%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GRP313-1 : 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 : n026.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 10:17:27 AM UTC 2026
% Result : Unsatisfiable 0.17s 0.47s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 60
% Syntax : Number of formulae : 397 ( 26 unt; 22 def)
% Number of atoms : 1278 ( 370 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 1651 ( 770 ~; 859 |; 0 &)
% ( 22 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 24 ( 22 usr; 23 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 10 con; 0-2 aty)
% Number of variables : 57 ( 0 sgn 57 !; 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_c8,sk_c9) = sk_c7
| multiply(sk_c4,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,plain,
( multiply(sk_c8,sk_c9) = sk_c7
| sk_c8 = multiply(sk_c4,sk_c9) ),
inference(reorient_equations,[],[f5]) ).
fof(f7,negated_conjecture,
( multiply(sk_c8,sk_c9) = sk_c7
| inverse(sk_c4) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_2) ).
fof(f8,plain,
( multiply(sk_c8,sk_c9) = sk_c7
| sk_c9 = inverse(sk_c4) ),
inference(reorient_equations,[],[f7]) ).
fof(f9,negated_conjecture,
( multiply(sk_c8,sk_c9) = sk_c7
| multiply(sk_c5,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_3) ).
fof(f10,plain,
( multiply(sk_c8,sk_c9) = sk_c7
| sk_c7 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f9]) ).
fof(f11,negated_conjecture,
( multiply(sk_c8,sk_c9) = sk_c7
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_4) ).
fof(f12,plain,
( multiply(sk_c8,sk_c9) = sk_c7
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f11]) ).
fof(f15,negated_conjecture,
( multiply(sk_c8,sk_c9) = sk_c7
| multiply(sk_c6,sk_c7) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_6) ).
fof(f16,plain,
( multiply(sk_c8,sk_c9) = sk_c7
| sk_c9 = multiply(sk_c6,sk_c7) ),
inference(reorient_equations,[],[f15]) ).
fof(f17,negated_conjecture,
( multiply(sk_c8,sk_c9) = sk_c7
| inverse(sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_7) ).
fof(f18,plain,
( multiply(sk_c8,sk_c9) = sk_c7
| sk_c7 = inverse(sk_c6) ),
inference(reorient_equations,[],[f17]) ).
fof(f19,negated_conjecture,
( multiply(sk_c1,sk_c9) = sk_c8
| multiply(sk_c4,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_8) ).
fof(f20,plain,
( sk_c8 = multiply(sk_c1,sk_c9)
| sk_c8 = multiply(sk_c4,sk_c9) ),
inference(reorient_equations,[],[f19]) ).
fof(f21,negated_conjecture,
( multiply(sk_c1,sk_c9) = sk_c8
| inverse(sk_c4) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_9) ).
fof(f22,plain,
( sk_c8 = multiply(sk_c1,sk_c9)
| sk_c9 = inverse(sk_c4) ),
inference(reorient_equations,[],[f21]) ).
fof(f27,negated_conjecture,
( multiply(sk_c1,sk_c9) = sk_c8
| multiply(sk_c7,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_12) ).
fof(f28,plain,
( sk_c8 = multiply(sk_c1,sk_c9)
| sk_c8 = multiply(sk_c7,sk_c9) ),
inference(reorient_equations,[],[f27]) ).
fof(f33,negated_conjecture,
( inverse(sk_c1) = sk_c9
| multiply(sk_c4,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_15) ).
fof(f34,plain,
( sk_c9 = inverse(sk_c1)
| sk_c8 = multiply(sk_c4,sk_c9) ),
inference(reorient_equations,[],[f33]) ).
fof(f35,negated_conjecture,
( inverse(sk_c1) = sk_c9
| inverse(sk_c4) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_16) ).
fof(f36,plain,
( sk_c9 = inverse(sk_c1)
| sk_c9 = inverse(sk_c4) ),
inference(reorient_equations,[],[f35]) ).
fof(f41,negated_conjecture,
( inverse(sk_c1) = sk_c9
| multiply(sk_c7,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_19) ).
fof(f42,plain,
( sk_c9 = inverse(sk_c1)
| sk_c8 = multiply(sk_c7,sk_c9) ),
inference(reorient_equations,[],[f41]) ).
fof(f49,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c7
| inverse(sk_c4) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_23) ).
fof(f50,plain,
( sk_c7 = multiply(sk_c2,sk_c8)
| sk_c9 = inverse(sk_c4) ),
inference(reorient_equations,[],[f49]) ).
fof(f55,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c7
| multiply(sk_c7,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_26) ).
fof(f56,plain,
( sk_c7 = multiply(sk_c2,sk_c8)
| sk_c8 = multiply(sk_c7,sk_c9) ),
inference(reorient_equations,[],[f55]) ).
fof(f57,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c7
| multiply(sk_c6,sk_c7) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_27) ).
fof(f58,plain,
( sk_c7 = multiply(sk_c2,sk_c8)
| sk_c9 = multiply(sk_c6,sk_c7) ),
inference(reorient_equations,[],[f57]) ).
fof(f59,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c7
| inverse(sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_28) ).
fof(f60,plain,
( sk_c7 = multiply(sk_c2,sk_c8)
| sk_c7 = inverse(sk_c6) ),
inference(reorient_equations,[],[f59]) ).
fof(f63,negated_conjecture,
( inverse(sk_c2) = sk_c8
| inverse(sk_c4) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_30) ).
fof(f64,plain,
( sk_c8 = inverse(sk_c2)
| sk_c9 = inverse(sk_c4) ),
inference(reorient_equations,[],[f63]) ).
fof(f69,negated_conjecture,
( inverse(sk_c2) = sk_c8
| multiply(sk_c7,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_33) ).
fof(f70,plain,
( sk_c8 = inverse(sk_c2)
| sk_c8 = multiply(sk_c7,sk_c9) ),
inference(reorient_equations,[],[f69]) ).
fof(f71,negated_conjecture,
( inverse(sk_c2) = sk_c8
| multiply(sk_c6,sk_c7) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_34) ).
fof(f72,plain,
( sk_c8 = inverse(sk_c2)
| sk_c9 = multiply(sk_c6,sk_c7) ),
inference(reorient_equations,[],[f71]) ).
fof(f73,negated_conjecture,
( inverse(sk_c2) = sk_c8
| inverse(sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_35) ).
fof(f74,plain,
( sk_c8 = inverse(sk_c2)
| sk_c7 = inverse(sk_c6) ),
inference(reorient_equations,[],[f73]) ).
fof(f75,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c9
| multiply(sk_c4,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_36) ).
fof(f76,plain,
( sk_c9 = multiply(sk_c3,sk_c8)
| sk_c8 = multiply(sk_c4,sk_c9) ),
inference(reorient_equations,[],[f75]) ).
fof(f77,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c9
| inverse(sk_c4) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_37) ).
fof(f78,plain,
( sk_c9 = multiply(sk_c3,sk_c8)
| sk_c9 = inverse(sk_c4) ),
inference(reorient_equations,[],[f77]) ).
fof(f79,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c9
| multiply(sk_c5,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_38) ).
fof(f80,plain,
( sk_c9 = multiply(sk_c3,sk_c8)
| sk_c7 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f79]) ).
fof(f81,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c9
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_39) ).
fof(f82,plain,
( sk_c9 = multiply(sk_c3,sk_c8)
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f81]) ).
fof(f83,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c9
| multiply(sk_c7,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_40) ).
fof(f84,plain,
( sk_c9 = multiply(sk_c3,sk_c8)
| sk_c8 = multiply(sk_c7,sk_c9) ),
inference(reorient_equations,[],[f83]) ).
fof(f85,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c9
| multiply(sk_c6,sk_c7) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_41) ).
