%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP389-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n005.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 10:13:49 AM UTC 2026
% Result : Unsatisfiable 2.67s 1.30s
% Output : Refutation 3.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 52
% Syntax : Number of formulae : 306 ( 24 unt; 23 def)
% Number of atoms : 895 ( 311 equ)
% Maximal formula atoms : 15 ( 2 avg)
% Number of connectives : 1100 ( 511 ~; 566 |; 0 &)
% ( 23 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 25 ( 23 usr; 24 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 12 con; 0-2 aty)
% Number of variables : 53 ( 0 sgn 53 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_identity) ).
fof(f2,axiom,
! [X0] : multiply(inverse(X0),X0) = identity,
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',associativity) ).
fof(f5,negated_conjecture,
( inverse(sk_c10) = sk_c9
| multiply(sk_c4,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,plain,
( inverse(sk_c10) = sk_c9
| sk_c10 = multiply(sk_c4,sk_c11) ),
inference(reorient_equations,[],[f5]) ).
fof(f7,negated_conjecture,
( inverse(sk_c10) = sk_c9
| inverse(sk_c4) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_2) ).
fof(f8,plain,
( inverse(sk_c10) = sk_c9
| sk_c11 = inverse(sk_c4) ),
inference(reorient_equations,[],[f7]) ).
fof(f9,negated_conjecture,
( inverse(sk_c10) = sk_c9
| multiply(sk_c5,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_3) ).
fof(f10,plain,
( inverse(sk_c10) = sk_c9
| sk_c9 = multiply(sk_c5,sk_c10) ),
inference(reorient_equations,[],[f9]) ).
fof(f11,negated_conjecture,
( inverse(sk_c10) = sk_c9
| inverse(sk_c5) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_4) ).
fof(f12,plain,
( inverse(sk_c10) = sk_c9
| sk_c10 = inverse(sk_c5) ),
inference(reorient_equations,[],[f11]) ).
fof(f23,negated_conjecture,
( inverse(sk_c1) = sk_c11
| multiply(sk_c4,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_10) ).
fof(f24,plain,
( sk_c11 = inverse(sk_c1)
| sk_c10 = multiply(sk_c4,sk_c11) ),
inference(reorient_equations,[],[f23]) ).
fof(f25,negated_conjecture,
( inverse(sk_c1) = sk_c11
| inverse(sk_c4) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_11) ).
fof(f26,plain,
( sk_c11 = inverse(sk_c1)
| sk_c11 = inverse(sk_c4) ),
inference(reorient_equations,[],[f25]) ).
fof(f31,negated_conjecture,
( inverse(sk_c1) = sk_c11
| inverse(sk_c6) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_14) ).
fof(f32,plain,
( sk_c11 = inverse(sk_c1)
| sk_c11 = inverse(sk_c6) ),
inference(reorient_equations,[],[f31]) ).
fof(f33,negated_conjecture,
( inverse(sk_c1) = sk_c11
| multiply(sk_c6,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_15) ).
fof(f34,plain,
( sk_c11 = inverse(sk_c1)
| sk_c11 = multiply(sk_c6,sk_c10) ),
inference(reorient_equations,[],[f33]) ).
fof(f41,negated_conjecture,
( multiply(sk_c1,sk_c10) = sk_c11
| multiply(sk_c4,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_19) ).
fof(f42,plain,
( sk_c11 = multiply(sk_c1,sk_c10)
| sk_c10 = multiply(sk_c4,sk_c11) ),
inference(reorient_equations,[],[f41]) ).
fof(f43,negated_conjecture,
( multiply(sk_c1,sk_c10) = sk_c11
| inverse(sk_c4) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_20) ).
fof(f44,plain,
( sk_c11 = multiply(sk_c1,sk_c10)
| sk_c11 = inverse(sk_c4) ),
inference(reorient_equations,[],[f43]) ).
fof(f49,negated_conjecture,
( multiply(sk_c1,sk_c10) = sk_c11
| inverse(sk_c6) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_23) ).
fof(f50,plain,
( sk_c11 = multiply(sk_c1,sk_c10)
| sk_c11 = inverse(sk_c6) ),
inference(reorient_equations,[],[f49]) ).
fof(f51,negated_conjecture,
( multiply(sk_c1,sk_c10) = sk_c11
| multiply(sk_c6,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_24) ).
fof(f52,plain,
( sk_c11 = multiply(sk_c1,sk_c10)
| sk_c11 = multiply(sk_c6,sk_c10) ),
inference(reorient_equations,[],[f51]) ).
fof(f59,negated_conjecture,
( multiply(sk_c2,sk_c3) = sk_c10
| multiply(sk_c4,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_28) ).
fof(f60,plain,
( sk_c10 = multiply(sk_c2,sk_c3)
| sk_c10 = multiply(sk_c4,sk_c11) ),
inference(reorient_equations,[],[f59]) ).
fof(f61,negated_conjecture,
( multiply(sk_c2,sk_c3) = sk_c10
| inverse(sk_c4) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_29) ).
fof(f62,plain,
( sk_c10 = multiply(sk_c2,sk_c3)
| sk_c11 = inverse(sk_c4) ),
inference(reorient_equations,[],[f61]) ).
fof(f63,negated_conjecture,
( multiply(sk_c2,sk_c3) = sk_c10
| multiply(sk_c5,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_30) ).
fof(f64,plain,
( sk_c10 = multiply(sk_c2,sk_c3)
| sk_c9 = multiply(sk_c5,sk_c10) ),
inference(reorient_equations,[],[f63]) ).
fof(f65,negated_conjecture,
( multiply(sk_c2,sk_c3) = sk_c10
| inverse(sk_c5) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_31) ).
fof(f66,plain,
( sk_c10 = multiply(sk_c2,sk_c3)
| sk_c10 = inverse(sk_c5) ),
inference(reorient_equations,[],[f65]) ).
fof(f71,negated_conjecture,
( multiply(sk_c2,sk_c3) = sk_c10
| multiply(sk_c7,sk_c8) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_34) ).
fof(f72,plain,
( sk_c10 = multiply(sk_c2,sk_c3)
| sk_c10 = multiply(sk_c7,sk_c8) ),
inference(reorient_equations,[],[f71]) ).
fof(f73,negated_conjecture,
( multiply(sk_c2,sk_c3) = sk_c10
| inverse(sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_35) ).
fof(f74,plain,
( sk_c10 = multiply(sk_c2,sk_c3)
| sk_c8 = inverse(sk_c7) ),
inference(reorient_equations,[],[f73]) ).
fof(f77,negated_conjecture,
( inverse(sk_c2) = sk_c3
| multiply(sk_c4,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_37) ).
fof(f78,plain,
( sk_c3 = inverse(sk_c2)
| sk_c10 = multiply(sk_c4,sk_c11) ),
inference(reorient_equations,[],[f77]) ).
