%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GRP273-1 : 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 : n009.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 10:17:21 AM UTC 2026
% Result : Unsatisfiable 0.36s 0.47s
% Output : Refutation 0.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 38
% Number of leaves : 51
% Syntax : Number of formulae : 370 ( 25 unt; 21 def)
% Number of atoms : 1391 ( 431 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 2016 ( 995 ~;1000 |; 0 &)
% ( 21 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 23 ( 21 usr; 22 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 10 con; 0-2 aty)
% Number of variables : 95 ( 0 sgn 95 !; 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_c1,sk_c11) = sk_c10
| multiply(sk_c3,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,plain,
( multiply(sk_c1,sk_c11) = sk_c10
| sk_c10 = multiply(sk_c3,sk_c11) ),
inference(reorient_equations,[],[f5]) ).
fof(f7,negated_conjecture,
( multiply(sk_c1,sk_c11) = sk_c10
| inverse(sk_c3) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_2) ).
fof(f8,plain,
( multiply(sk_c1,sk_c11) = sk_c10
| sk_c11 = inverse(sk_c3) ),
inference(reorient_equations,[],[f7]) ).
fof(f12,negated_conjecture,
( multiply(sk_c1,sk_c11) = sk_c10
| multiply(sk_c5,sk_c8) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_5) ).
fof(f13,plain,
( multiply(sk_c1,sk_c11) = sk_c10
| sk_c11 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f12]) ).
fof(f14,negated_conjecture,
( multiply(sk_c1,sk_c11) = sk_c10
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_6) ).
fof(f15,plain,
( multiply(sk_c1,sk_c11) = sk_c10
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f14]) ).
fof(f23,negated_conjecture,
( inverse(sk_c1) = sk_c11
| multiply(sk_c3,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_11) ).
fof(f24,plain,
( sk_c11 = inverse(sk_c1)
| sk_c10 = multiply(sk_c3,sk_c11) ),
inference(reorient_equations,[],[f23]) ).
fof(f25,negated_conjecture,
( inverse(sk_c1) = sk_c11
| inverse(sk_c3) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_12) ).
fof(f26,plain,
( sk_c11 = inverse(sk_c1)
| sk_c11 = inverse(sk_c3) ),
inference(reorient_equations,[],[f25]) ).
fof(f27,negated_conjecture,
( inverse(sk_c1) = sk_c11
| multiply(sk_c4,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_13) ).
fof(f28,plain,
( sk_c11 = inverse(sk_c1)
| multiply(sk_c4,sk_c10) = sk_c9 ),
inference(reorient_equations,[],[f27]) ).
fof(f29,negated_conjecture,
( inverse(sk_c1) = sk_c11
| inverse(sk_c4) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_14) ).
fof(f30,plain,
( sk_c11 = inverse(sk_c1)
| sk_c10 = inverse(sk_c4) ),
inference(reorient_equations,[],[f29]) ).
fof(f31,negated_conjecture,
( inverse(sk_c1) = sk_c11
| multiply(sk_c5,sk_c8) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_15) ).
fof(f32,plain,
( sk_c11 = inverse(sk_c1)
| sk_c11 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f31]) ).
fof(f33,negated_conjecture,
( inverse(sk_c1) = sk_c11
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_16) ).
fof(f34,plain,
( sk_c11 = inverse(sk_c1)
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f33]) ).
fof(f43,negated_conjecture,
( multiply(sk_c11,sk_c9) = sk_c10
| multiply(sk_c3,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_21) ).
fof(f44,plain,
( sk_c10 = multiply(sk_c11,sk_c9)
| sk_c10 = multiply(sk_c3,sk_c11) ),
inference(reorient_equations,[],[f43]) ).
fof(f45,negated_conjecture,
( multiply(sk_c11,sk_c9) = sk_c10
| inverse(sk_c3) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_22) ).
fof(f46,plain,
( sk_c10 = multiply(sk_c11,sk_c9)
| sk_c11 = inverse(sk_c3) ),
inference(reorient_equations,[],[f45]) ).
fof(f47,negated_conjecture,
( multiply(sk_c11,sk_c9) = sk_c10
| multiply(sk_c4,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_23) ).
fof(f48,plain,
( sk_c10 = multiply(sk_c11,sk_c9)
| multiply(sk_c4,sk_c10) = sk_c9 ),
inference(reorient_equations,[],[f47]) ).
fof(f49,negated_conjecture,
( multiply(sk_c11,sk_c9) = sk_c10
| inverse(sk_c4) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_24) ).
fof(f50,plain,
( sk_c10 = multiply(sk_c11,sk_c9)
| sk_c10 = inverse(sk_c4) ),
inference(reorient_equations,[],[f49]) ).
fof(f51,negated_conjecture,
( multiply(sk_c11,sk_c9) = sk_c10
| multiply(sk_c5,sk_c8) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_25) ).
fof(f52,plain,
( sk_c10 = multiply(sk_c11,sk_c9)
| sk_c11 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f51]) ).
fof(f53,negated_conjecture,
( multiply(sk_c11,sk_c9) = sk_c10
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_26) ).
fof(f54,plain,
( sk_c10 = multiply(sk_c11,sk_c9)
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f53]) ).
fof(f63,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c11
| multiply(sk_c3,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_31) ).
fof(f64,plain,
( sk_c11 = multiply(sk_c2,sk_c9)
| sk_c10 = multiply(sk_c3,sk_c11) ),
inference(reorient_equations,[],[f63]) ).
fof(f65,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c11
| inverse(sk_c3) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_32) ).
fof(f66,plain,
( sk_c11 = multiply(sk_c2,sk_c9)
| sk_c11 = inverse(sk_c3) ),
inference(reorient_equations,[],[f65]) ).
fof(f69,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c11
| inverse(sk_c4) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_34) ).
fof(f70,plain,
( sk_c11 = multiply(sk_c2,sk_c9)
| sk_c10 = inverse(sk_c4) ),
inference(reorient_equations,[],[f69]) ).
fof(f71,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c11
| multiply(sk_c5,sk_c8) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_35) ).
fof(f72,plain,
( sk_c11 = multiply(sk_c2,sk_c9)
| sk_c11 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f71]) ).
fof(f73,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c11
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_36) ).
fof(f74,plain,
( sk_c11 = multiply(sk_c2,sk_c9)
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f73]) ).
fof(f83,negated_conjecture,
( inverse(sk_c2) = sk_c9
| multiply(sk_c3,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_41) ).
fof(f84,plain,
( sk_c9 = inverse(sk_c2)
| sk_c10 = multiply(sk_c3,sk_c11) ),
inference(reorient_equations,[],[f83]) ).
fof(f85,negated_conjecture,
( inverse(sk_c2) = sk_c9
| inverse(sk_c3) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_42) ).
fof(f86,plain,
( sk_c9 = inverse(sk_c2)
| sk_c11 = inverse(sk_c3) ),
inference(reorient_equations,[],[f85]) ).
fof(f89,negated_conjecture,
( inverse(sk_c2) = sk_c9
| inverse(sk_c4) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_44) ).
fof(f90,plain,
( sk_c9 = inverse(sk_c2)
| sk_c10 = inverse(sk_c4) ),
inference(reorient_equations,[],[f89]) ).
fof(f91,negated_conjecture,
( inverse(sk_c2) = sk_c9
| multiply(sk_c5,sk_c8) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_45) ).
fof(f92,plain,
( sk_c9 = inverse(sk_c2)
| sk_c11 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f91]) ).
fof(f93,negated_conjecture,
( inverse(sk_c2) = sk_c9
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_46) ).
fof(f94,plain,
( sk_c9 = inverse(sk_c2)
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f93]) ).
fof(f103,negated_conjecture,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( multiply(X0,sk_c11) != sk_c10
| inverse(X0) != sk_c11
| multiply(sk_c11,sk_c9) != sk_c10
| multiply(X1,sk_c9) != sk_c11
| inverse(X1) != sk_c9
| 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_51) ).
fof(f104,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( sk_c10 != multiply(X0,sk_c11)
| inverse(X0) != sk_c11
| sk_c10 != multiply(sk_c11,sk_c9)
| sk_c11 != multiply(X1,sk_c9)
| sk_c9 != inverse(X1)
| 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,[],[f103]) ).