fof(f86,plain,
( sk_c9 = multiply(sk_c3,sk_c8)
| sk_c9 = multiply(sk_c6,sk_c7) ),
inference(reorient_equations,[],[f85]) ).
fof(f87,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c9
| inverse(sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_42) ).
fof(f88,plain,
( sk_c9 = multiply(sk_c3,sk_c8)
| sk_c7 = inverse(sk_c6) ),
inference(reorient_equations,[],[f87]) ).
fof(f89,negated_conjecture,
( inverse(sk_c3) = sk_c8
| multiply(sk_c4,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_43) ).
fof(f90,plain,
( sk_c8 = inverse(sk_c3)
| sk_c8 = multiply(sk_c4,sk_c9) ),
inference(reorient_equations,[],[f89]) ).
fof(f91,negated_conjecture,
( inverse(sk_c3) = sk_c8
| inverse(sk_c4) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_44) ).
fof(f92,plain,
( sk_c8 = inverse(sk_c3)
| sk_c9 = inverse(sk_c4) ),
inference(reorient_equations,[],[f91]) ).
fof(f93,negated_conjecture,
( inverse(sk_c3) = sk_c8
| multiply(sk_c5,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_45) ).
fof(f94,plain,
( sk_c8 = inverse(sk_c3)
| sk_c7 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f93]) ).
fof(f95,negated_conjecture,
( inverse(sk_c3) = sk_c8
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_46) ).
fof(f96,plain,
( sk_c8 = inverse(sk_c3)
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f95]) ).
fof(f97,negated_conjecture,
( inverse(sk_c3) = sk_c8
| multiply(sk_c7,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_47) ).
fof(f98,plain,
( sk_c8 = inverse(sk_c3)
| sk_c8 = multiply(sk_c7,sk_c9) ),
inference(reorient_equations,[],[f97]) ).
fof(f99,negated_conjecture,
( inverse(sk_c3) = sk_c8
| multiply(sk_c6,sk_c7) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_48) ).
fof(f100,plain,
( sk_c8 = inverse(sk_c3)
| sk_c9 = multiply(sk_c6,sk_c7) ),
inference(reorient_equations,[],[f99]) ).
fof(f101,negated_conjecture,
( inverse(sk_c3) = sk_c8
| inverse(sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_49) ).
fof(f102,plain,
( sk_c8 = inverse(sk_c3)
| sk_c7 = inverse(sk_c6) ),
inference(reorient_equations,[],[f101]) ).
fof(f103,negated_conjecture,
! [X2,X3,X0,X1,X4,X5] :
( multiply(sk_c8,sk_c9) != sk_c7
| multiply(X0,sk_c9) != sk_c8
| inverse(X0) != sk_c9
| multiply(X1,sk_c8) != sk_c7
| inverse(X1) != sk_c8
| multiply(X2,sk_c8) != sk_c9
| inverse(X2) != sk_c8
| multiply(X3,sk_c9) != sk_c8
| inverse(X3) != sk_c9
| multiply(X4,sk_c8) != sk_c7
| inverse(X4) != sk_c8
| multiply(sk_c7,sk_c9) != sk_c8
| multiply(X5,sk_c7) != sk_c9
| inverse(X5) != sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_50) ).
fof(f104,plain,
! [X2,X3,X0,X1,X4,X5] :
( multiply(sk_c8,sk_c9) != sk_c7
| sk_c8 != multiply(X0,sk_c9)
| inverse(X0) != sk_c9
| sk_c7 != multiply(X1,sk_c8)
| sk_c8 != inverse(X1)
| sk_c9 != multiply(X2,sk_c8)
| sk_c8 != inverse(X2)
| sk_c8 != multiply(X3,sk_c9)
| sk_c9 != inverse(X3)
| sk_c7 != multiply(X4,sk_c8)
| sk_c8 != inverse(X4)
| sk_c8 != multiply(sk_c7,sk_c9)
| sk_c9 != multiply(X5,sk_c7)
| sk_c7 != inverse(X5) ),
inference(reorient_equations,[],[f103]) ).
fof(f106,definition,
( spl0_1
<=> ! [X5] :
( sk_c9 != multiply(X5,sk_c7)
| sk_c7 != inverse(X5) ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f107,plain,
( ! [X5] :
( sk_c9 != multiply(X5,sk_c7)
| sk_c7 != inverse(X5) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f106]) ).
fof(f109,definition,
( spl0_2
<=> sk_c8 = multiply(sk_c7,sk_c9) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f110,plain,
( sk_c8 = multiply(sk_c7,sk_c9)
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f109]) ).
fof(f111,plain,
( sk_c8 != multiply(sk_c7,sk_c9)
| spl0_2 ),
inference(avatar_component_clause,[],[f109]) ).
fof(f113,definition,
( spl0_3
<=> ! [X4] :
( sk_c7 != multiply(X4,sk_c8)
| sk_c8 != inverse(X4) ) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f114,plain,
( ! [X4] :
( sk_c7 != multiply(X4,sk_c8)
| sk_c8 != inverse(X4) )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f113]) ).
fof(f116,definition,
( spl0_4
<=> ! [X3] :
( sk_c8 != multiply(X3,sk_c9)
| sk_c9 != inverse(X3) ) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f117,plain,
( ! [X3] :
( sk_c8 != multiply(X3,sk_c9)
| sk_c9 != inverse(X3) )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f116]) ).
fof(f119,definition,
( spl0_5
<=> ! [X2] :
( sk_c9 != multiply(X2,sk_c8)
| sk_c8 != inverse(X2) ) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f120,plain,
( ! [X2] :
( sk_c9 != multiply(X2,sk_c8)
| sk_c8 != inverse(X2) )
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f119]) ).
fof(f122,definition,
( spl0_6
<=> multiply(sk_c8,sk_c9) = sk_c7 ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f123,plain,
( multiply(sk_c8,sk_c9) = sk_c7
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f122]) ).
fof(f124,plain,
( multiply(sk_c8,sk_c9) != sk_c7
| spl0_6 ),
inference(avatar_component_clause,[],[f122]) ).
fof(f125,plain,
( spl0_1
| ~ spl0_2
| spl0_3
| spl0_4
| spl0_5
| spl0_3
| spl0_4
| ~ spl0_6 ),
inference(avatar_split_clause,[],[f104,f122,f116,f113,f119,f116,f113,f109,f106]) ).
fof(f127,definition,
( spl0_7
<=> sk_c7 = inverse(sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f129,plain,
( sk_c7 = inverse(sk_c6)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f127]) ).
fof(f131,definition,
( spl0_8
<=> sk_c8 = inverse(sk_c3) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f133,plain,
( sk_c8 = inverse(sk_c3)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f131]) ).
fof(f134,plain,
( spl0_7
| spl0_8 ),
inference(avatar_split_clause,[],[f102,f131,f127]) ).
fof(f136,definition,
( spl0_9
<=> sk_c9 = multiply(sk_c6,sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f137,plain,
( sk_c9 != multiply(sk_c6,sk_c7)
| spl0_9 ),
inference(avatar_component_clause,[],[f136]) ).
fof(f138,plain,
( sk_c9 = multiply(sk_c6,sk_c7)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f136]) ).
fof(f139,plain,
( spl0_9
| spl0_8 ),
inference(avatar_split_clause,[],[f100,f131,f136]) ).
fof(f140,plain,
( spl0_2
| spl0_8 ),
inference(avatar_split_clause,[],[f98,f131,f109]) ).
fof(f142,definition,
( spl0_10
<=> sk_c8 = inverse(sk_c5) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f144,plain,
( sk_c8 = inverse(sk_c5)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f142]) ).
fof(f145,plain,
( spl0_10
| spl0_8 ),
inference(avatar_split_clause,[],[f96,f131,f142]) ).
