%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP252-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n013.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 10:13:27 AM UTC 2026
% Result : Unsatisfiable 2.55s 1.27s
% Output : Refutation 3.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 57
% Syntax : Number of formulae : 289 ( 18 unt; 19 def)
% Number of atoms : 744 ( 289 equ)
% Maximal formula atoms : 13 ( 2 avg)
% Number of connectives : 805 ( 350 ~; 436 |; 0 &)
% ( 19 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 21 ( 19 usr; 20 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 11 con; 0-2 aty)
% Number of variables : 51 ( 0 sgn 51 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_identity) ).
fof(f2,axiom,
! [X0] : multiply(inverse(X0),X0) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_inverse) ).
fof(f3,plain,
! [X0] : identity = multiply(inverse(X0),X0),
inference(reorient_equations,[],[f2]) ).
fof(f4,axiom,
! [X2,X0,X1] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity) ).
fof(f5,negated_conjecture,
( multiply(sk_c1,sk_c10) = sk_c9
| multiply(sk_c4,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,plain,
( multiply(sk_c1,sk_c10) = sk_c9
| sk_c9 = multiply(sk_c4,sk_c10) ),
inference(reorient_equations,[],[f5]) ).
fof(f7,negated_conjecture,
( multiply(sk_c1,sk_c10) = sk_c9
| inverse(sk_c4) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_2) ).
fof(f8,plain,
( multiply(sk_c1,sk_c10) = sk_c9
| sk_c10 = inverse(sk_c4) ),
inference(reorient_equations,[],[f7]) ).
fof(f9,negated_conjecture,
( multiply(sk_c1,sk_c10) = sk_c9
| multiply(sk_c5,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_3) ).
fof(f10,plain,
( multiply(sk_c1,sk_c10) = sk_c9
| sk_c9 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f9]) ).
fof(f11,negated_conjecture,
( multiply(sk_c1,sk_c10) = sk_c9
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_4) ).
fof(f12,plain,
( multiply(sk_c1,sk_c10) = sk_c9
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f11]) ).
fof(f13,negated_conjecture,
( multiply(sk_c1,sk_c10) = sk_c9
| multiply(sk_c8,sk_c7) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_5) ).
fof(f14,plain,
( multiply(sk_c1,sk_c10) = sk_c9
| sk_c9 = multiply(sk_c8,sk_c7) ),
inference(reorient_equations,[],[f13]) ).
fof(f15,negated_conjecture,
( multiply(sk_c1,sk_c10) = sk_c9
| multiply(sk_c6,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_6) ).
fof(f16,plain,
( multiply(sk_c1,sk_c10) = sk_c9
| sk_c7 = multiply(sk_c6,sk_c8) ),
inference(reorient_equations,[],[f15]) ).
fof(f17,negated_conjecture,
( multiply(sk_c1,sk_c10) = sk_c9
| inverse(sk_c6) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_7) ).
fof(f18,plain,
( multiply(sk_c1,sk_c10) = sk_c9
| sk_c8 = inverse(sk_c6) ),
inference(reorient_equations,[],[f17]) ).
fof(f19,negated_conjecture,
( inverse(sk_c1) = sk_c10
| multiply(sk_c4,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_8) ).
fof(f20,plain,
( sk_c10 = inverse(sk_c1)
| sk_c9 = multiply(sk_c4,sk_c10) ),
inference(reorient_equations,[],[f19]) ).
fof(f21,negated_conjecture,
( inverse(sk_c1) = sk_c10
| inverse(sk_c4) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_9) ).
fof(f22,plain,
( sk_c10 = inverse(sk_c1)
| sk_c10 = inverse(sk_c4) ),
inference(reorient_equations,[],[f21]) ).
fof(f23,negated_conjecture,
( inverse(sk_c1) = sk_c10
| multiply(sk_c5,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_10) ).
fof(f24,plain,
( sk_c10 = inverse(sk_c1)
| sk_c9 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f23]) ).
fof(f25,negated_conjecture,
( inverse(sk_c1) = sk_c10
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_11) ).
fof(f26,plain,
( sk_c10 = inverse(sk_c1)
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f25]) ).
fof(f27,negated_conjecture,
( inverse(sk_c1) = sk_c10
| multiply(sk_c8,sk_c7) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_12) ).
fof(f28,plain,
( sk_c10 = inverse(sk_c1)
| sk_c9 = multiply(sk_c8,sk_c7) ),
inference(reorient_equations,[],[f27]) ).
fof(f29,negated_conjecture,
( inverse(sk_c1) = sk_c10
| multiply(sk_c6,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_13) ).
fof(f30,plain,
( sk_c10 = inverse(sk_c1)
| sk_c7 = multiply(sk_c6,sk_c8) ),
inference(reorient_equations,[],[f29]) ).
fof(f31,negated_conjecture,
( inverse(sk_c1) = sk_c10
| inverse(sk_c6) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_14) ).
fof(f32,plain,
( sk_c10 = inverse(sk_c1)
| sk_c8 = inverse(sk_c6) ),
inference(reorient_equations,[],[f31]) ).
fof(f37,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c8
| multiply(sk_c5,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_17) ).
fof(f38,plain,
( sk_c8 = multiply(sk_c2,sk_c9)
| sk_c9 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f37]) ).
fof(f39,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c8
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_18) ).
fof(f40,plain,
( sk_c8 = multiply(sk_c2,sk_c9)
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f39]) ).
fof(f41,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c8
| multiply(sk_c8,sk_c7) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_19) ).
fof(f42,plain,
( sk_c8 = multiply(sk_c2,sk_c9)
| sk_c9 = multiply(sk_c8,sk_c7) ),
inference(reorient_equations,[],[f41]) ).
fof(f43,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c8
| multiply(sk_c6,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_20) ).
fof(f44,plain,
( sk_c8 = multiply(sk_c2,sk_c9)
| sk_c7 = multiply(sk_c6,sk_c8) ),
inference(reorient_equations,[],[f43]) ).
fof(f45,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c8
| inverse(sk_c6) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_21) ).
fof(f46,plain,
( sk_c8 = multiply(sk_c2,sk_c9)
| sk_c8 = inverse(sk_c6) ),
inference(reorient_equations,[],[f45]) ).