fof(f79,negated_conjecture,
( inverse(sk_c2) = sk_c3
| inverse(sk_c4) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_38) ).
fof(f80,plain,
( sk_c3 = inverse(sk_c2)
| sk_c11 = inverse(sk_c4) ),
inference(reorient_equations,[],[f79]) ).
fof(f81,negated_conjecture,
( inverse(sk_c2) = sk_c3
| multiply(sk_c5,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_39) ).
fof(f82,plain,
( sk_c3 = inverse(sk_c2)
| sk_c9 = multiply(sk_c5,sk_c10) ),
inference(reorient_equations,[],[f81]) ).
fof(f83,negated_conjecture,
( inverse(sk_c2) = sk_c3
| inverse(sk_c5) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_40) ).
fof(f84,plain,
( sk_c3 = inverse(sk_c2)
| sk_c10 = inverse(sk_c5) ),
inference(reorient_equations,[],[f83]) ).
fof(f89,negated_conjecture,
( inverse(sk_c2) = sk_c3
| multiply(sk_c7,sk_c8) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_43) ).
fof(f90,plain,
( sk_c3 = inverse(sk_c2)
| sk_c10 = multiply(sk_c7,sk_c8) ),
inference(reorient_equations,[],[f89]) ).
fof(f91,negated_conjecture,
( inverse(sk_c2) = sk_c3
| inverse(sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_44) ).
fof(f92,plain,
( sk_c3 = inverse(sk_c2)
| sk_c8 = inverse(sk_c7) ),
inference(reorient_equations,[],[f91]) ).
fof(f99,negated_conjecture,
( multiply(sk_c3,sk_c9) = sk_c10
| multiply(sk_c5,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_48) ).
fof(f100,plain,
( sk_c10 = multiply(sk_c3,sk_c9)
| sk_c9 = multiply(sk_c5,sk_c10) ),
inference(reorient_equations,[],[f99]) ).
fof(f113,negated_conjecture,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( inverse(sk_c10) != sk_c9
| inverse(X0) != sk_c11
| multiply(X0,sk_c10) != sk_c11
| multiply(X1,X2) != sk_c10
| inverse(X1) != X2
| multiply(X2,sk_c9) != sk_c10
| multiply(X3,sk_c11) != sk_c10
| inverse(X3) != sk_c11
| multiply(X4,sk_c10) != sk_c9
| inverse(X4) != sk_c10
| inverse(X5) != sk_c11
| multiply(X5,sk_c10) != sk_c11
| multiply(X6,X7) != sk_c10
| inverse(X6) != X7
| multiply(X7,sk_c9) != sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_55) ).
fof(f114,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( inverse(sk_c10) != sk_c9
| inverse(X0) != sk_c11
| sk_c11 != multiply(X0,sk_c10)
| multiply(X1,X2) != sk_c10
| inverse(X1) != X2
| sk_c10 != multiply(X2,sk_c9)
| sk_c10 != multiply(X3,sk_c11)
| sk_c11 != inverse(X3)
| sk_c9 != multiply(X4,sk_c10)
| sk_c10 != inverse(X4)
| sk_c11 != inverse(X5)
| sk_c11 != multiply(X5,sk_c10)
| sk_c10 != multiply(X6,X7)
| inverse(X6) != X7
| sk_c10 != multiply(X7,sk_c9) ),
inference(reorient_equations,[],[f113]) ).
fof(f115,plain,
! [X3,X0,X1,X6,X7,X4,X5] :
( inverse(sk_c10) != sk_c9
| inverse(X0) != sk_c11
| sk_c11 != multiply(X0,sk_c10)
| sk_c10 != multiply(X1,inverse(X1))
| sk_c10 != multiply(inverse(X1),sk_c9)
| sk_c10 != multiply(X3,sk_c11)
| sk_c11 != inverse(X3)
| sk_c9 != multiply(X4,sk_c10)
| sk_c10 != inverse(X4)
| sk_c11 != inverse(X5)
| sk_c11 != multiply(X5,sk_c10)
| sk_c10 != multiply(X6,X7)
| inverse(X6) != X7
| sk_c10 != multiply(X7,sk_c9) ),
inference(equality_resolution,[],[f114]) ).
fof(f116,plain,
! [X3,X0,X1,X6,X4,X5] :
( inverse(sk_c10) != sk_c9
| inverse(X0) != sk_c11
| sk_c11 != multiply(X0,sk_c10)
| sk_c10 != multiply(X1,inverse(X1))
| sk_c10 != multiply(inverse(X1),sk_c9)
| sk_c10 != multiply(X3,sk_c11)
| sk_c11 != inverse(X3)
| sk_c9 != multiply(X4,sk_c10)
| sk_c10 != inverse(X4)
| sk_c11 != inverse(X5)
| sk_c11 != multiply(X5,sk_c10)
| sk_c10 != multiply(X6,inverse(X6))
| sk_c10 != multiply(inverse(X6),sk_c9) ),
inference(equality_resolution,[],[f115]) ).
fof(f118,definition,
( spl0_1
<=> ! [X6] :
( sk_c10 != multiply(X6,inverse(X6))
| sk_c10 != multiply(inverse(X6),sk_c9) ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f119,plain,
( ! [X6] :
( sk_c10 != multiply(X6,inverse(X6))
| sk_c10 != multiply(inverse(X6),sk_c9) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f118]) ).
fof(f121,definition,
( spl0_2
<=> ! [X5] :
( sk_c11 != inverse(X5)
| sk_c11 != multiply(X5,sk_c10) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f122,plain,
( ! [X5] :
( sk_c11 != inverse(X5)
| sk_c11 != multiply(X5,sk_c10) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f121]) ).
fof(f124,definition,
( spl0_3
<=> ! [X4] :
( sk_c9 != multiply(X4,sk_c10)
| sk_c10 != inverse(X4) ) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f125,plain,
( ! [X4] :
( sk_c9 != multiply(X4,sk_c10)
| sk_c10 != inverse(X4) )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f124]) ).
fof(f127,definition,
( spl0_4
<=> ! [X3] :
( sk_c10 != multiply(X3,sk_c11)
| sk_c11 != inverse(X3) ) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f128,plain,
( ! [X3] :
( sk_c10 != multiply(X3,sk_c11)
| sk_c11 != inverse(X3) )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f127]) ).
fof(f130,definition,
( spl0_5
<=> inverse(sk_c10) = sk_c9 ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f131,plain,
( inverse(sk_c10) = sk_c9
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f130]) ).
fof(f132,plain,
( inverse(sk_c10) != sk_c9
| spl0_5 ),
inference(avatar_component_clause,[],[f130]) ).
fof(f133,plain,
( spl0_1
| spl0_2
| spl0_3
| spl0_4
| spl0_1
| spl0_2
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f116,f130,f121,f118,f127,f124,f121,f118]) ).
