%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GRP228-1 : 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 : n007.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 10:17:13 AM UTC 2026
% Result : Unsatisfiable 0.11s 0.47s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 39
% Number of leaves : 42
% Syntax : Number of formulae : 278 ( 16 unt; 13 def)
% Number of atoms : 1055 ( 353 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 1512 ( 735 ~; 764 |; 0 &)
% ( 13 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 15 ( 13 usr; 14 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 81 ( 0 sgn 81 !; 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,
( inverse(sk_c1) = sk_c10
| inverse(sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,negated_conjecture,
( inverse(sk_c1) = sk_c10
| inverse(sk_c4) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_2) ).
fof(f7,plain,
( inverse(sk_c1) = sk_c10
| sk_c10 = inverse(sk_c4) ),
inference(reorient_equations,[],[f6]) ).
fof(f8,negated_conjecture,
( inverse(sk_c1) = sk_c10
| multiply(sk_c4,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_3) ).
fof(f9,plain,
( inverse(sk_c1) = sk_c10
| sk_c10 = multiply(sk_c4,sk_c9) ),
inference(reorient_equations,[],[f8]) ).
fof(f10,negated_conjecture,
( inverse(sk_c1) = sk_c10
| multiply(sk_c5,sk_c8) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_4) ).
fof(f11,plain,
( inverse(sk_c1) = sk_c10
| sk_c10 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f10]) ).
fof(f12,negated_conjecture,
( inverse(sk_c1) = sk_c10
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_5) ).
fof(f13,plain,
( inverse(sk_c1) = sk_c10
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f12]) ).
fof(f21,negated_conjecture,
( multiply(sk_c1,sk_c9) = sk_c10
| inverse(sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_10) ).
fof(f22,plain,
( sk_c10 = multiply(sk_c1,sk_c9)
| inverse(sk_c10) = sk_c9 ),
inference(reorient_equations,[],[f21]) ).
fof(f23,negated_conjecture,
( multiply(sk_c1,sk_c9) = sk_c10
| inverse(sk_c4) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_11) ).
fof(f24,plain,
( sk_c10 = multiply(sk_c1,sk_c9)
| sk_c10 = inverse(sk_c4) ),
inference(reorient_equations,[],[f23]) ).
fof(f25,negated_conjecture,
( multiply(sk_c1,sk_c9) = sk_c10
| multiply(sk_c4,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_12) ).
fof(f26,plain,
( sk_c10 = multiply(sk_c1,sk_c9)
| sk_c10 = multiply(sk_c4,sk_c9) ),
inference(reorient_equations,[],[f25]) ).
fof(f27,negated_conjecture,
( multiply(sk_c1,sk_c9) = sk_c10
| multiply(sk_c5,sk_c8) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_13) ).
fof(f28,plain,
( sk_c10 = multiply(sk_c1,sk_c9)
| sk_c10 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f27]) ).
fof(f29,negated_conjecture,
( multiply(sk_c1,sk_c9) = sk_c10
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_14) ).
fof(f30,plain,
( sk_c10 = multiply(sk_c1,sk_c9)
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f29]) ).
fof(f39,negated_conjecture,
( multiply(sk_c10,sk_c3) = sk_c9
| inverse(sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_19) ).
fof(f40,plain,
( sk_c9 = multiply(sk_c10,sk_c3)
| inverse(sk_c10) = sk_c9 ),
inference(reorient_equations,[],[f39]) ).
fof(f41,negated_conjecture,
( multiply(sk_c10,sk_c3) = sk_c9
| inverse(sk_c4) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_20) ).
fof(f42,plain,
( sk_c9 = multiply(sk_c10,sk_c3)
| sk_c10 = inverse(sk_c4) ),
inference(reorient_equations,[],[f41]) ).
fof(f43,negated_conjecture,
( multiply(sk_c10,sk_c3) = sk_c9
| multiply(sk_c4,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_21) ).
fof(f44,plain,
( sk_c9 = multiply(sk_c10,sk_c3)
| sk_c10 = multiply(sk_c4,sk_c9) ),
inference(reorient_equations,[],[f43]) ).
fof(f45,negated_conjecture,
( multiply(sk_c10,sk_c3) = sk_c9
| multiply(sk_c5,sk_c8) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_22) ).
fof(f46,plain,
( sk_c9 = multiply(sk_c10,sk_c3)
| sk_c10 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f45]) ).
fof(f47,negated_conjecture,
( multiply(sk_c10,sk_c3) = sk_c9
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_23) ).
fof(f48,plain,
( sk_c9 = multiply(sk_c10,sk_c3)
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f47]) ).
fof(f57,negated_conjecture,
( multiply(sk_c2,sk_c10) = sk_c3
| inverse(sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_28) ).
fof(f58,plain,
( sk_c3 = multiply(sk_c2,sk_c10)
| inverse(sk_c10) = sk_c9 ),
inference(reorient_equations,[],[f57]) ).
fof(f59,negated_conjecture,
( multiply(sk_c2,sk_c10) = sk_c3
| inverse(sk_c4) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_29) ).
fof(f60,plain,
( sk_c3 = multiply(sk_c2,sk_c10)
| sk_c10 = inverse(sk_c4) ),
inference(reorient_equations,[],[f59]) ).
fof(f61,negated_conjecture,
( multiply(sk_c2,sk_c10) = sk_c3
| multiply(sk_c4,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_30) ).
fof(f62,plain,
( sk_c3 = multiply(sk_c2,sk_c10)
| sk_c10 = multiply(sk_c4,sk_c9) ),
inference(reorient_equations,[],[f61]) ).
fof(f63,negated_conjecture,
( multiply(sk_c2,sk_c10) = sk_c3
| multiply(sk_c5,sk_c8) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_31) ).