fof(f105,plain,
! [X2,X3,X0,X1,X6,X7,X4] :
( sk_c10 != multiply(X0,sk_c11)
| inverse(X0) != sk_c11
| sk_c10 != multiply(sk_c11,sk_c9)
| sk_c11 != multiply(X1,sk_c9)
| sk_c9 != inverse(X1)
| 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,[],[f104]) ).
fof(f106,plain,
! [X2,X3,X0,X1,X6,X4] :
( sk_c10 != multiply(X0,sk_c11)
| inverse(X0) != sk_c11
| sk_c10 != multiply(sk_c11,sk_c9)
| sk_c11 != multiply(X1,sk_c9)
| sk_c9 != inverse(X1)
| 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,[],[f105]) ).
fof(f108,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(f109,plain,
( ! [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) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f108]) ).
fof(f111,definition,
( spl0_2
<=> ! [X3] :
( sk_c9 != multiply(X3,sk_c10)
| sk_c10 != inverse(X3) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f112,plain,
( ! [X3] :
( sk_c9 != multiply(X3,sk_c10)
| sk_c10 != inverse(X3) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f111]) ).
fof(f114,definition,
( spl0_3
<=> ! [X2] :
( sk_c10 != multiply(X2,sk_c11)
| sk_c11 != inverse(X2) ) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f115,plain,
( ! [X2] :
( sk_c10 != multiply(X2,sk_c11)
| sk_c11 != inverse(X2) )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f114]) ).
fof(f117,definition,
( spl0_4
<=> ! [X1] :
( sk_c11 != multiply(X1,sk_c9)
| sk_c9 != inverse(X1) ) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f118,plain,
( ! [X1] :
( sk_c11 != multiply(X1,sk_c9)
| sk_c9 != inverse(X1) )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f117]) ).
fof(f120,definition,
( spl0_5
<=> sk_c10 = multiply(sk_c11,sk_c9) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f121,plain,
( sk_c10 = multiply(sk_c11,sk_c9)
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f120]) ).
fof(f122,plain,
( sk_c10 != multiply(sk_c11,sk_c9)
| spl0_5 ),
inference(avatar_component_clause,[],[f120]) ).
fof(f123,plain,
( spl0_1
| spl0_2
| spl0_3
| spl0_4
| ~ spl0_5
| spl0_3 ),
inference(avatar_split_clause,[],[f106,f114,f120,f117,f114,f111,f108]) ).
fof(f129,definition,
( spl0_7
<=> sk_c9 = inverse(sk_c2) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f131,plain,
( sk_c9 = inverse(sk_c2)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f129]) ).
fof(f149,definition,
( spl0_11
<=> sk_c8 = inverse(sk_c5) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f151,plain,
( sk_c8 = inverse(sk_c5)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f149]) ).
fof(f152,plain,
( spl0_11
| spl0_7 ),
inference(avatar_split_clause,[],[f94,f129,f149]) ).
fof(f154,definition,
( spl0_12
<=> sk_c11 = multiply(sk_c5,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f156,plain,
( sk_c11 = multiply(sk_c5,sk_c8)
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f154]) ).
fof(f157,plain,
( spl0_12
| spl0_7 ),
inference(avatar_split_clause,[],[f92,f129,f154]) ).
fof(f159,definition,
( spl0_13
<=> sk_c10 = inverse(sk_c4) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f161,plain,
( sk_c10 = inverse(sk_c4)
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f159]) ).
fof(f162,plain,
( spl0_13
| spl0_7 ),
inference(avatar_split_clause,[],[f90,f129,f159]) ).
fof(f164,definition,
( spl0_14
<=> multiply(sk_c4,sk_c10) = sk_c9 ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
fof(f166,plain,
( multiply(sk_c4,sk_c10) = sk_c9
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f164]) ).
fof(f169,definition,
( spl0_15
<=> sk_c11 = inverse(sk_c3) ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
fof(f171,plain,
( sk_c11 = inverse(sk_c3)
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f169]) ).
fof(f172,plain,
( spl0_15
| spl0_7 ),
inference(avatar_split_clause,[],[f86,f129,f169]) ).
fof(f174,definition,
( spl0_16
<=> sk_c10 = multiply(sk_c3,sk_c11) ),
introduced(definition,[new_symbols(definition,[spl0_16])],[avatar_definition]) ).
fof(f175,plain,
( sk_c10 != multiply(sk_c3,sk_c11)
| spl0_16 ),
inference(avatar_component_clause,[],[f174]) ).
fof(f176,plain,
( sk_c10 = multiply(sk_c3,sk_c11)
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f174]) ).
fof(f177,plain,
( spl0_16
| spl0_7 ),
inference(avatar_split_clause,[],[f84,f129,f174]) ).
fof(f179,definition,
( spl0_17
<=> sk_c11 = multiply(sk_c2,sk_c9) ),
introduced(definition,[new_symbols(definition,[spl0_17])],[avatar_definition]) ).
fof(f181,plain,
( sk_c11 = multiply(sk_c2,sk_c9)
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f179]) ).
fof(f186,plain,
( spl0_11
| spl0_17 ),
inference(avatar_split_clause,[],[f74,f179,f149]) ).
fof(f187,plain,
( spl0_12
| spl0_17 ),
inference(avatar_split_clause,[],[f72,f179,f154]) ).
fof(f188,plain,
( spl0_13
| spl0_17 ),
inference(avatar_split_clause,[],[f70,f179,f159]) ).
fof(f190,plain,
( spl0_15
| spl0_17 ),
inference(avatar_split_clause,[],[f66,f179,f169]) ).
fof(f191,plain,
( spl0_16
| spl0_17 ),
inference(avatar_split_clause,[],[f64,f179,f174]) ).
fof(f196,plain,
( spl0_11
| spl0_5 ),
inference(avatar_split_clause,[],[f54,f120,f149]) ).
fof(f197,plain,
( spl0_12
| spl0_5 ),
inference(avatar_split_clause,[],[f52,f120,f154]) ).
fof(f198,plain,
( spl0_13
| spl0_5 ),
inference(avatar_split_clause,[],[f50,f120,f159]) ).
fof(f199,plain,
( spl0_14
| spl0_5 ),
inference(avatar_split_clause,[],[f48,f120,f164]) ).
fof(f200,plain,
( spl0_15
| spl0_5 ),
inference(avatar_split_clause,[],[f46,f120,f169]) ).
fof(f201,plain,
( spl0_16
| spl0_5 ),
inference(avatar_split_clause,[],[f44,f120,f174]) ).
fof(f203,definition,
( spl0_18
<=> sk_c11 = inverse(sk_c1) ),
introduced(definition,[new_symbols(definition,[spl0_18])],[avatar_definition]) ).
fof(f205,plain,
( sk_c11 = inverse(sk_c1)
| ~ spl0_18 ),
inference(avatar_component_clause,[],[f203]) ).
fof(f210,plain,
( spl0_11
| spl0_18 ),
inference(avatar_split_clause,[],[f34,f203,f149]) ).
fof(f211,plain,
( spl0_12
| spl0_18 ),
inference(avatar_split_clause,[],[f32,f203,f154]) ).
fof(f212,plain,
( spl0_13
| spl0_18 ),
inference(avatar_split_clause,[],[f30,f203,f159]) ).
fof(f213,plain,
( spl0_14
| spl0_18 ),
inference(avatar_split_clause,[],[f28,f203,f164]) ).
fof(f214,plain,
( spl0_15
| spl0_18 ),
inference(avatar_split_clause,[],[f26,f203,f169]) ).
fof(f215,plain,
( spl0_16
| spl0_18 ),
inference(avatar_split_clause,[],[f24,f203,f174]) ).
fof(f217,definition,
( spl0_19
<=> multiply(sk_c1,sk_c11) = sk_c10 ),
introduced(definition,[new_symbols(definition,[spl0_19])],[avatar_definition]) ).
fof(f219,plain,
( multiply(sk_c1,sk_c11) = sk_c10
| ~ spl0_19 ),
inference(avatar_component_clause,[],[f217]) ).