fof(f139,definition,
( spl0_7
<=> sk_c10 = multiply(sk_c3,sk_c9) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f141,plain,
( sk_c10 = multiply(sk_c3,sk_c9)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f139]) ).
fof(f144,definition,
( spl0_8
<=> sk_c8 = inverse(sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f146,plain,
( sk_c8 = inverse(sk_c7)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f144]) ).
fof(f149,definition,
( spl0_9
<=> sk_c10 = multiply(sk_c7,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f151,plain,
( sk_c10 = multiply(sk_c7,sk_c8)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f149]) ).
fof(f154,definition,
( spl0_10
<=> sk_c11 = multiply(sk_c6,sk_c10) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f156,plain,
( sk_c11 = multiply(sk_c6,sk_c10)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f154]) ).
fof(f159,definition,
( spl0_11
<=> sk_c11 = inverse(sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f161,plain,
( sk_c11 = inverse(sk_c6)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f159]) ).
fof(f164,definition,
( spl0_12
<=> sk_c10 = inverse(sk_c5) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f166,plain,
( sk_c10 = inverse(sk_c5)
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f164]) ).
fof(f169,definition,
( spl0_13
<=> sk_c9 = multiply(sk_c5,sk_c10) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f171,plain,
( sk_c9 = multiply(sk_c5,sk_c10)
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f169]) ).
fof(f172,plain,
( spl0_13
| spl0_7 ),
inference(avatar_split_clause,[],[f100,f139,f169]) ).
fof(f174,definition,
( spl0_14
<=> sk_c11 = inverse(sk_c4) ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
fof(f176,plain,
( sk_c11 = inverse(sk_c4)
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f174]) ).
fof(f179,definition,
( spl0_15
<=> sk_c10 = multiply(sk_c4,sk_c11) ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
fof(f181,plain,
( sk_c10 = multiply(sk_c4,sk_c11)
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f179]) ).
fof(f184,definition,
( spl0_16
<=> sk_c3 = inverse(sk_c2) ),
introduced(definition,[new_symbols(definition,[spl0_16])],[avatar_definition]) ).
fof(f186,plain,
( sk_c3 = inverse(sk_c2)
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f184]) ).
fof(f188,plain,
( spl0_8
| spl0_16 ),
inference(avatar_split_clause,[],[f92,f184,f144]) ).
fof(f189,plain,
( spl0_9
| spl0_16 ),
inference(avatar_split_clause,[],[f90,f184,f149]) ).
fof(f192,plain,
( spl0_12
| spl0_16 ),
inference(avatar_split_clause,[],[f84,f184,f164]) ).
fof(f193,plain,
( spl0_13
| spl0_16 ),
inference(avatar_split_clause,[],[f82,f184,f169]) ).
fof(f194,plain,
( spl0_14
| spl0_16 ),
inference(avatar_split_clause,[],[f80,f184,f174]) ).
fof(f195,plain,
( spl0_15
| spl0_16 ),
inference(avatar_split_clause,[],[f78,f184,f179]) ).
fof(f197,definition,
( spl0_17
<=> sk_c10 = multiply(sk_c2,sk_c3) ),
introduced(definition,[new_symbols(definition,[spl0_17])],[avatar_definition]) ).
fof(f199,plain,
( sk_c10 = multiply(sk_c2,sk_c3)
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f197]) ).
fof(f201,plain,
( spl0_8
| spl0_17 ),
inference(avatar_split_clause,[],[f74,f197,f144]) ).
fof(f202,plain,
( spl0_9
| spl0_17 ),
inference(avatar_split_clause,[],[f72,f197,f149]) ).
fof(f205,plain,
( spl0_12
| spl0_17 ),
inference(avatar_split_clause,[],[f66,f197,f164]) ).
fof(f206,plain,
( spl0_13
| spl0_17 ),
inference(avatar_split_clause,[],[f64,f197,f169]) ).
fof(f207,plain,
( spl0_14
| spl0_17 ),
inference(avatar_split_clause,[],[f62,f197,f174]) ).
fof(f208,plain,
( spl0_15
| spl0_17 ),
inference(avatar_split_clause,[],[f60,f197,f179]) ).
fof(f210,definition,
( spl0_18
<=> sk_c11 = multiply(sk_c1,sk_c10) ),
introduced(definition,[new_symbols(definition,[spl0_18])],[avatar_definition]) ).
fof(f212,plain,
( sk_c11 = multiply(sk_c1,sk_c10)
| ~ spl0_18 ),
inference(avatar_component_clause,[],[f210]) ).
fof(f216,plain,
( spl0_10
| spl0_18 ),
inference(avatar_split_clause,[],[f52,f210,f154]) ).
fof(f217,plain,
( spl0_11
| spl0_18 ),
inference(avatar_split_clause,[],[f50,f210,f159]) ).
fof(f220,plain,
( spl0_14
| spl0_18 ),
inference(avatar_split_clause,[],[f44,f210,f174]) ).
fof(f221,plain,
( spl0_15
| spl0_18 ),
inference(avatar_split_clause,[],[f42,f210,f179]) ).
fof(f223,definition,
( spl0_19
<=> sk_c11 = inverse(sk_c1) ),
introduced(definition,[new_symbols(definition,[spl0_19])],[avatar_definition]) ).
fof(f225,plain,
( sk_c11 = inverse(sk_c1)
| ~ spl0_19 ),
inference(avatar_component_clause,[],[f223]) ).
fof(f229,plain,
( spl0_10
| spl0_19 ),
inference(avatar_split_clause,[],[f34,f223,f154]) ).
fof(f230,plain,
( spl0_11
| spl0_19 ),
inference(avatar_split_clause,[],[f32,f223,f159]) ).
fof(f233,plain,
( spl0_14
| spl0_19 ),
inference(avatar_split_clause,[],[f26,f223,f174]) ).
fof(f234,plain,
( spl0_15
| spl0_19 ),
inference(avatar_split_clause,[],[f24,f223,f179]) ).
fof(f240,plain,
( spl0_12
| spl0_5 ),
inference(avatar_split_clause,[],[f12,f130,f164]) ).
fof(f241,plain,
( spl0_13
| spl0_5 ),
inference(avatar_split_clause,[],[f10,f130,f169]) ).
fof(f242,plain,
( spl0_14
| spl0_5 ),
inference(avatar_split_clause,[],[f8,f130,f174]) ).
fof(f243,plain,
( spl0_15
| spl0_5 ),
inference(avatar_split_clause,[],[f6,f130,f179]) ).
fof(f244,plain,
( identity = multiply(sk_c11,sk_c4)
| ~ spl0_14 ),
inference(superposition,[],[f3,f176]) ).
fof(f245,plain,
( identity = multiply(sk_c10,sk_c5)
| ~ spl0_12 ),
inference(superposition,[],[f3,f166]) ).
fof(f250,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[],[f4,f3]) ).
fof(f252,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c11,multiply(sk_c4,X0))
| ~ spl0_14 ),
inference(superposition,[],[f4,f244]) ).
