~ spl0_8
| ~ spl0_17 ),
inference(superposition,[],[f311,f173]) ).
fof(f933,plain,
( sk_c11 = multiply(inverse(sk_c10),sk_c9)
| ~ spl0_8 ),
inference(superposition,[],[f315,f173]) ).
fof(f934,plain,
( ! [X0] : multiply(sk_c9,X0) = multiply(sk_c10,multiply(sk_c11,X0))
| ~ spl0_8 ),
inference(superposition,[],[f4,f173]) ).
fof(f935,plain,
( sk_c11 = multiply(sk_c9,sk_c9)
| ~ spl0_7
| ~ spl0_8 ),
inference(forward_demodulation,[],[f933,f169]) ).
fof(f936,plain,
( sk_c10 = multiply(sk_c4,sk_c9)
| ~ spl0_6
| ~ spl0_8
| ~ spl0_17 ),
inference(forward_demodulation,[],[f932,f165]) ).
fof(f937,plain,
( sk_c9 = multiply(inverse(sk_c2),sk_c10)
| ~ spl0_10 ),
inference(superposition,[],[f315,f183]) ).
fof(f939,plain,
( sk_c9 = multiply(sk_c10,sk_c10)
| ~ spl0_10
| ~ spl0_20 ),
inference(forward_demodulation,[],[f937,f233]) ).
fof(f940,plain,
( sk_c10 = multiply(inverse(sk_c1),sk_c11)
| ~ spl0_21 ),
inference(superposition,[],[f315,f247]) ).
fof(f942,plain,
( sk_c10 = multiply(sk_c11,sk_c11)
| ~ spl0_21
| ~ spl0_22 ),
inference(forward_demodulation,[],[f940,f261]) ).
fof(f960,definition,
( spl0_36
<=> sk_c11 = sk_c9 ),
introduced(definition,[new_symbols(definition,[spl0_36])],[avatar_definition]) ).
fof(f961,plain,
( sk_c11 = sk_c9
| ~ spl0_36 ),
inference(avatar_component_clause,[],[f960]) ).
fof(f969,definition,
( spl0_38
<=> identity = sk_c9 ),
introduced(definition,[new_symbols(definition,[spl0_38])],[avatar_definition]) ).
fof(f970,plain,
( identity = sk_c9
| ~ spl0_38 ),
inference(avatar_component_clause,[],[f969]) ).
fof(f971,plain,
( identity != sk_c9
| spl0_38 ),
inference(avatar_component_clause,[],[f969]) ).
fof(f979,definition,
( spl0_40
<=> sk_c10 = sk_c9 ),
introduced(definition,[new_symbols(definition,[spl0_40])],[avatar_definition]) ).
fof(f980,plain,
( sk_c10 = sk_c9
| ~ spl0_40 ),
inference(avatar_component_clause,[],[f979]) ).
fof(f981,plain,
( sk_c10 != sk_c9
| spl0_40 ),
inference(avatar_component_clause,[],[f979]) ).
fof(f984,definition,
( spl0_41
<=> sk_c10 = sk_c11 ),
introduced(definition,[new_symbols(definition,[spl0_41])],[avatar_definition]) ).
fof(f985,plain,
( sk_c10 = sk_c11
| ~ spl0_41 ),
inference(avatar_component_clause,[],[f984]) ).
fof(f986,plain,
( sk_c10 != sk_c11
| spl0_41 ),
inference(avatar_component_clause,[],[f984]) ).
fof(f1030,plain,
( multiply(sk_c9,sk_c10) = multiply(sk_c4,sk_c9)
| ~ spl0_10
| ~ spl0_17
| ~ spl0_20 ),
inference(superposition,[],[f311,f939]) ).
fof(f1031,plain,
( sk_c9 != sk_c9
| sk_c10 != inverse(sk_c10)
| ~ spl0_2
| ~ spl0_10
| ~ spl0_20 ),
inference(superposition,[],[f153,f939]) ).
fof(f1034,plain,
( sk_c10 != inverse(sk_c10)
| ~ spl0_2
| ~ spl0_10
| ~ spl0_20 ),
inference(trivial_inequality_removal,[],[f1031]) ).
fof(f1036,plain,
( sk_c10 != sk_c9
| ~ spl0_2
| ~ spl0_7
| ~ spl0_10
| ~ spl0_20 ),
inference(forward_demodulation,[],[f1034,f169]) ).
fof(f1037,plain,
( sk_c10 = multiply(sk_c9,sk_c10)
| ~ spl0_6
| ~ spl0_8
| ~ spl0_10
| ~ spl0_17
| ~ spl0_20 ),
inference(forward_demodulation,[],[f1030,f936]) ).
fof(f1038,plain,
( ~ spl0_40
| ~ spl0_2
| ~ spl0_7
| ~ spl0_10
| ~ spl0_20 ),
inference(avatar_split_clause,[],[f1036,f231,f181,f168,f152,f979]) ).
fof(f1039,plain,
( identity = sk_c10
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_17
| ~ spl0_20 ),
inference(forward_demodulation,[],[f1037,f924]) ).
fof(f1042,plain,
( sk_c9 = multiply(identity,sk_c11)
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_17
| ~ spl0_20 ),
inference(superposition,[],[f173,f1039]) ).
fof(f1051,plain,
( sk_c9 = multiply(identity,identity)
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_17
| ~ spl0_20 ),
inference(superposition,[],[f939,f1039]) ).
fof(f1052,plain,
( identity = sk_c9
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_17
| ~ spl0_20 ),
inference(forward_demodulation,[],[f1051,f1]) ).
fof(f1057,plain,
( sk_c11 = sk_c9
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_17
| ~ spl0_20 ),
inference(forward_demodulation,[],[f1042,f1]) ).
fof(f1064,plain,
( identity != sk_c11
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_17
| ~ spl0_20
| spl0_41 ),
inference(forward_demodulation,[],[f986,f1039]) ).
fof(f1065,plain,
( spl0_38
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_17
| ~ spl0_20 ),
inference(avatar_split_clause,[],[f1052,f231,f216,f181,f172,f168,f164,f969]) ).