fof(f147,definition,
( spl0_11
<=> sk_c7 = multiply(sk_c5,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f149,plain,
( sk_c7 = multiply(sk_c5,sk_c8)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f147]) ).
fof(f150,plain,
( spl0_11
| spl0_8 ),
inference(avatar_split_clause,[],[f94,f131,f147]) ).
fof(f152,definition,
( spl0_12
<=> sk_c9 = inverse(sk_c4) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f154,plain,
( sk_c9 = inverse(sk_c4)
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f152]) ).
fof(f155,plain,
( spl0_12
| spl0_8 ),
inference(avatar_split_clause,[],[f92,f131,f152]) ).
fof(f157,definition,
( spl0_13
<=> sk_c8 = multiply(sk_c4,sk_c9) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f158,plain,
( sk_c8 != multiply(sk_c4,sk_c9)
| spl0_13 ),
inference(avatar_component_clause,[],[f157]) ).
fof(f159,plain,
( sk_c8 = multiply(sk_c4,sk_c9)
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f157]) ).
fof(f160,plain,
( spl0_13
| spl0_8 ),
inference(avatar_split_clause,[],[f90,f131,f157]) ).
fof(f162,definition,
( spl0_14
<=> sk_c9 = multiply(sk_c3,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
fof(f163,plain,
( sk_c9 != multiply(sk_c3,sk_c8)
| spl0_14 ),
inference(avatar_component_clause,[],[f162]) ).
fof(f164,plain,
( sk_c9 = multiply(sk_c3,sk_c8)
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f162]) ).
fof(f165,plain,
( spl0_7
| spl0_14 ),
inference(avatar_split_clause,[],[f88,f162,f127]) ).
fof(f166,plain,
( spl0_9
| spl0_14 ),
inference(avatar_split_clause,[],[f86,f162,f136]) ).
fof(f167,plain,
( spl0_2
| spl0_14 ),
inference(avatar_split_clause,[],[f84,f162,f109]) ).
fof(f168,plain,
( spl0_10
| spl0_14 ),
inference(avatar_split_clause,[],[f82,f162,f142]) ).
fof(f169,plain,
( spl0_11
| spl0_14 ),
inference(avatar_split_clause,[],[f80,f162,f147]) ).
fof(f170,plain,
( spl0_12
| spl0_14 ),
inference(avatar_split_clause,[],[f78,f162,f152]) ).
fof(f171,plain,
( spl0_13
| spl0_14 ),
inference(avatar_split_clause,[],[f76,f162,f157]) ).
fof(f173,definition,
( spl0_15
<=> sk_c8 = inverse(sk_c2) ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
fof(f175,plain,
( sk_c8 = inverse(sk_c2)
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f173]) ).
fof(f176,plain,
( spl0_7
| spl0_15 ),
inference(avatar_split_clause,[],[f74,f173,f127]) ).
fof(f177,plain,
( spl0_9
| spl0_15 ),
inference(avatar_split_clause,[],[f72,f173,f136]) ).
fof(f178,plain,
( spl0_2
| spl0_15 ),
inference(avatar_split_clause,[],[f70,f173,f109]) ).
fof(f181,plain,
( spl0_12
| spl0_15 ),
inference(avatar_split_clause,[],[f64,f173,f152]) ).
fof(f184,definition,
( spl0_16
<=> sk_c7 = multiply(sk_c2,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_16])],[avatar_definition]) ).
fof(f186,plain,
( sk_c7 = multiply(sk_c2,sk_c8)
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f184]) ).
fof(f187,plain,
( spl0_7
| spl0_16 ),
inference(avatar_split_clause,[],[f60,f184,f127]) ).
fof(f188,plain,
( spl0_9
| spl0_16 ),
inference(avatar_split_clause,[],[f58,f184,f136]) ).
fof(f189,plain,
( spl0_2
| spl0_16 ),
inference(avatar_split_clause,[],[f56,f184,f109]) ).
fof(f192,plain,
( spl0_12
| spl0_16 ),
inference(avatar_split_clause,[],[f50,f184,f152]) ).
fof(f195,definition,
( spl0_17
<=> sk_c9 = inverse(sk_c1) ),
introduced(definition,[new_symbols(definition,[spl0_17])],[avatar_definition]) ).
fof(f197,plain,
( sk_c9 = inverse(sk_c1)
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f195]) ).
fof(f200,plain,
( spl0_2
| spl0_17 ),
inference(avatar_split_clause,[],[f42,f195,f109]) ).
fof(f203,plain,
( spl0_12
| spl0_17 ),
inference(avatar_split_clause,[],[f36,f195,f152]) ).
fof(f204,plain,
( spl0_13
| spl0_17 ),
inference(avatar_split_clause,[],[f34,f195,f157]) ).
fof(f206,definition,
( spl0_18
<=> sk_c8 = multiply(sk_c1,sk_c9) ),
introduced(definition,[new_symbols(definition,[spl0_18])],[avatar_definition]) ).
fof(f208,plain,
( sk_c8 = multiply(sk_c1,sk_c9)
| ~ spl0_18 ),
inference(avatar_component_clause,[],[f206]) ).
fof(f211,plain,
( spl0_2
| spl0_18 ),
inference(avatar_split_clause,[],[f28,f206,f109]) ).
fof(f214,plain,
( spl0_12
| spl0_18 ),
inference(avatar_split_clause,[],[f22,f206,f152]) ).
fof(f215,plain,
( spl0_13
| spl0_18 ),
inference(avatar_split_clause,[],[f20,f206,f157]) ).
fof(f216,plain,
( spl0_7
| spl0_6 ),
inference(avatar_split_clause,[],[f18,f122,f127]) ).
fof(f217,plain,
( spl0_9
| spl0_6 ),
inference(avatar_split_clause,[],[f16,f122,f136]) ).
fof(f219,plain,
( spl0_10
| spl0_6 ),
inference(avatar_split_clause,[],[f12,f122,f142]) ).
fof(f220,plain,
( spl0_11
| spl0_6 ),
inference(avatar_split_clause,[],[f10,f122,f147]) ).
fof(f221,plain,
( spl0_12
| spl0_6 ),
inference(avatar_split_clause,[],[f8,f122,f152]) ).
fof(f222,plain,
( spl0_13
| spl0_6 ),
inference(avatar_split_clause,[],[f6,f122,f157]) ).
fof(f223,plain,
( identity = multiply(sk_c7,sk_c6)
| ~ spl0_7 ),
inference(superposition,[],[f3,f129]) ).
fof(f224,plain,
( identity = multiply(sk_c8,sk_c5)
| ~ spl0_10 ),
inference(superposition,[],[f3,f144]) ).
fof(f225,plain,
( identity = multiply(sk_c9,sk_c4)
| ~ spl0_12 ),
inference(superposition,[],[f3,f154]) ).
fof(f228,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[],[f4,f3]) ).
fof(f230,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c7,multiply(sk_c6,X0))
| ~ spl0_7 ),
inference(superposition,[],[f4,f223]) ).
fof(f232,plain,
( ! [X0] : multiply(sk_c5,multiply(sk_c8,X0)) = multiply(sk_c7,X0)
| ~ spl0_11 ),
inference(superposition,[],[f4,f149]) ).
fof(f233,plain,
( ! [X0] : multiply(sk_c9,X0) = multiply(sk_c6,multiply(sk_c7,X0))
| ~ spl0_9 ),
inference(superposition,[],[f4,f138]) ).
fof(f234,plain,
( ! [X0] : multiply(sk_c7,multiply(sk_c6,X0)) = X0
| ~ spl0_7 ),
inference(forward_demodulation,[],[f230,f1]) ).
fof(f235,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f228,f1]) ).