fof(f64,plain,
( sk_c3 = multiply(sk_c2,sk_c10)
| sk_c10 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f63]) ).
fof(f65,negated_conjecture,
( multiply(sk_c2,sk_c10) = sk_c3
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_32) ).
fof(f66,plain,
( sk_c3 = multiply(sk_c2,sk_c10)
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f65]) ).
fof(f75,negated_conjecture,
( inverse(sk_c2) = sk_c10
| inverse(sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_37) ).
fof(f76,plain,
( sk_c10 = inverse(sk_c2)
| inverse(sk_c10) = sk_c9 ),
inference(reorient_equations,[],[f75]) ).
fof(f77,negated_conjecture,
( inverse(sk_c2) = sk_c10
| inverse(sk_c4) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_38) ).
fof(f78,plain,
( sk_c10 = inverse(sk_c2)
| sk_c10 = inverse(sk_c4) ),
inference(reorient_equations,[],[f77]) ).
fof(f79,negated_conjecture,
( inverse(sk_c2) = sk_c10
| multiply(sk_c4,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_39) ).
fof(f80,plain,
( sk_c10 = inverse(sk_c2)
| sk_c10 = multiply(sk_c4,sk_c9) ),
inference(reorient_equations,[],[f79]) ).
fof(f81,negated_conjecture,
( inverse(sk_c2) = sk_c10
| multiply(sk_c5,sk_c8) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_40) ).
fof(f82,plain,
( sk_c10 = inverse(sk_c2)
| sk_c10 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f81]) ).
fof(f83,negated_conjecture,
( inverse(sk_c2) = sk_c10
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_41) ).
fof(f84,plain,
( sk_c10 = inverse(sk_c2)
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f83]) ).
fof(f93,negated_conjecture,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( inverse(X0) != sk_c10
| multiply(X0,sk_c9) != sk_c10
| multiply(sk_c10,X1) != sk_c9
| multiply(X2,sk_c10) != X1
| inverse(X2) != sk_c10
| inverse(sk_c10) != sk_c9
| inverse(X3) != sk_c10
| multiply(X3,sk_c9) != sk_c10
| multiply(X4,X5) != sk_c10
| inverse(X4) != X5
| multiply(X5,sk_c9) != sk_c10
| inverse(X6) != X7
| inverse(X7) != X5
| multiply(X6,X5) != X7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_46) ).
fof(f94,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( inverse(X0) != sk_c10
| sk_c10 != multiply(X0,sk_c9)
| sk_c9 != multiply(sk_c10,X1)
| multiply(X2,sk_c10) != X1
| sk_c10 != inverse(X2)
| inverse(sk_c10) != sk_c9
| sk_c10 != inverse(X3)
| sk_c10 != multiply(X3,sk_c9)
| sk_c10 != multiply(X4,X5)
| inverse(X4) != X5
| sk_c10 != multiply(X5,sk_c9)
| inverse(X6) != X7
| inverse(X7) != X5
| multiply(X6,X5) != X7 ),
inference(reorient_equations,[],[f93]) ).
fof(f95,plain,
! [X2,X3,X0,X6,X7,X4,X5] :
( inverse(X0) != sk_c10
| sk_c10 != multiply(X0,sk_c9)
| sk_c9 != multiply(sk_c10,multiply(X2,sk_c10))
| sk_c10 != inverse(X2)
| inverse(sk_c10) != sk_c9
| sk_c10 != inverse(X3)
| sk_c10 != multiply(X3,sk_c9)
| sk_c10 != multiply(X4,X5)
| inverse(X4) != X5
| sk_c10 != multiply(X5,sk_c9)
| inverse(X6) != X7
| inverse(X7) != X5
| multiply(X6,X5) != X7 ),
inference(equality_resolution,[],[f94]) ).
fof(f96,plain,
! [X2,X3,X0,X6,X7,X4] :
( inverse(X0) != sk_c10
| sk_c10 != multiply(X0,sk_c9)
| sk_c9 != multiply(sk_c10,multiply(X2,sk_c10))
| sk_c10 != inverse(X2)
| inverse(sk_c10) != sk_c9
| sk_c10 != inverse(X3)
| sk_c10 != multiply(X3,sk_c9)
| sk_c10 != multiply(X4,inverse(X4))
| sk_c10 != multiply(inverse(X4),sk_c9)
| inverse(X6) != X7
| inverse(X4) != inverse(X7)
| multiply(X6,inverse(X4)) != X7 ),
inference(equality_resolution,[],[f95]) ).
fof(f97,plain,
! [X2,X3,X0,X6,X4] :
( inverse(X0) != sk_c10
| sk_c10 != multiply(X0,sk_c9)
| sk_c9 != multiply(sk_c10,multiply(X2,sk_c10))
| sk_c10 != inverse(X2)
| inverse(sk_c10) != sk_c9
| sk_c10 != inverse(X3)
| sk_c10 != multiply(X3,sk_c9)
| sk_c10 != multiply(X4,inverse(X4))
| sk_c10 != multiply(inverse(X4),sk_c9)
| inverse(X4) != inverse(inverse(X6))
| inverse(X6) != multiply(X6,inverse(X4)) ),
inference(equality_resolution,[],[f96]) ).
fof(f99,definition,
( spl0_1
<=> ! [X6,X4] :
( sk_c10 != multiply(X4,inverse(X4))
| inverse(X6) != multiply(X6,inverse(X4))
| inverse(X4) != inverse(inverse(X6))
| sk_c10 != multiply(inverse(X4),sk_c9) ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f100,plain,
( ! [X6,X4] :
( sk_c10 != multiply(X4,inverse(X4))
| inverse(X6) != multiply(X6,inverse(X4))
| inverse(X4) != inverse(inverse(X6))
| sk_c10 != multiply(inverse(X4),sk_c9) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f99]) ).