fof(f1066,plain,
( spl0_36
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_17
| ~ spl0_20 ),
inference(avatar_split_clause,[],[f1057,f231,f216,f181,f172,f168,f164,f960]) ).
fof(f1075,plain,
( sk_c10 != sk_c11
| ~ spl0_36
| spl0_40 ),
inference(superposition,[],[f981,f961]) ).
fof(f1087,plain,
( identity = sk_c11
| ~ spl0_36
| ~ spl0_38 ),
inference(superposition,[],[f970,f961]) ).
fof(f1088,plain,
( sk_c10 = multiply(identity,sk_c11)
| ~ spl0_6
| ~ spl0_38 ),
inference(superposition,[],[f165,f970]) ).
fof(f1092,plain,
( sk_c11 = multiply(identity,identity)
| ~ spl0_7
| ~ spl0_8
| ~ spl0_38 ),
inference(superposition,[],[f935,f970]) ).
fof(f1096,plain,
( identity != sk_c10
| ~ spl0_38
| spl0_40 ),
inference(superposition,[],[f981,f970]) ).
fof(f1097,plain,
( $false
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_17
| ~ spl0_20
| ~ spl0_38
| spl0_40 ),
inference(forward_subsumption_resolution,[],[f1096,f1039]) ).
fof(f1098,plain,
( ~ spl0_6
| ~ spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_17
| ~ spl0_20
| ~ spl0_38
| spl0_40 ),
inference(avatar_contradiction_clause,[],[f1097]) ).
fof(f1103,plain,
( identity = sk_c11
| ~ spl0_7
| ~ spl0_8
| ~ spl0_38 ),
inference(forward_demodulation,[],[f1092,f1]) ).
fof(f1107,plain,
( sk_c10 = sk_c11
| ~ spl0_6
| ~ spl0_38 ),
inference(forward_demodulation,[],[f1088,f1]) ).
fof(f1108,plain,
( $false
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_17
| ~ spl0_20
| ~ spl0_36
| ~ spl0_38
| spl0_41 ),
inference(forward_subsumption_resolution,[],[f1087,f1064]) ).
fof(f1109,plain,
( ~ spl0_6
| ~ spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_17
| ~ spl0_20
| ~ spl0_36
| ~ spl0_38
| spl0_41 ),
inference(avatar_contradiction_clause,[],[f1108]) ).
fof(f1114,plain,
( identity = sk_c11
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_17
| ~ spl0_20
| ~ spl0_38 ),
inference(forward_demodulation,[],[f1107,f1039]) ).
fof(f1117,plain,
( $false
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_17
| ~ spl0_20
| ~ spl0_38
| spl0_41 ),
inference(forward_subsumption_resolution,[],[f1114,f1064]) ).
fof(f1118,plain,
( ~ spl0_6
| ~ spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_17
| ~ spl0_20
| ~ spl0_38
| spl0_41 ),
inference(avatar_contradiction_clause,[],[f1117]) ).
fof(f1121,plain,
( ~ spl0_41
| ~ spl0_36
| spl0_40 ),
inference(avatar_split_clause,[],[f1075,f979,f960,f984]) ).
fof(f1122,plain,
( spl0_41
| ~ spl0_6
| ~ spl0_38 ),
inference(avatar_split_clause,[],[f1107,f969,f164,f984]) ).
fof(f1183,plain,
( multiply(sk_c9,sk_c11) = multiply(sk_c10,sk_c10)
| ~ spl0_8
| ~ spl0_21
| ~ spl0_22 ),
inference(superposition,[],[f934,f942]) ).
fof(f1190,plain,
( sk_c9 = multiply(sk_c9,sk_c11)
| ~ spl0_8
| ~ spl0_10
| ~ spl0_20
| ~ spl0_21
| ~ spl0_22 ),
inference(forward_demodulation,[],[f1183,f939]) ).
fof(f1191,plain,
( sk_c10 = sk_c9
| ~ spl0_6
| ~ spl0_8
| ~ spl0_10
| ~ spl0_20
| ~ spl0_21
| ~ spl0_22 ),
inference(forward_demodulation,[],[f1190,f165]) ).
fof(f1194,plain,
( $false
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19
| spl0_38 ),
inference(forward_subsumption_resolution,[],[f471,f971]) ).
fof(f1195,plain,
( ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19
| spl0_38 ),
inference(avatar_contradiction_clause,[],[f1194]) ).
fof(f1197,plain,
( spl0_36
| ~ spl0_8
| ~ spl0_18
| ~ spl0_19 ),
inference(avatar_split_clause,[],[f750,f226,f221,f172,f960]) ).
fof(f1202,plain,
( spl0_40
| ~ spl0_6
| ~ spl0_8
| ~ spl0_10
| ~ spl0_20
| ~ spl0_21
| ~ spl0_22 ),
inference(avatar_split_clause,[],[f1191,f259,f245,f231,f181,f172,f164,f979]) ).
fof(f1204,plain,
( identity = multiply(sk_c10,sk_c10)
| ~ spl0_7
| ~ spl0_40 ),
inference(superposition,[],[f924,f980]) ).
fof(f1208,plain,
( identity != sk_c10
| spl0_38
| ~ spl0_40 ),
inference(superposition,[],[f971,f980]) ).
fof(f1234,plain,
( sk_c10 = multiply(sk_c2,sk_c10)
| ~ spl0_10
| ~ spl0_40 ),
inference(forward_demodulation,[],[f183,f980]) ).
fof(f1241,plain,
( sk_c10 = multiply(inverse(sk_c2),sk_c10)
| ~ spl0_10
| ~ spl0_40 ),
inference(superposition,[],[f315,f1234]) ).
fof(f1243,plain,
( sk_c10 = multiply(sk_c10,sk_c10)
| ~ spl0_10
| ~ spl0_20
| ~ spl0_40 ),
inference(forward_demodulation,[],[f1241,f233]) ).
fof(f1257,plain,
( sk_c11 != sk_c11
| sk_c11 != inverse(sk_c1)
| ~ spl0_5
| ~ spl0_21 ),
inference(superposition,[],[f162,f247]) ).