fof(f253,plain,
( ! [X0] : multiply(sk_c5,multiply(sk_c10,X0)) = multiply(sk_c9,X0)
| ~ spl0_13 ),
inference(superposition,[],[f4,f171]) ).
fof(f257,plain,
( ! [X0] : multiply(sk_c11,multiply(sk_c4,X0)) = X0
| ~ spl0_14 ),
inference(forward_demodulation,[],[f252,f1]) ).
fof(f258,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f250,f1]) ).
fof(f272,plain,
( sk_c11 = multiply(sk_c11,sk_c10)
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f257,f181]) ).
fof(f319,plain,
( sk_c5 = multiply(inverse(sk_c10),identity)
| ~ spl0_12 ),
inference(superposition,[],[f258,f245]) ).
fof(f326,plain,
( sk_c10 = multiply(inverse(sk_c11),sk_c11)
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f258,f272]) ).
fof(f329,plain,
( sk_c10 = multiply(inverse(sk_c5),sk_c9)
| ~ spl0_13 ),
inference(superposition,[],[f258,f171]) ).
fof(f333,plain,
( sk_c8 = multiply(inverse(sk_c7),sk_c10)
| ~ spl0_9 ),
inference(superposition,[],[f258,f151]) ).
fof(f341,plain,
( sk_c8 = multiply(sk_c8,sk_c10)
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f333,f146]) ).
fof(f345,plain,
( sk_c10 = multiply(sk_c10,sk_c9)
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f329,f166]) ).
fof(f346,plain,
( identity = sk_c10
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f326,f3]) ).
fof(f353,plain,
( sk_c10 = multiply(inverse(sk_c8),sk_c8)
| ~ spl0_8
| ~ spl0_9 ),
inference(superposition,[],[f258,f341]) ).
fof(f355,plain,
( identity = sk_c10
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f353,f3]) ).
fof(f362,plain,
( sk_c9 = multiply(inverse(sk_c10),sk_c10)
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f258,f345]) ).
fof(f364,plain,
( identity = sk_c9
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f362,f3]) ).
fof(f367,plain,
( sk_c10 = sk_c9
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f364,f346]) ).
fof(f372,plain,
( sk_c5 = multiply(inverse(sk_c10),sk_c10)
| ~ spl0_12
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f319,f346]) ).
fof(f373,plain,
( identity = sk_c5
| ~ spl0_12
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f372,f3]) ).
fof(f374,plain,
( sk_c10 = sk_c5
| ~ spl0_12
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f373,f346]) ).
fof(f379,plain,
( sk_c10 = inverse(sk_c10)
| ~ spl0_12
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f166,f374]) ).
fof(f384,plain,
( sk_c10 != sk_c9
| spl0_5
| ~ spl0_12
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f132,f379]) ).
fof(f388,plain,
( $false
| spl0_5
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f384,f367]) ).
fof(f389,plain,
( spl0_5
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(avatar_contradiction_clause,[],[f388]) ).
fof(f428,plain,
( identity = multiply(sk_c9,sk_c10)
| ~ spl0_5 ),
inference(superposition,[],[f3,f131]) ).
fof(f438,plain,
( identity = multiply(sk_c11,sk_c1)
| ~ spl0_19 ),
inference(superposition,[],[f3,f225]) ).
fof(f441,plain,
( sk_c3 = multiply(inverse(sk_c2),sk_c10)
| ~ spl0_17 ),
inference(superposition,[],[f258,f199]) ).
fof(f442,plain,
( ! [X0] : multiply(sk_c10,X0) = multiply(sk_c2,multiply(sk_c3,X0))
| ~ spl0_17 ),
inference(superposition,[],[f4,f199]) ).
fof(f443,plain,
( sk_c3 = multiply(sk_c3,sk_c10)
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f441,f186]) ).
fof(f444,plain,
( sk_c10 = multiply(inverse(sk_c1),sk_c11)
| ~ spl0_18 ),
inference(superposition,[],[f258,f212]) ).
fof(f446,plain,
( sk_c10 = multiply(sk_c11,sk_c11)
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_demodulation,[],[f444,f225]) ).
fof(f464,definition,
( spl0_25
<=> sk_c10 = sk_c3 ),
introduced(definition,[new_symbols(definition,[spl0_25])],[avatar_definition]) ).
fof(f465,plain,
( sk_c10 = sk_c3
| ~ spl0_25 ),
inference(avatar_component_clause,[],[f464]) ).
fof(f482,plain,
( ! [X0] : multiply(sk_c10,X0) = multiply(sk_c3,multiply(sk_c9,X0))
| ~ spl0_7 ),
inference(superposition,[],[f4,f141]) ).
fof(f486,plain,
( sk_c9 != sk_c9
| sk_c10 != inverse(sk_c5)
| ~ spl0_3
| ~ spl0_13 ),
inference(superposition,[],[f125,f171]) ).
fof(f489,plain,
( sk_c10 != inverse(sk_c5)
| ~ spl0_3
| ~ spl0_13 ),
inference(trivial_inequality_removal,[],[f486]) ).
fof(f504,definition,
( spl0_27
<=> sk_c10 = sk_c9 ),
introduced(definition,[new_symbols(definition,[spl0_27])],[avatar_definition]) ).
fof(f505,plain,
( sk_c10 = sk_c9
| ~ spl0_27 ),
inference(avatar_component_clause,[],[f504]) ).
fof(f513,plain,
( ~ spl0_12
| ~ spl0_3
| ~ spl0_13 ),
inference(avatar_split_clause,[],[f489,f169,f124,f164]) ).
fof(f516,definition,
( spl0_29
<=> sk_c10 = inverse(identity) ),
introduced(definition,[new_symbols(definition,[spl0_29])],[avatar_definition]) ).
fof(f517,plain,
( sk_c10 = inverse(identity)
| ~ spl0_29 ),
inference(avatar_component_clause,[],[f516]) ).
fof(f518,plain,
( sk_c10 != inverse(identity)
| spl0_29 ),
inference(avatar_component_clause,[],[f516]) ).
fof(f533,plain,
( sk_c1 = multiply(inverse(sk_c11),identity)
| ~ spl0_19 ),
inference(superposition,[],[f258,f438]) ).
fof(f543,plain,
( multiply(sk_c2,sk_c3) = multiply(sk_c10,sk_c10)
| ~ spl0_16
| ~ spl0_17 ),
inference(superposition,[],[f442,f443]) ).
fof(f545,plain,
( sk_c10 = multiply(inverse(sk_c3),sk_c3)
| ~ spl0_16
| ~ spl0_17 ),
inference(superposition,[],[f258,f443]) ).
fof(f547,plain,
( identity = sk_c10
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f545,f3]) ).
fof(f557,plain,
( sk_c10 = multiply(sk_c10,sk_c10)
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f543,f199]) ).