fof(f51,negated_conjecture,
( inverse(sk_c2) = sk_c9
| multiply(sk_c5,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_24) ).
fof(f52,plain,
( sk_c9 = inverse(sk_c2)
| sk_c9 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f51]) ).
fof(f53,negated_conjecture,
( inverse(sk_c2) = sk_c9
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_25) ).
fof(f54,plain,
( sk_c9 = inverse(sk_c2)
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f53]) ).
fof(f55,negated_conjecture,
( inverse(sk_c2) = sk_c9
| multiply(sk_c8,sk_c7) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_26) ).
fof(f56,plain,
( sk_c9 = inverse(sk_c2)
| sk_c9 = multiply(sk_c8,sk_c7) ),
inference(reorient_equations,[],[f55]) ).
fof(f57,negated_conjecture,
( inverse(sk_c2) = sk_c9
| multiply(sk_c6,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_27) ).
fof(f58,plain,
( sk_c9 = inverse(sk_c2)
| sk_c7 = multiply(sk_c6,sk_c8) ),
inference(reorient_equations,[],[f57]) ).
fof(f59,negated_conjecture,
( inverse(sk_c2) = sk_c9
| inverse(sk_c6) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_28) ).
fof(f60,plain,
( sk_c9 = inverse(sk_c2)
| sk_c8 = inverse(sk_c6) ),
inference(reorient_equations,[],[f59]) ).
fof(f65,negated_conjecture,
( inverse(sk_c3) = sk_c9
| multiply(sk_c5,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_31) ).
fof(f66,plain,
( sk_c9 = inverse(sk_c3)
| sk_c9 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f65]) ).
fof(f67,negated_conjecture,
( inverse(sk_c3) = sk_c9
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_32) ).
fof(f68,plain,
( sk_c9 = inverse(sk_c3)
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f67]) ).
fof(f69,negated_conjecture,
( inverse(sk_c3) = sk_c9
| multiply(sk_c8,sk_c7) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_33) ).
fof(f70,plain,
( sk_c9 = inverse(sk_c3)
| sk_c9 = multiply(sk_c8,sk_c7) ),
inference(reorient_equations,[],[f69]) ).
fof(f71,negated_conjecture,
( inverse(sk_c3) = sk_c9
| multiply(sk_c6,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_34) ).
fof(f72,plain,
( sk_c9 = inverse(sk_c3)
| sk_c7 = multiply(sk_c6,sk_c8) ),
inference(reorient_equations,[],[f71]) ).
fof(f73,negated_conjecture,
( inverse(sk_c3) = sk_c9
| inverse(sk_c6) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_35) ).
fof(f74,plain,
( sk_c9 = inverse(sk_c3)
| sk_c8 = inverse(sk_c6) ),
inference(reorient_equations,[],[f73]) ).
fof(f79,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c9
| multiply(sk_c5,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_38) ).
fof(f80,plain,
( sk_c9 = multiply(sk_c3,sk_c8)
| sk_c9 = 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/sandbox2/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_c8,sk_c7) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_40) ).
fof(f84,plain,
( sk_c9 = multiply(sk_c3,sk_c8)
| sk_c9 = multiply(sk_c8,sk_c7) ),
inference(reorient_equations,[],[f83]) ).
fof(f85,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c9
| multiply(sk_c6,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_41) ).
fof(f86,plain,
( sk_c9 = multiply(sk_c3,sk_c8)
| sk_c7 = multiply(sk_c6,sk_c8) ),
inference(reorient_equations,[],[f85]) ).
fof(f87,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c9
| inverse(sk_c6) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_42) ).
fof(f88,plain,
( sk_c9 = multiply(sk_c3,sk_c8)
| sk_c8 = inverse(sk_c6) ),
inference(reorient_equations,[],[f87]) ).
fof(f89,negated_conjecture,
! [X2,X3,X0,X1,X6,X4,X5] :
( multiply(X0,sk_c10) != sk_c9
| inverse(X0) != sk_c10
| multiply(X1,sk_c9) != sk_c8
| inverse(X1) != sk_c9
| inverse(X2) != sk_c9
| multiply(X2,sk_c8) != sk_c9
| multiply(X3,sk_c10) != sk_c9
| inverse(X3) != sk_c10
| multiply(X4,sk_c8) != sk_c9
| inverse(X4) != sk_c8
| multiply(sk_c8,X5) != sk_c9
| multiply(X6,sk_c8) != X5
| inverse(X6) != sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_43) ).
fof(f90,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( sk_c9 != multiply(X0,sk_c10)
| inverse(X0) != sk_c10
| sk_c8 != multiply(X1,sk_c9)
| sk_c9 != inverse(X1)
| sk_c9 != inverse(X2)
| sk_c9 != multiply(X2,sk_c8)
| sk_c9 != multiply(X3,sk_c10)
| sk_c10 != inverse(X3)
| sk_c9 != multiply(X4,sk_c8)
| sk_c8 != inverse(X4)
| sk_c9 != multiply(sk_c8,X5)
| multiply(X6,sk_c8) != X5
| sk_c8 != inverse(X6) ),
inference(reorient_equations,[],[f89]) ).
fof(f91,plain,
! [X2,X3,X0,X1,X6,X4] :
( sk_c9 != multiply(X0,sk_c10)
| inverse(X0) != sk_c10
| sk_c8 != multiply(X1,sk_c9)
| sk_c9 != inverse(X1)
| sk_c9 != inverse(X2)
| sk_c9 != multiply(X2,sk_c8)
| sk_c9 != multiply(X3,sk_c10)
| sk_c10 != inverse(X3)
| sk_c9 != multiply(X4,sk_c8)
| sk_c8 != inverse(X4)
| sk_c9 != multiply(sk_c8,multiply(X6,sk_c8))
| sk_c8 != inverse(X6) ),
inference(equality_resolution,[],[f90]) ).
fof(f93,definition,
( spl0_1
<=> ! [X6] :
( sk_c9 != multiply(sk_c8,multiply(X6,sk_c8))
| sk_c8 != inverse(X6) ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f94,plain,
( ! [X6] :
( sk_c9 != multiply(sk_c8,multiply(X6,sk_c8))
| sk_c8 != inverse(X6) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f93]) ).
