%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP227-1 : 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 : n019.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 10:13:23 AM UTC 2026
% Result : Unsatisfiable 2.64s 1.32s
% Output : Refutation 3.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 46
% Syntax : Number of formulae : 278 ( 19 unt; 21 def)
% Number of atoms : 782 ( 264 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 955 ( 451 ~; 483 |; 0 &)
% ( 21 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 23 ( 21 usr; 22 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 46 ( 0 sgn 46 !; 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_c1) = sk_c8
| inverse(sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,negated_conjecture,
( inverse(sk_c1) = sk_c8
| multiply(sk_c4,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_2) ).
fof(f7,plain,
( inverse(sk_c1) = sk_c8
| sk_c7 = multiply(sk_c4,sk_c8) ),
inference(reorient_equations,[],[f6]) ).
fof(f8,negated_conjecture,
( inverse(sk_c1) = sk_c8
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_3) ).
fof(f9,plain,
( inverse(sk_c1) = sk_c8
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f8]) ).
fof(f10,negated_conjecture,
( inverse(sk_c1) = sk_c8
| multiply(sk_c5,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_4) ).
fof(f11,plain,
( inverse(sk_c1) = sk_c8
| sk_c7 = multiply(sk_c5,sk_c6) ),
inference(reorient_equations,[],[f10]) ).
fof(f12,negated_conjecture,
( inverse(sk_c1) = sk_c8
| inverse(sk_c5) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_5) ).
fof(f13,plain,
( inverse(sk_c1) = sk_c8
| sk_c6 = inverse(sk_c5) ),
inference(reorient_equations,[],[f12]) ).
fof(f14,negated_conjecture,
( inverse(sk_c1) = sk_c8
| multiply(sk_c6,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_6) ).
fof(f15,plain,
( inverse(sk_c1) = sk_c8
| sk_c7 = multiply(sk_c6,sk_c8) ),
inference(reorient_equations,[],[f14]) ).
fof(f16,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c8
| inverse(sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_7) ).
fof(f17,plain,
( sk_c8 = multiply(sk_c1,sk_c7)
| inverse(sk_c8) = sk_c7 ),
inference(reorient_equations,[],[f16]) ).
fof(f18,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c8
| multiply(sk_c4,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_8) ).
fof(f19,plain,
( sk_c8 = multiply(sk_c1,sk_c7)
| sk_c7 = multiply(sk_c4,sk_c8) ),
inference(reorient_equations,[],[f18]) ).
fof(f20,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c8
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_9) ).
fof(f21,plain,
( sk_c8 = multiply(sk_c1,sk_c7)
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f20]) ).
fof(f22,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c8
| multiply(sk_c5,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_10) ).
fof(f23,plain,
( sk_c8 = multiply(sk_c1,sk_c7)
| sk_c7 = multiply(sk_c5,sk_c6) ),
inference(reorient_equations,[],[f22]) ).
fof(f24,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c8
| inverse(sk_c5) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_11) ).
fof(f25,plain,
( sk_c8 = multiply(sk_c1,sk_c7)
| sk_c6 = inverse(sk_c5) ),
inference(reorient_equations,[],[f24]) ).
fof(f26,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c8
| multiply(sk_c6,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_12) ).
fof(f27,plain,
( sk_c8 = multiply(sk_c1,sk_c7)
| sk_c7 = multiply(sk_c6,sk_c8) ),
inference(reorient_equations,[],[f26]) ).
fof(f28,negated_conjecture,
( multiply(sk_c8,sk_c3) = sk_c7
| inverse(sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_13) ).
fof(f29,plain,
( sk_c7 = multiply(sk_c8,sk_c3)
| inverse(sk_c8) = sk_c7 ),
inference(reorient_equations,[],[f28]) ).
fof(f34,negated_conjecture,
( multiply(sk_c8,sk_c3) = sk_c7
| multiply(sk_c5,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_16) ).
fof(f35,plain,
( sk_c7 = multiply(sk_c8,sk_c3)
| sk_c7 = multiply(sk_c5,sk_c6) ),
inference(reorient_equations,[],[f34]) ).
fof(f36,negated_conjecture,
( multiply(sk_c8,sk_c3) = sk_c7
| inverse(sk_c5) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_17) ).
fof(f37,plain,
( sk_c7 = multiply(sk_c8,sk_c3)
| sk_c6 = inverse(sk_c5) ),
inference(reorient_equations,[],[f36]) ).
fof(f40,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c3
| inverse(sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_19) ).
fof(f41,plain,
( sk_c3 = multiply(sk_c2,sk_c8)
| inverse(sk_c8) = sk_c7 ),
inference(reorient_equations,[],[f40]) ).
fof(f46,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c3
| multiply(sk_c5,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_22) ).
fof(f47,plain,
( sk_c3 = multiply(sk_c2,sk_c8)
| sk_c7 = multiply(sk_c5,sk_c6) ),
inference(reorient_equations,[],[f46]) ).
fof(f48,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c3
| inverse(sk_c5) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_23) ).
fof(f49,plain,
( sk_c3 = multiply(sk_c2,sk_c8)
| sk_c6 = inverse(sk_c5) ),
inference(reorient_equations,[],[f48]) ).
fof(f52,negated_conjecture,
( inverse(sk_c2) = sk_c8
| inverse(sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_25) ).
fof(f53,plain,
( sk_c8 = inverse(sk_c2)
| inverse(sk_c8) = sk_c7 ),
inference(reorient_equations,[],[f52]) ).
fof(f58,negated_conjecture,
( inverse(sk_c2) = sk_c8
| multiply(sk_c5,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_28) ).
fof(f59,plain,
( sk_c8 = inverse(sk_c2)
| sk_c7 = multiply(sk_c5,sk_c6) ),
inference(reorient_equations,[],[f58]) ).
fof(f60,negated_conjecture,
( inverse(sk_c2) = sk_c8
| inverse(sk_c5) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_29) ).