fof(f224,plain,
( spl0_11
| spl0_19 ),
inference(avatar_split_clause,[],[f15,f217,f149]) ).
fof(f225,plain,
( spl0_12
| spl0_19 ),
inference(avatar_split_clause,[],[f13,f217,f154]) ).
fof(f228,plain,
( spl0_15
| spl0_19 ),
inference(avatar_split_clause,[],[f8,f217,f169]) ).
fof(f229,plain,
( spl0_16
| spl0_19 ),
inference(avatar_split_clause,[],[f6,f217,f174]) ).
fof(f230,plain,
( identity = multiply(sk_c11,sk_c3)
| ~ spl0_15 ),
inference(superposition,[],[f3,f171]) ).
fof(f231,plain,
( identity = multiply(sk_c10,sk_c4)
| ~ spl0_13 ),
inference(superposition,[],[f3,f161]) ).
fof(f237,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[],[f4,f3]) ).
fof(f243,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f237,f1]) ).
fof(f246,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c11,multiply(sk_c3,X0))
| ~ spl0_15 ),
inference(superposition,[],[f4,f230]) ).
fof(f247,plain,
( ! [X0] : multiply(sk_c11,multiply(sk_c3,X0)) = X0
| ~ spl0_15 ),
inference(forward_demodulation,[],[f246,f1]) ).
fof(f260,plain,
( sk_c11 = multiply(sk_c11,sk_c10)
| ~ spl0_15
| ~ spl0_16 ),
inference(superposition,[],[f247,f176]) ).
fof(f309,plain,
( sk_c10 = multiply(inverse(sk_c11),sk_c11)
| ~ spl0_15
| ~ spl0_16 ),
inference(superposition,[],[f243,f260]) ).
fof(f314,plain,
( sk_c10 = multiply(inverse(sk_c4),sk_c9)
| ~ spl0_14 ),
inference(superposition,[],[f243,f166]) ).
fof(f317,plain,
( sk_c8 = multiply(inverse(sk_c5),sk_c11)
| ~ spl0_12 ),
inference(superposition,[],[f243,f156]) ).
fof(f334,plain,
( sk_c8 = multiply(sk_c8,sk_c11)
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f317,f151]) ).
fof(f337,plain,
( sk_c10 = multiply(sk_c10,sk_c9)
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f314,f161]) ).
fof(f341,plain,
( identity = sk_c10
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f309,f3]) ).
fof(f374,plain,
( sk_c11 = multiply(inverse(sk_c8),sk_c8)
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f243,f334]) ).
fof(f376,plain,
( identity = sk_c11
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f374,f3]) ).
fof(f381,plain,
( identity = multiply(identity,sk_c3)
| ~ spl0_11
| ~ spl0_12
| ~ spl0_15 ),
inference(superposition,[],[f230,f376]) ).
fof(f390,plain,
( identity = sk_c3
| ~ spl0_11
| ~ spl0_12
| ~ spl0_15 ),
inference(forward_demodulation,[],[f381,f1]) ).
fof(f396,plain,
( identity = multiply(identity,sk_c9)
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f337,f341]) ).
fof(f397,plain,
( identity = sk_c9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f396,f1]) ).
fof(f399,plain,
( sk_c10 != multiply(sk_c11,identity)
| spl0_5
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(superposition,[],[f122,f397]) ).
fof(f400,plain,
( sk_c10 != multiply(identity,identity)
| spl0_5
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f399,f376]) ).
fof(f402,plain,
( identity != sk_c10
| spl0_5
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f400,f1]) ).
fof(f403,plain,
( $false
| spl0_5
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_subsumption_resolution,[],[f402,f341]) ).
fof(f404,plain,
( spl0_5
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(avatar_contradiction_clause,[],[f403]) ).
fof(f405,plain,
( ! [X2] :
( sk_c10 != multiply(X2,identity)
| sk_c11 != inverse(X2) )
| ~ spl0_3
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f115,f376]) ).
fof(f407,plain,
( ! [X2] :
( identity != multiply(X2,identity)
| sk_c11 != inverse(X2) )
| ~ spl0_3
| ~ spl0_11
| ~ spl0_12
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f405,f341]) ).
fof(f409,plain,
( ! [X2] :
( identity != multiply(X2,identity)
| identity != inverse(X2) )
| ~ spl0_3
| ~ spl0_11
| ~ spl0_12
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f407,f376]) ).
fof(f411,plain,
( identity != identity
| identity != inverse(identity)
| ~ spl0_3
| ~ spl0_11
| ~ spl0_12
| ~ spl0_15
| ~ spl0_16 ),
inference(superposition,[],[f409,f1]) ).
fof(f416,plain,
( identity != inverse(identity)
| ~ spl0_3
| ~ spl0_11
| ~ spl0_12
| ~ spl0_15
| ~ spl0_16 ),
inference(trivial_inequality_removal,[],[f411]) ).
fof(f430,plain,
( sk_c11 = inverse(identity)
| ~ spl0_11
| ~ spl0_12
| ~ spl0_15 ),
inference(superposition,[],[f171,f390]) ).
fof(f431,plain,
( identity = inverse(identity)
| ~ spl0_11
| ~ spl0_12
| ~ spl0_15 ),
inference(forward_demodulation,[],[f430,f376]) ).
fof(f479,plain,
( $false
| ~ spl0_3
| ~ spl0_11
| ~ spl0_12
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_subsumption_resolution,[],[f431,f416]) ).
fof(f480,plain,
( ~ spl0_3
| ~ spl0_11
| ~ spl0_12
| ~ spl0_15
| ~ spl0_16 ),
inference(avatar_contradiction_clause,[],[f479]) ).
fof(f481,plain,
( sk_c10 != multiply(sk_c3,identity)
| ~ spl0_11
| ~ spl0_12
| spl0_16 ),
inference(forward_demodulation,[],[f175,f376]) ).
fof(f483,plain,
( identity = inverse(sk_c1)
| ~ spl0_11
| ~ spl0_12
| ~ spl0_18 ),
inference(forward_demodulation,[],[f205,f376]) ).
fof(f484,plain,
( sk_c10 = multiply(sk_c1,identity)
| ~ spl0_11
| ~ spl0_12
| ~ spl0_19 ),
inference(forward_demodulation,[],[f219,f376]) ).
fof(f486,plain,
( sk_c10 = multiply(identity,sk_c9)
| ~ spl0_5
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f121,f376]) ).
fof(f488,plain,
( sk_c10 != multiply(identity,identity)
| ~ spl0_11
| ~ spl0_12
| ~ spl0_15
| spl0_16 ),
inference(forward_demodulation,[],[f481,f390]) ).
fof(f490,plain,
( sk_c10 = sk_c9
| ~ spl0_5
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f486,f1]) ).
fof(f491,plain,
( identity != sk_c10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_15
| spl0_16 ),
inference(forward_demodulation,[],[f488,f1]) ).
fof(f494,plain,
( identity = multiply(identity,sk_c1)
| ~ spl0_11
| ~ spl0_12
| ~ spl0_18 ),
inference(superposition,[],[f3,f483]) ).
fof(f495,plain,
( identity = sk_c1
| ~ spl0_11
| ~ spl0_12
| ~ spl0_18 ),
inference(forward_demodulation,[],[f494,f1]) ).
fof(f499,plain,
( identity = inverse(identity)
| ~ spl0_11
| ~ spl0_12
| ~ spl0_18 ),
inference(superposition,[],[f483,f495]) ).
fof(f504,plain,
( sk_c10 = multiply(identity,identity)
| ~ spl0_11
| ~ spl0_12
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_demodulation,[],[f484,f495]) ).
fof(f505,plain,
( identity = sk_c10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_demodulation,[],[f504,f1]) ).
fof(f506,plain,
( $false
| ~ spl0_11
| ~ spl0_12
| ~ spl0_15
| spl0_16
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_subsumption_resolution,[],[f505,f491]) ).
fof(f507,plain,
( ~ spl0_11
| ~ spl0_12
| ~ spl0_15
| spl0_16
| ~ spl0_18
| ~ spl0_19 ),
inference(avatar_contradiction_clause,[],[f506]) ).