fof(f242,plain,
( sk_c7 = multiply(sk_c7,sk_c9)
| ~ spl0_7
| ~ spl0_9 ),
inference(superposition,[],[f234,f138]) ).
fof(f245,plain,
( sk_c8 = sk_c7
| ~ spl0_2
| ~ spl0_7
| ~ spl0_9 ),
inference(forward_demodulation,[],[f242,f110]) ).
fof(f254,plain,
( sk_c9 = multiply(sk_c6,sk_c8)
| ~ spl0_2
| ~ spl0_7
| ~ spl0_9 ),
inference(superposition,[],[f138,f245]) ).
fof(f262,plain,
( multiply(sk_c7,sk_c5) = multiply(sk_c5,identity)
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f232,f224]) ).
fof(f275,plain,
( multiply(sk_c6,sk_c8) = multiply(sk_c9,sk_c9)
| ~ spl0_2
| ~ spl0_9 ),
inference(superposition,[],[f233,f110]) ).
fof(f284,plain,
( sk_c9 = multiply(sk_c9,sk_c9)
| ~ spl0_2
| ~ spl0_7
| ~ spl0_9 ),
inference(forward_demodulation,[],[f275,f254]) ).
fof(f296,plain,
! [X0] : multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[],[f235,f3]) ).
fof(f297,plain,
! [X0,X1] : multiply(X1,X0) = multiply(inverse(inverse(X1)),X0),
inference(superposition,[],[f235,f235]) ).
fof(f298,plain,
( sk_c5 = multiply(inverse(sk_c8),identity)
| ~ spl0_10 ),
inference(superposition,[],[f235,f224]) ).
fof(f300,plain,
( sk_c4 = multiply(inverse(sk_c9),identity)
| ~ spl0_12 ),
inference(superposition,[],[f235,f225]) ).
fof(f301,plain,
( sk_c9 = multiply(inverse(sk_c9),sk_c9)
| ~ spl0_2
| ~ spl0_7
| ~ spl0_9 ),
inference(superposition,[],[f235,f284]) ).
fof(f302,plain,
( sk_c9 = multiply(inverse(sk_c7),sk_c8)
| ~ spl0_2 ),
inference(superposition,[],[f235,f110]) ).
fof(f304,plain,
( ! [X0] : multiply(sk_c6,X0) = multiply(inverse(sk_c7),X0)
| ~ spl0_7 ),
inference(superposition,[],[f235,f234]) ).
fof(f306,plain,
( sk_c9 = multiply(inverse(sk_c4),sk_c8)
| ~ spl0_13 ),
inference(superposition,[],[f235,f159]) ).
fof(f308,plain,
( sk_c8 = multiply(inverse(sk_c5),sk_c7)
| ~ spl0_11 ),
inference(superposition,[],[f235,f149]) ).
fof(f309,plain,
( ! [X0] : multiply(sk_c8,X0) = multiply(inverse(sk_c5),multiply(sk_c7,X0))
| ~ spl0_11 ),
inference(superposition,[],[f235,f232]) ).
fof(f319,plain,
( sk_c8 = multiply(inverse(sk_c5),sk_c8)
| ~ spl0_2
| ~ spl0_7
| ~ spl0_9
| ~ spl0_11 ),
inference(forward_demodulation,[],[f308,f245]) ).
fof(f321,plain,
( sk_c9 = multiply(sk_c9,sk_c8)
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f306,f154]) ).
fof(f326,plain,
( identity = sk_c9
| ~ spl0_2
| ~ spl0_7
| ~ spl0_9 ),
inference(forward_demodulation,[],[f301,f3]) ).
fof(f327,plain,
! [X0] : multiply(X0,identity) = X0,
inference(forward_demodulation,[],[f296,f297]) ).
fof(f331,plain,
( sk_c8 = multiply(sk_c8,sk_c8)
| ~ spl0_2
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f319,f144]) ).
fof(f338,plain,
( sk_c8 = multiply(inverse(sk_c9),sk_c9)
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f235,f321]) ).
fof(f340,plain,
( identity = sk_c8
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f338,f3]) ).
fof(f344,plain,
( sk_c8 = sk_c9
| ~ spl0_2
| ~ spl0_7
| ~ spl0_9
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f326,f340]) ).
fof(f345,plain,
( ! [X0] : multiply(sk_c8,X0) = X0
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f1,f340]) ).
fof(f353,plain,
( sk_c7 != multiply(sk_c8,sk_c8)
| ~ spl0_2
| spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f124,f344]) ).
fof(f355,plain,
( identity = multiply(sk_c8,sk_c4)
| ~ spl0_2
| ~ spl0_7
| ~ spl0_9
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f225,f344]) ).
fof(f362,plain,
( identity = sk_c4
| ~ spl0_2
| ~ spl0_7
| ~ spl0_9
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f355,f345]) ).
fof(f363,plain,
( sk_c8 != sk_c7
| ~ spl0_2
| spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f353,f331]) ).
fof(f366,plain,
( sk_c9 = sk_c4
| ~ spl0_2
| ~ spl0_7
| ~ spl0_9
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f362,f326]) ).
fof(f367,plain,
( $false
| ~ spl0_2
| spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f363,f245]) ).
fof(f368,plain,
( ~ spl0_2
| spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[],[f367]) ).
fof(f369,plain,
( sk_c8 = sk_c4
| ~ spl0_2
| ~ spl0_7
| ~ spl0_9
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f366,f344]) ).
fof(f382,plain,
( multiply(sk_c5,sk_c8) = multiply(sk_c7,sk_c5)
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f262,f340]) ).
fof(f384,plain,
( ! [X0] : multiply(sk_c8,X0) = multiply(sk_c8,multiply(sk_c7,X0))
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f309,f144]) ).
fof(f388,plain,
( sk_c9 = multiply(sk_c6,sk_c8)
| ~ spl0_2
| ~ spl0_7 ),
inference(forward_demodulation,[],[f302,f304]) ).
fof(f389,plain,
( ! [X0] : multiply(X0,sk_c8) = X0
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f327,f340]) ).
fof(f392,plain,
( sk_c9 = sk_c7
| ~ spl0_6
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f123,f345]) ).
fof(f394,plain,
( sk_c7 = multiply(sk_c7,sk_c5)
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f382,f149]) ).
fof(f395,plain,
( ! [X0] : multiply(sk_c8,X0) = multiply(sk_c7,X0)
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f384,f345]) ).
fof(f400,plain,
( ! [X0] : multiply(sk_c9,X0) = multiply(sk_c8,X0)
| ~ spl0_6
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f395,f392]) ).
fof(f402,plain,
( ! [X0] : multiply(sk_c9,X0) = X0
| ~ spl0_6
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f400,f345]) ).
fof(f404,plain,
( identity = multiply(sk_c9,sk_c6)
| ~ spl0_6
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f223,f392]) ).
fof(f409,plain,
( identity = sk_c6
| ~ spl0_6
| ~ spl0_7
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f404,f402]) ).
fof(f412,plain,
( sk_c8 = sk_c6
| ~ spl0_6
| ~ spl0_7
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f409,f340]) ).
fof(f414,plain,
( identity = multiply(sk_c8,sk_c3)
| ~ spl0_8 ),
inference(superposition,[],[f3,f133]) ).
fof(f415,plain,
( identity = sk_c3
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f414,f345]) ).
fof(f417,plain,
( sk_c8 = sk_c3
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f415,f340]) ).
fof(f434,plain,
( identity = multiply(sk_c8,sk_c2)
| ~ spl0_15 ),
inference(superposition,[],[f3,f175]) ).
fof(f435,plain,
( identity = sk_c2
| ~ spl0_12
| ~ spl0_13
| ~ spl0_15 ),
inference(forward_demodulation,[],[f434,f345]) ).