fof(f61,plain,
( sk_c8 = inverse(sk_c2)
| sk_c6 = inverse(sk_c5) ),
inference(reorient_equations,[],[f60]) ).
fof(f64,negated_conjecture,
! [X2,X3,X0,X1,X4,X5] :
( inverse(X0) != sk_c8
| multiply(X0,sk_c7) != sk_c8
| multiply(sk_c8,X1) != sk_c7
| multiply(X2,sk_c8) != X1
| inverse(X2) != sk_c8
| inverse(sk_c8) != sk_c7
| multiply(X3,sk_c8) != sk_c7
| inverse(X3) != sk_c8
| multiply(X4,X5) != sk_c7
| inverse(X4) != X5
| multiply(X5,sk_c8) != sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_31) ).
fof(f65,plain,
! [X2,X3,X0,X1,X4,X5] :
( inverse(X0) != sk_c8
| sk_c8 != multiply(X0,sk_c7)
| sk_c7 != multiply(sk_c8,X1)
| multiply(X2,sk_c8) != X1
| sk_c8 != inverse(X2)
| inverse(sk_c8) != sk_c7
| sk_c7 != multiply(X3,sk_c8)
| sk_c8 != inverse(X3)
| sk_c7 != multiply(X4,X5)
| inverse(X4) != X5
| sk_c7 != multiply(X5,sk_c8) ),
inference(reorient_equations,[],[f64]) ).
fof(f66,plain,
! [X2,X3,X0,X4,X5] :
( inverse(X0) != sk_c8
| sk_c8 != multiply(X0,sk_c7)
| sk_c7 != multiply(sk_c8,multiply(X2,sk_c8))
| sk_c8 != inverse(X2)
| inverse(sk_c8) != sk_c7
| sk_c7 != multiply(X3,sk_c8)
| sk_c8 != inverse(X3)
| sk_c7 != multiply(X4,X5)
| inverse(X4) != X5
| sk_c7 != multiply(X5,sk_c8) ),
inference(equality_resolution,[],[f65]) ).
fof(f67,plain,
! [X2,X3,X0,X4] :
( inverse(X0) != sk_c8
| sk_c8 != multiply(X0,sk_c7)
| sk_c7 != multiply(sk_c8,multiply(X2,sk_c8))
| sk_c8 != inverse(X2)
| inverse(sk_c8) != sk_c7
| sk_c7 != multiply(X3,sk_c8)
| sk_c8 != inverse(X3)
| sk_c7 != multiply(X4,inverse(X4))
| sk_c7 != multiply(inverse(X4),sk_c8) ),
inference(equality_resolution,[],[f66]) ).
fof(f69,definition,
( spl0_1
<=> ! [X4] :
( sk_c7 != multiply(X4,inverse(X4))
| sk_c7 != multiply(inverse(X4),sk_c8) ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f70,plain,
( ! [X4] :
( sk_c7 != multiply(inverse(X4),sk_c8)
| sk_c7 != multiply(X4,inverse(X4)) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f69]) ).
fof(f72,definition,
( spl0_2
<=> ! [X3] :
( sk_c7 != multiply(X3,sk_c8)
| sk_c8 != inverse(X3) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f73,plain,
( ! [X3] :
( sk_c7 != multiply(X3,sk_c8)
| sk_c8 != inverse(X3) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f72]) ).
fof(f75,definition,
( spl0_3
<=> inverse(sk_c8) = sk_c7 ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f76,plain,
( inverse(sk_c8) = sk_c7
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f75]) ).
fof(f77,plain,
( inverse(sk_c8) != sk_c7
| spl0_3 ),
inference(avatar_component_clause,[],[f75]) ).
fof(f79,definition,
( spl0_4
<=> ! [X2] :
( sk_c7 != multiply(sk_c8,multiply(X2,sk_c8))
| sk_c8 != inverse(X2) ) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f80,plain,
( ! [X2] :
( sk_c8 != inverse(X2)
| sk_c7 != multiply(sk_c8,multiply(X2,sk_c8)) )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f79]) ).
fof(f82,definition,
( spl0_5
<=> ! [X0] :
( inverse(X0) != sk_c8
| sk_c8 != multiply(X0,sk_c7) ) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f83,plain,
( ! [X0] :
( inverse(X0) != sk_c8
| sk_c8 != multiply(X0,sk_c7) )
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f82]) ).
fof(f84,plain,
( spl0_1
| spl0_2
| ~ spl0_3
| spl0_4
| spl0_5 ),
inference(avatar_split_clause,[],[f67,f82,f79,f75,f72,f69]) ).
fof(f86,definition,
( spl0_6
<=> sk_c7 = multiply(sk_c6,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f88,plain,
( sk_c7 = multiply(sk_c6,sk_c8)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f86]) ).
fof(f90,definition,
( spl0_7
<=> sk_c8 = inverse(sk_c2) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f92,plain,
( sk_c8 = inverse(sk_c2)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f90]) ).
fof(f95,definition,
( spl0_8
<=> sk_c6 = inverse(sk_c5) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f97,plain,
( sk_c6 = inverse(sk_c5)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f95]) ).
fof(f98,plain,
( spl0_8
| spl0_7 ),
inference(avatar_split_clause,[],[f61,f90,f95]) ).
fof(f100,definition,
( spl0_9
<=> sk_c7 = multiply(sk_c5,sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f102,plain,
( sk_c7 = multiply(sk_c5,sk_c6)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f100]) ).
fof(f103,plain,
( spl0_9
| spl0_7 ),
inference(avatar_split_clause,[],[f59,f90,f100]) ).
fof(f105,definition,
( spl0_10
<=> sk_c8 = inverse(sk_c4) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f107,plain,
( sk_c8 = inverse(sk_c4)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f105]) ).
fof(f110,definition,
( spl0_11
<=> sk_c7 = multiply(sk_c4,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f112,plain,
( sk_c7 = multiply(sk_c4,sk_c8)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f110]) ).