fof(f565,plain,
( multiply(sk_c10,sk_c10) = multiply(sk_c3,identity)
| ~ spl0_5
| ~ spl0_7 ),
inference(superposition,[],[f482,f428]) ).
fof(f570,plain,
( multiply(sk_c10,sk_c10) = multiply(sk_c3,sk_c10)
| ~ spl0_5
| ~ spl0_7
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f565,f547]) ).
fof(f572,plain,
( sk_c3 = multiply(sk_c10,sk_c10)
| ~ spl0_5
| ~ spl0_7
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f570,f443]) ).
fof(f617,plain,
( sk_c10 = sk_c3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_16
| ~ spl0_17 ),
inference(superposition,[],[f572,f557]) ).
fof(f620,plain,
( multiply(sk_c5,sk_c10) = multiply(sk_c9,sk_c10)
| ~ spl0_13
| ~ spl0_16
| ~ spl0_17 ),
inference(superposition,[],[f253,f557]) ).
fof(f622,plain,
( sk_c10 != sk_c9
| sk_c10 != inverse(sk_c10)
| ~ spl0_3
| ~ spl0_16
| ~ spl0_17 ),
inference(superposition,[],[f125,f557]) ).
fof(f626,plain,
( identity = multiply(sk_c5,sk_c10)
| ~ spl0_5
| ~ spl0_13
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f620,f428]) ).
fof(f629,plain,
( spl0_25
| ~ spl0_5
| ~ spl0_7
| ~ spl0_16
| ~ spl0_17 ),
inference(avatar_split_clause,[],[f617,f197,f184,f139,f130,f464]) ).
fof(f630,plain,
( identity = sk_c9
| ~ spl0_5
| ~ spl0_13
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f626,f171]) ).
fof(f637,plain,
( sk_c10 = sk_c9
| ~ spl0_5
| ~ spl0_13
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f630,f547]) ).
fof(f642,plain,
( sk_c10 != inverse(sk_c10)
| ~ spl0_16
| ~ spl0_17
| spl0_29 ),
inference(forward_demodulation,[],[f518,f547]) ).
fof(f646,plain,
( sk_c10 != sk_c9
| sk_c10 != sk_c9
| ~ spl0_3
| ~ spl0_5
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f622,f131]) ).
fof(f647,plain,
( sk_c10 != sk_c9
| ~ spl0_3
| ~ spl0_5
| ~ spl0_16
| ~ spl0_17 ),
inference(duplicate_literal_removal,[],[f646]) ).
fof(f655,plain,
( spl0_27
| ~ spl0_5
| ~ spl0_13
| ~ spl0_16
| ~ spl0_17 ),
inference(avatar_split_clause,[],[f637,f197,f184,f169,f130,f504]) ).
fof(f656,plain,
( sk_c10 != sk_c9
| ~ spl0_5
| ~ spl0_16
| ~ spl0_17
| spl0_29 ),
inference(forward_demodulation,[],[f642,f131]) ).
fof(f659,plain,
( ~ spl0_27
| ~ spl0_3
| ~ spl0_5
| ~ spl0_16
| ~ spl0_17 ),
inference(avatar_split_clause,[],[f647,f197,f184,f130,f124,f504]) ).
fof(f661,plain,
( ~ spl0_27
| ~ spl0_5
| ~ spl0_16
| ~ spl0_17
| spl0_29 ),
inference(avatar_split_clause,[],[f656,f516,f197,f184,f130,f504]) ).
fof(f669,plain,
( sk_c10 = multiply(sk_c10,sk_c9)
| ~ spl0_7
| ~ spl0_25 ),
inference(superposition,[],[f141,f465]) ).
fof(f691,plain,
( sk_c9 = multiply(inverse(sk_c10),sk_c10)
| ~ spl0_7
| ~ spl0_25 ),
inference(superposition,[],[f258,f669]) ).
fof(f693,plain,
( identity = sk_c9
| ~ spl0_7
| ~ spl0_25 ),
inference(forward_demodulation,[],[f691,f3]) ).
fof(f696,plain,
( sk_c10 = sk_c9
| ~ spl0_7
| ~ spl0_16
| ~ spl0_17
| ~ spl0_25 ),
inference(forward_demodulation,[],[f693,f547]) ).
fof(f699,plain,
( sk_c10 = inverse(sk_c10)
| ~ spl0_16
| ~ spl0_17
| ~ spl0_29 ),
inference(forward_demodulation,[],[f517,f547]) ).
fof(f702,plain,
( spl0_27
| ~ spl0_7
| ~ spl0_16
| ~ spl0_17
| ~ spl0_25 ),
inference(avatar_split_clause,[],[f696,f464,f197,f184,f139,f504]) ).
fof(f705,plain,
( sk_c11 != sk_c11
| sk_c11 != multiply(sk_c6,sk_c10)
| ~ spl0_2
| ~ spl0_11 ),
inference(superposition,[],[f122,f161]) ).
fof(f707,plain,
( sk_c11 != sk_c11
| sk_c11 != multiply(sk_c1,sk_c10)
| ~ spl0_2
| ~ spl0_19 ),
inference(superposition,[],[f122,f225]) ).
fof(f709,plain,
( sk_c11 != multiply(sk_c1,sk_c10)
| ~ spl0_2
| ~ spl0_19 ),
inference(trivial_inequality_removal,[],[f707]) ).
fof(f710,plain,
( sk_c11 != multiply(sk_c6,sk_c10)
| ~ spl0_2
| ~ spl0_11 ),
inference(trivial_inequality_removal,[],[f705]) ).
fof(f713,plain,
( $false
| ~ spl0_2
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_subsumption_resolution,[],[f709,f212]) ).
fof(f714,plain,
( ~ spl0_2
| ~ spl0_18
| ~ spl0_19 ),
inference(avatar_contradiction_clause,[],[f713]) ).
fof(f724,plain,
( $false
| ~ spl0_2
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f710,f156]) ).
fof(f725,plain,
( ~ spl0_2
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_contradiction_clause,[],[f724]) ).
fof(f855,plain,
( sk_c1 = multiply(inverse(sk_c11),sk_c10)
| ~ spl0_16
| ~ spl0_17
| ~ spl0_19 ),
inference(forward_demodulation,[],[f533,f547]) ).
fof(f923,plain,
( sk_c10 != sk_c10
| sk_c11 != inverse(sk_c11)
| ~ spl0_4
| ~ spl0_18
| ~ spl0_19 ),
inference(superposition,[],[f128,f446]) ).
fof(f924,plain,
( sk_c11 = multiply(inverse(sk_c11),sk_c10)
| ~ spl0_18
| ~ spl0_19 ),
inference(superposition,[],[f258,f446]) ).
fof(f926,plain,
( sk_c11 != inverse(sk_c11)
| ~ spl0_4
| ~ spl0_18
| ~ spl0_19 ),
inference(trivial_inequality_removal,[],[f923]) ).
