TSTP Solution File: GRP222-1 by SnakeForV-SAT---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV-SAT---1.0
% Problem : GRP222-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Aug 31 16:20:56 EDT 2022
% Result : Unsatisfiable 0.20s 0.55s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 49
% Syntax : Number of formulae : 224 ( 41 unt; 0 def)
% Number of atoms : 623 ( 252 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 763 ( 364 ~; 381 |; 0 &)
% ( 18 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 20 ( 18 usr; 19 prp; 0-2 aty)
% Number of functors : 23 ( 23 usr; 17 con; 0-2 aty)
% Number of variables : 38 ( 38 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f925,plain,
$false,
inference(avatar_sat_refutation,[],[f68,f78,f79,f93,f98,f103,f104,f105,f107,f108,f109,f110,f112,f113,f123,f208,f220,f265,f270,f360,f402,f540,f578,f697,f742,f756,f862,f914,f923]) ).
fof(f923,plain,
( ~ spl13_1
| ~ spl13_6
| spl13_15
| ~ spl13_26 ),
inference(avatar_contradiction_clause,[],[f922]) ).
fof(f922,plain,
( $false
| ~ spl13_1
| ~ spl13_6
| spl13_15
| ~ spl13_26 ),
inference(subsumption_resolution,[],[f921,f268]) ).
fof(f268,plain,
( sk_c7 = inverse(sk_c4)
| ~ spl13_26 ),
inference(avatar_component_clause,[],[f267]) ).
fof(f267,plain,
( spl13_26
<=> sk_c7 = inverse(sk_c4) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_26])]) ).
fof(f921,plain,
( sk_c7 != inverse(sk_c4)
| ~ spl13_1
| ~ spl13_6
| spl13_15 ),
inference(forward_demodulation,[],[f207,f821]) ).
fof(f821,plain,
( sk_c4 = sk_c5
| ~ spl13_1
| ~ spl13_6 ),
inference(forward_demodulation,[],[f817,f809]) ).
fof(f809,plain,
( sk_c4 = multiply(inverse(sk_c7),identity)
| ~ spl13_1 ),
inference(superposition,[],[f302,f598]) ).
fof(f598,plain,
( identity = multiply(sk_c7,sk_c4)
| ~ spl13_1 ),
inference(superposition,[],[f127,f63]) ).
fof(f63,plain,
( sk_c7 = sF0
| ~ spl13_1 ),
inference(avatar_component_clause,[],[f61]) ).
fof(f61,plain,
( spl13_1
<=> sk_c7 = sF0 ),
introduced(avatar_definition,[new_symbols(naming,[spl13_1])]) ).
fof(f127,plain,
identity = multiply(sF0,sk_c4),
inference(superposition,[],[f2,f26]) ).
fof(f26,plain,
inverse(sk_c4) = sF0,
introduced(function_definition,[]) ).
fof(f2,axiom,
! [X0] : identity = multiply(inverse(X0),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_inverse) ).
fof(f302,plain,
! [X12,X13] : multiply(inverse(X12),multiply(X12,X13)) = X13,
inference(forward_demodulation,[],[f276,f1]) ).
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_identity) ).
fof(f276,plain,
! [X12,X13] : multiply(inverse(X12),multiply(X12,X13)) = multiply(identity,X13),
inference(superposition,[],[f3,f2]) ).
fof(f3,axiom,
! [X2,X0,X1] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity) ).
fof(f817,plain,
( sk_c5 = multiply(inverse(sk_c7),identity)
| ~ spl13_6 ),
inference(superposition,[],[f302,f616]) ).
fof(f616,plain,
( identity = multiply(sk_c7,sk_c5)
| ~ spl13_6 ),
inference(superposition,[],[f128,f87]) ).
fof(f87,plain,
( sk_c7 = sF6
| ~ spl13_6 ),
inference(avatar_component_clause,[],[f85]) ).
fof(f85,plain,
( spl13_6
<=> sk_c7 = sF6 ),
introduced(avatar_definition,[new_symbols(naming,[spl13_6])]) ).
fof(f128,plain,
identity = multiply(sF6,sk_c5),
inference(superposition,[],[f2,f35]) ).
fof(f35,plain,
inverse(sk_c5) = sF6,
introduced(function_definition,[]) ).
fof(f207,plain,
( sk_c7 != inverse(sk_c5)
| spl13_15 ),
inference(avatar_component_clause,[],[f205]) ).
fof(f205,plain,
( spl13_15
<=> sk_c7 = inverse(sk_c5) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_15])]) ).
fof(f914,plain,
( ~ spl13_1
| ~ spl13_3
| ~ spl13_6
| ~ spl13_20
| spl13_23 ),
inference(avatar_contradiction_clause,[],[f913]) ).