fof(f1259,plain,
( sk_c11 != inverse(sk_c1)
| ~ spl0_5
| ~ spl0_21 ),
inference(trivial_inequality_removal,[],[f1257]) ).
fof(f1261,plain,
( $false
| ~ spl0_5
| ~ spl0_21
| ~ spl0_22 ),
inference(forward_subsumption_resolution,[],[f1259,f261]) ).
fof(f1262,plain,
( ~ spl0_5
| ~ spl0_21
| ~ spl0_22 ),
inference(avatar_contradiction_clause,[],[f1261]) ).
fof(f1287,plain,
( ! [X0] :
( inverse(X0) != inverse(inverse(inverse(inverse(X0))))
| sk_c11 != multiply(X0,inverse(X0))
| identity != inverse(inverse(inverse(X0)))
| sk_c11 != multiply(inverse(X0),sk_c10) )
| ~ spl0_1 ),
inference(superposition,[],[f150,f3]) ).
fof(f1338,definition,
( spl0_52
<=> identity = sk_c11 ),
introduced(definition,[new_symbols(definition,[spl0_52])],[avatar_definition]) ).
fof(f1375,plain,
( sk_c9 != inverse(inverse(inverse(sk_c9)))
| sk_c11 != multiply(sk_c10,sk_c9)
| identity != inverse(inverse(sk_c9))
| sk_c11 != multiply(sk_c9,sk_c10)
| ~ spl0_1
| ~ spl0_7 ),
inference(superposition,[],[f1287,f169]) ).
fof(f1382,plain,
( sk_c10 != inverse(inverse(inverse(sk_c10)))
| sk_c11 != multiply(sk_c2,sk_c10)
| identity != inverse(inverse(sk_c10))
| sk_c11 != multiply(sk_c10,sk_c10)
| ~ spl0_1
| ~ spl0_20 ),
inference(superposition,[],[f1287,f233]) ).
fof(f1383,plain,
( sk_c10 != inverse(inverse(inverse(sk_c10)))
| sk_c11 != multiply(sk_c10,sk_c9)
| identity != inverse(inverse(sk_c9))
| sk_c11 != multiply(sk_c9,sk_c10)
| ~ spl0_1
| ~ spl0_7
| ~ spl0_40 ),
inference(forward_demodulation,[],[f1375,f980]) ).
fof(f1384,plain,
( sk_c10 != inverse(inverse(sk_c9))
| sk_c11 != multiply(sk_c10,sk_c9)
| identity != inverse(inverse(sk_c9))
| sk_c11 != multiply(sk_c9,sk_c10)
| ~ spl0_1
| ~ spl0_7
| ~ spl0_40 ),
inference(forward_demodulation,[],[f1383,f169]) ).
fof(f1385,plain,
( sk_c10 != inverse(inverse(sk_c10))
| sk_c11 != multiply(sk_c10,sk_c9)
| identity != inverse(inverse(sk_c9))
| sk_c11 != multiply(sk_c9,sk_c10)
| ~ spl0_1
| ~ spl0_7
| ~ spl0_40 ),
inference(forward_demodulation,[],[f1384,f980]) ).
fof(f1386,plain,
( sk_c10 != inverse(sk_c9)
| sk_c11 != multiply(sk_c10,sk_c9)
| identity != inverse(inverse(sk_c9))
| sk_c11 != multiply(sk_c9,sk_c10)
| ~ spl0_1
| ~ spl0_7
| ~ spl0_40 ),
inference(forward_demodulation,[],[f1385,f169]) ).
fof(f1387,plain,
( sk_c10 != inverse(sk_c10)
| sk_c11 != multiply(sk_c10,sk_c9)
| identity != inverse(inverse(sk_c9))
| sk_c11 != multiply(sk_c9,sk_c10)
| ~ spl0_1
| ~ spl0_7
| ~ spl0_40 ),
inference(forward_demodulation,[],[f1386,f980]) ).
fof(f1388,plain,
( sk_c10 != sk_c9
| sk_c11 != multiply(sk_c10,sk_c9)
| identity != inverse(inverse(sk_c9))
| sk_c11 != multiply(sk_c9,sk_c10)
| ~ spl0_1
| ~ spl0_7
| ~ spl0_40 ),
inference(forward_demodulation,[],[f1387,f169]) ).
fof(f1389,plain,
( sk_c11 != multiply(sk_c10,sk_c9)
| identity != inverse(inverse(sk_c9))
| sk_c11 != multiply(sk_c9,sk_c10)
| ~ spl0_1
| ~ spl0_7
| ~ spl0_40 ),
inference(forward_subsumption_resolution,[],[f1388,f980]) ).
fof(f1390,plain,
( sk_c11 != multiply(sk_c10,sk_c10)
| identity != inverse(inverse(sk_c9))
| sk_c11 != multiply(sk_c9,sk_c10)
| ~ spl0_1
| ~ spl0_7
| ~ spl0_40 ),
inference(forward_demodulation,[],[f1389,f980]) ).
fof(f1467,plain,
( identity = sk_c10
| ~ spl0_7
| ~ spl0_10
| ~ spl0_20
| ~ spl0_40 ),
inference(forward_demodulation,[],[f1243,f1204]) ).
fof(f1468,plain,
( $false
| ~ spl0_7
| ~ spl0_10
| ~ spl0_20
| spl0_38
| ~ spl0_40 ),
inference(forward_subsumption_resolution,[],[f1467,f1208]) ).
fof(f1469,plain,
( ~ spl0_7
| ~ spl0_10
| ~ spl0_20
| spl0_38
| ~ spl0_40 ),
inference(avatar_contradiction_clause,[],[f1468]) ).
fof(f1485,plain,
( spl0_52
| ~ spl0_36
| ~ spl0_38 ),
inference(avatar_split_clause,[],[f1087,f969,f960,f1338]) ).
fof(f1486,plain,
( spl0_52
| ~ spl0_7
| ~ spl0_8
| ~ spl0_38 ),
inference(avatar_split_clause,[],[f1103,f969,f172,f168,f1338]) ).