fof(f102,definition,
( spl0_2
<=> ! [X3] :
( sk_c10 != inverse(X3)
| sk_c10 != multiply(X3,sk_c9) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f103,plain,
( ! [X3] :
( sk_c10 != multiply(X3,sk_c9)
| sk_c10 != inverse(X3) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f102]) ).
fof(f105,definition,
( spl0_3
<=> inverse(sk_c10) = sk_c9 ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f106,plain,
( inverse(sk_c10) = sk_c9
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f105]) ).
fof(f107,plain,
( inverse(sk_c10) != sk_c9
| spl0_3 ),
inference(avatar_component_clause,[],[f105]) ).
fof(f109,definition,
( spl0_4
<=> ! [X2] :
( sk_c9 != multiply(sk_c10,multiply(X2,sk_c10))
| sk_c10 != inverse(X2) ) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f110,plain,
( ! [X2] :
( sk_c9 != multiply(sk_c10,multiply(X2,sk_c10))
| sk_c10 != inverse(X2) )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f109]) ).
fof(f111,plain,
( spl0_1
| spl0_2
| ~ spl0_3
| spl0_4
| spl0_2 ),
inference(avatar_split_clause,[],[f97,f102,f109,f105,f102,f99]) ).
fof(f117,definition,
( spl0_6
<=> sk_c10 = inverse(sk_c2) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f119,plain,
( sk_c10 = inverse(sk_c2)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f117]) ).
fof(f137,definition,
( spl0_10
<=> sk_c8 = inverse(sk_c5) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f139,plain,
( sk_c8 = inverse(sk_c5)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f137]) ).
fof(f140,plain,
( spl0_10
| spl0_6 ),
inference(avatar_split_clause,[],[f84,f117,f137]) ).
fof(f142,definition,
( spl0_11
<=> sk_c10 = multiply(sk_c5,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f144,plain,
( sk_c10 = multiply(sk_c5,sk_c8)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f142]) ).
fof(f145,plain,
( spl0_11
| spl0_6 ),
inference(avatar_split_clause,[],[f82,f117,f142]) ).
fof(f147,definition,
( spl0_12
<=> sk_c10 = multiply(sk_c4,sk_c9) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f148,plain,
( sk_c10 != multiply(sk_c4,sk_c9)
| spl0_12 ),
inference(avatar_component_clause,[],[f147]) ).
fof(f149,plain,
( sk_c10 = multiply(sk_c4,sk_c9)
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f147]) ).
fof(f150,plain,
( spl0_12
| spl0_6 ),
inference(avatar_split_clause,[],[f80,f117,f147]) ).
fof(f152,definition,
( spl0_13
<=> sk_c10 = inverse(sk_c4) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f154,plain,
( sk_c10 = inverse(sk_c4)
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f152]) ).
fof(f155,plain,
( spl0_13
| spl0_6 ),
inference(avatar_split_clause,[],[f78,f117,f152]) ).
fof(f156,plain,
( spl0_3
| spl0_6 ),
inference(avatar_split_clause,[],[f76,f117,f105]) ).
fof(f158,definition,
( spl0_14
<=> sk_c3 = multiply(sk_c2,sk_c10) ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
fof(f160,plain,
( sk_c3 = multiply(sk_c2,sk_c10)
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f158]) ).
fof(f165,plain,
( spl0_10
| spl0_14 ),
inference(avatar_split_clause,[],[f66,f158,f137]) ).
fof(f166,plain,
( spl0_11
| spl0_14 ),
inference(avatar_split_clause,[],[f64,f158,f142]) ).
fof(f167,plain,
( spl0_12
| spl0_14 ),
inference(avatar_split_clause,[],[f62,f158,f147]) ).
fof(f168,plain,
( spl0_13
| spl0_14 ),
inference(avatar_split_clause,[],[f60,f158,f152]) ).
fof(f169,plain,
( spl0_3
| spl0_14 ),
inference(avatar_split_clause,[],[f58,f158,f105]) ).
fof(f171,definition,
( spl0_15
<=> sk_c9 = multiply(sk_c10,sk_c3) ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
fof(f172,plain,
( sk_c9 != multiply(sk_c10,sk_c3)
| spl0_15 ),
inference(avatar_component_clause,[],[f171]) ).
fof(f173,plain,
( sk_c9 = multiply(sk_c10,sk_c3)
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f171]) ).
fof(f178,plain,
( spl0_10
| spl0_15 ),
inference(avatar_split_clause,[],[f48,f171,f137]) ).
fof(f179,plain,
( spl0_11
| spl0_15 ),
inference(avatar_split_clause,[],[f46,f171,f142]) ).
fof(f180,plain,
( spl0_12
| spl0_15 ),
inference(avatar_split_clause,[],[f44,f171,f147]) ).
fof(f181,plain,
( spl0_13
| spl0_15 ),
inference(avatar_split_clause,[],[f42,f171,f152]) ).
fof(f182,plain,
( spl0_3
| spl0_15 ),
inference(avatar_split_clause,[],[f40,f171,f105]) ).
fof(f184,definition,
( spl0_16
<=> sk_c10 = multiply(sk_c1,sk_c9) ),
introduced(definition,[new_symbols(definition,[spl0_16])],[avatar_definition]) ).
fof(f186,plain,
( sk_c10 = multiply(sk_c1,sk_c9)
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f184]) ).
fof(f191,plain,
( spl0_10
| spl0_16 ),
inference(avatar_split_clause,[],[f30,f184,f137]) ).
fof(f192,plain,
( spl0_11
| spl0_16 ),
inference(avatar_split_clause,[],[f28,f184,f142]) ).