fof(f437,plain,
( sk_c8 = sk_c2
| ~ spl0_12
| ~ spl0_13
| ~ spl0_15 ),
inference(forward_demodulation,[],[f435,f340]) ).
fof(f440,plain,
( identity = multiply(sk_c9,sk_c1)
| ~ spl0_17 ),
inference(superposition,[],[f3,f197]) ).
fof(f453,plain,
( sk_c9 = multiply(sk_c8,sk_c8)
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(superposition,[],[f164,f417]) ).
fof(f458,plain,
( sk_c8 = sk_c9
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f453,f345]) ).
fof(f469,plain,
( sk_c7 = multiply(sk_c8,sk_c8)
| ~ spl0_12
| ~ spl0_13
| ~ spl0_15
| ~ spl0_16 ),
inference(superposition,[],[f186,f437]) ).
fof(f474,plain,
( sk_c8 = sk_c7
| ~ spl0_12
| ~ spl0_13
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f469,f345]) ).
fof(f481,plain,
( sk_c8 = multiply(sk_c4,sk_c8)
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(superposition,[],[f159,f458]) ).
fof(f489,plain,
( sk_c8 = sk_c4
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f481,f389]) ).
fof(f507,plain,
( sk_c9 != multiply(sk_c6,sk_c8)
| spl0_9
| ~ spl0_12
| ~ spl0_13
| ~ spl0_15
| ~ spl0_16 ),
inference(superposition,[],[f137,f474]) ).
fof(f515,plain,
( $false
| ~ spl0_2
| ~ spl0_7
| spl0_9
| ~ spl0_12
| ~ spl0_13
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_subsumption_resolution,[],[f507,f388]) ).
fof(f516,plain,
( ~ spl0_2
| ~ spl0_7
| spl0_9
| ~ spl0_12
| ~ spl0_13
| ~ spl0_15
| ~ spl0_16 ),
inference(avatar_contradiction_clause,[],[f515]) ).
fof(f544,plain,
( sk_c8 != sk_c8
| sk_c9 != inverse(sk_c4)
| ~ spl0_4
| ~ spl0_13 ),
inference(superposition,[],[f117,f159]) ).
fof(f545,plain,
( sk_c8 != sk_c8
| sk_c9 != inverse(sk_c1)
| ~ spl0_4
| ~ spl0_18 ),
inference(superposition,[],[f117,f208]) ).
fof(f546,plain,
( sk_c9 != inverse(sk_c1)
| ~ spl0_4
| ~ spl0_18 ),
inference(trivial_inequality_removal,[],[f545]) ).
fof(f547,plain,
( sk_c9 != inverse(sk_c4)
| ~ spl0_4
| ~ spl0_13 ),
inference(trivial_inequality_removal,[],[f544]) ).
fof(f549,plain,
( $false
| ~ spl0_4
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[],[f546,f197]) ).
fof(f550,plain,
( ~ spl0_4
| ~ spl0_17
| ~ spl0_18 ),
inference(avatar_contradiction_clause,[],[f549]) ).
fof(f551,plain,
( $false
| ~ spl0_4
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f547,f154]) ).
fof(f552,plain,
( ~ spl0_4
| ~ spl0_12
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[],[f551]) ).
fof(f571,plain,
( ! [X4] :
( sk_c7 != X4
| sk_c8 != inverse(X4) )
| ~ spl0_3
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f114,f389]) ).
fof(f596,plain,
( ! [X2] :
( sk_c9 != X2
| sk_c8 != inverse(X2) )
| ~ spl0_5
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f120,f389]) ).
fof(f616,plain,
( ! [X5] :
( sk_c9 != multiply(X5,sk_c9)
| sk_c7 != inverse(X5) )
| ~ spl0_1
| ~ spl0_6
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f107,f392]) ).
fof(f617,plain,
( ! [X5] :
( sk_c8 != multiply(X5,sk_c8)
| sk_c7 != inverse(X5) )
| ~ spl0_1
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f616,f458]) ).
fof(f618,plain,
( ! [X5] :
( sk_c8 != X5
| sk_c7 != inverse(X5) )
| ~ spl0_1
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f617,f389]) ).
fof(f619,plain,
( ! [X5] :
( sk_c9 != inverse(X5)
| sk_c8 != X5 )
| ~ spl0_1
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f618,f392]) ).
fof(f620,plain,
( ! [X5] :
( sk_c8 != inverse(X5)
| sk_c8 != X5 )
| ~ spl0_1
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f619,f458]) ).
fof(f626,plain,
( sk_c8 != sk_c9
| sk_c8 != sk_c4
| ~ spl0_1
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(superposition,[],[f620,f154]) ).
fof(f642,plain,
( sk_c8 != sk_c4
| ~ spl0_1
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_subsumption_resolution,[],[f626,f458]) ).
fof(f645,plain,
( $false
| ~ spl0_1
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_subsumption_resolution,[],[f642,f489]) ).
fof(f646,plain,
( ~ spl0_1
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(avatar_contradiction_clause,[],[f645]) ).
fof(f657,plain,
( sk_c3 = multiply(inverse(sk_c8),identity)
| ~ spl0_8 ),
inference(superposition,[],[f235,f414]) ).
fof(f660,plain,
( sk_c5 = sk_c3
| ~ spl0_8
| ~ spl0_10 ),
inference(forward_demodulation,[],[f657,f298]) ).
fof(f664,plain,
( sk_c2 = multiply(inverse(sk_c8),identity)
| ~ spl0_15 ),
inference(superposition,[],[f235,f434]) ).
fof(f673,plain,
( sk_c3 = inverse(sk_c8)
| ~ spl0_8 ),
inference(forward_demodulation,[],[f657,f327]) ).
fof(f674,plain,
( sk_c2 = inverse(sk_c8)
| ~ spl0_15 ),
inference(forward_demodulation,[],[f664,f327]) ).
fof(f676,plain,
( identity = multiply(sk_c3,sk_c8)
| ~ spl0_8 ),
inference(superposition,[],[f3,f673]) ).
fof(f677,plain,
( identity = sk_c9
| ~ spl0_8
| ~ spl0_14 ),
inference(forward_demodulation,[],[f676,f164]) ).
fof(f678,plain,
( sk_c1 = multiply(inverse(sk_c9),identity)
| ~ spl0_17 ),
inference(superposition,[],[f235,f440]) ).
fof(f681,plain,
( sk_c4 = sk_c1
| ~ spl0_12
| ~ spl0_17 ),
inference(forward_demodulation,[],[f678,f300]) ).
fof(f683,plain,
( sk_c8 = multiply(sk_c4,sk_c9)
| ~ spl0_12
| ~ spl0_17
| ~ spl0_18 ),
inference(superposition,[],[f208,f681]) ).
fof(f685,plain,
( $false
| ~ spl0_12
| spl0_13
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[],[f683,f158]) ).
fof(f686,plain,
( ~ spl0_12
| spl0_13
| ~ spl0_17
| ~ spl0_18 ),
inference(avatar_contradiction_clause,[],[f685]) ).
fof(f702,plain,
( sk_c8 = inverse(sk_c6)
| ~ spl0_2
| ~ spl0_7
| ~ spl0_9 ),
inference(forward_demodulation,[],[f129,f245]) ).
fof(f710,plain,
( sk_c8 = multiply(sk_c8,sk_c5)
| ~ spl0_2
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f394,f245]) ).
fof(f719,plain,
( sk_c9 != sk_c3
| ~ spl0_12
| ~ spl0_13
| spl0_14 ),
inference(forward_demodulation,[],[f163,f389]) ).
fof(f724,plain,
( sk_c8 = inverse(sk_c8)
| ~ spl0_2
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f702,f412]) ).
fof(f728,plain,
( sk_c8 = sk_c5
| ~ spl0_2
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f710,f345]) ).