fof(f1491,plain,
( sk_c10 != inverse(inverse(sk_c9))
| sk_c11 != multiply(sk_c2,sk_c10)
| identity != inverse(inverse(sk_c10))
| sk_c11 != multiply(sk_c10,sk_c10)
| ~ spl0_1
| ~ spl0_7
| ~ spl0_20 ),
inference(forward_demodulation,[],[f1382,f169]) ).
fof(f1493,plain,
( identity != sk_c11
| identity != inverse(inverse(sk_c9))
| sk_c11 != multiply(sk_c9,sk_c10)
| ~ spl0_1
| ~ spl0_7
| ~ spl0_40 ),
inference(forward_demodulation,[],[f1390,f1204]) ).
fof(f1501,plain,
( sk_c10 != inverse(inverse(sk_c10))
| sk_c11 != multiply(sk_c2,sk_c10)
| identity != inverse(inverse(sk_c10))
| sk_c11 != multiply(sk_c10,sk_c10)
| ~ spl0_1
| ~ spl0_7
| ~ spl0_20
| ~ spl0_40 ),
inference(forward_demodulation,[],[f1491,f980]) ).
fof(f1503,plain,
( identity != inverse(inverse(sk_c10))
| identity != sk_c11
| sk_c11 != multiply(sk_c9,sk_c10)
| ~ spl0_1
| ~ spl0_7
| ~ spl0_40 ),
inference(forward_demodulation,[],[f1493,f980]) ).
fof(f1513,plain,
( sk_c10 != inverse(sk_c9)
| sk_c11 != multiply(sk_c2,sk_c10)
| identity != inverse(inverse(sk_c10))
| sk_c11 != multiply(sk_c10,sk_c10)
| ~ spl0_1
| ~ spl0_7
| ~ spl0_20
| ~ spl0_40 ),
inference(forward_demodulation,[],[f1501,f169]) ).
fof(f1515,plain,
( identity != inverse(sk_c9)
| identity != sk_c11
| sk_c11 != multiply(sk_c9,sk_c10)
| ~ spl0_1
| ~ spl0_7
| ~ spl0_40 ),
inference(forward_demodulation,[],[f1503,f169]) ).
fof(f1520,plain,
( sk_c10 != inverse(sk_c10)
| sk_c11 != multiply(sk_c2,sk_c10)
| identity != inverse(inverse(sk_c10))
| sk_c11 != multiply(sk_c10,sk_c10)
| ~ spl0_1
| ~ spl0_7
| ~ spl0_20
| ~ spl0_40 ),
inference(forward_demodulation,[],[f1513,f980]) ).
fof(f1522,plain,
( identity != inverse(sk_c10)
| identity != sk_c11
| sk_c11 != multiply(sk_c9,sk_c10)
| ~ spl0_1
| ~ spl0_7
| ~ spl0_40 ),
inference(forward_demodulation,[],[f1515,f980]) ).
fof(f1525,plain,
( sk_c10 != sk_c9
| sk_c11 != multiply(sk_c2,sk_c10)
| identity != inverse(inverse(sk_c10))
| sk_c11 != multiply(sk_c10,sk_c10)
| ~ spl0_1
| ~ spl0_7
| ~ spl0_20
| ~ spl0_40 ),
inference(forward_demodulation,[],[f1520,f169]) ).
fof(f1527,plain,
( identity != sk_c9
| identity != sk_c11
| sk_c11 != multiply(sk_c9,sk_c10)
| ~ spl0_1
| ~ spl0_7
| ~ spl0_40 ),
inference(forward_demodulation,[],[f1522,f169]) ).
fof(f1528,plain,
( sk_c11 != multiply(sk_c2,sk_c10)
| identity != inverse(inverse(sk_c10))
| sk_c11 != multiply(sk_c10,sk_c10)
| ~ spl0_1
| ~ spl0_7
| ~ spl0_20
| ~ spl0_40 ),
inference(forward_subsumption_resolution,[],[f1525,f980]) ).
fof(f1530,plain,
( identity != sk_c10
| identity != sk_c11
| sk_c11 != multiply(sk_c9,sk_c10)
| ~ spl0_1
| ~ spl0_7
| ~ spl0_40 ),
inference(forward_demodulation,[],[f1527,f980]) ).
fof(f1531,plain,
( sk_c10 != sk_c11
| identity != inverse(inverse(sk_c10))
| sk_c11 != multiply(sk_c10,sk_c10)
| ~ spl0_1
| ~ spl0_7
| ~ spl0_10
| ~ spl0_20
| ~ spl0_40 ),
inference(forward_demodulation,[],[f1528,f1234]) ).
fof(f1533,plain,
( identity != sk_c11
| identity != sk_c10
| identity != sk_c11
| ~ spl0_1
| ~ spl0_7
| ~ spl0_40 ),
inference(forward_demodulation,[],[f1530,f924]) ).
fof(f1534,plain,
( identity != sk_c11
| identity != sk_c10
| ~ spl0_1
| ~ spl0_7
| ~ spl0_40 ),
inference(duplicate_literal_removal,[],[f1533]) ).
fof(f1535,plain,
( identity != inverse(sk_c9)
| sk_c10 != sk_c11
| sk_c11 != multiply(sk_c10,sk_c10)
| ~ spl0_1
| ~ spl0_7
| ~ spl0_10
| ~ spl0_20
| ~ spl0_40 ),
inference(forward_demodulation,[],[f1531,f169]) ).
fof(f1538,definition,
( spl0_54
<=> identity = sk_c10 ),
introduced(definition,[new_symbols(definition,[spl0_54])],[avatar_definition]) ).
fof(f1541,plain,
( ~ spl0_54
| ~ spl0_52
| ~ spl0_1
| ~ spl0_7
| ~ spl0_40 ),
inference(avatar_split_clause,[],[f1534,f979,f168,f149,f1338,f1538]) ).
fof(f1542,plain,
( identity != inverse(sk_c10)
| sk_c10 != sk_c11
| sk_c11 != multiply(sk_c10,sk_c10)
| ~ spl0_1
| ~ spl0_7
| ~ spl0_10
| ~ spl0_20
| ~ spl0_40 ),
inference(forward_demodulation,[],[f1535,f980]) ).