fof(f913,plain,
( $false
| ~ spl13_1
| ~ spl13_3
| ~ spl13_6
| ~ spl13_20
| spl13_23 ),
inference(subsumption_resolution,[],[f912,f241]) ).
fof(f241,plain,
( identity = sk_c6
| ~ spl13_20 ),
inference(avatar_component_clause,[],[f240]) ).
fof(f240,plain,
( spl13_20
<=> identity = sk_c6 ),
introduced(avatar_definition,[new_symbols(naming,[spl13_20])]) ).
fof(f912,plain,
( identity != sk_c6
| ~ spl13_1
| ~ spl13_3
| ~ spl13_6
| ~ spl13_20
| spl13_23 ),
inference(superposition,[],[f255,f907]) ).
fof(f907,plain,
( identity = sF10(sk_c4)
| ~ spl13_1
| ~ spl13_3
| ~ spl13_6
| ~ spl13_20 ),
inference(superposition,[],[f898,f596]) ).
fof(f596,plain,
( sF10(sk_c4) = sF11(sk_c7)
| ~ spl13_1 ),
inference(superposition,[],[f166,f63]) ).
fof(f166,plain,
sF10(sk_c4) = sF11(sF0),
inference(superposition,[],[f153,f47]) ).
fof(f47,plain,
! [X6] : multiply(X6,sk_c7) = sF11(X6),
introduced(function_definition,[]) ).
fof(f153,plain,
sF10(sk_c4) = multiply(sF0,sk_c7),
inference(superposition,[],[f46,f26]) ).
fof(f46,plain,
! [X4] : sF10(X4) = multiply(inverse(X4),sk_c7),
introduced(function_definition,[]) ).
fof(f898,plain,
( identity = sF11(sk_c7)
| ~ spl13_3
| ~ spl13_6
| ~ spl13_20 ),
inference(forward_demodulation,[],[f892,f241]) ).
fof(f892,plain,
( sk_c6 = sF11(sk_c7)
| ~ spl13_3
| ~ spl13_6 ),
inference(superposition,[],[f732,f47]) ).
fof(f732,plain,
( sk_c6 = multiply(sk_c7,sk_c7)
| ~ spl13_3
| ~ spl13_6 ),
inference(forward_demodulation,[],[f621,f72]) ).
fof(f72,plain,
( sk_c7 = sF3
| ~ spl13_3 ),
inference(avatar_component_clause,[],[f70]) ).
fof(f70,plain,
( spl13_3
<=> sk_c7 = sF3 ),
introduced(avatar_definition,[new_symbols(naming,[spl13_3])]) ).
fof(f621,plain,
( sk_c6 = multiply(sk_c7,sF3)
| ~ spl13_6 ),
inference(superposition,[],[f339,f87]) ).
fof(f339,plain,
sk_c6 = multiply(sF6,sF3),
inference(forward_demodulation,[],[f329,f35]) ).
fof(f329,plain,
sk_c6 = multiply(inverse(sk_c5),sF3),
inference(superposition,[],[f302,f30]) ).
fof(f30,plain,
multiply(sk_c5,sk_c6) = sF3,
introduced(function_definition,[]) ).
fof(f255,plain,
( sk_c6 != sF10(sk_c4)
| spl13_23 ),
inference(avatar_component_clause,[],[f253]) ).
fof(f253,plain,
( spl13_23
<=> sk_c6 = sF10(sk_c4) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_23])]) ).
fof(f862,plain,
( spl13_20
| ~ spl13_1
| ~ spl13_7 ),
inference(avatar_split_clause,[],[f855,f90,f61,f240]) ).
fof(f90,plain,
( spl13_7
<=> sk_c6 = sF4 ),
introduced(avatar_definition,[new_symbols(naming,[spl13_7])]) ).
fof(f855,plain,
( identity = sk_c6
| ~ spl13_1
| ~ spl13_7 ),
inference(superposition,[],[f92,f851]) ).
fof(f851,plain,
( identity = sF4
| ~ spl13_1 ),
inference(forward_demodulation,[],[f850,f2]) ).
fof(f850,plain,
( sF4 = multiply(inverse(sk_c7),sk_c7)
| ~ spl13_1 ),
inference(forward_demodulation,[],[f845,f63]) ).
fof(f845,plain,
sF4 = multiply(inverse(sF0),sk_c7),
inference(superposition,[],[f302,f343]) ).
fof(f343,plain,
sk_c7 = multiply(sF0,sF4),
inference(forward_demodulation,[],[f327,f26]) ).
fof(f327,plain,
sk_c7 = multiply(inverse(sk_c4),sF4),
inference(superposition,[],[f302,f32]) ).