fof(f193,plain,
( spl0_12
| spl0_16 ),
inference(avatar_split_clause,[],[f26,f184,f147]) ).
fof(f194,plain,
( spl0_13
| spl0_16 ),
inference(avatar_split_clause,[],[f24,f184,f152]) ).
fof(f195,plain,
( spl0_3
| spl0_16 ),
inference(avatar_split_clause,[],[f22,f184,f105]) ).
fof(f197,definition,
( spl0_17
<=> inverse(sk_c1) = sk_c10 ),
introduced(definition,[new_symbols(definition,[spl0_17])],[avatar_definition]) ).
fof(f199,plain,
( inverse(sk_c1) = sk_c10
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f197]) ).
fof(f204,plain,
( spl0_10
| spl0_17 ),
inference(avatar_split_clause,[],[f13,f197,f137]) ).
fof(f205,plain,
( spl0_11
| spl0_17 ),
inference(avatar_split_clause,[],[f11,f197,f142]) ).
fof(f206,plain,
( spl0_12
| spl0_17 ),
inference(avatar_split_clause,[],[f9,f197,f147]) ).
fof(f207,plain,
( spl0_13
| spl0_17 ),
inference(avatar_split_clause,[],[f7,f197,f152]) ).
fof(f208,plain,
( spl0_3
| spl0_17 ),
inference(avatar_split_clause,[],[f5,f197,f105]) ).
fof(f209,plain,
( sk_c10 != sk_c10
| sk_c10 != inverse(sk_c4)
| ~ spl0_2
| ~ spl0_12 ),
inference(superposition,[],[f103,f149]) ).
fof(f212,plain,
( sk_c10 != inverse(sk_c4)
| ~ spl0_2
| ~ spl0_12 ),
inference(trivial_inequality_removal,[],[f209]) ).
fof(f213,plain,
( $false
| ~ spl0_2
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f212,f154]) ).
fof(f214,plain,
( ~ spl0_2
| ~ spl0_12
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[],[f213]) ).
fof(f215,plain,
( sk_c10 != sk_c10
| inverse(sk_c1) != sk_c10
| ~ spl0_2
| ~ spl0_16 ),
inference(superposition,[],[f103,f186]) ).
fof(f216,plain,
( inverse(sk_c1) != sk_c10
| ~ spl0_2
| ~ spl0_16 ),
inference(trivial_inequality_removal,[],[f215]) ).
fof(f217,plain,
( $false
| ~ spl0_2
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f216,f199]) ).
fof(f218,plain,
( ~ spl0_2
| ~ spl0_16
| ~ spl0_17 ),
inference(avatar_contradiction_clause,[],[f217]) ).
fof(f219,plain,
( sk_c9 != multiply(sk_c10,sk_c3)
| sk_c10 != inverse(sk_c2)
| ~ spl0_4
| ~ spl0_14 ),
inference(superposition,[],[f110,f160]) ).
fof(f220,plain,
( sk_c10 != inverse(sk_c2)
| ~ spl0_4
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f219,f173]) ).
fof(f221,plain,
( $false
| ~ spl0_4
| ~ spl0_6
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f220,f119]) ).
fof(f222,plain,
( ~ spl0_4
| ~ spl0_6
| ~ spl0_14
| ~ spl0_15 ),
inference(avatar_contradiction_clause,[],[f221]) ).
fof(f223,plain,
( identity = multiply(sk_c10,sk_c1)
| ~ spl0_17 ),
inference(superposition,[],[f3,f199]) ).
fof(f224,plain,
( identity = multiply(sk_c10,sk_c4)
| ~ spl0_13 ),
inference(superposition,[],[f3,f154]) ).
fof(f225,plain,
( identity = multiply(sk_c8,sk_c5)
| ~ spl0_10 ),
inference(superposition,[],[f3,f139]) ).
fof(f228,plain,
( identity = multiply(sk_c10,sk_c2)
| ~ spl0_6 ),
inference(superposition,[],[f3,f119]) ).
fof(f231,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[],[f4,f3]) ).
fof(f238,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f231,f1]) ).
fof(f245,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c8,multiply(sk_c5,X0))
| ~ spl0_10 ),
inference(superposition,[],[f4,f225]) ).
fof(f246,plain,
( ! [X0] : multiply(sk_c8,multiply(sk_c5,X0)) = X0
| ~ spl0_10 ),
inference(forward_demodulation,[],[f245,f1]) ).
fof(f272,plain,
( sk_c8 = multiply(sk_c8,sk_c10)
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f246,f144]) ).
fof(f334,plain,
( sk_c1 = multiply(inverse(sk_c10),identity)
| ~ spl0_17 ),
inference(superposition,[],[f238,f223]) ).
fof(f336,plain,
( sk_c4 = multiply(inverse(sk_c10),identity)
| ~ spl0_13 ),
inference(superposition,[],[f238,f224]) ).
fof(f337,plain,
( sk_c3 = multiply(inverse(sk_c10),sk_c9)
| ~ spl0_15 ),
inference(superposition,[],[f238,f173]) ).
fof(f338,plain,
( sk_c2 = multiply(inverse(sk_c10),identity)
| ~ spl0_6 ),
inference(superposition,[],[f238,f228]) ).
fof(f343,plain,
( sk_c10 = multiply(inverse(sk_c8),sk_c8)
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f238,f272]) ).
fof(f351,plain,
( sk_c10 = multiply(inverse(sk_c2),sk_c3)
| ~ spl0_14 ),
inference(superposition,[],[f238,f160]) ).
fof(f356,plain,
( sk_c10 = multiply(sk_c10,sk_c3)
| ~ spl0_6
| ~ spl0_14 ),
inference(forward_demodulation,[],[f351,f119]) ).