fof(f732,plain,
( sk_c9 != sk_c5
| ~ spl0_8
| ~ spl0_10
| ~ spl0_12
| ~ spl0_13
| spl0_14 ),
inference(forward_demodulation,[],[f719,f660]) ).
fof(f738,plain,
( sk_c8 != sk_c9
| ~ spl0_2
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| spl0_14 ),
inference(forward_demodulation,[],[f732,f728]) ).
fof(f755,plain,
( $false
| ~ spl0_2
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| spl0_14 ),
inference(forward_subsumption_resolution,[],[f738,f344]) ).
fof(f756,plain,
( ~ spl0_2
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| spl0_14 ),
inference(avatar_contradiction_clause,[],[f755]) ).
fof(f797,plain,
( sk_c9 != sk_c7
| sk_c7 != inverse(identity)
| ~ spl0_1 ),
inference(superposition,[],[f107,f1]) ).
fof(f799,plain,
( identity != sk_c9
| sk_c7 != inverse(inverse(sk_c7))
| ~ spl0_1 ),
inference(superposition,[],[f107,f3]) ).
fof(f802,plain,
( sk_c8 != sk_c9
| sk_c7 != inverse(identity)
| ~ spl0_1
| ~ spl0_2
| ~ spl0_7
| ~ spl0_9 ),
inference(forward_demodulation,[],[f797,f245]) ).
fof(f806,plain,
( sk_c7 != inverse(identity)
| ~ spl0_1
| ~ spl0_2
| ~ spl0_7
| ~ spl0_9
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f802,f344]) ).
fof(f810,plain,
( sk_c7 != inverse(sk_c9)
| ~ spl0_1
| ~ spl0_2
| ~ spl0_7
| ~ spl0_9
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f806,f326]) ).
fof(f814,plain,
( sk_c7 != inverse(sk_c8)
| ~ spl0_1
| ~ spl0_2
| ~ spl0_7
| ~ spl0_9
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f810,f344]) ).
fof(f815,plain,
( sk_c8 != sk_c7
| ~ spl0_1
| ~ spl0_2
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f814,f724]) ).
fof(f816,plain,
( $false
| ~ spl0_1
| ~ spl0_2
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f815,f245]) ).
fof(f817,plain,
( ~ spl0_1
| ~ spl0_2
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[],[f816]) ).
fof(f819,plain,
( ! [X2] :
( sk_c8 != inverse(X2)
| sk_c8 != X2 )
| ~ spl0_2
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f596,f344]) ).
fof(f825,plain,
( sk_c8 != sk_c9
| sk_c8 != sk_c4
| ~ spl0_2
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f819,f154]) ).
fof(f835,plain,
( sk_c8 != sk_c4
| ~ spl0_2
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f825,f344]) ).
fof(f838,plain,
( $false
| ~ spl0_2
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f835,f369]) ).
fof(f839,plain,
( ~ spl0_2
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_12
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[],[f838]) ).
fof(f841,plain,
( ! [X4] :
( sk_c8 != inverse(X4)
| sk_c8 != X4 )
| ~ spl0_2
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f571,f245]) ).
fof(f858,plain,
( sk_c8 != sk_c9
| sk_c8 != sk_c4
| ~ spl0_2
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f841,f154]) ).
fof(f868,plain,
( sk_c8 != sk_c4
| ~ spl0_2
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f858,f344]) ).
fof(f871,plain,
( $false
| ~ spl0_2
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f868,f369]) ).
fof(f872,plain,
( ~ spl0_2
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_12
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[],[f871]) ).
fof(f878,definition,
( spl0_20
<=> sk_c9 = sk_c7 ),
introduced(definition,[new_symbols(definition,[spl0_20])],[avatar_definition]) ).
fof(f879,plain,
( sk_c9 = sk_c7
| ~ spl0_20 ),
inference(avatar_component_clause,[],[f878]) ).
fof(f880,plain,
( sk_c9 != sk_c7
| spl0_20 ),
inference(avatar_component_clause,[],[f878]) ).
fof(f883,definition,
( spl0_21
<=> sk_c7 = inverse(inverse(sk_c7)) ),
introduced(definition,[new_symbols(definition,[spl0_21])],[avatar_definition]) ).
fof(f885,plain,
( sk_c7 != inverse(inverse(sk_c7))
| spl0_21 ),
inference(avatar_component_clause,[],[f883]) ).
fof(f887,definition,
( spl0_22
<=> identity = sk_c9 ),
introduced(definition,[new_symbols(definition,[spl0_22])],[avatar_definition]) ).
fof(f888,plain,
( identity = sk_c9
| ~ spl0_22 ),
inference(avatar_component_clause,[],[f887]) ).
fof(f890,plain,
( ~ spl0_21
| ~ spl0_22
| ~ spl0_1 ),
inference(avatar_split_clause,[],[f799,f106,f887,f883]) ).
fof(f891,plain,
( spl0_22
| ~ spl0_8
| ~ spl0_14 ),
inference(avatar_split_clause,[],[f677,f162,f131,f887]) ).
fof(f897,plain,
( sk_c1 = inverse(sk_c9)
| ~ spl0_17 ),
inference(forward_demodulation,[],[f678,f327]) ).
fof(f902,plain,
( sk_c9 != inverse(inverse(sk_c9))
| ~ spl0_20
| spl0_21 ),
inference(forward_demodulation,[],[f885,f879]) ).
fof(f903,plain,
( sk_c9 != inverse(sk_c1)
| ~ spl0_17
| ~ spl0_20
| spl0_21 ),
inference(forward_demodulation,[],[f902,f897]) ).
fof(f904,plain,
( $false
| ~ spl0_17
| ~ spl0_20
| spl0_21 ),
inference(forward_subsumption_resolution,[],[f903,f197]) ).
fof(f905,plain,
( ~ spl0_17
| ~ spl0_20
| spl0_21 ),
inference(avatar_contradiction_clause,[],[f904]) ).
fof(f914,plain,
( ! [X0] : multiply(sk_c9,X0) = X0
| ~ spl0_22 ),
inference(superposition,[],[f1,f888]) ).
fof(f933,plain,
( identity != sk_c9
| sk_c8 != inverse(inverse(sk_c8))
| ~ spl0_5 ),
inference(superposition,[],[f120,f3]) ).
fof(f941,definition,
( spl0_23
<=> sk_c8 = sk_c9 ),
introduced(definition,[new_symbols(definition,[spl0_23])],[avatar_definition]) ).
fof(f943,plain,
( sk_c8 != sk_c9
| spl0_23 ),
inference(avatar_component_clause,[],[f941]) ).
fof(f949,plain,
( ! [X4] :
( sk_c9 != multiply(X4,sk_c8)
| sk_c8 != inverse(X4) )
| ~ spl0_3
| ~ spl0_20 ),
inference(forward_demodulation,[],[f114,f879]) ).
fof(f950,plain,
( spl0_5
| ~ spl0_3
| ~ spl0_20 ),
inference(avatar_split_clause,[],[f949,f878,f113,f119]) ).
fof(f967,plain,
( identity = multiply(sk_c2,sk_c8)
| ~ spl0_15 ),
inference(superposition,[],[f3,f674]) ).
fof(f968,plain,
( identity = sk_c7
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f967,f186]) ).
fof(f969,plain,
( sk_c9 = sk_c7
| ~ spl0_15
| ~ spl0_16
| ~ spl0_22 ),
inference(forward_demodulation,[],[f968,f888]) ).
fof(f970,plain,
( $false
| ~ spl0_15
| ~ spl0_16
| spl0_20
| ~ spl0_22 ),
inference(forward_subsumption_resolution,[],[f969,f880]) ).