fof(f509,plain,
( identity = multiply(sk_c9,sk_c2)
| ~ spl0_7 ),
inference(superposition,[],[f3,f131]) ).
fof(f514,plain,
( sk_c9 = multiply(inverse(sk_c2),sk_c11)
| ~ spl0_17 ),
inference(superposition,[],[f243,f181]) ).
fof(f516,plain,
( sk_c9 = multiply(sk_c9,sk_c11)
| ~ spl0_7
| ~ spl0_17 ),
inference(forward_demodulation,[],[f514,f131]) ).
fof(f523,plain,
( sk_c10 != sk_c10
| sk_c11 != inverse(sk_c1)
| ~ spl0_3
| ~ spl0_19 ),
inference(superposition,[],[f115,f219]) ).
fof(f524,plain,
( sk_c11 != inverse(sk_c1)
| ~ spl0_3
| ~ spl0_19 ),
inference(trivial_inequality_removal,[],[f523]) ).
fof(f525,plain,
( $false
| ~ spl0_3
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_subsumption_resolution,[],[f524,f205]) ).
fof(f526,plain,
( ~ spl0_3
| ~ spl0_18
| ~ spl0_19 ),
inference(avatar_contradiction_clause,[],[f525]) ).
fof(f532,definition,
( spl0_23
<=> identity = sk_c10 ),
introduced(definition,[new_symbols(definition,[spl0_23])],[avatar_definition]) ).
fof(f533,plain,
( identity = sk_c10
| ~ spl0_23 ),
inference(avatar_component_clause,[],[f532]) ).
fof(f545,plain,
( spl0_23
| ~ spl0_15
| ~ spl0_16 ),
inference(avatar_split_clause,[],[f341,f174,f169,f532]) ).
fof(f550,plain,
( identity = multiply(identity,sk_c4)
| ~ spl0_13
| ~ spl0_23 ),
inference(superposition,[],[f231,f533]) ).
fof(f555,plain,
( identity = sk_c4
| ~ spl0_13
| ~ spl0_23 ),
inference(forward_demodulation,[],[f550,f1]) ).
fof(f573,plain,
( sk_c10 = inverse(identity)
| ~ spl0_13
| ~ spl0_23 ),
inference(superposition,[],[f161,f555]) ).
fof(f574,plain,
( identity = inverse(identity)
| ~ spl0_13
| ~ spl0_23 ),
inference(forward_demodulation,[],[f573,f533]) ).
fof(f615,plain,
( ! [X3] :
( sk_c9 != multiply(X3,identity)
| sk_c10 != inverse(X3) )
| ~ spl0_2
| ~ spl0_23 ),
inference(forward_demodulation,[],[f112,f533]) ).
fof(f616,plain,
( ! [X3] :
( sk_c10 != multiply(X3,identity)
| sk_c10 != inverse(X3) )
| ~ spl0_2
| ~ spl0_5
| ~ spl0_11
| ~ spl0_12
| ~ spl0_23 ),
inference(forward_demodulation,[],[f615,f490]) ).
fof(f617,plain,
( ! [X3] :
( identity != multiply(X3,identity)
| sk_c10 != inverse(X3) )
| ~ spl0_2
| ~ spl0_5
| ~ spl0_11
| ~ spl0_12
| ~ spl0_23 ),
inference(forward_demodulation,[],[f616,f533]) ).
fof(f618,plain,
( ! [X3] :
( identity != multiply(X3,identity)
| identity != inverse(X3) )
| ~ spl0_2
| ~ spl0_5
| ~ spl0_11
| ~ spl0_12
| ~ spl0_23 ),
inference(forward_demodulation,[],[f617,f533]) ).
fof(f627,plain,
( identity != identity
| identity != inverse(inverse(identity))
| ~ spl0_2
| ~ spl0_5
| ~ spl0_11
| ~ spl0_12
| ~ spl0_23 ),
inference(superposition,[],[f618,f3]) ).
fof(f633,plain,
( identity != inverse(inverse(identity))
| ~ spl0_2
| ~ spl0_5
| ~ spl0_11
| ~ spl0_12
| ~ spl0_23 ),
inference(trivial_inequality_removal,[],[f627]) ).
fof(f636,plain,
( identity != inverse(identity)
| ~ spl0_2
| ~ spl0_5
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_23 ),
inference(forward_demodulation,[],[f633,f574]) ).
fof(f641,plain,
( $false
| ~ spl0_2
| ~ spl0_5
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_23 ),
inference(forward_subsumption_resolution,[],[f636,f574]) ).
fof(f642,plain,
( ~ spl0_2
| ~ spl0_5
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_23 ),
inference(avatar_contradiction_clause,[],[f641]) ).
fof(f643,plain,
( ! [X1] :
( sk_c11 != multiply(X1,sk_c10)
| sk_c9 != inverse(X1) )
| ~ spl0_4
| ~ spl0_5
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f118,f490]) ).
fof(f644,plain,
( ! [X1] :
( sk_c11 != multiply(X1,identity)
| sk_c9 != inverse(X1) )
| ~ spl0_4
| ~ spl0_5
| ~ spl0_11
| ~ spl0_12
| ~ spl0_23 ),
inference(forward_demodulation,[],[f643,f533]) ).
fof(f645,plain,
( ! [X1] :
( identity != multiply(X1,identity)
| sk_c9 != inverse(X1) )
| ~ spl0_4
| ~ spl0_5
| ~ spl0_11
| ~ spl0_12
| ~ spl0_23 ),
inference(forward_demodulation,[],[f644,f376]) ).
fof(f646,plain,
( ! [X1] :
( sk_c10 != inverse(X1)
| identity != multiply(X1,identity) )
| ~ spl0_4
| ~ spl0_5
| ~ spl0_11
| ~ spl0_12
| ~ spl0_23 ),
inference(forward_demodulation,[],[f645,f490]) ).
fof(f647,plain,
( ! [X1] :
( identity != multiply(X1,identity)
| identity != inverse(X1) )
| ~ spl0_4
| ~ spl0_5
| ~ spl0_11
| ~ spl0_12
| ~ spl0_23 ),
inference(forward_demodulation,[],[f646,f533]) ).
fof(f653,plain,
( identity != identity
| identity != inverse(inverse(identity))
| ~ spl0_4
| ~ spl0_5
| ~ spl0_11
| ~ spl0_12
| ~ spl0_23 ),
inference(superposition,[],[f647,f3]) ).
fof(f659,plain,
( identity != inverse(inverse(identity))
| ~ spl0_4
| ~ spl0_5
| ~ spl0_11
| ~ spl0_12
| ~ spl0_23 ),
inference(trivial_inequality_removal,[],[f653]) ).
fof(f662,plain,
( identity != inverse(identity)
| ~ spl0_4
| ~ spl0_5
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_23 ),
inference(forward_demodulation,[],[f659,f574]) ).
fof(f667,plain,
( $false
| ~ spl0_4
| ~ spl0_5
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_23 ),
inference(forward_subsumption_resolution,[],[f662,f574]) ).
fof(f668,plain,
( ~ spl0_4
| ~ spl0_5
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_23 ),
inference(avatar_contradiction_clause,[],[f667]) ).
fof(f669,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_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f109,f376]) ).
fof(f670,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_11
| ~ spl0_12
| ~ spl0_23 ),
inference(forward_demodulation,[],[f669,f533]) ).
fof(f671,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_11
| ~ spl0_12
| ~ spl0_23 ),
inference(forward_demodulation,[],[f670,f376]) ).
fof(f675,plain,
( ! [X0] :
( inverse(X0) != multiply(X0,sk_c11)
| identity != multiply(sk_c3,sk_c11)
| identity != multiply(sk_c11,identity)
| sk_c11 != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_11
| ~ spl0_12
| ~ spl0_15
| ~ spl0_23 ),
inference(superposition,[],[f671,f171]) ).
fof(f676,plain,
( ! [X0] :
( inverse(X0) != multiply(X0,sk_c10)
| identity != multiply(sk_c4,sk_c10)
| identity != multiply(sk_c10,identity)
| sk_c10 != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_23 ),
inference(superposition,[],[f671,f161]) ).