fof(f114,plain,
( spl0_3
| spl0_7 ),
inference(avatar_split_clause,[],[f53,f90,f75]) ).
fof(f116,definition,
( spl0_12
<=> sk_c3 = multiply(sk_c2,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f118,plain,
( sk_c3 = multiply(sk_c2,sk_c8)
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f116]) ).
fof(f120,plain,
( spl0_8
| spl0_12 ),
inference(avatar_split_clause,[],[f49,f116,f95]) ).
fof(f121,plain,
( spl0_9
| spl0_12 ),
inference(avatar_split_clause,[],[f47,f116,f100]) ).
fof(f124,plain,
( spl0_3
| spl0_12 ),
inference(avatar_split_clause,[],[f41,f116,f75]) ).
fof(f126,definition,
( spl0_13
<=> sk_c7 = multiply(sk_c8,sk_c3) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f128,plain,
( sk_c7 = multiply(sk_c8,sk_c3)
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f126]) ).
fof(f130,plain,
( spl0_8
| spl0_13 ),
inference(avatar_split_clause,[],[f37,f126,f95]) ).
fof(f131,plain,
( spl0_9
| spl0_13 ),
inference(avatar_split_clause,[],[f35,f126,f100]) ).
fof(f134,plain,
( spl0_3
| spl0_13 ),
inference(avatar_split_clause,[],[f29,f126,f75]) ).
fof(f136,definition,
( spl0_14
<=> sk_c8 = multiply(sk_c1,sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
fof(f138,plain,
( sk_c8 = multiply(sk_c1,sk_c7)
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f136]) ).
fof(f139,plain,
( spl0_6
| spl0_14 ),
inference(avatar_split_clause,[],[f27,f136,f86]) ).
fof(f140,plain,
( spl0_8
| spl0_14 ),
inference(avatar_split_clause,[],[f25,f136,f95]) ).
fof(f141,plain,
( spl0_9
| spl0_14 ),
inference(avatar_split_clause,[],[f23,f136,f100]) ).
fof(f142,plain,
( spl0_10
| spl0_14 ),
inference(avatar_split_clause,[],[f21,f136,f105]) ).
fof(f143,plain,
( spl0_11
| spl0_14 ),
inference(avatar_split_clause,[],[f19,f136,f110]) ).
fof(f144,plain,
( spl0_3
| spl0_14 ),
inference(avatar_split_clause,[],[f17,f136,f75]) ).
fof(f146,definition,
( spl0_15
<=> inverse(sk_c1) = sk_c8 ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
fof(f148,plain,
( inverse(sk_c1) = sk_c8
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f146]) ).
fof(f149,plain,
( spl0_6
| spl0_15 ),
inference(avatar_split_clause,[],[f15,f146,f86]) ).
fof(f150,plain,
( spl0_8
| spl0_15 ),
inference(avatar_split_clause,[],[f13,f146,f95]) ).
fof(f151,plain,
( spl0_9
| spl0_15 ),
inference(avatar_split_clause,[],[f11,f146,f100]) ).
fof(f152,plain,
( spl0_10
| spl0_15 ),
inference(avatar_split_clause,[],[f9,f146,f105]) ).
fof(f153,plain,
( spl0_11
| spl0_15 ),
inference(avatar_split_clause,[],[f7,f146,f110]) ).
fof(f154,plain,
( spl0_3
| spl0_15 ),
inference(avatar_split_clause,[],[f5,f146,f75]) ).
fof(f156,plain,
( sk_c7 != sk_c7
| sk_c8 != inverse(sk_c4)
| ~ spl0_2
| ~ spl0_11 ),
inference(superposition,[],[f73,f112]) ).
fof(f157,plain,
( sk_c8 != inverse(sk_c4)
| ~ spl0_2
| ~ spl0_11 ),
inference(trivial_inequality_removal,[],[f156]) ).
fof(f161,plain,
( ~ spl0_10
| ~ spl0_2
| ~ spl0_11 ),
inference(avatar_split_clause,[],[f157,f110,f72,f105]) ).
fof(f166,definition,
( spl0_16
<=> sk_c8 = inverse(identity) ),
introduced(definition,[new_symbols(definition,[spl0_16])],[avatar_definition]) ).
fof(f167,plain,
( sk_c8 = inverse(identity)
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f166]) ).
fof(f168,plain,
( sk_c8 != inverse(identity)
| spl0_16 ),
inference(avatar_component_clause,[],[f166]) ).
fof(f170,definition,
( spl0_17
<=> sk_c8 = sk_c7 ),
introduced(definition,[new_symbols(definition,[spl0_17])],[avatar_definition]) ).
fof(f171,plain,
( sk_c8 = sk_c7
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f170]) ).
fof(f172,plain,
( sk_c8 != sk_c7
| spl0_17 ),
inference(avatar_component_clause,[],[f170]) ).
fof(f174,plain,
( identity = multiply(sk_c8,sk_c1)
| ~ spl0_15 ),
inference(superposition,[],[f3,f148]) ).
fof(f175,plain,
( identity = multiply(sk_c7,sk_c8)
| ~ spl0_3 ),
inference(superposition,[],[f3,f76]) ).
fof(f181,definition,
( spl0_18
<=> identity = sk_c7 ),
introduced(definition,[new_symbols(definition,[spl0_18])],[avatar_definition]) ).
fof(f182,plain,
( identity = sk_c7
| ~ spl0_18 ),
inference(avatar_component_clause,[],[f181]) ).
fof(f183,plain,
( identity != sk_c7
| spl0_18 ),
inference(avatar_component_clause,[],[f181]) ).
fof(f185,definition,
( spl0_19
<=> sk_c8 = inverse(sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_19])],[avatar_definition]) ).
fof(f186,plain,
( sk_c8 = inverse(sk_c7)
| ~ spl0_19 ),
inference(avatar_component_clause,[],[f185]) ).