fof(f362,plain,
( identity = sk_c10
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f343,f3]) ).
fof(f445,plain,
( sk_c4 = multiply(inverse(identity),identity)
| ~ spl0_10
| ~ spl0_11
| ~ spl0_13 ),
inference(forward_demodulation,[],[f336,f362]) ).
fof(f446,plain,
( identity = sk_c4
| ~ spl0_10
| ~ spl0_11
| ~ spl0_13 ),
inference(forward_demodulation,[],[f445,f3]) ).
fof(f458,plain,
( sk_c10 = sk_c9
| ~ spl0_6
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f356,f173]) ).
fof(f470,plain,
( sk_c10 = multiply(sk_c1,sk_c10)
| ~ spl0_6
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(superposition,[],[f186,f458]) ).
fof(f473,plain,
( sk_c1 = sk_c4
| ~ spl0_13
| ~ spl0_17 ),
inference(forward_demodulation,[],[f336,f334]) ).
fof(f476,plain,
( sk_c10 != multiply(sk_c1,sk_c9)
| spl0_12
| ~ spl0_13
| ~ spl0_17 ),
inference(superposition,[],[f148,f473]) ).
fof(f478,plain,
( $false
| spl0_12
| ~ spl0_13
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f476,f186]) ).
fof(f479,plain,
( spl0_12
| ~ spl0_13
| ~ spl0_16
| ~ spl0_17 ),
inference(avatar_contradiction_clause,[],[f478]) ).
fof(f480,plain,
( sk_c3 = multiply(inverse(sk_c10),sk_c10)
| ~ spl0_6
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f337,f458]) ).
fof(f481,plain,
( identity = sk_c3
| ~ spl0_6
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f480,f3]) ).
fof(f487,plain,
( sk_c1 = sk_c2
| ~ spl0_6
| ~ spl0_17 ),
inference(forward_demodulation,[],[f338,f334]) ).
fof(f490,plain,
( sk_c3 = multiply(sk_c1,sk_c10)
| ~ spl0_6
| ~ spl0_14
| ~ spl0_17 ),
inference(superposition,[],[f160,f487]) ).
fof(f492,plain,
( identity = multiply(sk_c1,sk_c10)
| ~ spl0_6
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17 ),
inference(forward_demodulation,[],[f490,f481]) ).
fof(f534,plain,
( identity = sk_c10
| ~ spl0_6
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f470,f492]) ).
fof(f538,plain,
( sk_c9 != inverse(identity)
| spl0_3
| ~ spl0_6
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(superposition,[],[f107,f534]) ).
fof(f547,plain,
( sk_c1 = multiply(inverse(identity),identity)
| ~ spl0_6
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(superposition,[],[f334,f534]) ).
fof(f554,plain,
( identity = sk_c1
| ~ spl0_6
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f547,f3]) ).
fof(f563,plain,
( sk_c10 != inverse(identity)
| spl0_3
| ~ spl0_6
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f538,f458]) ).
fof(f568,plain,
( identity != inverse(identity)
| spl0_3
| ~ spl0_6
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f563,f534]) ).
fof(f574,plain,
( sk_c10 = inverse(identity)
| ~ spl0_6
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(superposition,[],[f199,f554]) ).
fof(f583,plain,
( identity = inverse(identity)
| ~ spl0_6
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f574,f534]) ).
fof(f684,plain,
( $false
| spl0_3
| ~ spl0_6
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f583,f568]) ).
fof(f685,plain,
( spl0_3
| ~ spl0_6
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(avatar_contradiction_clause,[],[f684]) ).
fof(f686,plain,
( ! [X6,X4] :
( identity != multiply(X4,inverse(X4))
| inverse(X6) != multiply(X6,inverse(X4))
| inverse(X4) != inverse(inverse(X6))
| sk_c10 != multiply(inverse(X4),sk_c9) )
| ~ spl0_1
| ~ spl0_6
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f100,f534]) ).
fof(f687,plain,
( sk_c10 = inverse(sk_c10)
| ~ spl0_3
| ~ spl0_6
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f106,f458]) ).
fof(f688,plain,
( ! [X6,X4] :
( sk_c10 != multiply(inverse(X4),sk_c10)
| identity != multiply(X4,inverse(X4))
| inverse(X6) != multiply(X6,inverse(X4))
| inverse(X4) != inverse(inverse(X6)) )
| ~ spl0_1
| ~ spl0_6
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f686,f458]) ).
fof(f689,plain,
( identity = inverse(identity)
| ~ spl0_3
| ~ spl0_6
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f687,f534]) ).
fof(f690,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_6
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f688,f534]) ).
fof(f694,plain,
( ! [X0] :
( inverse(X0) != multiply(X0,identity)
| identity != multiply(identity,identity)
| identity != multiply(identity,identity)
| identity != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_3
| ~ spl0_6
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(superposition,[],[f690,f689]) ).
fof(f701,plain,
( ! [X0] :
( inverse(X0) != multiply(X0,identity)
| identity != multiply(identity,identity)
| identity != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_3
| ~ spl0_6
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(duplicate_literal_removal,[],[f694]) ).
fof(f717,plain,
( ! [X0] :
( inverse(X0) != multiply(X0,identity)
| identity != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_3
| ~ spl0_6
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f701,f1]) ).
fof(f733,plain,
( sk_c1 != inverse(inverse(sk_c10))
| identity != inverse(inverse(inverse(sk_c10)))
| ~ spl0_1
| ~ spl0_3
| ~ spl0_6
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(superposition,[],[f717,f334]) ).