fof(f701,plain,
( ! [X0] :
( inverse(X0) != multiply(X0,identity)
| identity != multiply(sk_c4,sk_c10)
| identity != multiply(sk_c10,identity)
| sk_c10 != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_23 ),
inference(forward_demodulation,[],[f676,f533]) ).
fof(f702,plain,
( ! [X0] :
( inverse(X0) != multiply(X0,identity)
| identity != multiply(sk_c3,sk_c11)
| identity != multiply(sk_c11,identity)
| sk_c11 != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_11
| ~ spl0_12
| ~ spl0_15
| ~ spl0_23 ),
inference(forward_demodulation,[],[f675,f376]) ).
fof(f715,plain,
( ! [X0] :
( identity != sk_c9
| inverse(X0) != multiply(X0,identity)
| identity != multiply(sk_c10,identity)
| sk_c10 != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_23 ),
inference(forward_demodulation,[],[f701,f166]) ).
fof(f716,plain,
( ! [X0] :
( identity != multiply(sk_c3,identity)
| inverse(X0) != multiply(X0,identity)
| identity != multiply(sk_c11,identity)
| sk_c11 != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_11
| ~ spl0_12
| ~ spl0_15
| ~ spl0_23 ),
inference(forward_demodulation,[],[f702,f376]) ).
fof(f721,plain,
( ! [X0] :
( inverse(X0) != multiply(X0,identity)
| identity != multiply(sk_c10,identity)
| sk_c10 != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_23 ),
inference(forward_subsumption_resolution,[],[f715,f397]) ).
fof(f722,plain,
( ! [X0] :
( identity != multiply(identity,identity)
| inverse(X0) != multiply(X0,identity)
| identity != multiply(sk_c11,identity)
| sk_c11 != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_11
| ~ spl0_12
| ~ spl0_15
| ~ spl0_23 ),
inference(forward_demodulation,[],[f716,f390]) ).
fof(f725,plain,
( ! [X0] :
( identity != multiply(identity,identity)
| inverse(X0) != multiply(X0,identity)
| sk_c10 != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_23 ),
inference(forward_demodulation,[],[f721,f533]) ).
fof(f726,plain,
( ! [X0] :
( inverse(X0) != multiply(X0,identity)
| identity != multiply(sk_c11,identity)
| sk_c11 != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_11
| ~ spl0_12
| ~ spl0_15
| ~ spl0_23 ),
inference(forward_subsumption_resolution,[],[f722,f1]) ).
fof(f728,plain,
( ! [X0] :
( inverse(X0) != multiply(X0,identity)
| sk_c10 != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_23 ),
inference(forward_subsumption_resolution,[],[f725,f1]) ).
fof(f729,plain,
( ! [X0] :
( identity != multiply(identity,identity)
| inverse(X0) != multiply(X0,identity)
| sk_c11 != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_11
| ~ spl0_12
| ~ spl0_15
| ~ spl0_23 ),
inference(forward_demodulation,[],[f726,f376]) ).
fof(f731,plain,
( ! [X0] :
( inverse(X0) != multiply(X0,identity)
| identity != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_23 ),
inference(forward_demodulation,[],[f728,f533]) ).
fof(f732,plain,
( ! [X0] :
( inverse(X0) != multiply(X0,identity)
| sk_c11 != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_11
| ~ spl0_12
| ~ spl0_15
| ~ spl0_23 ),
inference(forward_subsumption_resolution,[],[f729,f1]) ).
fof(f734,plain,
( ! [X0] :
( inverse(X0) != multiply(X0,identity)
| identity != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_11
| ~ spl0_12
| ~ spl0_15
| ~ spl0_23 ),
inference(forward_demodulation,[],[f732,f376]) ).
fof(f783,plain,
( identity != inverse(inverse(identity))
| identity != inverse(inverse(inverse(identity)))
| ~ spl0_1
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_23 ),
inference(superposition,[],[f731,f3]) ).
fof(f803,definition,
( spl0_34
<=> identity = inverse(sk_c1) ),
introduced(definition,[new_symbols(definition,[spl0_34])],[avatar_definition]) ).
fof(f804,plain,
( identity = inverse(sk_c1)
| ~ spl0_34 ),
inference(avatar_component_clause,[],[f803]) ).
fof(f805,plain,
( identity != inverse(sk_c1)
| spl0_34 ),
inference(avatar_component_clause,[],[f803]) ).
fof(f808,plain,
( identity != inverse(identity)
| identity != inverse(inverse(inverse(identity)))
| ~ spl0_1
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_23 ),
inference(forward_demodulation,[],[f783,f574]) ).
fof(f811,plain,
( identity != inverse(inverse(inverse(identity)))
| ~ spl0_1
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_23 ),
inference(forward_subsumption_resolution,[],[f808,f574]) ).
fof(f814,plain,
( identity != inverse(inverse(identity))
| ~ spl0_1
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_23 ),
inference(forward_demodulation,[],[f811,f574]) ).
fof(f818,plain,
( identity != inverse(identity)
| ~ spl0_1
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_23 ),
inference(forward_demodulation,[],[f814,f574]) ).
fof(f820,plain,
( $false
| ~ spl0_1
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_23 ),
inference(forward_subsumption_resolution,[],[f818,f574]) ).
fof(f821,plain,
( ~ spl0_1
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_23 ),
inference(avatar_contradiction_clause,[],[f820]) ).
fof(f826,plain,
( spl0_34
| ~ spl0_11
| ~ spl0_12
| ~ spl0_18 ),
inference(avatar_split_clause,[],[f483,f203,f154,f149,f803]) ).
fof(f856,plain,
( identity != inverse(inverse(identity))
| identity != inverse(inverse(inverse(identity)))
| ~ spl0_1
| ~ spl0_11
| ~ spl0_12
| ~ spl0_15
| ~ spl0_23 ),
inference(superposition,[],[f734,f3]) ).
fof(f865,plain,
( identity != inverse(identity)
| identity != inverse(inverse(inverse(identity)))
| ~ spl0_1
| ~ spl0_11
| ~ spl0_12
| ~ spl0_15
| ~ spl0_18
| ~ spl0_23 ),
inference(forward_demodulation,[],[f856,f499]) ).
fof(f870,plain,
( identity != inverse(inverse(inverse(identity)))
| ~ spl0_1
| ~ spl0_11
| ~ spl0_12
| ~ spl0_15
| ~ spl0_18
| ~ spl0_23 ),
inference(forward_subsumption_resolution,[],[f865,f499]) ).
fof(f875,plain,
( identity != inverse(inverse(identity))
| ~ spl0_1
| ~ spl0_11
| ~ spl0_12
| ~ spl0_15
| ~ spl0_18
| ~ spl0_23 ),
inference(forward_demodulation,[],[f870,f499]) ).
fof(f881,plain,
( identity != inverse(identity)
| ~ spl0_1
| ~ spl0_11
| ~ spl0_12
| ~ spl0_15
| ~ spl0_18
| ~ spl0_23 ),
inference(forward_demodulation,[],[f875,f499]) ).
fof(f887,plain,
( $false
| ~ spl0_1
| ~ spl0_11
| ~ spl0_12
| ~ spl0_15
| ~ spl0_18
| ~ spl0_23 ),
inference(forward_subsumption_resolution,[],[f881,f499]) ).
fof(f888,plain,
( ~ spl0_1
| ~ spl0_11
| ~ spl0_12
| ~ spl0_15
| ~ spl0_18
| ~ spl0_23 ),
inference(avatar_contradiction_clause,[],[f887]) ).
fof(f905,plain,
( identity != inverse(identity)
| ~ spl0_2
| ~ spl0_5
| ~ spl0_11
| ~ spl0_12
| ~ spl0_18
| ~ spl0_23 ),
inference(forward_demodulation,[],[f633,f499]) ).
fof(f919,plain,
( $false
| ~ spl0_2
| ~ spl0_5
| ~ spl0_11
| ~ spl0_12
| ~ spl0_18
| ~ spl0_23 ),
inference(forward_subsumption_resolution,[],[f905,f499]) ).
fof(f920,plain,
( ~ spl0_2
| ~ spl0_5
| ~ spl0_11
| ~ spl0_12
| ~ spl0_18
| ~ spl0_23 ),
inference(avatar_contradiction_clause,[],[f919]) ).