fof(f96,definition,
( spl0_2
<=> ! [X4] :
( sk_c9 != multiply(X4,sk_c8)
| sk_c8 != inverse(X4) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f97,plain,
( ! [X4] :
( sk_c9 != multiply(X4,sk_c8)
| sk_c8 != inverse(X4) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f96]) ).
fof(f99,definition,
( spl0_3
<=> ! [X3] :
( sk_c9 != multiply(X3,sk_c10)
| sk_c10 != inverse(X3) ) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f100,plain,
( ! [X3] :
( sk_c9 != multiply(X3,sk_c10)
| sk_c10 != inverse(X3) )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f99]) ).
fof(f102,definition,
( spl0_4
<=> ! [X2] :
( sk_c9 != inverse(X2)
| sk_c9 != multiply(X2,sk_c8) ) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f103,plain,
( ! [X2] :
( sk_c9 != inverse(X2)
| sk_c9 != multiply(X2,sk_c8) )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f102]) ).
fof(f105,definition,
( spl0_5
<=> ! [X1] :
( sk_c8 != multiply(X1,sk_c9)
| sk_c9 != inverse(X1) ) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f106,plain,
( ! [X1] :
( sk_c9 != inverse(X1)
| sk_c8 != multiply(X1,sk_c9) )
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f105]) ).
fof(f107,plain,
( spl0_1
| spl0_2
| spl0_3
| spl0_4
| spl0_5
| spl0_3 ),
inference(avatar_split_clause,[],[f91,f99,f105,f102,f99,f96,f93]) ).
fof(f109,definition,
( spl0_6
<=> sk_c8 = inverse(sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f111,plain,
( sk_c8 = inverse(sk_c6)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f109]) ).
fof(f113,definition,
( spl0_7
<=> sk_c9 = multiply(sk_c3,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f115,plain,
( sk_c9 = multiply(sk_c3,sk_c8)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f113]) ).
fof(f116,plain,
( spl0_6
| spl0_7 ),
inference(avatar_split_clause,[],[f88,f113,f109]) ).
fof(f118,definition,
( spl0_8
<=> sk_c7 = multiply(sk_c6,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f120,plain,
( sk_c7 = multiply(sk_c6,sk_c8)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f118]) ).
fof(f121,plain,
( spl0_8
| spl0_7 ),
inference(avatar_split_clause,[],[f86,f113,f118]) ).
fof(f123,definition,
( spl0_9
<=> sk_c9 = multiply(sk_c8,sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f125,plain,
( sk_c9 = multiply(sk_c8,sk_c7)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f123]) ).
fof(f126,plain,
( spl0_9
| spl0_7 ),
inference(avatar_split_clause,[],[f84,f113,f123]) ).
fof(f128,definition,
( spl0_10
<=> sk_c8 = inverse(sk_c5) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f130,plain,
( sk_c8 = inverse(sk_c5)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f128]) ).
fof(f131,plain,
( spl0_10
| spl0_7 ),
inference(avatar_split_clause,[],[f82,f113,f128]) ).
fof(f133,definition,
( spl0_11
<=> sk_c9 = multiply(sk_c5,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f135,plain,
( sk_c9 = multiply(sk_c5,sk_c8)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f133]) ).
fof(f136,plain,
( spl0_11
| spl0_7 ),
inference(avatar_split_clause,[],[f80,f113,f133]) ).
fof(f138,definition,
( spl0_12
<=> sk_c10 = inverse(sk_c4) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f140,plain,
( sk_c10 = inverse(sk_c4)
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f138]) ).
fof(f143,definition,
( spl0_13
<=> sk_c9 = multiply(sk_c4,sk_c10) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f145,plain,
( sk_c9 = multiply(sk_c4,sk_c10)
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f143]) ).
fof(f148,definition,
( spl0_14
<=> sk_c9 = inverse(sk_c3) ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
fof(f150,plain,
( sk_c9 = inverse(sk_c3)
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f148]) ).
fof(f151,plain,
( spl0_6
| spl0_14 ),
inference(avatar_split_clause,[],[f74,f148,f109]) ).
fof(f152,plain,
( spl0_8
| spl0_14 ),
inference(avatar_split_clause,[],[f72,f148,f118]) ).
fof(f153,plain,
( spl0_9
| spl0_14 ),
inference(avatar_split_clause,[],[f70,f148,f123]) ).
fof(f154,plain,
( spl0_10
| spl0_14 ),
inference(avatar_split_clause,[],[f68,f148,f128]) ).
fof(f155,plain,
( spl0_11
| spl0_14 ),
inference(avatar_split_clause,[],[f66,f148,f133]) ).
fof(f159,definition,
( spl0_15
<=> sk_c9 = inverse(sk_c2) ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
fof(f161,plain,
( sk_c9 = inverse(sk_c2)
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f159]) ).
fof(f162,plain,
( spl0_6
| spl0_15 ),
inference(avatar_split_clause,[],[f60,f159,f109]) ).
fof(f163,plain,
( spl0_8
| spl0_15 ),
inference(avatar_split_clause,[],[f58,f159,f118]) ).
fof(f164,plain,
( spl0_9
| spl0_15 ),
inference(avatar_split_clause,[],[f56,f159,f123]) ).
fof(f165,plain,
( spl0_10
| spl0_15 ),
inference(avatar_split_clause,[],[f54,f159,f128]) ).
fof(f166,plain,
( spl0_11
| spl0_15 ),
inference(avatar_split_clause,[],[f52,f159,f133]) ).
fof(f170,definition,
( spl0_16
<=> sk_c8 = multiply(sk_c2,sk_c9) ),
introduced(definition,[new_symbols(definition,[spl0_16])],[avatar_definition]) ).
fof(f173,plain,
( spl0_6
| spl0_16 ),
inference(avatar_split_clause,[],[f46,f170,f109]) ).
fof(f174,plain,
( spl0_8
| spl0_16 ),
inference(avatar_split_clause,[],[f44,f170,f118]) ).
fof(f175,plain,
( spl0_9
| spl0_16 ),
inference(avatar_split_clause,[],[f42,f170,f123]) ).