fof(f756,plain,
( sk_c1 != inverse(inverse(identity))
| identity != inverse(inverse(inverse(sk_c10)))
| ~ spl0_1
| ~ spl0_3
| ~ spl0_6
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f733,f534]) ).
fof(f760,plain,
( sk_c1 != inverse(identity)
| identity != inverse(inverse(inverse(sk_c10)))
| ~ spl0_1
| ~ spl0_3
| ~ spl0_6
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f756,f689]) ).
fof(f764,plain,
( identity != sk_c1
| identity != inverse(inverse(inverse(sk_c10)))
| ~ spl0_1
| ~ spl0_3
| ~ spl0_6
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f760,f689]) ).
fof(f769,plain,
( identity != inverse(inverse(inverse(sk_c10)))
| ~ spl0_1
| ~ spl0_3
| ~ spl0_6
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f764,f554]) ).
fof(f773,plain,
( identity != inverse(inverse(inverse(identity)))
| ~ spl0_1
| ~ spl0_3
| ~ spl0_6
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f769,f534]) ).
fof(f776,plain,
( identity != inverse(inverse(identity))
| ~ spl0_1
| ~ spl0_3
| ~ spl0_6
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f773,f689]) ).
fof(f777,plain,
( identity != inverse(identity)
| ~ spl0_1
| ~ spl0_3
| ~ spl0_6
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f776,f689]) ).
fof(f778,plain,
( $false
| ~ spl0_1
| ~ spl0_3
| ~ spl0_6
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f777,f689]) ).
fof(f779,plain,
( ~ spl0_1
| ~ spl0_3
| ~ spl0_6
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(avatar_contradiction_clause,[],[f778]) ).
fof(f805,plain,
( sk_c10 != sk_c9
| ~ spl0_6
| ~ spl0_14
| spl0_15 ),
inference(forward_demodulation,[],[f172,f356]) ).
fof(f826,plain,
( sk_c10 = inverse(identity)
| ~ spl0_10
| ~ spl0_11
| ~ spl0_13 ),
inference(forward_demodulation,[],[f154,f446]) ).
fof(f832,plain,
( sk_c10 = multiply(identity,sk_c9)
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f149,f446]) ).
fof(f833,plain,
( sk_c10 = sk_c9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f832,f1]) ).
fof(f834,plain,
( $false
| ~ spl0_6
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| spl0_15 ),
inference(forward_subsumption_resolution,[],[f833,f805]) ).
fof(f835,plain,
( ~ spl0_6
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| spl0_15 ),
inference(avatar_contradiction_clause,[],[f834]) ).
fof(f858,plain,
( ! [X6,X4] :
( identity != multiply(X4,inverse(X4))
| inverse(X6) != multiply(X6,inverse(X4))
| inverse(X4) != inverse(inverse(X6))
| sk_c10 != multiply(inverse(X4),sk_c9) )
| ~ spl0_1
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f100,f362]) ).
fof(f859,plain,
( ! [X6,X4] :
( sk_c10 != multiply(inverse(X4),sk_c10)
| identity != multiply(X4,inverse(X4))
| inverse(X6) != multiply(X6,inverse(X4))
| inverse(X4) != inverse(inverse(X6)) )
| ~ spl0_1
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f858,f833]) ).
fof(f860,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_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f859,f362]) ).
fof(f861,plain,
( ! [X0] :
( inverse(X0) != multiply(X0,sk_c10)
| identity != multiply(identity,sk_c10)
| identity != multiply(sk_c10,identity)
| sk_c10 != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f860,f826]) ).
fof(f886,plain,
( ! [X0] :
( inverse(X0) != multiply(X0,identity)
| identity != multiply(identity,sk_c10)
| identity != multiply(sk_c10,identity)
| sk_c10 != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f861,f362]) ).
fof(f891,plain,
( ! [X0] :
( identity != sk_c10
| inverse(X0) != multiply(X0,identity)
| identity != multiply(sk_c10,identity)
| sk_c10 != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f886,f1]) ).
fof(f896,plain,
( ! [X0] :
( inverse(X0) != multiply(X0,identity)
| identity != multiply(sk_c10,identity)
| sk_c10 != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f891,f362]) ).
fof(f900,plain,
( ! [X0] :
( identity != multiply(identity,identity)
| inverse(X0) != multiply(X0,identity)
| sk_c10 != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f896,f362]) ).
fof(f904,plain,
( ! [X0] :
( inverse(X0) != multiply(X0,identity)
| sk_c10 != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f900,f1]) ).
fof(f909,plain,
( ! [X0] :
( inverse(X0) != multiply(X0,identity)
| identity != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f904,f362]) ).
fof(f1047,plain,
( identity != inverse(inverse(identity))
| identity != inverse(inverse(inverse(identity)))
| ~ spl0_1
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f909,f3]) ).
fof(f1058,plain,
( identity != inverse(sk_c10)
| identity != inverse(inverse(inverse(identity)))
| ~ spl0_1
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f1047,f826]) ).
fof(f1065,plain,
( identity != sk_c9
| identity != inverse(inverse(inverse(identity)))
| ~ spl0_1
| ~ spl0_3
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f1058,f106]) ).
fof(f1072,plain,
( identity != sk_c10
| identity != inverse(inverse(inverse(identity)))
| ~ spl0_1
| ~ spl0_3
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f1065,f833]) ).
fof(f1079,plain,
( identity != inverse(inverse(inverse(identity)))
| ~ spl0_1
| ~ spl0_3
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f1072,f362]) ).
fof(f1087,plain,
( identity != inverse(inverse(sk_c10))
| ~ spl0_1
| ~ spl0_3
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f1079,f826]) ).
fof(f1095,plain,
( identity != inverse(sk_c9)
| ~ spl0_1
| ~ spl0_3
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f1087,f106]) ).