fof(f975,plain,
( identity = multiply(sk_c11,sk_c1)
| ~ spl0_18 ),
inference(superposition,[],[f3,f205]) ).
fof(f976,plain,
( identity = sk_c11
| ~ spl0_18
| ~ spl0_34 ),
inference(superposition,[],[f804,f205]) ).
fof(f987,plain,
( sk_c10 = multiply(identity,sk_c9)
| ~ spl0_5
| ~ spl0_18
| ~ spl0_34 ),
inference(superposition,[],[f121,f976]) ).
fof(f988,plain,
( sk_c10 = multiply(sk_c1,identity)
| ~ spl0_18
| ~ spl0_19
| ~ spl0_34 ),
inference(superposition,[],[f219,f976]) ).
fof(f995,plain,
( sk_c10 = sk_c9
| ~ spl0_5
| ~ spl0_18
| ~ spl0_34 ),
inference(forward_demodulation,[],[f987,f1]) ).
fof(f996,plain,
( identity = sk_c9
| ~ spl0_5
| ~ spl0_18
| ~ spl0_23
| ~ spl0_34 ),
inference(forward_demodulation,[],[f995,f533]) ).
fof(f1011,definition,
( spl0_36
<=> identity = sk_c9 ),
introduced(definition,[new_symbols(definition,[spl0_36])],[avatar_definition]) ).
fof(f1012,plain,
( identity = sk_c9
| ~ spl0_36 ),
inference(avatar_component_clause,[],[f1011]) ).
fof(f1019,plain,
( identity != sk_c11
| ~ spl0_18
| spl0_34 ),
inference(forward_demodulation,[],[f805,f205]) ).
fof(f1024,plain,
( sk_c11 != sk_c11
| sk_c9 != inverse(sk_c2)
| ~ spl0_4
| ~ spl0_17 ),
inference(superposition,[],[f118,f181]) ).
fof(f1025,plain,
( sk_c9 != inverse(sk_c2)
| ~ spl0_4
| ~ spl0_17 ),
inference(trivial_inequality_removal,[],[f1024]) ).
fof(f1026,plain,
( $false
| ~ spl0_4
| ~ spl0_7
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f1025,f131]) ).
fof(f1027,plain,
( ~ spl0_4
| ~ spl0_7
| ~ spl0_17 ),
inference(avatar_contradiction_clause,[],[f1026]) ).
fof(f1035,plain,
( ! [X3] :
( sk_c9 != multiply(X3,identity)
| identity != inverse(X3) )
| ~ spl0_2
| ~ spl0_23 ),
inference(forward_demodulation,[],[f615,f533]) ).
fof(f1041,plain,
( identity != sk_c9
| identity != inverse(identity)
| ~ spl0_2
| ~ spl0_23 ),
inference(superposition,[],[f1035,f1]) ).
fof(f1051,definition,
( spl0_39
<=> identity = inverse(identity) ),
introduced(definition,[new_symbols(definition,[spl0_39])],[avatar_definition]) ).
fof(f1052,plain,
( identity = inverse(identity)
| ~ spl0_39 ),
inference(avatar_component_clause,[],[f1051]) ).
fof(f1054,plain,
( ~ spl0_39
| ~ spl0_36
| ~ spl0_2
| ~ spl0_23 ),
inference(avatar_split_clause,[],[f1041,f532,f111,f1011,f1051]) ).
fof(f1058,plain,
( sk_c11 = multiply(inverse(sk_c9),sk_c9)
| ~ spl0_7
| ~ spl0_17 ),
inference(superposition,[],[f243,f516]) ).
fof(f1060,plain,
( identity = sk_c11
| ~ spl0_7
| ~ spl0_17 ),
inference(forward_demodulation,[],[f1058,f3]) ).
fof(f1061,plain,
( $false
| ~ spl0_7
| ~ spl0_17
| ~ spl0_18
| spl0_34 ),
inference(forward_subsumption_resolution,[],[f1060,f1019]) ).
fof(f1062,plain,
( ~ spl0_7
| ~ spl0_17
| ~ spl0_18
| spl0_34 ),
inference(avatar_contradiction_clause,[],[f1061]) ).
fof(f1069,plain,
( spl0_36
| ~ spl0_5
| ~ spl0_18
| ~ spl0_23
| ~ spl0_34 ),
inference(avatar_split_clause,[],[f996,f803,f532,f203,f120,f1011]) ).
fof(f1071,plain,
( identity = multiply(identity,sk_c2)
| ~ spl0_7
| ~ spl0_36 ),
inference(superposition,[],[f509,f1012]) ).
fof(f1075,plain,
( identity = sk_c2
| ~ spl0_7
| ~ spl0_36 ),
inference(forward_demodulation,[],[f1071,f1]) ).
fof(f1079,plain,
( sk_c9 = inverse(identity)
| ~ spl0_7
| ~ spl0_36 ),
inference(superposition,[],[f131,f1075]) ).
fof(f1080,plain,
( identity = inverse(identity)
| ~ spl0_7
| ~ spl0_36 ),
inference(forward_demodulation,[],[f1079,f1012]) ).
fof(f1083,plain,
( spl0_39
| ~ spl0_7
| ~ spl0_36 ),
inference(avatar_split_clause,[],[f1080,f1011,f129,f1051]) ).
fof(f1085,plain,
( ! [X6,X4] :
( inverse(X6) != multiply(X6,inverse(X4))
| sk_c11 != multiply(X4,inverse(X4))
| sk_c11 != multiply(inverse(X4),identity)
| inverse(X4) != inverse(inverse(X6)) )
| ~ spl0_1
| ~ spl0_23 ),
inference(forward_demodulation,[],[f109,f533]) ).
fof(f1091,plain,
( ! [X0] :
( inverse(X0) != multiply(X0,sk_c9)
| sk_c11 != multiply(sk_c2,sk_c9)
| sk_c11 != multiply(sk_c9,identity)
| sk_c9 != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_23 ),
inference(superposition,[],[f1085,f131]) ).
fof(f1095,plain,
( ! [X0] :
( inverse(X0) != multiply(X0,sk_c9)
| sk_c11 != multiply(sk_c9,identity)
| sk_c9 != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_17
| ~ spl0_23 ),
inference(forward_subsumption_resolution,[],[f1091,f181]) ).
fof(f1108,plain,
( ! [X0] :
( inverse(X0) != multiply(X0,identity)
| sk_c11 != multiply(sk_c9,identity)
| sk_c9 != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_17
| ~ spl0_23
| ~ spl0_36 ),
inference(forward_demodulation,[],[f1095,f1012]) ).
fof(f1126,definition,
( spl0_46
<=> identity = sk_c11 ),
introduced(definition,[new_symbols(definition,[spl0_46])],[avatar_definition]) ).
fof(f1127,plain,
( identity = sk_c11
| ~ spl0_46 ),
inference(avatar_component_clause,[],[f1126]) ).
fof(f1131,plain,
( ! [X0] :
( sk_c11 != multiply(identity,identity)
| inverse(X0) != multiply(X0,identity)
| sk_c9 != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_17
| ~ spl0_23
| ~ spl0_36 ),
inference(forward_demodulation,[],[f1108,f1012]) ).
fof(f1133,plain,
( ! [X0] :
( identity != sk_c11
| inverse(X0) != multiply(X0,identity)
| sk_c9 != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_17
| ~ spl0_23
| ~ spl0_36 ),
inference(forward_demodulation,[],[f1131,f1]) ).
fof(f1134,plain,
( ! [X0] :
( identity != inverse(inverse(X0))
| identity != sk_c11
| inverse(X0) != multiply(X0,identity) )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_17
| ~ spl0_23
| ~ spl0_36 ),
inference(forward_demodulation,[],[f1133,f1012]) ).
fof(f1136,definition,
( spl0_47
<=> ! [X0] :
( identity != inverse(inverse(X0))
| inverse(X0) != multiply(X0,identity) ) ),
introduced(definition,[new_symbols(definition,[spl0_47])],[avatar_definition]) ).