fof(f176,plain,
( spl0_10
| spl0_16 ),
inference(avatar_split_clause,[],[f40,f170,f128]) ).
fof(f177,plain,
( spl0_11
| spl0_16 ),
inference(avatar_split_clause,[],[f38,f170,f133]) ).
fof(f181,definition,
( spl0_17
<=> sk_c10 = inverse(sk_c1) ),
introduced(definition,[new_symbols(definition,[spl0_17])],[avatar_definition]) ).
fof(f183,plain,
( sk_c10 = inverse(sk_c1)
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f181]) ).
fof(f184,plain,
( spl0_6
| spl0_17 ),
inference(avatar_split_clause,[],[f32,f181,f109]) ).
fof(f185,plain,
( spl0_8
| spl0_17 ),
inference(avatar_split_clause,[],[f30,f181,f118]) ).
fof(f186,plain,
( spl0_9
| spl0_17 ),
inference(avatar_split_clause,[],[f28,f181,f123]) ).
fof(f187,plain,
( spl0_10
| spl0_17 ),
inference(avatar_split_clause,[],[f26,f181,f128]) ).
fof(f188,plain,
( spl0_11
| spl0_17 ),
inference(avatar_split_clause,[],[f24,f181,f133]) ).
fof(f189,plain,
( spl0_12
| spl0_17 ),
inference(avatar_split_clause,[],[f22,f181,f138]) ).
fof(f190,plain,
( spl0_13
| spl0_17 ),
inference(avatar_split_clause,[],[f20,f181,f143]) ).
fof(f192,definition,
( spl0_18
<=> multiply(sk_c1,sk_c10) = sk_c9 ),
introduced(definition,[new_symbols(definition,[spl0_18])],[avatar_definition]) ).
fof(f194,plain,
( multiply(sk_c1,sk_c10) = sk_c9
| ~ spl0_18 ),
inference(avatar_component_clause,[],[f192]) ).
fof(f195,plain,
( spl0_6
| spl0_18 ),
inference(avatar_split_clause,[],[f18,f192,f109]) ).
fof(f196,plain,
( spl0_8
| spl0_18 ),
inference(avatar_split_clause,[],[f16,f192,f118]) ).
fof(f197,plain,
( spl0_9
| spl0_18 ),
inference(avatar_split_clause,[],[f14,f192,f123]) ).
fof(f198,plain,
( spl0_10
| spl0_18 ),
inference(avatar_split_clause,[],[f12,f192,f128]) ).
fof(f199,plain,
( spl0_11
| spl0_18 ),
inference(avatar_split_clause,[],[f10,f192,f133]) ).
fof(f200,plain,
( spl0_12
| spl0_18 ),
inference(avatar_split_clause,[],[f8,f192,f138]) ).
fof(f201,plain,
( spl0_13
| spl0_18 ),
inference(avatar_split_clause,[],[f6,f192,f143]) ).
fof(f202,plain,
( sk_c9 != sk_c9
| sk_c8 != inverse(sk_c5)
| ~ spl0_2
| ~ spl0_11 ),
inference(superposition,[],[f97,f135]) ).
fof(f204,plain,
( sk_c8 != inverse(sk_c5)
| ~ spl0_2
| ~ spl0_11 ),
inference(trivial_inequality_removal,[],[f202]) ).
fof(f208,plain,
( ~ spl0_10
| ~ spl0_2
| ~ spl0_11 ),
inference(avatar_split_clause,[],[f204,f133,f96,f128]) ).
fof(f209,plain,
( sk_c9 != sk_c9
| sk_c8 != inverse(sk_c3)
| ~ spl0_2
| ~ spl0_7 ),
inference(superposition,[],[f97,f115]) ).
fof(f210,plain,
( sk_c8 != inverse(sk_c3)
| ~ spl0_2
| ~ spl0_7 ),
inference(trivial_inequality_removal,[],[f209]) ).
fof(f211,plain,
( sk_c9 != sk_c8
| ~ spl0_2
| ~ spl0_7
| ~ spl0_14 ),
inference(forward_demodulation,[],[f210,f150]) ).
fof(f213,plain,
( identity = multiply(sk_c10,sk_c1)
| ~ spl0_17 ),
inference(superposition,[],[f3,f183]) ).
fof(f215,plain,
( identity = multiply(sk_c8,sk_c6)
| ~ spl0_6 ),
inference(superposition,[],[f3,f111]) ).
fof(f216,plain,
( identity = multiply(sk_c9,sk_c2)
| ~ spl0_15 ),
inference(superposition,[],[f3,f161]) ).
fof(f230,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[],[f4,f3]) ).
fof(f231,plain,
( ! [X0] : multiply(sk_c1,multiply(sk_c10,X0)) = multiply(sk_c9,X0)
| ~ spl0_18 ),
inference(superposition,[],[f4,f194]) ).
fof(f239,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f230,f1]) ).
fof(f242,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c10,multiply(sk_c1,X0))
| ~ spl0_17 ),
inference(superposition,[],[f4,f213]) ).
fof(f243,plain,
( ! [X0] : multiply(sk_c10,multiply(sk_c1,X0)) = X0
| ~ spl0_17 ),
inference(forward_demodulation,[],[f242,f1]) ).
fof(f246,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c8,multiply(sk_c6,X0))
| ~ spl0_6 ),
inference(superposition,[],[f4,f215]) ).
fof(f247,plain,
( ! [X0] : multiply(sk_c8,multiply(sk_c6,X0)) = X0
| ~ spl0_6 ),
inference(forward_demodulation,[],[f246,f1]) ).
fof(f248,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c9,multiply(sk_c2,X0))
| ~ spl0_15 ),
inference(superposition,[],[f4,f216]) ).
fof(f249,plain,
( ! [X0] : multiply(sk_c9,multiply(sk_c2,X0)) = X0
| ~ spl0_15 ),
inference(forward_demodulation,[],[f248,f1]) ).
fof(f252,plain,
( sk_c10 = multiply(sk_c10,sk_c9)
| ~ spl0_17
| ~ spl0_18 ),
inference(superposition,[],[f243,f194]) ).