fof(f1100,plain,
( identity != inverse(sk_c10)
| ~ spl0_1
| ~ spl0_3
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f1095,f833]) ).
fof(f1103,plain,
( identity != sk_c9
| ~ spl0_1
| ~ spl0_3
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f1100,f106]) ).
fof(f1106,plain,
( identity != sk_c10
| ~ spl0_1
| ~ spl0_3
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f1103,f833]) ).
fof(f1109,plain,
( $false
| ~ spl0_1
| ~ spl0_3
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f1106,f362]) ).
fof(f1110,plain,
( ~ spl0_1
| ~ spl0_3
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[],[f1109]) ).
fof(f1117,plain,
( ! [X2] :
( sk_c9 != multiply(identity,multiply(X2,identity))
| sk_c10 != inverse(X2) )
| ~ spl0_4
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f110,f362]) ).
fof(f1118,plain,
( ! [X2] :
( sk_c9 != multiply(X2,identity)
| sk_c10 != inverse(X2) )
| ~ spl0_4
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f1117,f1]) ).
fof(f1119,plain,
( ! [X2] :
( sk_c10 != multiply(X2,identity)
| sk_c10 != inverse(X2) )
| ~ spl0_4
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f1118,f833]) ).
fof(f1120,plain,
( ! [X2] :
( identity != multiply(X2,identity)
| sk_c10 != inverse(X2) )
| ~ spl0_4
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f1119,f362]) ).
fof(f1121,plain,
( ! [X2] :
( identity != multiply(X2,identity)
| identity != inverse(X2) )
| ~ spl0_4
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f1120,f362]) ).
fof(f1124,plain,
( identity != identity
| identity != inverse(inverse(identity))
| ~ spl0_4
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f1121,f3]) ).
fof(f1132,plain,
( identity != inverse(inverse(identity))
| ~ spl0_4
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(trivial_inequality_removal,[],[f1124]) ).
fof(f1139,plain,
( identity != inverse(sk_c10)
| ~ spl0_4
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f1132,f826]) ).
fof(f1149,plain,
( identity != sk_c9
| ~ spl0_3
| ~ spl0_4
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f1139,f106]) ).
fof(f1154,plain,
( identity != sk_c10
| ~ spl0_3
| ~ spl0_4
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f1149,f833]) ).
fof(f1158,plain,
( $false
| ~ spl0_3
| ~ spl0_4
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f1154,f362]) ).
fof(f1159,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[],[f1158]) ).
cnf(s1,plain,
( spl0_2
| spl0_1
| spl0_2
| ~ spl0_3
| spl0_4 ),
inference(sat_conversion,[],[f111]) ).
cnf(s2,plain,
( spl0_1
| spl0_2
| ~ spl0_3
| spl0_4 ),
inference(rat,[],[s1]) ).
cnf(s7,plain,
( spl0_6
| spl0_10 ),
inference(sat_conversion,[],[f140]) ).
cnf(s8,plain,
( spl0_6
| spl0_11 ),
inference(sat_conversion,[],[f145]) ).
cnf(s9,plain,
( spl0_6
| spl0_12 ),
inference(sat_conversion,[],[f150]) ).
cnf(s10,plain,
( spl0_6
| spl0_13 ),
inference(sat_conversion,[],[f155]) ).
cnf(s11,plain,
( spl0_3
| spl0_6 ),
inference(sat_conversion,[],[f156]) ).
cnf(s16,plain,
( spl0_10
| spl0_14 ),
inference(sat_conversion,[],[f165]) ).
cnf(s17,plain,
( spl0_11
| spl0_14 ),
inference(sat_conversion,[],[f166]) ).
cnf(s18,plain,
( spl0_12
| spl0_14 ),
inference(sat_conversion,[],[f167]) ).
cnf(s19,plain,
( spl0_13
| spl0_14 ),
inference(sat_conversion,[],[f168]) ).
cnf(s20,plain,
( spl0_3
| spl0_14 ),
inference(sat_conversion,[],[f169]) ).
cnf(s25,plain,
( spl0_10
| spl0_15 ),
inference(sat_conversion,[],[f178]) ).
cnf(s26,plain,
( spl0_11
| spl0_15 ),
inference(sat_conversion,[],[f179]) ).
cnf(s27,plain,
( spl0_12
| spl0_15 ),
inference(sat_conversion,[],[f180]) ).
cnf(s28,plain,
( spl0_13
| spl0_15 ),
inference(sat_conversion,[],[f181]) ).
cnf(s29,plain,
( spl0_3
| spl0_15 ),
inference(sat_conversion,[],[f182]) ).
cnf(s34,plain,
( spl0_10
| spl0_16 ),
inference(sat_conversion,[],[f191]) ).
cnf(s35,plain,
( spl0_11
| spl0_16 ),
inference(sat_conversion,[],[f192]) ).
cnf(s36,plain,
( spl0_12
| spl0_16 ),
inference(sat_conversion,[],[f193]) ).
cnf(s37,plain,
( spl0_13
| spl0_16 ),
inference(sat_conversion,[],[f194]) ).
cnf(s38,plain,
( spl0_3
| spl0_16 ),
inference(sat_conversion,[],[f195]) ).
cnf(s43,plain,
( spl0_10
| spl0_17 ),
inference(sat_conversion,[],[f204]) ).
cnf(s44,plain,
( spl0_11
| spl0_17 ),
inference(sat_conversion,[],[f205]) ).
cnf(s45,plain,
( spl0_12
| spl0_17 ),
inference(sat_conversion,[],[f206]) ).
cnf(s46,plain,
( spl0_13
| spl0_17 ),
inference(sat_conversion,[],[f207]) ).