fof(f971,plain,
( ~ spl0_15
| ~ spl0_16
| spl0_20
| ~ spl0_22 ),
inference(avatar_contradiction_clause,[],[f970]) ).
fof(f974,plain,
( sk_c8 != inverse(inverse(sk_c8))
| ~ spl0_5
| ~ spl0_22 ),
inference(forward_subsumption_resolution,[],[f933,f888]) ).
fof(f981,plain,
( sk_c8 != inverse(sk_c3)
| ~ spl0_5
| ~ spl0_8
| ~ spl0_22 ),
inference(forward_demodulation,[],[f974,f673]) ).
fof(f986,plain,
( $false
| ~ spl0_5
| ~ spl0_8
| ~ spl0_22 ),
inference(forward_subsumption_resolution,[],[f981,f133]) ).
fof(f987,plain,
( ~ spl0_5
| ~ spl0_8
| ~ spl0_22 ),
inference(avatar_contradiction_clause,[],[f986]) ).
fof(f988,plain,
( sk_c8 != multiply(sk_c9,sk_c9)
| spl0_2
| ~ spl0_20 ),
inference(forward_demodulation,[],[f111,f879]) ).
fof(f989,plain,
( sk_c8 != sk_c9
| spl0_2
| ~ spl0_20
| ~ spl0_22 ),
inference(forward_demodulation,[],[f988,f914]) ).
fof(f990,plain,
( ~ spl0_23
| spl0_2
| ~ spl0_20
| ~ spl0_22 ),
inference(avatar_split_clause,[],[f989,f887,f878,f109,f941]) ).
fof(f1032,plain,
( identity = multiply(sk_c1,sk_c9)
| ~ spl0_17 ),
inference(superposition,[],[f3,f897]) ).
fof(f1033,plain,
( identity = sk_c8
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f1032,f208]) ).
fof(f1047,plain,
( sk_c8 = sk_c9
| ~ spl0_17
| ~ spl0_18
| ~ spl0_22 ),
inference(superposition,[],[f1033,f888]) ).
fof(f1054,plain,
( $false
| ~ spl0_17
| ~ spl0_18
| ~ spl0_22
| spl0_23 ),
inference(forward_subsumption_resolution,[],[f1047,f943]) ).
fof(f1055,plain,
( ~ spl0_17
| ~ spl0_18
| ~ spl0_22
| spl0_23 ),
inference(avatar_contradiction_clause,[],[f1054]) ).
cnf(s1,plain,
( spl0_3
| spl0_4
| spl0_1
| spl0_3
| ~ spl0_2
| spl0_4
| spl0_5
| ~ spl0_6 ),
inference(sat_conversion,[],[f125]) ).
cnf(s2,plain,
( spl0_1
| ~ spl0_2
| spl0_3
| spl0_4
| spl0_5
| ~ spl0_6 ),
inference(rat,[],[s1]) ).
cnf(s3,plain,
( spl0_7
| spl0_8 ),
inference(sat_conversion,[],[f134]) ).
cnf(s4,plain,
( spl0_8
| spl0_9 ),
inference(sat_conversion,[],[f139]) ).
cnf(s5,plain,
( spl0_2
| spl0_8 ),
inference(sat_conversion,[],[f140]) ).
cnf(s6,plain,
( spl0_8
| spl0_10 ),
inference(sat_conversion,[],[f145]) ).
cnf(s7,plain,
( spl0_8
| spl0_11 ),
inference(sat_conversion,[],[f150]) ).
cnf(s8,plain,
( spl0_8
| spl0_12 ),
inference(sat_conversion,[],[f155]) ).
cnf(s9,plain,
( spl0_8
| spl0_13 ),
inference(sat_conversion,[],[f160]) ).
cnf(s10,plain,
( spl0_7
| spl0_14 ),
inference(sat_conversion,[],[f165]) ).
cnf(s11,plain,
( spl0_9
| spl0_14 ),
inference(sat_conversion,[],[f166]) ).
cnf(s12,plain,
( spl0_2
| spl0_14 ),
inference(sat_conversion,[],[f167]) ).
cnf(s13,plain,
( spl0_10
| spl0_14 ),
inference(sat_conversion,[],[f168]) ).
cnf(s14,plain,
( spl0_11
| spl0_14 ),
inference(sat_conversion,[],[f169]) ).
cnf(s15,plain,
( spl0_12
| spl0_14 ),
inference(sat_conversion,[],[f170]) ).
cnf(s16,plain,
( spl0_13
| spl0_14 ),
inference(sat_conversion,[],[f171]) ).
cnf(s17,plain,
( spl0_7
| spl0_15 ),
inference(sat_conversion,[],[f176]) ).
cnf(s18,plain,
( spl0_9
| spl0_15 ),
inference(sat_conversion,[],[f177]) ).
cnf(s19,plain,
( spl0_2
| spl0_15 ),
inference(sat_conversion,[],[f178]) ).
cnf(s22,plain,
( spl0_12
| spl0_15 ),
inference(sat_conversion,[],[f181]) ).
cnf(s24,plain,
( spl0_7
| spl0_16 ),
inference(sat_conversion,[],[f187]) ).
cnf(s25,plain,
( spl0_9
| spl0_16 ),
inference(sat_conversion,[],[f188]) ).
cnf(s26,plain,
( spl0_2
| spl0_16 ),
inference(sat_conversion,[],[f189]) ).
cnf(s29,plain,
( spl0_12
| spl0_16 ),
inference(sat_conversion,[],[f192]) ).
cnf(s33,plain,
( spl0_2
| spl0_17 ),
inference(sat_conversion,[],[f200]) ).
cnf(s36,plain,
( spl0_12
| spl0_17 ),
inference(sat_conversion,[],[f203]) ).
cnf(s37,plain,
( spl0_13
| spl0_17 ),
inference(sat_conversion,[],[f204]) ).
cnf(s40,plain,
( spl0_2
| spl0_18 ),
inference(sat_conversion,[],[f211]) ).
cnf(s43,plain,
( spl0_12
| spl0_18 ),
inference(sat_conversion,[],[f214]) ).
cnf(s44,plain,
( spl0_13
| spl0_18 ),
inference(sat_conversion,[],[f215]) ).
cnf(s45,plain,
( spl0_6
| spl0_7 ),
inference(sat_conversion,[],[f216]) ).
cnf(s46,plain,
( spl0_6
| spl0_9 ),
inference(sat_conversion,[],[f217]) ).
cnf(s48,plain,
( spl0_6
| spl0_10 ),
inference(sat_conversion,[],[f219]) ).
cnf(s49,plain,
( spl0_6
| spl0_11 ),
inference(sat_conversion,[],[f220]) ).
cnf(s50,plain,
( spl0_6
| spl0_12 ),
inference(sat_conversion,[],[f221]) ).
cnf(s51,plain,
( spl0_6
| spl0_13 ),
inference(sat_conversion,[],[f222]) ).
cnf(s52,plain,
( ~ spl0_2
| spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(sat_conversion,[],[f368]) ).
cnf(s55,plain,
( ~ spl0_2
| ~ spl0_7
| spl0_9
| ~ spl0_12
| ~ spl0_13
| ~ spl0_15
| ~ spl0_16 ),
inference(sat_conversion,[],[f516]) ).
cnf(s56,plain,
( ~ spl0_4
| ~ spl0_17
| ~ spl0_18 ),
inference(sat_conversion,[],[f550]) ).
cnf(s57,plain,
( ~ spl0_4
| ~ spl0_12
| ~ spl0_13 ),
inference(sat_conversion,[],[f552]) ).
cnf(s73,plain,
( ~ spl0_1
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(sat_conversion,[],[f646]) ).
cnf(s76,plain,
( ~ spl0_12
| spl0_13
| ~ spl0_17
| ~ spl0_18 ),
inference(sat_conversion,[],[f686]) ).