fof(f1544,plain,
( identity != sk_c9
| sk_c10 != sk_c11
| sk_c11 != multiply(sk_c10,sk_c10)
| ~ spl0_1
| ~ spl0_7
| ~ spl0_10
| ~ spl0_20
| ~ spl0_40 ),
inference(forward_demodulation,[],[f1542,f169]) ).
fof(f1546,plain,
( identity != sk_c10
| sk_c10 != sk_c11
| sk_c11 != multiply(sk_c10,sk_c10)
| ~ spl0_1
| ~ spl0_7
| ~ spl0_10
| ~ spl0_20
| ~ spl0_40 ),
inference(forward_demodulation,[],[f1544,f980]) ).
fof(f1548,plain,
( identity != sk_c11
| identity != sk_c10
| sk_c10 != sk_c11
| ~ spl0_1
| ~ spl0_7
| ~ spl0_10
| ~ spl0_20
| ~ spl0_40 ),
inference(forward_demodulation,[],[f1546,f1204]) ).
fof(f1550,plain,
( ~ spl0_41
| ~ spl0_54
| ~ spl0_52
| ~ spl0_1
| ~ spl0_7
| ~ spl0_10
| ~ spl0_20
| ~ spl0_40 ),
inference(avatar_split_clause,[],[f1548,f979,f231,f181,f168,f149,f1338,f1538,f984]) ).
fof(f1573,plain,
( ! [X1] :
( sk_c10 != multiply(X1,sk_c10)
| sk_c10 != inverse(X1) )
| ~ spl0_4
| ~ spl0_40 ),
inference(forward_demodulation,[],[f159,f980]) ).
fof(f1604,plain,
( identity = multiply(identity,sk_c10)
| ~ spl0_7
| ~ spl0_38 ),
inference(superposition,[],[f924,f970]) ).
fof(f1611,plain,
( identity = sk_c10
| ~ spl0_7
| ~ spl0_38 ),
inference(forward_demodulation,[],[f1604,f1]) ).
fof(f1613,plain,
( spl0_54
| ~ spl0_7
| ~ spl0_38 ),
inference(avatar_split_clause,[],[f1611,f969,f168,f1538]) ).
fof(f1617,plain,
( identity != sk_c10
| sk_c10 != inverse(sk_c10)
| ~ spl0_4
| ~ spl0_7
| ~ spl0_40 ),
inference(superposition,[],[f1573,f1204]) ).
fof(f1621,plain,
( sk_c10 != sk_c10
| sk_c10 != inverse(sk_c2)
| ~ spl0_4
| ~ spl0_10
| ~ spl0_40 ),
inference(superposition,[],[f1573,f1234]) ).
fof(f1622,plain,
( sk_c10 != inverse(sk_c2)
| ~ spl0_4
| ~ spl0_10
| ~ spl0_40 ),
inference(trivial_inequality_removal,[],[f1621]) ).
fof(f1624,plain,
( $false
| ~ spl0_4
| ~ spl0_10
| ~ spl0_20
| ~ spl0_40 ),
inference(forward_subsumption_resolution,[],[f1622,f233]) ).
fof(f1625,plain,
( ~ spl0_4
| ~ spl0_10
| ~ spl0_20
| ~ spl0_40 ),
inference(avatar_contradiction_clause,[],[f1624]) ).
fof(f1628,plain,
( sk_c10 != sk_c9
| identity != sk_c10
| ~ spl0_4
| ~ spl0_7
| ~ spl0_40 ),
inference(forward_demodulation,[],[f1617,f169]) ).
fof(f1632,plain,
( identity != sk_c10
| ~ spl0_4
| ~ spl0_7
| ~ spl0_40 ),
inference(forward_subsumption_resolution,[],[f1628,f980]) ).
fof(f1637,plain,
( ~ spl0_54
| ~ spl0_4
| ~ spl0_7
| ~ spl0_40 ),
inference(avatar_split_clause,[],[f1632,f979,f168,f158,f1538]) ).
fof(f1640,plain,
( ! [X2] :
( sk_c10 != multiply(X2,sk_c10)
| sk_c11 != inverse(X2) )
| ~ spl0_3
| ~ spl0_41 ),
inference(forward_demodulation,[],[f156,f985]) ).
fof(f1641,plain,
( ! [X2] :
( sk_c10 != multiply(X2,sk_c10)
| sk_c10 != inverse(X2) )
| ~ spl0_3
| ~ spl0_41 ),
inference(forward_demodulation,[],[f1640,f985]) ).
fof(f1648,plain,
( sk_c10 != sk_c11
| sk_c10 != inverse(sk_c1)
| ~ spl0_3
| ~ spl0_21
| ~ spl0_41 ),
inference(superposition,[],[f1641,f247]) ).
fof(f1654,plain,
( sk_c10 != inverse(sk_c1)
| ~ spl0_3
| ~ spl0_21
| ~ spl0_41 ),
inference(forward_subsumption_resolution,[],[f1648,f985]) ).
fof(f1658,plain,
( sk_c10 != sk_c11
| ~ spl0_3
| ~ spl0_21
| ~ spl0_22
| ~ spl0_41 ),
inference(forward_demodulation,[],[f1654,f261]) ).
fof(f1662,plain,
( $false
| ~ spl0_3
| ~ spl0_21
| ~ spl0_22
| ~ spl0_41 ),
inference(forward_subsumption_resolution,[],[f1658,f985]) ).
fof(f1663,plain,
( ~ spl0_3
| ~ spl0_21
| ~ spl0_22
| ~ spl0_41 ),
inference(avatar_contradiction_clause,[],[f1662]) ).
cnf(s1,plain,
( spl0_1
| spl0_2
| spl0_3
| spl0_4
| spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8 ),
inference(sat_conversion,[],[f175]) ).
cnf(s6,plain,
( spl0_10
| spl0_14 ),
inference(sat_conversion,[],[f204]) ).