fof(f262,plain,
( multiply(sk_c1,sk_c10) = multiply(sk_c9,sk_c9)
| ~ spl0_17
| ~ spl0_18 ),
inference(superposition,[],[f231,f252]) ).
fof(f264,plain,
( sk_c9 = multiply(sk_c9,sk_c9)
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f262,f194]) ).
fof(f295,plain,
( sk_c8 = multiply(sk_c8,sk_c7)
| ~ spl0_6
| ~ spl0_8 ),
inference(superposition,[],[f247,f120]) ).
fof(f302,plain,
( sk_c9 = sk_c8
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f295,f125]) ).
fof(f396,plain,
( sk_c8 = multiply(inverse(sk_c3),sk_c9)
| ~ spl0_7 ),
inference(superposition,[],[f239,f115]) ).
fof(f402,plain,
( sk_c8 = multiply(sk_c9,sk_c9)
| ~ spl0_7
| ~ spl0_14 ),
inference(forward_demodulation,[],[f396,f150]) ).
fof(f412,plain,
( sk_c9 = sk_c8
| ~ spl0_7
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f402,f264]) ).
fof(f417,plain,
( $false
| ~ spl0_2
| ~ spl0_7
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[],[f412,f211]) ).
fof(f418,plain,
( ~ spl0_2
| ~ spl0_7
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(avatar_contradiction_clause,[],[f417]) ).
fof(f425,plain,
( sk_c9 != sk_c9
| sk_c9 != multiply(sk_c3,sk_c8)
| ~ spl0_4
| ~ spl0_14 ),
inference(superposition,[],[f103,f150]) ).
fof(f426,plain,
( sk_c9 != multiply(sk_c3,sk_c8)
| ~ spl0_4
| ~ spl0_14 ),
inference(trivial_inequality_removal,[],[f425]) ).
fof(f428,plain,
( $false
| ~ spl0_4
| ~ spl0_7
| ~ spl0_14 ),
inference(forward_subsumption_resolution,[],[f426,f115]) ).
fof(f429,plain,
( ~ spl0_4
| ~ spl0_7
| ~ spl0_14 ),
inference(avatar_contradiction_clause,[],[f428]) ).
fof(f435,definition,
( spl0_23
<=> sk_c9 = sk_c8 ),
introduced(definition,[new_symbols(definition,[spl0_23])],[avatar_definition]) ).
fof(f436,plain,
( sk_c9 = sk_c8
| ~ spl0_23 ),
inference(avatar_component_clause,[],[f435]) ).
fof(f453,plain,
( spl0_23
| ~ spl0_7
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(avatar_split_clause,[],[f412,f192,f181,f148,f113,f435]) ).
fof(f457,plain,
( sk_c9 != sk_c9
| sk_c8 != multiply(sk_c2,sk_c9)
| ~ spl0_5
| ~ spl0_15 ),
inference(superposition,[],[f106,f161]) ).
fof(f480,plain,
( sk_c9 = multiply(sk_c9,sk_c7)
| ~ spl0_9
| ~ spl0_23 ),
inference(superposition,[],[f125,f436]) ).
fof(f481,plain,
( sk_c9 = multiply(sk_c5,sk_c9)
| ~ spl0_11
| ~ spl0_23 ),
inference(superposition,[],[f135,f436]) ).
fof(f493,plain,
( sk_c9 != sk_c9
| sk_c10 != inverse(sk_c1)
| ~ spl0_3
| ~ spl0_18 ),
inference(superposition,[],[f100,f194]) ).
fof(f494,plain,
( sk_c9 != sk_c9
| sk_c10 != inverse(sk_c4)
| ~ spl0_3
| ~ spl0_13 ),
inference(superposition,[],[f100,f145]) ).
fof(f495,plain,
( sk_c10 != inverse(sk_c4)
| ~ spl0_3
| ~ spl0_13 ),
inference(trivial_inequality_removal,[],[f494]) ).
fof(f496,plain,
( sk_c10 != inverse(sk_c1)
| ~ spl0_3
| ~ spl0_18 ),
inference(trivial_inequality_removal,[],[f493]) ).
fof(f497,plain,
( $false
| ~ spl0_3
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f495,f140]) ).
fof(f498,plain,
( ~ spl0_3
| ~ spl0_12
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[],[f497]) ).
fof(f499,plain,
( $false
| ~ spl0_3
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[],[f496,f183]) ).
fof(f500,plain,
( ~ spl0_3
| ~ spl0_17
| ~ spl0_18 ),
inference(avatar_contradiction_clause,[],[f499]) ).
fof(f508,plain,
( ! [X6] :
( sk_c9 != multiply(sk_c9,multiply(X6,sk_c9))
| sk_c8 != inverse(X6) )
| ~ spl0_1
| ~ spl0_23 ),
inference(forward_demodulation,[],[f94,f436]) ).
fof(f509,plain,
( ! [X6] :
( sk_c9 != inverse(X6)
| sk_c9 != multiply(sk_c9,multiply(X6,sk_c9)) )
| ~ spl0_1
| ~ spl0_23 ),
inference(forward_demodulation,[],[f508,f436]) ).
fof(f514,plain,
( sk_c9 != sk_c9
| sk_c9 != multiply(sk_c9,multiply(sk_c2,sk_c9))
| ~ spl0_1
| ~ spl0_15
| ~ spl0_23 ),
inference(superposition,[],[f509,f161]) ).
fof(f517,plain,
( sk_c9 != multiply(sk_c9,multiply(sk_c2,sk_c9))
| ~ spl0_1
| ~ spl0_15
| ~ spl0_23 ),
inference(trivial_inequality_removal,[],[f514]) ).
fof(f518,plain,
( $false
| ~ spl0_1
| ~ spl0_15
| ~ spl0_23 ),
inference(forward_subsumption_resolution,[],[f517,f249]) ).
fof(f519,plain,
( ~ spl0_1
| ~ spl0_15
| ~ spl0_23 ),
inference(avatar_contradiction_clause,[],[f518]) ).
fof(f531,plain,
( sk_c8 != multiply(sk_c2,sk_c9)
| ~ spl0_5
| ~ spl0_15 ),
inference(trivial_inequality_removal,[],[f457]) ).