fof(f191,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[],[f4,f3]) ).
fof(f199,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f191,f1]) ).
fof(f202,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c8,multiply(sk_c1,X0))
| ~ spl0_15 ),
inference(superposition,[],[f4,f174]) ).
fof(f203,plain,
( ! [X0] : multiply(sk_c8,multiply(sk_c1,X0)) = X0
| ~ spl0_15 ),
inference(forward_demodulation,[],[f202,f1]) ).
fof(f205,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c7,multiply(sk_c8,X0))
| ~ spl0_3 ),
inference(superposition,[],[f4,f175]) ).
fof(f206,plain,
( ! [X0] : multiply(sk_c7,multiply(sk_c8,X0)) = X0
| ~ spl0_3 ),
inference(forward_demodulation,[],[f205,f1]) ).
fof(f211,plain,
( sk_c7 = multiply(sk_c8,sk_c8)
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f203,f138]) ).
fof(f225,plain,
( sk_c1 = multiply(sk_c7,identity)
| ~ spl0_3
| ~ spl0_15 ),
inference(superposition,[],[f206,f174]) ).
fof(f226,plain,
( sk_c8 = multiply(sk_c7,sk_c7)
| ~ spl0_3
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f206,f211]) ).
fof(f343,plain,
( sk_c6 = multiply(inverse(sk_c5),sk_c7)
| ~ spl0_9 ),
inference(superposition,[],[f199,f102]) ).
fof(f349,plain,
( sk_c8 = multiply(inverse(sk_c2),sk_c3)
| ~ spl0_12 ),
inference(superposition,[],[f199,f118]) ).
fof(f355,plain,
( sk_c8 = multiply(sk_c8,sk_c3)
| ~ spl0_7
| ~ spl0_12 ),
inference(forward_demodulation,[],[f349,f92]) ).
fof(f358,plain,
( sk_c6 = multiply(sk_c6,sk_c7)
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f343,f97]) ).
fof(f374,plain,
( sk_c7 = multiply(inverse(sk_c6),sk_c6)
| ~ spl0_8
| ~ spl0_9 ),
inference(superposition,[],[f199,f358]) ).
fof(f376,plain,
( identity = sk_c7
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f374,f3]) ).
fof(f390,plain,
( spl0_18
| ~ spl0_8
| ~ spl0_9 ),
inference(avatar_split_clause,[],[f376,f100,f95,f181]) ).
fof(f395,plain,
( sk_c1 = multiply(sk_c7,sk_c7)
| ~ spl0_3
| ~ spl0_15
| ~ spl0_18 ),
inference(superposition,[],[f225,f182]) ).
fof(f399,plain,
( sk_c1 = sk_c8
| ~ spl0_3
| ~ spl0_14
| ~ spl0_15
| ~ spl0_18 ),
inference(forward_demodulation,[],[f395,f226]) ).
fof(f404,plain,
( sk_c8 = inverse(sk_c8)
| ~ spl0_3
| ~ spl0_14
| ~ spl0_15
| ~ spl0_18 ),
inference(superposition,[],[f148,f399]) ).
fof(f440,plain,
( sk_c8 = sk_c7
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f128,f355]) ).
fof(f464,plain,
( spl0_17
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13 ),
inference(avatar_split_clause,[],[f440,f126,f116,f90,f170]) ).
fof(f465,plain,
( sk_c8 = multiply(sk_c1,sk_c8)
| ~ spl0_14
| ~ spl0_17 ),
inference(superposition,[],[f138,f171]) ).
fof(f472,plain,
( sk_c8 != sk_c7
| inverse(sk_c1) != sk_c8
| ~ spl0_2
| ~ spl0_14
| ~ spl0_17 ),
inference(superposition,[],[f73,f465]) ).
fof(f476,plain,
( inverse(sk_c1) != sk_c8
| ~ spl0_2
| ~ spl0_14
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f472,f171]) ).
fof(f478,plain,
( $false
| ~ spl0_2
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f476,f148]) ).
fof(f479,plain,
( ~ spl0_2
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17 ),
inference(avatar_contradiction_clause,[],[f478]) ).
fof(f483,plain,
( identity = multiply(sk_c7,sk_c8)
| ~ spl0_3 ),
inference(superposition,[],[f3,f76]) ).
fof(f484,plain,
( sk_c7 = multiply(sk_c7,sk_c8)
| ~ spl0_3
| ~ spl0_18 ),
inference(forward_demodulation,[],[f483,f182]) ).
fof(f508,plain,
( sk_c8 = inverse(sk_c7)
| ~ spl0_16
| ~ spl0_18 ),
inference(forward_demodulation,[],[f167,f182]) ).
fof(f509,plain,
( spl0_19
| ~ spl0_16
| ~ spl0_18 ),
inference(avatar_split_clause,[],[f508,f181,f166,f185]) ).
fof(f513,plain,
( sk_c8 != sk_c8
| sk_c7 != multiply(sk_c8,multiply(sk_c1,sk_c8))
| ~ spl0_4
| ~ spl0_15 ),
inference(superposition,[],[f80,f148]) ).
fof(f516,plain,
( sk_c8 != sk_c8
| sk_c7 != multiply(sk_c8,multiply(sk_c4,sk_c8))
| ~ spl0_4
| ~ spl0_10 ),
inference(superposition,[],[f80,f107]) ).
fof(f520,plain,
( sk_c7 != multiply(sk_c8,multiply(sk_c4,sk_c8))
| ~ spl0_4
| ~ spl0_10 ),
inference(trivial_inequality_removal,[],[f516]) ).
fof(f522,plain,
( sk_c7 != multiply(sk_c8,multiply(sk_c1,sk_c8))
| ~ spl0_4
| ~ spl0_15 ),
inference(trivial_inequality_removal,[],[f513]) ).
fof(f533,plain,
( sk_c7 != multiply(sk_c8,sk_c7)
| ~ spl0_4
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f520,f112]) ).