cnf(s78,plain,
( ~ spl0_2
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| spl0_14 ),
inference(sat_conversion,[],[f756]) ).
cnf(s81,plain,
( ~ spl0_1
| ~ spl0_2
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(sat_conversion,[],[f817]) ).
cnf(s85,plain,
( ~ spl0_2
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_12
| ~ spl0_13 ),
inference(sat_conversion,[],[f839]) ).
cnf(s89,plain,
( ~ spl0_2
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_12
| ~ spl0_13 ),
inference(sat_conversion,[],[f872]) ).
cnf(s91,plain,
( ~ spl0_1
| ~ spl0_21
| ~ spl0_22 ),
inference(sat_conversion,[],[f890]) ).
cnf(s92,plain,
( ~ spl0_8
| ~ spl0_14
| spl0_22 ),
inference(sat_conversion,[],[f891]) ).
cnf(s96,plain,
( ~ spl0_17
| ~ spl0_20
| spl0_21 ),
inference(sat_conversion,[],[f905]) ).
cnf(s99,plain,
( ~ spl0_3
| spl0_5
| ~ spl0_20 ),
inference(sat_conversion,[],[f950]) ).
cnf(s100,plain,
( ~ spl0_15
| ~ spl0_16
| spl0_20
| ~ spl0_22 ),
inference(sat_conversion,[],[f971]) ).
cnf(s104,plain,
( ~ spl0_5
| ~ spl0_8
| ~ spl0_22 ),
inference(sat_conversion,[],[f987]) ).
cnf(s105,plain,
( spl0_2
| ~ spl0_20
| ~ spl0_22
| ~ spl0_23 ),
inference(sat_conversion,[],[f990]) ).
cnf(s107,plain,
( ~ spl0_17
| ~ spl0_18
| ~ spl0_22
| spl0_23 ),
inference(sat_conversion,[],[f1055]) ).
cnf(s108,plain,
spl0_2,
inference(rat,[],[s100,s105,s107,s92,s5,s12,s19,s26,s33,s40]) ).
cnf(s109,plain,
spl0_6,
inference(rat,[],[s52,s45,s46,s48,s49,s50,s51,s108]) ).
cnf(s110,plain,
( ~ spl0_8
| ~ spl0_7
| ~ spl0_5 ),
inference(rat,[],[s78,s11,s13,s14,s15,s16,s92,s104,s108]) ).
cnf(s111,plain,
( ~ spl0_7
| ~ spl0_5 ),
inference(rat,[],[s85,s4,s8,s9,s110,s108]) ).
cnf(s112,plain,
~ spl0_5,
inference(rat,[],[s104,s92,s3,s10,s111]) ).
cnf(s113,plain,
( spl0_13
| ~ spl0_4 ),
inference(rat,[],[s56,s37,s44]) ).
cnf(s114,plain,
( ~ spl0_13
| ~ spl0_4 ),
inference(rat,[],[s56,s36,s43,s57]) ).
cnf(s115,plain,
~ spl0_4,
inference(rat,[],[s114,s113]) ).
cnf(s116,plain,
( spl0_13
| ~ spl0_12 ),
inference(rat,[],[s76,s37,s44]) ).
cnf(s117,plain,
( ~ spl0_7
| ~ spl0_13
| ~ spl0_3
| ~ spl0_12 ),
inference(rat,[],[s55,s18,s25,s89,s108]) ).
cnf(s118,plain,
( spl0_7
| spl0_20 ),
inference(rat,[],[s92,s100,s3,s10,s17,s24]) ).
cnf(s119,plain,
( ~ spl0_12
| ~ spl0_3 ),
inference(rat,[],[s117,s116,s118,s99,s112]) ).
cnf(s120,plain,
~ spl0_3,
inference(rat,[],[s92,s100,s8,s15,s22,s29,s119,s99,s112]) ).
cnf(s121,plain,
spl0_1,
inference(rat,[],[s2,s112,s109,s108,s115,s120]) ).
cnf(s122,plain,
( ~ spl0_8
| ~ spl0_7
| ~ spl0_12 ),
inference(rat,[],[s78,s11,s13,s14,s73,s116,s108,s121,s109]) ).
cnf(s123,plain,
( ~ spl0_7
| ~ spl0_12 ),
inference(rat,[],[s81,s4,s6,s7,s122,s116,s108,s109,s121]) ).
cnf(s124,plain,
~ spl0_12,
inference(rat,[],[s73,s3,s10,s123,s116,s121,s109]) ).
cnf(s126,plain,
spl0_17,
inference(rat,[],[s36,s124]) ).
cnf(s127,plain,
spl0_16,
inference(rat,[],[s29,s124]) ).
cnf(s128,plain,
spl0_15,
inference(rat,[],[s22,s124]) ).
cnf(s129,plain,
spl0_14,
inference(rat,[],[s15,s124]) ).
cnf(s130,plain,
spl0_8,
inference(rat,[],[s8,s124]) ).
cnf(s131,plain,
spl0_22,
inference(rat,[],[s92,s130,s129]) ).
cnf(s133,plain,
spl0_20,
inference(rat,[],[s100,s128,s127,s131]) ).
cnf(s134,plain,
~ spl0_21,
inference(rat,[],[s91,s121,s131]) ).
cnf(s135,plain,
$false,
inference(rat,[],[s96,s126,s134,s133]) ).
fof(f1058,plain,
$false,
inference(avatar_sat_refutation,[],[s135]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP313-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.13/0.39 % Computer : n026.cluster.edu
% 0.13/0.39 % Model : x86_64 x86_64
% 0.13/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.39 % Memory : 8046.5625MB
% 0.13/0.39 % OS : Linux 6.8.0-71-generic
% 0.13/0.39 % CPULimit : 300
% 0.13/0.39 % WCLimit : 300
% 0.13/0.39 % DateTime : Sun Sep 27 09:52:26 UTC 2026
% 0.13/0.39 % CPUTime :
% 0.13/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.13/0.42 Running first-order model finding
% 0.13/0.42 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
% 0.17/0.47 % (2587716)Will run a generic schedule for satisfiability detection.
% 0.17/0.47 % (2587725)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2781814889:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.17/0.47 % (2587722)% WARNING: option uhcvi not known.
% 0.17/0.47 % (2587721)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=864825760_2999 on theBenchmark for (2999ds/0Mi)
% 0.17/0.47 % (2587722)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=11816129:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.17/0.47 % (2587723)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=757094423:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.17/0.47 % (2587724)dis+10_1_sil=32000:sp=arity:random_seed=1029282124:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.17/0.47 % (2587727)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3496418310:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.17/0.47 % (2587726)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3912190257:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.17/0.47 % (2587725) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2587716-2587725"...
% 0.17/0.47 % TRYING [1]
% 0.17/0.47 % TRYING [2]
% 0.17/0.47 % (2587725)...printing done.
% 0.17/0.47 % TRYING [3]
% 0.17/0.47 % (2587725)Refutation found. Thanks to Tanya!
% 0.17/0.47 % SZS status Unsatisfiable for theBenchmark
% 0.17/0.47 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/0.48 % (2587725)------------------------------
% 0.17/0.48 % (2587725)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.17/0.48 % (2587725)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/0.48 % (2587725)CaDiCaL version: 2.1.3
% 0.17/0.48 % (2587725)Termination reason: Refutation
% 0.17/0.48 % (2587725)Time elapsed: 0.012 s
% 0.17/0.48 % (2587725)Peak memory usage: 12 MB
% 0.17/0.48 % (2587725)Instructions burned: 32 (million)
% 0.17/0.48 % (2587716)Success in time 0.039 s
% 0.17/0.48 % Vampire exiting
%------------------------------------------------------------------------------