fof(f533,plain,
( ! [X1] :
( sk_c9 != inverse(X1)
| sk_c9 != multiply(X1,sk_c9) )
| ~ spl0_5
| ~ spl0_23 ),
inference(forward_demodulation,[],[f106,f436]) ).
fof(f541,plain,
( sk_c7 = multiply(sk_c6,sk_c9)
| ~ spl0_8
| ~ spl0_23 ),
inference(forward_demodulation,[],[f120,f436]) ).
fof(f543,plain,
( sk_c9 = inverse(sk_c5)
| ~ spl0_10
| ~ spl0_23 ),
inference(forward_demodulation,[],[f130,f436]) ).
fof(f566,plain,
( sk_c9 != sk_c9
| sk_c9 != multiply(sk_c5,sk_c9)
| ~ spl0_5
| ~ spl0_10
| ~ spl0_23 ),
inference(superposition,[],[f533,f543]) ).
fof(f572,plain,
( sk_c9 != multiply(sk_c5,sk_c9)
| ~ spl0_5
| ~ spl0_10
| ~ spl0_23 ),
inference(trivial_inequality_removal,[],[f566]) ).
fof(f588,plain,
( $false
| ~ spl0_5
| ~ spl0_10
| ~ spl0_11
| ~ spl0_23 ),
inference(forward_subsumption_resolution,[],[f481,f572]) ).
fof(f589,plain,
( ~ spl0_5
| ~ spl0_10
| ~ spl0_11
| ~ spl0_23 ),
inference(avatar_contradiction_clause,[],[f588]) ).
fof(f591,plain,
( ~ spl0_16
| ~ spl0_5
| ~ spl0_15 ),
inference(avatar_split_clause,[],[f531,f159,f105,f170]) ).
fof(f592,plain,
( spl0_23
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(avatar_split_clause,[],[f302,f123,f118,f109,f435]) ).
fof(f620,plain,
( sk_c9 != sk_c8
| sk_c9 != multiply(sk_c9,multiply(sk_c6,sk_c9))
| ~ spl0_1
| ~ spl0_6
| ~ spl0_23 ),
inference(superposition,[],[f509,f111]) ).
fof(f624,plain,
( sk_c9 != multiply(sk_c9,multiply(sk_c6,sk_c9))
| ~ spl0_1
| ~ spl0_6
| ~ spl0_23 ),
inference(forward_subsumption_resolution,[],[f620,f436]) ).
fof(f625,plain,
( sk_c9 != multiply(sk_c9,sk_c7)
| ~ spl0_1
| ~ spl0_6
| ~ spl0_8
| ~ spl0_23 ),
inference(forward_demodulation,[],[f624,f541]) ).
fof(f626,plain,
( $false
| ~ spl0_1
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_23 ),
inference(forward_subsumption_resolution,[],[f480,f625]) ).
fof(f627,plain,
( ~ spl0_1
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_23 ),
inference(avatar_contradiction_clause,[],[f626]) ).
fof(f628,plain,
( ! [X2] :
( sk_c9 != inverse(X2)
| sk_c9 != multiply(X2,sk_c9) )
| ~ spl0_4
| ~ spl0_23 ),
inference(forward_demodulation,[],[f103,f436]) ).
fof(f638,plain,
( sk_c9 != sk_c9
| sk_c9 != multiply(sk_c5,sk_c9)
| ~ spl0_4
| ~ spl0_10
| ~ spl0_23 ),
inference(superposition,[],[f628,f543]) ).
fof(f640,plain,
( sk_c9 != multiply(sk_c5,sk_c9)
| ~ spl0_4
| ~ spl0_10
| ~ spl0_23 ),
inference(trivial_inequality_removal,[],[f638]) ).
fof(f643,plain,
( $false
| ~ spl0_4
| ~ spl0_10
| ~ spl0_11
| ~ spl0_23 ),
inference(forward_subsumption_resolution,[],[f481,f640]) ).
fof(f644,plain,
( ~ spl0_4
| ~ spl0_10
| ~ spl0_11
| ~ spl0_23 ),
inference(avatar_contradiction_clause,[],[f643]) ).
cnf(s1,plain,
( spl0_3
| spl0_2
| spl0_1
| spl0_3
| spl0_4
| spl0_5 ),
inference(sat_conversion,[],[f107]) ).
cnf(s2,plain,
( spl0_1
| spl0_2
| spl0_3
| spl0_4
| spl0_5 ),
inference(rat,[],[s1]) ).
cnf(s3,plain,
( spl0_6
| spl0_7 ),
inference(sat_conversion,[],[f116]) ).
cnf(s4,plain,
( spl0_7
| spl0_8 ),
inference(sat_conversion,[],[f121]) ).
cnf(s5,plain,
( spl0_7
| spl0_9 ),
inference(sat_conversion,[],[f126]) ).
cnf(s6,plain,
( spl0_7
| spl0_10 ),
inference(sat_conversion,[],[f131]) ).
cnf(s7,plain,
( spl0_7
| spl0_11 ),
inference(sat_conversion,[],[f136]) ).
cnf(s10,plain,
( spl0_6
| spl0_14 ),
inference(sat_conversion,[],[f151]) ).
cnf(s11,plain,
( spl0_8
| spl0_14 ),
inference(sat_conversion,[],[f152]) ).
cnf(s12,plain,
( spl0_9
| spl0_14 ),
inference(sat_conversion,[],[f153]) ).
cnf(s13,plain,
( spl0_10
| spl0_14 ),
inference(sat_conversion,[],[f154]) ).
cnf(s14,plain,
( spl0_11
| spl0_14 ),
inference(sat_conversion,[],[f155]) ).
cnf(s17,plain,
( spl0_6
| spl0_15 ),
inference(sat_conversion,[],[f162]) ).
cnf(s18,plain,
( spl0_8
| spl0_15 ),
inference(sat_conversion,[],[f163]) ).
cnf(s19,plain,
( spl0_9
| spl0_15 ),
inference(sat_conversion,[],[f164]) ).
cnf(s20,plain,
( spl0_10
| spl0_15 ),
inference(sat_conversion,[],[f165]) ).