fof(f536,plain,
( sk_c8 != sk_c7
| ~ spl0_4
| ~ spl0_15 ),
inference(forward_demodulation,[],[f522,f203]) ).
fof(f544,plain,
( ~ spl0_17
| ~ spl0_4
| ~ spl0_15 ),
inference(avatar_split_clause,[],[f536,f146,f79,f170]) ).
fof(f550,plain,
( ! [X4] :
( sk_c8 != multiply(X4,inverse(X4))
| sk_c7 != multiply(inverse(X4),sk_c8) )
| ~ spl0_1
| ~ spl0_17 ),
inference(forward_demodulation,[],[f70,f171]) ).
fof(f551,plain,
( ! [X4] :
( sk_c8 != multiply(inverse(X4),sk_c8)
| sk_c8 != multiply(X4,inverse(X4)) )
| ~ spl0_1
| ~ spl0_17 ),
inference(forward_demodulation,[],[f550,f171]) ).
fof(f552,plain,
( sk_c8 = inverse(sk_c8)
| ~ spl0_17
| ~ spl0_19 ),
inference(forward_demodulation,[],[f186,f171]) ).
fof(f555,plain,
( sk_c8 != multiply(sk_c7,sk_c8)
| sk_c8 != multiply(sk_c8,sk_c7)
| ~ spl0_1
| ~ spl0_3
| ~ spl0_17 ),
inference(superposition,[],[f551,f76]) ).
fof(f565,plain,
( sk_c8 != multiply(sk_c8,sk_c8)
| sk_c8 != multiply(sk_c8,sk_c7)
| ~ spl0_1
| ~ spl0_3
| ~ spl0_17 ),
inference(forward_demodulation,[],[f555,f171]) ).
fof(f572,plain,
( sk_c8 != sk_c7
| sk_c8 != multiply(sk_c8,sk_c7)
| ~ spl0_1
| ~ spl0_3
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17 ),
inference(forward_demodulation,[],[f565,f211]) ).
fof(f580,plain,
( sk_c8 != multiply(sk_c8,sk_c7)
| ~ spl0_1
| ~ spl0_3
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f572,f171]) ).
fof(f588,plain,
( sk_c8 != multiply(sk_c8,sk_c8)
| ~ spl0_1
| ~ spl0_3
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17 ),
inference(forward_demodulation,[],[f580,f171]) ).
fof(f592,plain,
( sk_c8 != sk_c7
| ~ spl0_1
| ~ spl0_3
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17 ),
inference(forward_demodulation,[],[f588,f211]) ).
fof(f599,plain,
( $false
| ~ spl0_1
| ~ spl0_3
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f592,f171]) ).
fof(f600,plain,
( ~ spl0_1
| ~ spl0_3
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17 ),
inference(avatar_contradiction_clause,[],[f599]) ).
fof(f601,plain,
( ! [X0] :
( sk_c8 != multiply(X0,sk_c8)
| inverse(X0) != sk_c8 )
| ~ spl0_5
| ~ spl0_17 ),
inference(forward_demodulation,[],[f83,f171]) ).
fof(f602,plain,
( sk_c8 != sk_c8
| sk_c8 != inverse(identity)
| ~ spl0_5
| ~ spl0_17 ),
inference(superposition,[],[f601,f1]) ).
fof(f606,plain,
( sk_c8 != sk_c7
| sk_c8 != inverse(sk_c4)
| ~ spl0_5
| ~ spl0_11
| ~ spl0_17 ),
inference(superposition,[],[f601,f112]) ).
fof(f608,plain,
( sk_c8 != inverse(identity)
| ~ spl0_5
| ~ spl0_17 ),
inference(trivial_inequality_removal,[],[f602]) ).
fof(f610,plain,
( sk_c8 != inverse(sk_c4)
| ~ spl0_5
| ~ spl0_11
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f606,f171]) ).
fof(f613,plain,
( sk_c8 != inverse(sk_c7)
| ~ spl0_5
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f608,f182]) ).
fof(f614,plain,
( $false
| ~ spl0_5
| ~ spl0_10
| ~ spl0_11
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f610,f107]) ).
fof(f615,plain,
( ~ spl0_5
| ~ spl0_10
| ~ spl0_11
| ~ spl0_17 ),
inference(avatar_contradiction_clause,[],[f614]) ).
fof(f619,plain,
( sk_c8 != inverse(sk_c8)
| ~ spl0_5
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f613,f171]) ).
fof(f621,plain,
( $false
| ~ spl0_3
| ~ spl0_5
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[],[f619,f404]) ).
fof(f622,plain,
( ~ spl0_3
| ~ spl0_5
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17
| ~ spl0_18 ),
inference(avatar_contradiction_clause,[],[f621]) ).
fof(f635,plain,
( sk_c8 != multiply(sk_c8,sk_c8)
| ~ spl0_4
| ~ spl0_10
| ~ spl0_11
| ~ spl0_17 ),
inference(forward_demodulation,[],[f533,f171]) ).
fof(f663,plain,
( sk_c8 = multiply(sk_c8,sk_c8)
| ~ spl0_3
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f484,f171]) ).
fof(f664,plain,
( $false
| ~ spl0_3
| ~ spl0_4
| ~ spl0_10
| ~ spl0_11
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[],[f663,f635]) ).
fof(f665,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_10
| ~ spl0_11
| ~ spl0_17
| ~ spl0_18 ),
inference(avatar_contradiction_clause,[],[f664]) ).
fof(f668,plain,
( sk_c7 != multiply(sk_c6,sk_c8)
| sk_c7 != multiply(sk_c5,sk_c6)
| ~ spl0_1
| ~ spl0_8 ),
inference(superposition,[],[f70,f97]) ).
fof(f677,definition,
( spl0_27
<=> sk_c7 = multiply(sk_c8,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_27])],[avatar_definition]) ).