cnf(s7,plain,
( spl0_10
| spl0_15 ),
inference(sat_conversion,[],[f209]) ).
cnf(s8,plain,
( spl0_10
| spl0_16 ),
inference(sat_conversion,[],[f214]) ).
cnf(s9,plain,
( spl0_10
| spl0_17 ),
inference(sat_conversion,[],[f219]) ).
cnf(s10,plain,
( spl0_10
| spl0_18 ),
inference(sat_conversion,[],[f224]) ).
cnf(s11,plain,
( spl0_10
| spl0_19 ),
inference(sat_conversion,[],[f229]) ).
cnf(s16,plain,
( spl0_14
| spl0_20 ),
inference(sat_conversion,[],[f238]) ).
cnf(s17,plain,
( spl0_15
| spl0_20 ),
inference(sat_conversion,[],[f239]) ).
cnf(s18,plain,
( spl0_16
| spl0_20 ),
inference(sat_conversion,[],[f240]) ).
cnf(s19,plain,
( spl0_17
| spl0_20 ),
inference(sat_conversion,[],[f241]) ).
cnf(s20,plain,
( spl0_18
| spl0_20 ),
inference(sat_conversion,[],[f242]) ).
cnf(s21,plain,
( spl0_19
| spl0_20 ),
inference(sat_conversion,[],[f243]) ).
cnf(s28,plain,
( spl0_16
| spl0_21 ),
inference(sat_conversion,[],[f254]) ).
cnf(s29,plain,
( spl0_17
| spl0_21 ),
inference(sat_conversion,[],[f255]) ).
cnf(s30,plain,
( spl0_18
| spl0_21 ),
inference(sat_conversion,[],[f256]) ).
cnf(s31,plain,
( spl0_19
| spl0_21 ),
inference(sat_conversion,[],[f257]) ).
cnf(s38,plain,
( spl0_16
| spl0_22 ),
inference(sat_conversion,[],[f268]) ).
cnf(s39,plain,
( spl0_17
| spl0_22 ),
inference(sat_conversion,[],[f269]) ).
cnf(s40,plain,
( spl0_18
| spl0_22 ),
inference(sat_conversion,[],[f270]) ).
cnf(s41,plain,
( spl0_19
| spl0_22 ),
inference(sat_conversion,[],[f271]) ).
cnf(s46,plain,
( spl0_6
| spl0_14 ),
inference(sat_conversion,[],[f276]) ).
cnf(s47,plain,
( spl0_6
| spl0_15 ),
inference(sat_conversion,[],[f277]) ).
cnf(s48,plain,
( spl0_6
| spl0_16 ),
inference(sat_conversion,[],[f278]) ).
cnf(s49,plain,
( spl0_6
| spl0_17 ),
inference(sat_conversion,[],[f279]) ).
cnf(s50,plain,
( spl0_6
| spl0_18 ),
inference(sat_conversion,[],[f280]) ).
cnf(s51,plain,
( spl0_6
| spl0_19 ),
inference(sat_conversion,[],[f281]) ).
cnf(s56,plain,
( spl0_7
| spl0_14 ),
inference(sat_conversion,[],[f286]) ).
cnf(s57,plain,
( spl0_7
| spl0_15 ),
inference(sat_conversion,[],[f287]) ).
cnf(s58,plain,
( spl0_7
| spl0_16 ),
inference(sat_conversion,[],[f288]) ).
cnf(s59,plain,
( spl0_7
| spl0_17 ),
inference(sat_conversion,[],[f289]) ).
cnf(s60,plain,
( spl0_7
| spl0_18 ),
inference(sat_conversion,[],[f290]) ).
cnf(s61,plain,
( spl0_7
| spl0_19 ),
inference(sat_conversion,[],[f291]) ).
cnf(s66,plain,
( spl0_8
| spl0_14 ),
inference(sat_conversion,[],[f296]) ).
cnf(s67,plain,
( spl0_8
| spl0_15 ),
inference(sat_conversion,[],[f297]) ).
cnf(s68,plain,
( spl0_8
| spl0_16 ),
inference(sat_conversion,[],[f298]) ).
cnf(s69,plain,
( spl0_8
| spl0_17 ),
inference(sat_conversion,[],[f299]) ).
cnf(s70,plain,
( spl0_8
| spl0_18 ),
inference(sat_conversion,[],[f300]) ).
cnf(s71,plain,
( spl0_8
| spl0_19 ),
inference(sat_conversion,[],[f301]) ).
cnf(s72,plain,
( spl0_8
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19 ),
inference(sat_conversion,[],[f492]) ).
cnf(s73,plain,
( spl0_6
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19 ),
inference(sat_conversion,[],[f500]) ).
cnf(s74,plain,
( spl0_7
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19 ),
inference(sat_conversion,[],[f512]) ).
cnf(s78,plain,
( ~ spl0_5
| ~ spl0_7
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19 ),
inference(sat_conversion,[],[f550]) ).
cnf(s85,plain,
( ~ spl0_1
| ~ spl0_7
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19 ),
inference(sat_conversion,[],[f635]) ).
cnf(s88,plain,
( ~ spl0_2
| ~ spl0_7
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19 ),
inference(sat_conversion,[],[f657]) ).
cnf(s94,plain,
( ~ spl0_3
| ~ spl0_7
| ~ spl0_8
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19 ),
inference(sat_conversion,[],[f742]) ).
cnf(s110,plain,
( ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_18
| ~ spl0_19
| ~ spl0_20 ),
inference(sat_conversion,[],[f922]) ).
cnf(s116,plain,
( ~ spl0_2
| ~ spl0_7
| ~ spl0_10
| ~ spl0_20
| ~ spl0_40 ),
inference(sat_conversion,[],[f1038]) ).
cnf(s119,plain,
( ~ spl0_6
| ~ spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_17
| ~ spl0_20
| spl0_38 ),
inference(sat_conversion,[],[f1065]) ).
cnf(s120,plain,
( ~ spl0_6
| ~ spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_17
| ~ spl0_20
| spl0_36 ),
inference(sat_conversion,[],[f1066]) ).