cnf(s21,plain,
( spl0_11
| spl0_15 ),
inference(sat_conversion,[],[f166]) ).
cnf(s24,plain,
( spl0_6
| spl0_16 ),
inference(sat_conversion,[],[f173]) ).
cnf(s25,plain,
( spl0_8
| spl0_16 ),
inference(sat_conversion,[],[f174]) ).
cnf(s26,plain,
( spl0_9
| spl0_16 ),
inference(sat_conversion,[],[f175]) ).
cnf(s27,plain,
( spl0_10
| spl0_16 ),
inference(sat_conversion,[],[f176]) ).
cnf(s28,plain,
( spl0_11
| spl0_16 ),
inference(sat_conversion,[],[f177]) ).
cnf(s31,plain,
( spl0_6
| spl0_17 ),
inference(sat_conversion,[],[f184]) ).
cnf(s32,plain,
( spl0_8
| spl0_17 ),
inference(sat_conversion,[],[f185]) ).
cnf(s33,plain,
( spl0_9
| spl0_17 ),
inference(sat_conversion,[],[f186]) ).
cnf(s34,plain,
( spl0_10
| spl0_17 ),
inference(sat_conversion,[],[f187]) ).
cnf(s35,plain,
( spl0_11
| spl0_17 ),
inference(sat_conversion,[],[f188]) ).
cnf(s36,plain,
( spl0_12
| spl0_17 ),
inference(sat_conversion,[],[f189]) ).
cnf(s37,plain,
( spl0_13
| spl0_17 ),
inference(sat_conversion,[],[f190]) ).
cnf(s38,plain,
( spl0_6
| spl0_18 ),
inference(sat_conversion,[],[f195]) ).
cnf(s39,plain,
( spl0_8
| spl0_18 ),
inference(sat_conversion,[],[f196]) ).
cnf(s40,plain,
( spl0_9
| spl0_18 ),
inference(sat_conversion,[],[f197]) ).
cnf(s41,plain,
( spl0_10
| spl0_18 ),
inference(sat_conversion,[],[f198]) ).
cnf(s42,plain,
( spl0_11
| spl0_18 ),
inference(sat_conversion,[],[f199]) ).
cnf(s43,plain,
( spl0_12
| spl0_18 ),
inference(sat_conversion,[],[f200]) ).
cnf(s44,plain,
( spl0_13
| spl0_18 ),
inference(sat_conversion,[],[f201]) ).
cnf(s46,plain,
( ~ spl0_2
| ~ spl0_10
| ~ spl0_11 ),
inference(sat_conversion,[],[f208]) ).
cnf(s52,plain,
( ~ spl0_2
| ~ spl0_7
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(sat_conversion,[],[f418]) ).
cnf(s55,plain,
( ~ spl0_4
| ~ spl0_7
| ~ spl0_14 ),
inference(sat_conversion,[],[f429]) ).
cnf(s59,plain,
( ~ spl0_7
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18
| spl0_23 ),
inference(sat_conversion,[],[f453]) ).
cnf(s64,plain,
( ~ spl0_3
| ~ spl0_12
| ~ spl0_13 ),
inference(sat_conversion,[],[f498]) ).
cnf(s65,plain,
( ~ spl0_3
| ~ spl0_17
| ~ spl0_18 ),
inference(sat_conversion,[],[f500]) ).
cnf(s67,plain,
( ~ spl0_1
| ~ spl0_15
| ~ spl0_23 ),
inference(sat_conversion,[],[f519]) ).
cnf(s74,plain,
( ~ spl0_5
| ~ spl0_10
| ~ spl0_11
| ~ spl0_23 ),
inference(sat_conversion,[],[f589]) ).
cnf(s76,plain,
( ~ spl0_5
| ~ spl0_15
| ~ spl0_16 ),
inference(sat_conversion,[],[f591]) ).
cnf(s78,plain,
( ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| spl0_23 ),
inference(sat_conversion,[],[f592]) ).
cnf(s80,plain,
( ~ spl0_1
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_23 ),
inference(sat_conversion,[],[f627]) ).
cnf(s81,plain,
( ~ spl0_4
| ~ spl0_10
| ~ spl0_11
| ~ spl0_23 ),
inference(sat_conversion,[],[f644]) ).
cnf(s82,plain,
( spl0_6
| ~ spl0_5 ),
inference(rat,[],[s76,s17,s24]) ).
cnf(s83,plain,
( spl0_16
| ~ spl0_5 ),
inference(rat,[],[s78,s74,s25,s26,s27,s28,s82]) ).
cnf(s84,plain,
~ spl0_5,
inference(rat,[],[s78,s74,s18,s19,s20,s21,s76,s83,s82]) ).
cnf(s86,plain,
( spl0_11
| ~ spl0_4 ),
inference(rat,[],[s55,s7,s14]) ).
cnf(s87,plain,
( spl0_10
| ~ spl0_4 ),
inference(rat,[],[s55,s6,s13]) ).
cnf(s88,plain,
( spl0_9
| spl0_23 ),
inference(rat,[],[s59,s5,s12,s33,s40]) ).
cnf(s89,plain,
( spl0_8
| spl0_23 ),
inference(rat,[],[s59,s4,s11,s32,s39]) ).
cnf(s90,plain,
( ~ spl0_8
| spl0_23
| ~ spl0_9 ),
inference(rat,[],[s59,s3,s10,s31,s38,s78]) ).
cnf(s91,plain,
spl0_23,
inference(rat,[],[s90,s89,s88]) ).
cnf(s92,plain,
~ spl0_4,
inference(rat,[],[s81,s87,s86,s91]) ).
cnf(s94,plain,
( spl0_18
| ~ spl0_3 ),
inference(rat,[],[s64,s43,s44]) ).
cnf(s95,plain,
( ~ spl0_18
| ~ spl0_3 ),
inference(rat,[],[s64,s36,s37,s65]) ).
cnf(s96,plain,
~ spl0_3,
inference(rat,[],[s95,s94]) ).
cnf(s97,plain,
( spl0_18
| ~ spl0_2 ),
inference(rat,[],[s46,s41,s42]) ).