fof(f678,plain,
( sk_c7 = multiply(sk_c8,sk_c8)
| ~ spl0_27 ),
inference(avatar_component_clause,[],[f677]) ).
fof(f681,plain,
( sk_c7 != multiply(sk_c5,sk_c6)
| ~ spl0_1
| ~ spl0_6
| ~ spl0_8 ),
inference(forward_subsumption_resolution,[],[f668,f88]) ).
fof(f684,definition,
( spl0_28
<=> sk_c7 = multiply(sk_c7,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_28])],[avatar_definition]) ).
fof(f685,plain,
( sk_c7 = multiply(sk_c7,sk_c8)
| ~ spl0_28 ),
inference(avatar_component_clause,[],[f684]) ).
fof(f686,plain,
( sk_c7 != multiply(sk_c7,sk_c8)
| spl0_28 ),
inference(avatar_component_clause,[],[f684]) ).
fof(f689,plain,
( $false
| ~ spl0_1
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_subsumption_resolution,[],[f681,f102]) ).
fof(f690,plain,
( ~ spl0_1
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(avatar_contradiction_clause,[],[f689]) ).
fof(f718,plain,
( spl0_28
| ~ spl0_3
| ~ spl0_18 ),
inference(avatar_split_clause,[],[f484,f181,f75,f684]) ).
fof(f720,plain,
( sk_c8 = multiply(inverse(sk_c7),sk_c7)
| ~ spl0_28 ),
inference(superposition,[],[f199,f685]) ).
fof(f722,plain,
( identity = sk_c8
| ~ spl0_28 ),
inference(forward_demodulation,[],[f720,f3]) ).
fof(f724,plain,
( sk_c8 = sk_c7
| ~ spl0_18
| ~ spl0_28 ),
inference(superposition,[],[f722,f182]) ).
fof(f729,plain,
( $false
| spl0_17
| ~ spl0_18
| ~ spl0_28 ),
inference(forward_subsumption_resolution,[],[f724,f172]) ).
fof(f730,plain,
( spl0_17
| ~ spl0_18
| ~ spl0_28 ),
inference(avatar_contradiction_clause,[],[f729]) ).
fof(f732,plain,
( spl0_27
| ~ spl0_14
| ~ spl0_15 ),
inference(avatar_split_clause,[],[f211,f146,f136,f677]) ).
fof(f734,plain,
( sk_c8 != inverse(sk_c8)
| spl0_16
| ~ spl0_28 ),
inference(forward_demodulation,[],[f168,f722]) ).
fof(f741,plain,
( identity = multiply(sk_c8,sk_c1)
| ~ spl0_15 ),
inference(superposition,[],[f3,f148]) ).
fof(f742,plain,
( sk_c8 = multiply(sk_c8,sk_c1)
| ~ spl0_15
| ~ spl0_28 ),
inference(forward_demodulation,[],[f741,f722]) ).
fof(f769,plain,
( sk_c1 = multiply(inverse(sk_c8),sk_c8)
| ~ spl0_15
| ~ spl0_28 ),
inference(superposition,[],[f199,f742]) ).
fof(f771,plain,
( identity = sk_c1
| ~ spl0_15
| ~ spl0_28 ),
inference(forward_demodulation,[],[f769,f3]) ).
fof(f774,plain,
( sk_c1 = sk_c8
| ~ spl0_15
| ~ spl0_28 ),
inference(forward_demodulation,[],[f771,f722]) ).
fof(f786,plain,
( identity != sk_c8
| ~ spl0_17
| spl0_18 ),
inference(forward_demodulation,[],[f183,f171]) ).
fof(f789,plain,
( $false
| ~ spl0_17
| spl0_18
| ~ spl0_28 ),
inference(forward_subsumption_resolution,[],[f786,f722]) ).
fof(f790,plain,
( ~ spl0_17
| spl0_18
| ~ spl0_28 ),
inference(avatar_contradiction_clause,[],[f789]) ).
fof(f791,plain,
( sk_c8 != multiply(sk_c8,sk_c8)
| ~ spl0_17
| spl0_28 ),
inference(forward_demodulation,[],[f686,f171]) ).
fof(f793,plain,
( sk_c8 = multiply(sk_c8,sk_c8)
| ~ spl0_17
| ~ spl0_27 ),
inference(forward_demodulation,[],[f678,f171]) ).
fof(f808,plain,
( $false
| ~ spl0_17
| ~ spl0_27
| spl0_28 ),
inference(forward_subsumption_resolution,[],[f793,f791]) ).
fof(f809,plain,
( ~ spl0_17
| ~ spl0_27
| spl0_28 ),
inference(avatar_contradiction_clause,[],[f808]) ).
fof(f841,plain,
( sk_c8 = inverse(sk_c8)
| ~ spl0_15
| ~ spl0_28 ),
inference(superposition,[],[f148,f774]) ).
fof(f848,plain,
( sk_c8 != sk_c7
| spl0_3
| ~ spl0_17
| ~ spl0_19 ),
inference(superposition,[],[f77,f552]) ).
fof(f852,plain,
( $false
| spl0_3
| ~ spl0_17
| ~ spl0_19 ),
inference(forward_subsumption_resolution,[],[f848,f171]) ).
fof(f853,plain,
( spl0_3
| ~ spl0_17
| ~ spl0_19 ),
inference(avatar_contradiction_clause,[],[f852]) ).
fof(f864,plain,
( $false
| ~ spl0_15
| spl0_16
| ~ spl0_28 ),
inference(forward_subsumption_resolution,[],[f841,f734]) ).
fof(f865,plain,
( ~ spl0_15
| spl0_16
| ~ spl0_28 ),
inference(avatar_contradiction_clause,[],[f864]) ).
cnf(s1,plain,
( spl0_1
| spl0_2
| ~ spl0_3
| spl0_4
| spl0_5 ),
inference(sat_conversion,[],[f84]) ).