fof(f972,plain,
( sk_c11 = sk_c1
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19 ),
inference(superposition,[],[f924,f855]) ).
fof(f982,plain,
( sk_c11 = inverse(sk_c11)
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19 ),
inference(superposition,[],[f225,f972]) ).
fof(f990,plain,
( $false
| ~ spl0_4
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_subsumption_resolution,[],[f982,f926]) ).
fof(f991,plain,
( ~ spl0_4
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19 ),
inference(avatar_contradiction_clause,[],[f990]) ).
fof(f992,plain,
( ! [X6] :
( sk_c10 != multiply(X6,inverse(X6))
| sk_c10 != multiply(inverse(X6),sk_c10) )
| ~ spl0_1
| ~ spl0_27 ),
inference(forward_demodulation,[],[f119,f505]) ).
fof(f994,plain,
( sk_c10 != multiply(sk_c10,sk_c9)
| sk_c10 != multiply(sk_c9,sk_c10)
| ~ spl0_1
| ~ spl0_5
| ~ spl0_27 ),
inference(superposition,[],[f992,f131]) ).
fof(f997,plain,
( sk_c10 != inverse(identity)
| sk_c10 != multiply(inverse(identity),sk_c10)
| ~ spl0_1
| ~ spl0_27 ),
inference(superposition,[],[f992,f1]) ).
fof(f1004,plain,
( sk_c10 != inverse(sk_c10)
| sk_c10 != multiply(inverse(identity),sk_c10)
| ~ spl0_1
| ~ spl0_16
| ~ spl0_17
| ~ spl0_27 ),
inference(forward_demodulation,[],[f997,f547]) ).
fof(f1012,plain,
( sk_c10 != multiply(inverse(identity),sk_c10)
| ~ spl0_1
| ~ spl0_16
| ~ spl0_17
| ~ spl0_27
| ~ spl0_29 ),
inference(forward_subsumption_resolution,[],[f1004,f699]) ).
fof(f1019,plain,
( sk_c10 != multiply(inverse(sk_c10),sk_c10)
| ~ spl0_1
| ~ spl0_16
| ~ spl0_17
| ~ spl0_27
| ~ spl0_29 ),
inference(forward_demodulation,[],[f1012,f547]) ).
fof(f1026,plain,
( identity != sk_c10
| ~ spl0_1
| ~ spl0_16
| ~ spl0_17
| ~ spl0_27
| ~ spl0_29 ),
inference(forward_demodulation,[],[f1019,f3]) ).
fof(f1028,plain,
( $false
| ~ spl0_1
| ~ spl0_16
| ~ spl0_17
| ~ spl0_27
| ~ spl0_29 ),
inference(forward_subsumption_resolution,[],[f1026,f547]) ).
fof(f1029,plain,
( ~ spl0_1
| ~ spl0_16
| ~ spl0_17
| ~ spl0_27
| ~ spl0_29 ),
inference(avatar_contradiction_clause,[],[f1028]) ).
fof(f1049,plain,
( sk_c10 = multiply(sk_c5,sk_c10)
| ~ spl0_13
| ~ spl0_27 ),
inference(forward_demodulation,[],[f171,f505]) ).
fof(f1061,plain,
( sk_c10 = inverse(sk_c10)
| ~ spl0_12
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f166,f374]) ).
fof(f1098,plain,
( sk_c10 = sk_c9
| ~ spl0_5
| ~ spl0_12
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f131,f1061]) ).
fof(f1114,plain,
( sk_c10 != multiply(sk_c10,sk_c10)
| sk_c10 != multiply(sk_c9,sk_c10)
| ~ spl0_1
| ~ spl0_5
| ~ spl0_27 ),
inference(forward_demodulation,[],[f994,f505]) ).
fof(f1115,plain,
( identity != sk_c10
| sk_c10 != multiply(sk_c10,sk_c10)
| ~ spl0_1
| ~ spl0_5
| ~ spl0_27 ),
inference(forward_demodulation,[],[f1114,f428]) ).
fof(f1117,definition,
( spl0_37
<=> sk_c10 = multiply(sk_c10,sk_c10) ),
introduced(definition,[new_symbols(definition,[spl0_37])],[avatar_definition]) ).
fof(f1121,definition,
( spl0_38
<=> identity = sk_c10 ),
introduced(definition,[new_symbols(definition,[spl0_38])],[avatar_definition]) ).
fof(f1124,plain,
( ~ spl0_37
| ~ spl0_38
| ~ spl0_1
| ~ spl0_5
| ~ spl0_27 ),
inference(avatar_split_clause,[],[f1115,f504,f130,f118,f1121,f1117]) ).
fof(f1135,plain,
( sk_c10 = multiply(sk_c10,sk_c10)
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_27 ),
inference(forward_demodulation,[],[f1049,f374]) ).
fof(f1136,plain,
( spl0_37
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_27 ),
inference(avatar_split_clause,[],[f1135,f504,f179,f174,f169,f164,f1117]) ).
fof(f1147,plain,
( spl0_38
| ~ spl0_8
| ~ spl0_9 ),
inference(avatar_split_clause,[],[f355,f149,f144,f1121]) ).
fof(f1151,plain,
( sk_c10 != sk_c10
| sk_c11 != inverse(sk_c4)
| ~ spl0_4
| ~ spl0_15 ),
inference(superposition,[],[f128,f181]) ).
fof(f1152,plain,
( sk_c11 != inverse(sk_c4)
| ~ spl0_4
| ~ spl0_15 ),
inference(trivial_inequality_removal,[],[f1151]) ).
fof(f1153,plain,
( $false
| ~ spl0_4
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f1152,f176]) ).
fof(f1154,plain,
( ~ spl0_4
| ~ spl0_14
| ~ spl0_15 ),
inference(avatar_contradiction_clause,[],[f1153]) ).
fof(f1164,plain,
( spl0_27
| ~ spl0_5
| ~ spl0_12
| ~ spl0_14
| ~ spl0_15 ),
inference(avatar_split_clause,[],[f1098,f179,f174,f164,f130,f504]) ).
cnf(s1,plain,
( spl0_1
| spl0_2
| spl0_1
| spl0_2
| spl0_3
| spl0_4
| ~ spl0_5 ),
inference(sat_conversion,[],[f133]) ).
cnf(s2,plain,
( spl0_1
| spl0_2
| spl0_3
| spl0_4
| ~ spl0_5 ),
inference(rat,[],[s1]) ).
cnf(s9,plain,
( spl0_7
| spl0_13 ),
inference(sat_conversion,[],[f172]) ).
cnf(s13,plain,
( spl0_8
| spl0_16 ),
inference(sat_conversion,[],[f188]) ).
cnf(s14,plain,
( spl0_9
| spl0_16 ),
inference(sat_conversion,[],[f189]) ).
cnf(s17,plain,
( spl0_12
| spl0_16 ),
inference(sat_conversion,[],[f192]) ).