cnf(s122,plain,
( ~ spl0_6
| ~ spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_17
| ~ spl0_20
| ~ spl0_38
| spl0_40 ),
inference(sat_conversion,[],[f1098]) ).
cnf(s124,plain,
( ~ spl0_6
| ~ spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_17
| ~ spl0_20
| ~ spl0_36
| ~ spl0_38
| spl0_41 ),
inference(sat_conversion,[],[f1109]) ).
cnf(s126,plain,
( ~ spl0_6
| ~ spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_17
| ~ spl0_20
| ~ spl0_38
| spl0_41 ),
inference(sat_conversion,[],[f1118]) ).
cnf(s127,plain,
( ~ spl0_36
| spl0_40
| ~ spl0_41 ),
inference(sat_conversion,[],[f1121]) ).
cnf(s128,plain,
( ~ spl0_6
| ~ spl0_38
| spl0_41 ),
inference(sat_conversion,[],[f1122]) ).
cnf(s131,plain,
( ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19
| spl0_38 ),
inference(sat_conversion,[],[f1195]) ).
cnf(s132,plain,
( ~ spl0_8
| ~ spl0_18
| ~ spl0_19
| spl0_36 ),
inference(sat_conversion,[],[f1197]) ).
cnf(s134,plain,
( ~ spl0_6
| ~ spl0_8
| ~ spl0_10
| ~ spl0_20
| ~ spl0_21
| ~ spl0_22
| spl0_40 ),
inference(sat_conversion,[],[f1202]) ).
cnf(s138,plain,
( ~ spl0_5
| ~ spl0_21
| ~ spl0_22 ),
inference(sat_conversion,[],[f1262]) ).
cnf(s146,plain,
( ~ spl0_7
| ~ spl0_10
| ~ spl0_20
| spl0_38
| ~ spl0_40 ),
inference(sat_conversion,[],[f1469]) ).
cnf(s155,plain,
( ~ spl0_36
| ~ spl0_38
| spl0_52 ),
inference(sat_conversion,[],[f1485]) ).
cnf(s157,plain,
( ~ spl0_7
| ~ spl0_8
| ~ spl0_38
| spl0_52 ),
inference(sat_conversion,[],[f1486]) ).
cnf(s163,plain,
( ~ spl0_1
| ~ spl0_7
| ~ spl0_40
| ~ spl0_52
| ~ spl0_54 ),
inference(sat_conversion,[],[f1541]) ).
cnf(s165,plain,
( ~ spl0_1
| ~ spl0_7
| ~ spl0_10
| ~ spl0_20
| ~ spl0_40
| ~ spl0_41
| ~ spl0_52
| ~ spl0_54 ),
inference(sat_conversion,[],[f1550]) ).
cnf(s177,plain,
( ~ spl0_7
| ~ spl0_38
| spl0_54 ),
inference(sat_conversion,[],[f1613]) ).
cnf(s178,plain,
( ~ spl0_4
| ~ spl0_10
| ~ spl0_20
| ~ spl0_40 ),
inference(sat_conversion,[],[f1625]) ).
cnf(s180,plain,
( ~ spl0_4
| ~ spl0_7
| ~ spl0_40
| ~ spl0_54 ),
inference(sat_conversion,[],[f1637]) ).
cnf(s185,plain,
( ~ spl0_3
| ~ spl0_21
| ~ spl0_22
| ~ spl0_41 ),
inference(sat_conversion,[],[f1663]) ).
cnf(s189,plain,
spl0_6,
inference(rat,[],[s73,s46,s47,s48,s49,s50,s51]) ).
cnf(s190,plain,
spl0_7,
inference(rat,[],[s74,s56,s57,s58,s59,s60,s61]) ).
cnf(s191,plain,
spl0_8,
inference(rat,[],[s72,s66,s67,s68,s69,s70,s71]) ).
cnf(s192,plain,
( spl0_10
| ~ spl0_5 ),
inference(rat,[],[s78,s6,s7,s8,s9,s10,s11,s190]) ).
cnf(s193,plain,
( spl0_19
| ~ spl0_5 ),
inference(rat,[],[s138,s31,s41]) ).
cnf(s194,plain,
( spl0_18
| ~ spl0_5 ),
inference(rat,[],[s138,s30,s40]) ).
cnf(s195,plain,
( ~ spl0_18
| ~ spl0_19
| ~ spl0_5
| ~ spl0_10 ),
inference(rat,[],[s16,s78,s17,s18,s19,s110,s191,s190]) ).
cnf(s196,plain,
~ spl0_5,
inference(rat,[],[s195,s194,s193,s192]) ).
cnf(s197,plain,
( spl0_19
| ~ spl0_4 ),
inference(rat,[],[s134,s178,s11,s21,s31,s41,s189,s191]) ).
cnf(s198,plain,
( ~ spl0_18
| ~ spl0_17
| ~ spl0_16
| ~ spl0_4 ),
inference(rat,[],[s127,s180,s128,s177,s131,s132,s197,s190,s189,s191]) ).
cnf(s199,plain,
( spl0_18
| ~ spl0_4 ),
inference(rat,[],[s134,s178,s10,s20,s30,s40,s189,s191]) ).
cnf(s200,plain,
( spl0_17
| ~ spl0_4 ),
inference(rat,[],[s134,s178,s9,s19,s29,s39,s189,s191]) ).
cnf(s201,plain,
( ~ spl0_17
| ~ spl0_4
| ~ spl0_18 ),
inference(rat,[],[s134,s178,s8,s18,s28,s38,s198,s191,s189]) ).
cnf(s202,plain,
~ spl0_4,
inference(rat,[],[s201,s200,s199]) ).
cnf(s203,plain,
( spl0_19
| ~ spl0_17
| ~ spl0_3 ),
inference(rat,[],[s126,s119,s185,s11,s21,s31,s41,s189,s190,s191]) ).
cnf(s204,plain,
( ~ spl0_19
| ~ spl0_17
| ~ spl0_16
| ~ spl0_3 ),
inference(rat,[],[s126,s119,s185,s10,s20,s30,s40,s94,s191,s190,s189]) ).