cnf(s3,plain,
( spl0_7
| spl0_8 ),
inference(sat_conversion,[],[f98]) ).
cnf(s4,plain,
( spl0_7
| spl0_9 ),
inference(sat_conversion,[],[f103]) ).
cnf(s7,plain,
( spl0_3
| spl0_7 ),
inference(sat_conversion,[],[f114]) ).
cnf(s9,plain,
( spl0_8
| spl0_12 ),
inference(sat_conversion,[],[f120]) ).
cnf(s10,plain,
( spl0_9
| spl0_12 ),
inference(sat_conversion,[],[f121]) ).
cnf(s13,plain,
( spl0_3
| spl0_12 ),
inference(sat_conversion,[],[f124]) ).
cnf(s15,plain,
( spl0_8
| spl0_13 ),
inference(sat_conversion,[],[f130]) ).
cnf(s16,plain,
( spl0_9
| spl0_13 ),
inference(sat_conversion,[],[f131]) ).
cnf(s19,plain,
( spl0_3
| spl0_13 ),
inference(sat_conversion,[],[f134]) ).
cnf(s20,plain,
( spl0_6
| spl0_14 ),
inference(sat_conversion,[],[f139]) ).
cnf(s21,plain,
( spl0_8
| spl0_14 ),
inference(sat_conversion,[],[f140]) ).
cnf(s22,plain,
( spl0_9
| spl0_14 ),
inference(sat_conversion,[],[f141]) ).
cnf(s23,plain,
( spl0_10
| spl0_14 ),
inference(sat_conversion,[],[f142]) ).
cnf(s24,plain,
( spl0_11
| spl0_14 ),
inference(sat_conversion,[],[f143]) ).
cnf(s25,plain,
( spl0_3
| spl0_14 ),
inference(sat_conversion,[],[f144]) ).
cnf(s26,plain,
( spl0_6
| spl0_15 ),
inference(sat_conversion,[],[f149]) ).
cnf(s27,plain,
( spl0_8
| spl0_15 ),
inference(sat_conversion,[],[f150]) ).
cnf(s28,plain,
( spl0_9
| spl0_15 ),
inference(sat_conversion,[],[f151]) ).
cnf(s29,plain,
( spl0_10
| spl0_15 ),
inference(sat_conversion,[],[f152]) ).
cnf(s30,plain,
( spl0_11
| spl0_15 ),
inference(sat_conversion,[],[f153]) ).
cnf(s31,plain,
( spl0_3
| spl0_15 ),
inference(sat_conversion,[],[f154]) ).
cnf(s33,plain,
( ~ spl0_2
| ~ spl0_10
| ~ spl0_11 ),
inference(sat_conversion,[],[f161]) ).
cnf(s40,plain,
( ~ spl0_8
| ~ spl0_9
| spl0_18 ),
inference(sat_conversion,[],[f390]) ).
cnf(s52,plain,
( ~ spl0_7
| ~ spl0_12
| ~ spl0_13
| spl0_17 ),
inference(sat_conversion,[],[f464]) ).
cnf(s54,plain,
( ~ spl0_2
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17 ),
inference(sat_conversion,[],[f479]) ).
cnf(s59,plain,
( ~ spl0_16
| ~ spl0_18
| spl0_19 ),
inference(sat_conversion,[],[f509]) ).
cnf(s63,plain,
( ~ spl0_4
| ~ spl0_15
| ~ spl0_17 ),
inference(sat_conversion,[],[f544]) ).
cnf(s71,plain,
( ~ spl0_1
| ~ spl0_3
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17 ),
inference(sat_conversion,[],[f600]) ).
cnf(s72,plain,
( ~ spl0_5
| ~ spl0_10
| ~ spl0_11
| ~ spl0_17 ),
inference(sat_conversion,[],[f615]) ).
cnf(s74,plain,
( ~ spl0_3
| ~ spl0_5
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17
| ~ spl0_18 ),
inference(sat_conversion,[],[f622]) ).
cnf(s77,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_10
| ~ spl0_11
| ~ spl0_17
| ~ spl0_18 ),
inference(sat_conversion,[],[f665]) ).
cnf(s80,plain,
( ~ spl0_1
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(sat_conversion,[],[f690]) ).
cnf(s95,plain,
( ~ spl0_3
| ~ spl0_18
| spl0_28 ),
inference(sat_conversion,[],[f718]) ).
cnf(s97,plain,
( spl0_17
| ~ spl0_18
| ~ spl0_28 ),
inference(sat_conversion,[],[f730]) ).
cnf(s100,plain,
( ~ spl0_14
| ~ spl0_15
| spl0_27 ),
inference(sat_conversion,[],[f732]) ).
cnf(s103,plain,
( ~ spl0_17
| spl0_18
| ~ spl0_28 ),
inference(sat_conversion,[],[f790]) ).
cnf(s104,plain,
( ~ spl0_17
| ~ spl0_27
| spl0_28 ),
inference(sat_conversion,[],[f809]) ).
cnf(s105,plain,
( spl0_3
| ~ spl0_17
| ~ spl0_19 ),
inference(sat_conversion,[],[f853]) ).
cnf(s106,plain,
( ~ spl0_15
| spl0_16
| ~ spl0_28 ),
inference(sat_conversion,[],[f865]) ).
cnf(s107,plain,
spl0_3,
inference(rat,[],[s106,s59,s103,s104,s105,s52,s100,s7,s13,s19,s25,s31]) ).
cnf(s109,plain,
( ~ spl0_15
| ~ spl0_14
| ~ spl0_17
| ~ spl0_5 ),
inference(rat,[],[s103,s104,s74,s100,s107]) ).
cnf(s110,plain,
( spl0_15
| ~ spl0_17
| ~ spl0_5 ),
inference(rat,[],[s72,s29,s30]) ).
cnf(s111,plain,
( ~ spl0_15
| ~ spl0_17
| ~ spl0_5 ),
inference(rat,[],[s72,s23,s24,s109]) ).