cnf(s18,plain,
( spl0_13
| spl0_16 ),
inference(sat_conversion,[],[f193]) ).
cnf(s19,plain,
( spl0_14
| spl0_16 ),
inference(sat_conversion,[],[f194]) ).
cnf(s20,plain,
( spl0_15
| spl0_16 ),
inference(sat_conversion,[],[f195]) ).
cnf(s22,plain,
( spl0_8
| spl0_17 ),
inference(sat_conversion,[],[f201]) ).
cnf(s23,plain,
( spl0_9
| spl0_17 ),
inference(sat_conversion,[],[f202]) ).
cnf(s26,plain,
( spl0_12
| spl0_17 ),
inference(sat_conversion,[],[f205]) ).
cnf(s27,plain,
( spl0_13
| spl0_17 ),
inference(sat_conversion,[],[f206]) ).
cnf(s28,plain,
( spl0_14
| spl0_17 ),
inference(sat_conversion,[],[f207]) ).
cnf(s29,plain,
( spl0_15
| spl0_17 ),
inference(sat_conversion,[],[f208]) ).
cnf(s33,plain,
( spl0_10
| spl0_18 ),
inference(sat_conversion,[],[f216]) ).
cnf(s34,plain,
( spl0_11
| spl0_18 ),
inference(sat_conversion,[],[f217]) ).
cnf(s37,plain,
( spl0_14
| spl0_18 ),
inference(sat_conversion,[],[f220]) ).
cnf(s38,plain,
( spl0_15
| spl0_18 ),
inference(sat_conversion,[],[f221]) ).
cnf(s42,plain,
( spl0_10
| spl0_19 ),
inference(sat_conversion,[],[f229]) ).
cnf(s43,plain,
( spl0_11
| spl0_19 ),
inference(sat_conversion,[],[f230]) ).
cnf(s46,plain,
( spl0_14
| spl0_19 ),
inference(sat_conversion,[],[f233]) ).
cnf(s47,plain,
( spl0_15
| spl0_19 ),
inference(sat_conversion,[],[f234]) ).
cnf(s53,plain,
( spl0_5
| spl0_12 ),
inference(sat_conversion,[],[f240]) ).
cnf(s54,plain,
( spl0_5
| spl0_13 ),
inference(sat_conversion,[],[f241]) ).
cnf(s55,plain,
( spl0_5
| spl0_14 ),
inference(sat_conversion,[],[f242]) ).
cnf(s56,plain,
( spl0_5
| spl0_15 ),
inference(sat_conversion,[],[f243]) ).
cnf(s57,plain,
( spl0_5
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(sat_conversion,[],[f389]) ).
cnf(s74,plain,
( ~ spl0_3
| ~ spl0_12
| ~ spl0_13 ),
inference(sat_conversion,[],[f513]) ).
cnf(s78,plain,
( ~ spl0_5
| ~ spl0_7
| ~ spl0_16
| ~ spl0_17
| spl0_25 ),
inference(sat_conversion,[],[f629]) ).
cnf(s87,plain,
( ~ spl0_5
| ~ spl0_13
| ~ spl0_16
| ~ spl0_17
| spl0_27 ),
inference(sat_conversion,[],[f655]) ).
cnf(s88,plain,
( ~ spl0_3
| ~ spl0_5
| ~ spl0_16
| ~ spl0_17
| ~ spl0_27 ),
inference(sat_conversion,[],[f659]) ).
cnf(s90,plain,
( ~ spl0_5
| ~ spl0_16
| ~ spl0_17
| ~ spl0_27
| spl0_29 ),
inference(sat_conversion,[],[f661]) ).
cnf(s100,plain,
( ~ spl0_7
| ~ spl0_16
| ~ spl0_17
| ~ spl0_25
| spl0_27 ),
inference(sat_conversion,[],[f702]) ).
cnf(s102,plain,
( ~ spl0_2
| ~ spl0_18
| ~ spl0_19 ),
inference(sat_conversion,[],[f714]) ).
cnf(s104,plain,
( ~ spl0_2
| ~ spl0_10
| ~ spl0_11 ),
inference(sat_conversion,[],[f725]) ).
cnf(s115,plain,
( ~ spl0_4
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19 ),
inference(sat_conversion,[],[f991]) ).
cnf(s120,plain,
( ~ spl0_1
| ~ spl0_16
| ~ spl0_17
| ~ spl0_27
| ~ spl0_29 ),
inference(sat_conversion,[],[f1029]) ).
cnf(s128,plain,
( ~ spl0_1
| ~ spl0_5
| ~ spl0_27
| ~ spl0_37
| ~ spl0_38 ),
inference(sat_conversion,[],[f1124]) ).
cnf(s131,plain,
( ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_27
| spl0_37 ),
inference(sat_conversion,[],[f1136]) ).
cnf(s135,plain,
( ~ spl0_8
| ~ spl0_9
| spl0_38 ),
inference(sat_conversion,[],[f1147]) ).
cnf(s137,plain,
( ~ spl0_4
| ~ spl0_14
| ~ spl0_15 ),
inference(sat_conversion,[],[f1154]) ).
cnf(s142,plain,
( ~ spl0_5
| ~ spl0_12
| ~ spl0_14
| ~ spl0_15
| spl0_27 ),
inference(sat_conversion,[],[f1164]) ).
cnf(s148,plain,
spl0_5,
inference(rat,[],[s57,s53,s54,s55,s56]) ).
cnf(s150,plain,
( spl0_15
| ~ spl0_4 ),
inference(rat,[],[s115,s20,s29,s38,s47]) ).
cnf(s151,plain,
( ~ spl0_15
| ~ spl0_4 ),
inference(rat,[],[s115,s19,s28,s37,s46,s137]) ).
cnf(s152,plain,
~ spl0_4,
inference(rat,[],[s151,s150]) ).
cnf(s154,plain,
( spl0_27
| ~ spl0_17
| ~ spl0_16 ),
inference(rat,[],[s100,s78,s9,s87,s148]) ).
cnf(s156,plain,
( spl0_17
| ~ spl0_3 ),
inference(rat,[],[s74,s26,s27]) ).
cnf(s157,plain,
( spl0_16
| ~ spl0_3 ),
inference(rat,[],[s74,s17,s18]) ).
cnf(s158,plain,
( ~ spl0_17
| ~ spl0_16
| ~ spl0_3 ),
inference(rat,[],[s154,s88,s148]) ).
cnf(s159,plain,
~ spl0_3,
inference(rat,[],[s158,s157,s156]) ).
cnf(s161,plain,
( spl0_19
| ~ spl0_2 ),
inference(rat,[],[s104,s42,s43]) ).
cnf(s162,plain,
( ~ spl0_19
| ~ spl0_2 ),
inference(rat,[],[s104,s33,s34,s102]) ).
cnf(s163,plain,
~ spl0_2,
inference(rat,[],[s162,s161]) ).