fof(f1137,plain,
( ! [X0] :
( inverse(X0) != multiply(X0,identity)
| identity != inverse(inverse(X0)) )
| ~ spl0_47 ),
inference(avatar_component_clause,[],[f1136]) ).
fof(f1138,plain,
( ~ spl0_46
| spl0_47
| ~ spl0_1
| ~ spl0_7
| ~ spl0_17
| ~ spl0_23
| ~ spl0_36 ),
inference(avatar_split_clause,[],[f1134,f1011,f532,f179,f129,f108,f1136,f1126]) ).
fof(f1148,plain,
( spl0_46
| ~ spl0_18
| ~ spl0_34 ),
inference(avatar_split_clause,[],[f976,f803,f203,f1126]) ).
fof(f1155,plain,
( identity = multiply(identity,sk_c1)
| ~ spl0_18
| ~ spl0_46 ),
inference(superposition,[],[f975,f1127]) ).
fof(f1156,plain,
( identity = sk_c1
| ~ spl0_18
| ~ spl0_46 ),
inference(forward_demodulation,[],[f1155,f1]) ).
fof(f1210,plain,
( identity != inverse(identity)
| identity != inverse(inverse(identity))
| ~ spl0_47 ),
inference(superposition,[],[f1137,f1]) ).
fof(f1216,plain,
( identity != inverse(inverse(identity))
| ~ spl0_39
| ~ spl0_47 ),
inference(forward_subsumption_resolution,[],[f1210,f1052]) ).
fof(f1218,plain,
( identity != inverse(identity)
| ~ spl0_39
| ~ spl0_47 ),
inference(forward_demodulation,[],[f1216,f1052]) ).
fof(f1220,plain,
( $false
| ~ spl0_39
| ~ spl0_47 ),
inference(forward_subsumption_resolution,[],[f1218,f1052]) ).
fof(f1221,plain,
( ~ spl0_39
| ~ spl0_47 ),
inference(avatar_contradiction_clause,[],[f1220]) ).
fof(f1229,plain,
( sk_c10 = multiply(identity,identity)
| ~ spl0_18
| ~ spl0_19
| ~ spl0_34
| ~ spl0_46 ),
inference(forward_demodulation,[],[f988,f1156]) ).
fof(f1240,plain,
( identity = sk_c10
| ~ spl0_18
| ~ spl0_19
| ~ spl0_34
| ~ spl0_46 ),
inference(forward_demodulation,[],[f1229,f1]) ).
fof(f1249,plain,
( spl0_23
| ~ spl0_18
| ~ spl0_19
| ~ spl0_34
| ~ spl0_46 ),
inference(avatar_split_clause,[],[f1240,f1126,f803,f217,f203,f532]) ).
cnf(s1,plain,
( spl0_3
| spl0_2
| spl0_1
| spl0_3
| spl0_4
| ~ spl0_5 ),
inference(sat_conversion,[],[f123]) ).
cnf(s2,plain,
( spl0_1
| spl0_2
| spl0_3
| spl0_4
| ~ spl0_5 ),
inference(rat,[],[s1]) ).
cnf(s7,plain,
( spl0_7
| spl0_11 ),
inference(sat_conversion,[],[f152]) ).
cnf(s8,plain,
( spl0_7
| spl0_12 ),
inference(sat_conversion,[],[f157]) ).
cnf(s9,plain,
( spl0_7
| spl0_13 ),
inference(sat_conversion,[],[f162]) ).
cnf(s11,plain,
( spl0_7
| spl0_15 ),
inference(sat_conversion,[],[f172]) ).
cnf(s12,plain,
( spl0_7
| spl0_16 ),
inference(sat_conversion,[],[f177]) ).
cnf(s17,plain,
( spl0_11
| spl0_17 ),
inference(sat_conversion,[],[f186]) ).
cnf(s18,plain,
( spl0_12
| spl0_17 ),
inference(sat_conversion,[],[f187]) ).
cnf(s19,plain,
( spl0_13
| spl0_17 ),
inference(sat_conversion,[],[f188]) ).
cnf(s21,plain,
( spl0_15
| spl0_17 ),
inference(sat_conversion,[],[f190]) ).
cnf(s22,plain,
( spl0_16
| spl0_17 ),
inference(sat_conversion,[],[f191]) ).
cnf(s27,plain,
( spl0_5
| spl0_11 ),
inference(sat_conversion,[],[f196]) ).
cnf(s28,plain,
( spl0_5
| spl0_12 ),
inference(sat_conversion,[],[f197]) ).
cnf(s29,plain,
( spl0_5
| spl0_13 ),
inference(sat_conversion,[],[f198]) ).
cnf(s30,plain,
( spl0_5
| spl0_14 ),
inference(sat_conversion,[],[f199]) ).
cnf(s31,plain,
( spl0_5
| spl0_15 ),
inference(sat_conversion,[],[f200]) ).
cnf(s32,plain,
( spl0_5
| spl0_16 ),
inference(sat_conversion,[],[f201]) ).
cnf(s37,plain,
( spl0_11
| spl0_18 ),
inference(sat_conversion,[],[f210]) ).
cnf(s38,plain,
( spl0_12
| spl0_18 ),
inference(sat_conversion,[],[f211]) ).
cnf(s39,plain,
( spl0_13
| spl0_18 ),
inference(sat_conversion,[],[f212]) ).
cnf(s40,plain,
( spl0_14
| spl0_18 ),
inference(sat_conversion,[],[f213]) ).
cnf(s41,plain,
( spl0_15
| spl0_18 ),
inference(sat_conversion,[],[f214]) ).
cnf(s42,plain,
( spl0_16
| spl0_18 ),
inference(sat_conversion,[],[f215]) ).
cnf(s47,plain,
( spl0_11
| spl0_19 ),
inference(sat_conversion,[],[f224]) ).
cnf(s48,plain,
( spl0_12
| spl0_19 ),
inference(sat_conversion,[],[f225]) ).
cnf(s51,plain,
( spl0_15
| spl0_19 ),
inference(sat_conversion,[],[f228]) ).
cnf(s52,plain,
( spl0_16
| spl0_19 ),
inference(sat_conversion,[],[f229]) ).
cnf(s53,plain,
( spl0_5
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(sat_conversion,[],[f404]) ).
cnf(s55,plain,
( ~ spl0_3
| ~ spl0_11
| ~ spl0_12
| ~ spl0_15
| ~ spl0_16 ),
inference(sat_conversion,[],[f480]) ).
cnf(s56,plain,
( ~ spl0_11
| ~ spl0_12
| ~ spl0_15
| spl0_16
| ~ spl0_18
| ~ spl0_19 ),
inference(sat_conversion,[],[f507]) ).
cnf(s57,plain,
( ~ spl0_3
| ~ spl0_18
| ~ spl0_19 ),
inference(sat_conversion,[],[f526]) ).
cnf(s60,plain,
( ~ spl0_15
| ~ spl0_16
| spl0_23 ),
inference(sat_conversion,[],[f545]) ).
cnf(s63,plain,
( ~ spl0_2
| ~ spl0_5
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_23 ),
inference(sat_conversion,[],[f642]) ).
cnf(s66,plain,
( ~ spl0_4
| ~ spl0_5
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_23 ),
inference(sat_conversion,[],[f668]) ).
cnf(s74,plain,
( ~ spl0_1
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_23 ),
inference(sat_conversion,[],[f821]) ).
cnf(s76,plain,
( ~ spl0_11
| ~ spl0_12
| ~ spl0_18
| spl0_34 ),
inference(sat_conversion,[],[f826]) ).
cnf(s83,plain,
( ~ spl0_1
| ~ spl0_11
| ~ spl0_12
| ~ spl0_15
| ~ spl0_18
| ~ spl0_23 ),
inference(sat_conversion,[],[f888]) ).
cnf(s90,plain,
( ~ spl0_2
| ~ spl0_5
| ~ spl0_11
| ~ spl0_12
| ~ spl0_18
| ~ spl0_23 ),
inference(sat_conversion,[],[f920]) ).
cnf(s106,plain,
( ~ spl0_4
| ~ spl0_7
| ~ spl0_17 ),
inference(sat_conversion,[],[f1027]) ).