cnf(s112,plain,
( ~ spl0_17
| ~ spl0_5 ),
inference(rat,[],[s111,s110]) ).
cnf(s113,plain,
( ~ spl0_18
| spl0_17 ),
inference(rat,[],[s97,s95,s107]) ).
cnf(s114,plain,
( spl0_12
| spl0_18 ),
inference(rat,[],[s40,s9,s10]) ).
cnf(s115,plain,
( spl0_13
| spl0_18 ),
inference(rat,[],[s40,s15,s16]) ).
cnf(s116,plain,
spl0_17,
inference(rat,[],[s40,s3,s4,s52,s115,s114,s113]) ).
cnf(s117,plain,
~ spl0_5,
inference(rat,[],[s112,s116]) ).
cnf(s118,plain,
~ spl0_4,
inference(rat,[],[s40,s77,s27,s28,s29,s30,s63,s107,s116]) ).
cnf(s119,plain,
( spl0_14
| ~ spl0_2 ),
inference(rat,[],[s33,s23,s24]) ).
cnf(s120,plain,
( ~ spl0_14
| ~ spl0_2 ),
inference(rat,[],[s33,s29,s30,s54,s116]) ).
cnf(s121,plain,
~ spl0_2,
inference(rat,[],[s120,s119]) ).
cnf(s122,plain,
spl0_1,
inference(rat,[],[s1,s117,s107,s118,s121]) ).
cnf(s123,plain,
spl0_14,
inference(rat,[],[s80,s20,s21,s22,s122]) ).
cnf(s124,plain,
~ spl0_15,
inference(rat,[],[s71,s122,s107,s116,s123]) ).
cnf(s127,plain,
spl0_9,
inference(rat,[],[s28,s124]) ).
cnf(s128,plain,
spl0_8,
inference(rat,[],[s27,s124]) ).
cnf(s129,plain,
spl0_6,
inference(rat,[],[s26,s124]) ).
cnf(s131,plain,
$false,
inference(rat,[],[s80,s129,s122,s127,s128]) ).
fof(f866,plain,
$false,
inference(avatar_sat_refutation,[],[s131]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP227-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.39 % Computer : n019.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Sun Sep 27 09:38:33 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 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
% 2.64/1.32 % (2839378)Input is clausal, will run a generic CNF schedule.
% 2.64/1.32 % (2839436)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=816640766:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.64/1.32 % (2839437)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=3023201634:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.64/1.32 % (2839440)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=2575706544:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.64/1.32 % (2839439)lrs+10_1_sil=8000:sp=occurrence:random_seed=3386864610:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.64/1.32 % (2839438)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=3804763139:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.64/1.32 % (2839441)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=230471970:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.64/1.32 % (2839441)First to succeed.
% 2.64/1.32 % (2839441)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2839378"
% 2.64/1.32 % (2839439)Instruction limit reached!
% 2.64/1.32 % (2839439)------------------------------
% 2.64/1.32 % (2839439)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.64/1.32 % (2839439)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.64/1.32 % (2839439)CaDiCaL version: 2.1.3
% 2.64/1.32 % (2839439)Termination reason: Instruction limit
% 2.64/1.32 % (2839439)Termination phase: Saturation
% 2.64/1.32 % (2839439)Time elapsed: 0.053 s
% 2.64/1.32 % (2839439)Peak memory usage: 89 MB
% 2.64/1.32 % (2839439)Instructions burned: 109 (million)
% 2.64/1.32 % (2839440)Instruction limit reached!
% 2.64/1.32 % (2839440)------------------------------
% 2.64/1.32 % (2839440)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.64/1.32 % (2839440)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.64/1.32 % (2839440)CaDiCaL version: 2.1.3
% 2.64/1.32 % (2839440)Termination reason: Instruction limit
% 2.64/1.32 % (2839440)Termination phase: Saturation
% 2.64/1.32 % (2839440)Time elapsed: 0.067 s
% 2.64/1.32 % (2839440)Peak memory usage: 89 MB
% 2.64/1.32 % (2839440)Instructions burned: 115 (million)
% 2.64/1.32 % (2839442)dis-21_1_sil=8000:lcm=predicate:random_seed=2382562566: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)
% 2.64/1.32 % (2839442)Refutation not found, incomplete strategy
% 2.64/1.32 % (2839442)------------------------------
% 2.64/1.32 % (2839442)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.64/1.32 % (2839442)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.64/1.32 % (2839442)CaDiCaL version: 2.1.3
% 2.64/1.32 % (2839442)Termination reason: Refutation not found, incomplete strategy
% 2.64/1.32 % (2839442)Time elapsed: 0.004 s
% 2.64/1.32 % (2839442)Peak memory usage: 88 MB
% 2.64/1.32 % (2839442)Instructions burned: 2 (million)
% 2.64/1.32 % (2839449)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=582351320:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 2.64/1.32 % (2839450)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=1881720486: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)
% 2.64/1.32 % (2839441)Refutation found. Thanks to Tanya!
% 2.64/1.32 % SZS status Unsatisfiable for theBenchmark
% 2.64/1.32 % SZS output start Proof for theBenchmark
% See solution above
% 3.69/1.42 % (2839441)------------------------------
% 3.69/1.42 % (2839441)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.69/1.42 % (2839441)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.69/1.42 % (2839441)CaDiCaL version: 2.1.3
% 3.69/1.42 % (2839441)Termination reason: Refutation
% 3.69/1.42 % (2839441)Time elapsed: 0.020 s
% 3.69/1.42 % (2839441)Peak memory usage: 90 MB
% 3.69/1.42 % (2839441)Instructions burned: 31 (million)
% 3.69/1.42 % (2839441)------------------------------
% 3.69/1.42 % (2839441)------------------------------
% 3.69/1.42 % (2839378)Success in time 0.462 s
% 3.69/1.42 % Vampire exiting
%------------------------------------------------------------------------------