cnf(s205,plain,
( ~ spl0_17
| ~ spl0_16
| ~ spl0_3 ),
inference(rat,[],[s204,s203]) ).
cnf(s206,plain,
( spl0_17
| ~ spl0_3 ),
inference(rat,[],[s146,s128,s134,s185,s9,s19,s29,s39,s190,s189,s191]) ).
cnf(s207,plain,
( ~ spl0_17
| ~ spl0_3 ),
inference(rat,[],[s126,s119,s185,s8,s18,s28,s38,s205,s191,s190,s189]) ).
cnf(s208,plain,
~ spl0_3,
inference(rat,[],[s207,s206]) ).
cnf(s209,plain,
( ~ spl0_20
| ~ spl0_22
| ~ spl0_21
| ~ spl0_10
| ~ spl0_2 ),
inference(rat,[],[s134,s116,s189,s191,s190]) ).
cnf(s210,plain,
( spl0_20
| ~ spl0_17
| ~ spl0_16
| ~ spl0_2 ),
inference(rat,[],[s88,s20,s21,s190]) ).
cnf(s211,plain,
( ~ spl0_10
| ~ spl0_20
| ~ spl0_17
| ~ spl0_2 ),
inference(rat,[],[s122,s119,s116,s189,s190,s191]) ).
cnf(s212,plain,
( ~ spl0_17
| ~ spl0_16
| ~ spl0_2 ),
inference(rat,[],[s88,s10,s11,s211,s210,s190]) ).
cnf(s213,plain,
( spl0_17
| ~ spl0_2 ),
inference(rat,[],[s209,s9,s19,s29,s39]) ).
cnf(s214,plain,
( ~ spl0_17
| ~ spl0_2 ),
inference(rat,[],[s209,s8,s18,s28,s38,s212]) ).
cnf(s215,plain,
~ spl0_2,
inference(rat,[],[s214,s213]) ).
cnf(s216,plain,
spl0_1,
inference(rat,[],[s1,s190,s196,s202,s191,s189,s208,s215]) ).
cnf(s217,plain,
( ~ spl0_36
| ~ spl0_20
| ~ spl0_10
| ~ spl0_17
| ~ spl0_38 ),
inference(rat,[],[s165,s122,s155,s177,s124,s191,s189,s190,s216]) ).
cnf(s218,plain,
( ~ spl0_20
| ~ spl0_10
| ~ spl0_17 ),
inference(rat,[],[s217,s119,s120,s191,s190,s189]) ).
cnf(s219,plain,
( spl0_20
| ~ spl0_17
| ~ spl0_16 ),
inference(rat,[],[s85,s16,s17,s20,s21,s190,s216]) ).
cnf(s220,plain,
( ~ spl0_17
| ~ spl0_16 ),
inference(rat,[],[s85,s6,s7,s10,s11,s218,s219,s216,s190]) ).
cnf(s221,plain,
( ~ spl0_40
| ~ spl0_20
| ~ spl0_10 ),
inference(rat,[],[s163,s157,s177,s146,s191,s216,s190]) ).
cnf(s222,plain,
( ~ spl0_21
| ~ spl0_10
| ~ spl0_20
| ~ spl0_22 ),
inference(rat,[],[s221,s134,s191,s189]) ).
cnf(s223,plain,
spl0_17,
inference(rat,[],[s222,s9,s19,s29,s39]) ).
cnf(s224,plain,
~ spl0_16,
inference(rat,[],[s220,s223]) ).
cnf(s225,plain,
spl0_22,
inference(rat,[],[s38,s224]) ).
cnf(s226,plain,
spl0_21,
inference(rat,[],[s28,s224]) ).
cnf(s227,plain,
spl0_20,
inference(rat,[],[s18,s224]) ).
cnf(s228,plain,
spl0_10,
inference(rat,[],[s8,s224]) ).
cnf(s229,plain,
$false,
inference(rat,[],[s222,s225,s227,s228,s226]) ).
fof(f1668,plain,
$false,
inference(avatar_sat_refutation,[],[s229]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP350-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.36 % Computer : n003.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 27 09:56:56 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.40 Running first-order model finding
% 0.10/0.40 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.48 % (262826)Will run a generic schedule for satisfiability detection.
% 0.10/0.48 % (262831)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=4142965186_2999 on theBenchmark for (2999ds/0Mi)
% 0.10/0.48 % TRYING [1]
% 0.10/0.48 % TRYING [2]
% 0.10/0.48 % TRYING [3]
% 0.10/0.48 % (262837)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1761369777:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.10/0.48 % (262833)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1924826715:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.10/0.48 % (262834)dis+10_1_sil=32000:sp=arity:random_seed=1622929382:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.10/0.48 % (262835)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2072653172:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.10/0.48 % TRYING [4]
% 0.10/0.48 % (262836)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3056797792:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.10/0.48 % (262832)% WARNING: option uhcvi not known.
% 0.10/0.48 % (262832)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=201581286:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.10/0.48 % TRYING [5]
% 0.10/0.48 % TRYING [6]
% 0.10/0.48 % (262834) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-262826-262834"...
% 0.10/0.48 % (262832) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-262826-262832"...
% 0.10/0.48 % (262834)...printing done.
% 0.10/0.48 % (262835) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-262826-262835"...
% 0.10/0.48 % (262834)Refutation found. Thanks to Tanya!
% 0.10/0.48 % SZS status Unsatisfiable for theBenchmark
% 0.10/0.48 % SZS output start Proof for theBenchmark
% See solution above
% 0.10/0.49 % (262834)------------------------------
% 0.10/0.49 % (262834)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.10/0.49 % (262834)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.10/0.49 % (262834)CaDiCaL version: 2.1.3
% 0.10/0.49 % (262834)Termination reason: Refutation
% 0.10/0.49 % (262834)Time elapsed: 0.037 s
% 0.10/0.49 % (262834)Peak memory usage: 13 MB
% 0.10/0.49 % (262834)Instructions burned: 60 (million)
% 0.10/0.49 % (262826)Success in time 0.074 s
% 0.10/0.49 % Vampire exiting
%------------------------------------------------------------------------------