cnf(s47,plain,
( spl0_3
| spl0_17 ),
inference(sat_conversion,[],[f208]) ).
cnf(s48,plain,
( ~ spl0_2
| ~ spl0_12
| ~ spl0_13 ),
inference(sat_conversion,[],[f214]) ).
cnf(s49,plain,
( ~ spl0_2
| ~ spl0_16
| ~ spl0_17 ),
inference(sat_conversion,[],[f218]) ).
cnf(s50,plain,
( ~ spl0_4
| ~ spl0_6
| ~ spl0_14
| ~ spl0_15 ),
inference(sat_conversion,[],[f222]) ).
cnf(s52,plain,
( spl0_12
| ~ spl0_13
| ~ spl0_16
| ~ spl0_17 ),
inference(sat_conversion,[],[f479]) ).
cnf(s54,plain,
( spl0_3
| ~ spl0_6
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(sat_conversion,[],[f685]) ).
cnf(s61,plain,
( ~ spl0_1
| ~ spl0_3
| ~ spl0_6
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(sat_conversion,[],[f779]) ).
cnf(s63,plain,
( ~ spl0_6
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| spl0_15 ),
inference(sat_conversion,[],[f835]) ).
cnf(s78,plain,
( ~ spl0_1
| ~ spl0_3
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(sat_conversion,[],[f1110]) ).
cnf(s86,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(sat_conversion,[],[f1159]) ).
cnf(s88,plain,
spl0_3,
inference(rat,[],[s54,s11,s20,s29,s38,s47]) ).
cnf(s90,plain,
( ~ spl0_14
| ~ spl0_6
| ~ spl0_4 ),
inference(rat,[],[s63,s25,s26,s27,s28,s50]) ).
cnf(s91,plain,
( spl0_14
| ~ spl0_4 ),
inference(rat,[],[s86,s16,s17,s18,s19,s88]) ).
cnf(s92,plain,
( ~ spl0_14
| ~ spl0_4 ),
inference(rat,[],[s86,s7,s8,s9,s10,s90,s88]) ).
cnf(s93,plain,
~ spl0_4,
inference(rat,[],[s92,s91]) ).
cnf(s94,plain,
( spl0_13
| ~ spl0_2 ),
inference(rat,[],[s49,s37,s46]) ).
cnf(s95,plain,
( ~ spl0_13
| ~ spl0_2 ),
inference(rat,[],[s49,s36,s45,s48]) ).
cnf(s96,plain,
~ spl0_2,
inference(rat,[],[s95,s94]) ).
cnf(s97,plain,
spl0_1,
inference(rat,[],[s2,s88,s93,s96]) ).
cnf(s98,plain,
spl0_13,
inference(rat,[],[s61,s10,s19,s28,s37,s46,s88,s97]) ).
cnf(s99,plain,
( spl0_11
| ~ spl0_14
| ~ spl0_6 ),
inference(rat,[],[s61,s26,s35,s44,s88,s97]) ).
cnf(s100,plain,
( ~ spl0_14
| ~ spl0_6
| ~ spl0_12 ),
inference(rat,[],[s61,s25,s34,s43,s78,s99,s88,s97,s98]) ).
cnf(s101,plain,
( spl0_14
| ~ spl0_12 ),
inference(rat,[],[s78,s16,s17,s98,s88,s97]) ).
cnf(s102,plain,
( ~ spl0_14
| ~ spl0_12 ),
inference(rat,[],[s78,s7,s8,s100,s97,s88,s98]) ).
cnf(s103,plain,
~ spl0_12,
inference(rat,[],[s102,s101]) ).
cnf(s104,plain,
spl0_17,
inference(rat,[],[s45,s103]) ).
cnf(s105,plain,
spl0_16,
inference(rat,[],[s36,s103]) ).
cnf(s109,plain,
$false,
inference(rat,[],[s52,s103,s98,s104,s105]) ).
fof(f1163,plain,
$false,
inference(avatar_sat_refutation,[],[s109]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP228-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.38 % Computer : n007.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sun Sep 27 09:36:25 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.41 Running first-order model finding
% 0.11/0.41 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
% 0.11/0.46 % (1161523)Will run a generic schedule for satisfiability detection.
% 0.11/0.46 % (1161531)dis+10_1_sil=32000:sp=arity:random_seed=3487579410:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.11/0.46 % (1161529)% WARNING: option uhcvi not known.
% 0.11/0.46 % (1161529)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3513491175:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.11/0.46 % (1161530)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=265017642:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.11/0.46 % (1161528)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2530556690_2999 on theBenchmark for (2999ds/0Mi)
% 0.11/0.46 % (1161532)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3837416113:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.11/0.46 % (1161531) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1161523-1161531"...
% 0.11/0.46 % TRYING [1]
% 0.11/0.46 % TRYING [2]
% 0.11/0.46 % TRYING [3]
% 0.11/0.46 % (1161531)...printing done.
% 0.11/0.46 % (1161531)Refutation found. Thanks to Tanya!
% 0.11/0.47 % SZS status Unsatisfiable for theBenchmark
% 0.11/0.47 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/0.47 % (1161531)------------------------------
% 0.17/0.47 % (1161531)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.17/0.47 % (1161531)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/0.47 % (1161531)CaDiCaL version: 2.1.3
% 0.17/0.47 % (1161531)Termination reason: Refutation
% 0.17/0.47 % (1161531)Time elapsed: 0.013 s
% 0.17/0.47 % (1161531)Peak memory usage: 12 MB
% 0.17/0.47 % (1161531)Instructions burned: 38 (million)
% 0.17/0.47 % (1161523)Success in time 0.042 s
% 0.17/0.47 % Vampire exiting
%------------------------------------------------------------------------------