cnf(s109,plain,
( ~ spl0_2
| ~ spl0_23
| ~ spl0_36
| ~ spl0_39 ),
inference(sat_conversion,[],[f1054]) ).
cnf(s110,plain,
( ~ spl0_7
| ~ spl0_17
| ~ spl0_18
| spl0_34 ),
inference(sat_conversion,[],[f1062]) ).
cnf(s113,plain,
( ~ spl0_5
| ~ spl0_18
| ~ spl0_23
| ~ spl0_34
| spl0_36 ),
inference(sat_conversion,[],[f1069]) ).
cnf(s115,plain,
( ~ spl0_7
| ~ spl0_36
| spl0_39 ),
inference(sat_conversion,[],[f1083]) ).
cnf(s120,plain,
( ~ spl0_1
| ~ spl0_7
| ~ spl0_17
| ~ spl0_23
| ~ spl0_36
| ~ spl0_46
| spl0_47 ),
inference(sat_conversion,[],[f1138]) ).
cnf(s123,plain,
( ~ spl0_18
| ~ spl0_34
| spl0_46 ),
inference(sat_conversion,[],[f1148]) ).
cnf(s130,plain,
( ~ spl0_39
| ~ spl0_47 ),
inference(sat_conversion,[],[f1221]) ).
cnf(s136,plain,
( ~ spl0_18
| ~ spl0_19
| spl0_23
| ~ spl0_34
| ~ spl0_46 ),
inference(sat_conversion,[],[f1249]) ).
cnf(s140,plain,
spl0_5,
inference(rat,[],[s53,s27,s28,s29,s30,s31,s32]) ).
cnf(s141,plain,
( spl0_7
| ~ spl0_4 ),
inference(rat,[],[s66,s60,s7,s8,s9,s11,s12,s140]) ).
cnf(s142,plain,
( ~ spl0_7
| ~ spl0_4 ),
inference(rat,[],[s66,s60,s17,s18,s19,s21,s22,s106,s140]) ).
cnf(s143,plain,
~ spl0_4,
inference(rat,[],[s142,s141]) ).
cnf(s145,plain,
( ~ spl0_15
| ~ spl0_12
| ~ spl0_3
| ~ spl0_11 ),
inference(rat,[],[s56,s42,s52,s55]) ).
cnf(s146,plain,
( spl0_15
| ~ spl0_3 ),
inference(rat,[],[s57,s41,s51]) ).
cnf(s147,plain,
( spl0_12
| ~ spl0_3 ),
inference(rat,[],[s57,s38,s48]) ).
cnf(s148,plain,
( ~ spl0_12
| ~ spl0_15
| ~ spl0_3 ),
inference(rat,[],[s57,s37,s47,s145]) ).
cnf(s149,plain,
~ spl0_3,
inference(rat,[],[s148,s147,s146]) ).
cnf(s150,plain,
( ~ spl0_18
| ~ spl0_15
| ~ spl0_12
| ~ spl0_11
| ~ spl0_2 ),
inference(rat,[],[s52,s136,s60,s123,s90,s76,s140]) ).
cnf(s151,plain,
( ~ spl0_15
| ~ spl0_12
| ~ spl0_2
| ~ spl0_11 ),
inference(rat,[],[s63,s60,s39,s42,s150,s140]) ).
cnf(s152,plain,
( ~ spl0_12
| ~ spl0_11
| ~ spl0_2 ),
inference(rat,[],[s136,s123,s90,s76,s41,s51,s151,s140]) ).
cnf(s153,plain,
( spl0_12
| ~ spl0_2 ),
inference(rat,[],[s115,s109,s113,s136,s123,s110,s8,s18,s38,s48,s140]) ).
cnf(s154,plain,
( ~ spl0_12
| ~ spl0_2 ),
inference(rat,[],[s115,s109,s113,s136,s123,s110,s7,s17,s37,s47,s152,s140]) ).
cnf(s155,plain,
~ spl0_2,
inference(rat,[],[s154,s153]) ).
cnf(s156,plain,
spl0_1,
inference(rat,[],[s2,s143,s149,s140,s155]) ).
cnf(s157,plain,
( ~ spl0_15
| ~ spl0_18
| ~ spl0_12
| ~ spl0_11 ),
inference(rat,[],[s52,s136,s60,s83,s123,s76,s156]) ).
cnf(s158,plain,
( ~ spl0_18
| ~ spl0_12
| ~ spl0_11 ),
inference(rat,[],[s130,s120,s115,s113,s136,s11,s21,s51,s157,s123,s76,s140,s156]) ).
cnf(s159,plain,
( ~ spl0_12
| ~ spl0_11 ),
inference(rat,[],[s74,s60,s39,s40,s41,s42,s158,s156]) ).
cnf(s160,plain,
spl0_12,
inference(rat,[],[s130,s120,s115,s113,s136,s123,s110,s8,s18,s38,s48,s156,s140]) ).
cnf(s161,plain,
~ spl0_11,
inference(rat,[],[s159,s160]) ).
cnf(s162,plain,
spl0_19,
inference(rat,[],[s47,s161]) ).
cnf(s163,plain,
spl0_18,
inference(rat,[],[s37,s161]) ).
cnf(s164,plain,
spl0_17,
inference(rat,[],[s17,s161]) ).
cnf(s165,plain,
spl0_7,
inference(rat,[],[s7,s161]) ).
cnf(s166,plain,
spl0_34,
inference(rat,[],[s110,s163,s165,s164]) ).
cnf(s167,plain,
spl0_46,
inference(rat,[],[s123,s163,s166]) ).
cnf(s168,plain,
spl0_23,
inference(rat,[],[s136,s167,s163,s162,s166]) ).
cnf(s170,plain,
spl0_36,
inference(rat,[],[s113,s166,s163,s140,s168]) ).
cnf(s172,plain,
spl0_39,
inference(rat,[],[s115,s165,s170]) ).
cnf(s173,plain,
spl0_47,
inference(rat,[],[s120,s168,s167,s165,s164,s156,s170]) ).
cnf(s175,plain,
$false,
inference(rat,[],[s130,s173,s172]) ).
fof(f1253,plain,
$false,
inference(avatar_sat_refutation,[],[s175]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP273-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.37 % Computer : n009.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sun Sep 27 09:43:45 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.40 Running first-order model finding
% 0.09/0.40 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
% 0.36/0.47 % (1783996)Will run a generic schedule for satisfiability detection.
% 0.36/0.47 % (1784007)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1911222000:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.36/0.47 % (1784002)% WARNING: option uhcvi not known.
% 0.36/0.47 % (1784001)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1508602652_2999 on theBenchmark for (2999ds/0Mi)
% 0.36/0.47 % (1784003)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3544034073:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.36/0.47 % (1784004)dis+10_1_sil=32000:sp=arity:random_seed=4233338243:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.36/0.47 % (1784005)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3479698345:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.36/0.47 % (1784006)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3987126013:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.36/0.47 % (1784002)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2685803561:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.36/0.47 % TRYING [1]
% 0.36/0.47 % TRYING [2]
% 0.36/0.47 % TRYING [3]
% 0.36/0.47 % TRYING [4]
% 0.36/0.47 % (1784004) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1783996-1784004"...
% 0.36/0.47 % TRYING [5]
% 0.36/0.47 % (1784004)...printing done.
% 0.36/0.47 % (1784004)Refutation found. Thanks to Tanya!
% 0.36/0.47 % SZS status Unsatisfiable for theBenchmark
% 0.36/0.47 % SZS output start Proof for theBenchmark
% See solution above
% 0.36/0.48 % (1784004)------------------------------
% 0.36/0.48 % (1784004)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.36/0.48 % (1784004)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.36/0.48 % (1784004)CaDiCaL version: 2.1.3
% 0.36/0.48 % (1784004)Termination reason: Refutation
% 0.36/0.48 % (1784004)Time elapsed: 0.026 s
% 0.36/0.48 % (1784004)Peak memory usage: 12 MB
% 0.36/0.48 % (1784004)Instructions burned: 40 (million)
% 0.36/0.48 % (1783996)Success in time 0.063 s
% 0.36/0.48 % Vampire exiting
%------------------------------------------------------------------------------