cnf(s164,plain,
spl0_1,
inference(rat,[],[s2,s148,s152,s159,s163]) ).
cnf(s165,plain,
( ~ spl0_27
| ~ spl0_17
| ~ spl0_16 ),
inference(rat,[],[s120,s90,s148,s164]) ).
cnf(s166,plain,
( ~ spl0_17
| ~ spl0_16 ),
inference(rat,[],[s165,s154]) ).
cnf(s167,plain,
spl0_17,
inference(rat,[],[s128,s135,s131,s142,s22,s23,s26,s27,s28,s29,s148,s164]) ).
cnf(s168,plain,
~ spl0_16,
inference(rat,[],[s166,s167]) ).
cnf(s169,plain,
spl0_15,
inference(rat,[],[s20,s168]) ).
cnf(s170,plain,
spl0_14,
inference(rat,[],[s19,s168]) ).
cnf(s171,plain,
spl0_13,
inference(rat,[],[s18,s168]) ).
cnf(s172,plain,
spl0_12,
inference(rat,[],[s17,s168]) ).
cnf(s175,plain,
spl0_9,
inference(rat,[],[s14,s168]) ).
cnf(s176,plain,
spl0_8,
inference(rat,[],[s13,s168]) ).
cnf(s178,plain,
spl0_27,
inference(rat,[],[s142,s169,s170,s148,s172]) ).
cnf(s180,plain,
spl0_37,
inference(rat,[],[s131,s178,s171,s169,s170,s172]) ).
cnf(s181,plain,
spl0_38,
inference(rat,[],[s135,s175,s176]) ).
cnf(s183,plain,
$false,
inference(rat,[],[s128,s178,s164,s148,s181,s180]) ).
fof(f1170,plain,
$false,
inference(avatar_sat_refutation,[],[s183]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP389-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n005.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 27 10:00:32 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.67/1.30 % (3752742)Input is clausal, will run a generic CNF schedule.
% 2.67/1.30 % (3752753)dis-21_1_sil=8000:lcm=predicate:random_seed=3532683103: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)
% 2.67/1.30 % (3752753)Refutation not found, incomplete strategy
% 2.67/1.30 % (3752753)------------------------------
% 2.67/1.30 % (3752753)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.67/1.30 % (3752753)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.67/1.30 % (3752753)CaDiCaL version: 2.1.3
% 2.67/1.30 % (3752753)Termination reason: Refutation not found, incomplete strategy
% 2.67/1.30 % (3752753)Time elapsed: 0.001 s
% 2.67/1.30 % (3752753)Peak memory usage: 88 MB
% 2.67/1.30 % (3752753)Instructions burned: 3 (million)
% 2.67/1.30 % (3752747)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=3440773201:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.67/1.30 % (3752750)lrs+10_1_sil=8000:sp=occurrence:random_seed=1896731154:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.67/1.30 % (3752748)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=896146437:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.67/1.30 % (3752749)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=810966271:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.67/1.30 % (3752750)Refutation not found, incomplete strategy
% 2.67/1.30 % (3752750)------------------------------
% 2.67/1.30 % (3752750)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.67/1.30 % (3752750)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.67/1.30 % (3752750)CaDiCaL version: 2.1.3
% 2.67/1.30 % (3752750)Termination reason: Refutation not found, incomplete strategy
% 2.67/1.30 % (3752750)Time elapsed: 0.004 s
% 2.67/1.30 % (3752750)Peak memory usage: 88 MB
% 2.67/1.30 % (3752750)Instructions burned: 5 (million)
% 2.67/1.30 % (3752751)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1325120942:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.67/1.30 % (3752752)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3675998232:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.67/1.30 % (3752752)First to succeed.
% 2.67/1.30 % (3752752)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3752742"
% 2.67/1.30 % (3752751)Instruction limit reached!
% 2.67/1.30 % (3752751)------------------------------
% 2.67/1.30 % (3752751)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.67/1.30 % (3752751)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.67/1.30 % (3752751)CaDiCaL version: 2.1.3
% 2.67/1.30 % (3752751)Termination reason: Instruction limit
% 2.67/1.30 % (3752751)Termination phase: Saturation
% 2.67/1.30 % (3752751)Time elapsed: 0.065 s
% 2.67/1.30 % (3752751)Peak memory usage: 89 MB
% 2.67/1.30 % (3752751)Instructions burned: 114 (million)
% 2.67/1.30 % (3752753)------------------------------
% 2.67/1.30 % (3752753)------------------------------
% 2.67/1.30 % (3752761)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=313888385:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 2.67/1.30 % (3752761)Refutation not found, incomplete strategy
% 2.67/1.30 % (3752761)------------------------------
% 2.67/1.30 % (3752761)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.67/1.30 % (3752761)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.67/1.30 % (3752761)CaDiCaL version: 2.1.3
% 2.67/1.30 % (3752761)Termination reason: Refutation not found, incomplete strategy
% 2.67/1.30 % (3752761)Time elapsed: 0.004 s
% 2.67/1.30 % (3752761)Peak memory usage: 88 MB
% 2.67/1.30 % (3752761)Instructions burned: 5 (million)
% 2.67/1.30 % (3752762)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=1718790868: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)
% 2.67/1.30 % (3752762)Refutation not found, incomplete strategy
% 2.67/1.30 % (3752762)------------------------------
% 2.67/1.30 % (3752762)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.67/1.30 % (3752762)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.67/1.30 % (3752762)CaDiCaL version: 2.1.3
% 2.67/1.30 % (3752762)Termination reason: Refutation not found, incomplete strategy
% 2.67/1.30 % (3752762)Time elapsed: 0.002 s
% 2.67/1.30 % (3752762)Peak memory usage: 88 MB
% 2.67/1.30 % (3752762)Instructions burned: 5 (million)
% 2.67/1.30 % (3752750)------------------------------
% 2.67/1.30 % (3752750)------------------------------
% 2.67/1.30 % (3752752)Refutation found. Thanks to Tanya!
% 2.67/1.30 % SZS status Unsatisfiable for theBenchmark
% 2.67/1.30 % SZS output start Proof for theBenchmark
% See solution above
% 3.71/1.49 % (3752752)------------------------------
% 3.71/1.49 % (3752752)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.71/1.49 % (3752752)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.71/1.49 % (3752752)CaDiCaL version: 2.1.3
% 3.71/1.49 % (3752752)Termination reason: Refutation
% 3.71/1.49 % (3752752)Time elapsed: 0.030 s
% 3.71/1.49 % (3752752)Peak memory usage: 90 MB
% 3.71/1.49 % (3752752)Instructions burned: 40 (million)
% 3.71/1.49 % (3752752)------------------------------
% 3.71/1.49 % (3752752)------------------------------
% 3.71/1.49 % (3752742)Success in time 0.445 s
% 3.71/1.49 % Vampire exiting
%------------------------------------------------------------------------------