cnf(s98,plain,
( spl0_10
| ~ spl0_17
| ~ spl0_2 ),
inference(rat,[],[s52,s6,s13,s97]) ).
cnf(s99,plain,
( ~ spl0_17
| ~ spl0_2 ),
inference(rat,[],[s52,s7,s14,s46,s98,s97]) ).
cnf(s100,plain,
~ spl0_2,
inference(rat,[],[s46,s34,s35,s99]) ).
cnf(s101,plain,
spl0_1,
inference(rat,[],[s2,s92,s84,s96,s100]) ).
cnf(s102,plain,
~ spl0_15,
inference(rat,[],[s67,s91,s101]) ).
cnf(s107,plain,
spl0_9,
inference(rat,[],[s19,s102]) ).
cnf(s108,plain,
spl0_8,
inference(rat,[],[s18,s102]) ).
cnf(s109,plain,
spl0_6,
inference(rat,[],[s17,s102]) ).
cnf(s110,plain,
$false,
inference(rat,[],[s80,s107,s101,s91,s109,s108]) ).
fof(f645,plain,
$false,
inference(avatar_sat_refutation,[],[s110]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP252-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.37 % Computer : n013.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sun Sep 27 09:42:22 UTC 2026
% 0.09/0.38 % CPUTime :
% 0.09/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.41 Running first-order theorem proving
% 0.09/0.41 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.55/1.27 % (4161435)Input is clausal, will run a generic CNF schedule.
% 2.55/1.27 % (4161442)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=3010827432:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.55/1.27 % (4161446)dis-21_1_sil=8000:lcm=predicate:random_seed=2374847721:st=5:avsq=on:i=117:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/117Mi)
% 2.55/1.27 % (4161441)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=3551723304:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.55/1.27 % (4161443)lrs+10_1_sil=8000:sp=occurrence:random_seed=2720897496:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.55/1.27 % (4161445)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3904352440:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.55/1.27 % (4161440)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=307372215:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.55/1.27 % (4161444)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=4025652522:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.55/1.27 % (4161446)Refutation not found, incomplete strategy
% 2.55/1.27 % (4161446)------------------------------
% 2.55/1.27 % (4161446)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.55/1.27 % (4161446)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.55/1.27 % (4161446)CaDiCaL version: 2.1.3
% 2.55/1.27 % (4161446)Termination reason: Refutation not found, incomplete strategy
% 2.55/1.27 % (4161446)Time elapsed: 0.002 s
% 2.55/1.27 % (4161446)Peak memory usage: 88 MB
% 2.55/1.27 % (4161446)Instructions burned: 2 (million)
% 2.55/1.27 % (4161445)First to succeed.
% 2.55/1.27 % (4161445)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-4161435"
% 2.55/1.27 % (4161443)Instruction limit reached!
% 2.55/1.27 % (4161443)------------------------------
% 2.55/1.27 % (4161443)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.55/1.27 % (4161443)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.55/1.27 % (4161443)CaDiCaL version: 2.1.3
% 2.55/1.27 % (4161443)Termination reason: Instruction limit
% 2.55/1.27 % (4161443)Termination phase: Saturation
% 2.55/1.27 % (4161443)Time elapsed: 0.052 s
% 2.55/1.27 % (4161443)Peak memory usage: 89 MB
% 2.55/1.27 % (4161443)Instructions burned: 107 (million)
% 2.55/1.27 % (4161444)Instruction limit reached!
% 2.55/1.27 % (4161444)------------------------------
% 2.55/1.27 % (4161444)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.55/1.27 % (4161444)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.55/1.27 % (4161444)CaDiCaL version: 2.1.3
% 2.55/1.27 % (4161444)Termination reason: Instruction limit
% 2.55/1.27 % (4161444)Termination phase: Saturation
% 2.55/1.27 % (4161444)Time elapsed: 0.066 s
% 2.55/1.27 % (4161444)Peak memory usage: 89 MB
% 2.55/1.27 % (4161444)Instructions burned: 116 (million)
% 2.55/1.27 % (4161454)dis+1010_3_sil=8000:plsq=on:drc=off:fde=none:plsqc=1:bsd=on:plsqr=7,2:sos=on:spb=goal_then_units:random_seed=2677863996:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 2.55/1.27 % (4161455)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=3593300280:st=3:avsq=on:s2a=on:i=189:s2at=1.2:avsqr=1,16:sd=2:bd=all:nm=64:ss=axioms:sgt=30_2997 on theBenchmark for (2997ds/189Mi)
% 2.55/1.27 % (4161446)------------------------------
% 2.55/1.27 % (4161446)------------------------------
% 2.55/1.27 % (4161454)Instruction limit reached!
% 2.55/1.27 % (4161454)------------------------------
% 2.55/1.27 % (4161454)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.55/1.27 % (4161454)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.55/1.27 % (4161454)CaDiCaL version: 2.1.3
% 2.55/1.27 % (4161454)Termination reason: Instruction limit
% 2.55/1.27 % (4161454)Termination phase: Saturation
% 2.55/1.27 % (4161454)Time elapsed: 0.068 s
% 2.55/1.27 % (4161454)Peak memory usage: 90 MB
% 2.55/1.27 % (4161454)Instructions burned: 143 (million)
% 2.55/1.27 % (4161445)Refutation found. Thanks to Tanya!
% 2.55/1.27 % SZS status Unsatisfiable for theBenchmark
% 2.55/1.27 % SZS output start Proof for theBenchmark
% See solution above
% 3.41/1.37 % (4161445)------------------------------
% 3.41/1.37 % (4161445)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.41/1.37 % (4161445)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.41/1.37 % (4161445)CaDiCaL version: 2.1.3
% 3.41/1.37 % (4161445)Termination reason: Refutation
% 3.41/1.37 % (4161445)Time elapsed: 0.016 s
% 3.41/1.37 % (4161445)Peak memory usage: 89 MB
% 3.41/1.37 % (4161445)Instructions burned: 24 (million)
% 3.41/1.37 % (4161445)------------------------------
% 3.41/1.37 % (4161445)------------------------------
% 3.41/1.37 % (4161435)Success in time 0.416 s
% 3.41/1.37 % Vampire exiting
%------------------------------------------------------------------------------