fof(f32,plain,
multiply(sk_c4,sk_c7) = sF4,
introduced(function_definition,[]) ).
fof(f92,plain,
( sk_c6 = sF4
| ~ spl13_7 ),
inference(avatar_component_clause,[],[f90]) ).
fof(f756,plain,
( ~ spl13_1
| spl13_26 ),
inference(avatar_contradiction_clause,[],[f755]) ).
fof(f755,plain,
( $false
| ~ spl13_1
| spl13_26 ),
inference(subsumption_resolution,[],[f754,f63]) ).
fof(f754,plain,
( sk_c7 != sF0
| spl13_26 ),
inference(superposition,[],[f269,f26]) ).
fof(f269,plain,
( sk_c7 != inverse(sk_c4)
| spl13_26 ),
inference(avatar_component_clause,[],[f267]) ).
fof(f742,plain,
( ~ spl13_1
| ~ spl13_7
| ~ spl13_12
| ~ spl13_23 ),
inference(avatar_contradiction_clause,[],[f741]) ).
fof(f741,plain,
( $false
| ~ spl13_1
| ~ spl13_7
| ~ spl13_12
| ~ spl13_23 ),
inference(subsumption_resolution,[],[f740,f254]) ).
fof(f254,plain,
( sk_c6 = sF10(sk_c4)
| ~ spl13_23 ),
inference(avatar_component_clause,[],[f253]) ).
fof(f740,plain,
( sk_c6 != sF10(sk_c4)
| ~ spl13_1
| ~ spl13_7
| ~ spl13_12 ),
inference(trivial_inequality_removal,[],[f738]) ).
fof(f738,plain,
( sk_c6 != sF10(sk_c4)
| sk_c6 != sk_c6
| ~ spl13_1
| ~ spl13_7
| ~ spl13_12 ),
inference(superposition,[],[f122,f708]) ).
fof(f708,plain,
( sk_c6 = sF12(sk_c4)
| ~ spl13_1
| ~ spl13_7 ),
inference(forward_demodulation,[],[f603,f92]) ).
fof(f603,plain,
( sF4 = sF12(sk_c4)
| ~ spl13_1 ),
inference(forward_demodulation,[],[f595,f32]) ).
fof(f595,plain,
( multiply(sk_c4,sk_c7) = sF12(sk_c4)
| ~ spl13_1 ),
inference(superposition,[],[f180,f63]) ).
fof(f180,plain,
sF12(sk_c4) = multiply(sk_c4,sF0),
inference(superposition,[],[f48,f26]) ).
fof(f48,plain,
! [X4] : multiply(X4,inverse(X4)) = sF12(X4),
introduced(function_definition,[]) ).
fof(f122,plain,
( ! [X4] :
( sk_c6 != sF12(X4)
| sk_c6 != sF10(X4) )
| ~ spl13_12 ),
inference(avatar_component_clause,[],[f121]) ).
fof(f121,plain,
( spl13_12
<=> ! [X4] :
( sk_c6 != sF10(X4)
| sk_c6 != sF12(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_12])]) ).
fof(f697,plain,
( ~ spl13_1
| ~ spl13_4
| ~ spl13_7
| ~ spl13_12
| ~ spl13_20
| ~ spl13_24 ),
inference(avatar_contradiction_clause,[],[f696]) ).
fof(f696,plain,
( $false
| ~ spl13_1
| ~ spl13_4
| ~ spl13_7
| ~ spl13_12
| ~ spl13_20
| ~ spl13_24 ),
inference(subsumption_resolution,[],[f695,f609]) ).
fof(f609,plain,
( identity = sF10(sk_c4)
| ~ spl13_1
| ~ spl13_4
| ~ spl13_20
| ~ spl13_24 ),
inference(forward_demodulation,[],[f606,f241]) ).
fof(f606,plain,
( sk_c6 = sF10(sk_c4)
| ~ spl13_1
| ~ spl13_4
| ~ spl13_24 ),
inference(forward_demodulation,[],[f605,f259]) ).
fof(f259,plain,
( sk_c6 = sF10(sk_c1)
| ~ spl13_24 ),
inference(avatar_component_clause,[],[f258]) ).
fof(f258,plain,
( spl13_24
<=> sk_c6 = sF10(sk_c1) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_24])]) ).
fof(f605,plain,
( sF10(sk_c4) = sF10(sk_c1)
| ~ spl13_1
| ~ spl13_4 ),
inference(forward_demodulation,[],[f597,f163]) ).
fof(f163,plain,
( multiply(sk_c7,sk_c7) = sF10(sk_c1)
| ~ spl13_4 ),
inference(forward_demodulation,[],[f152,f77]) ).
fof(f77,plain,
( sk_c7 = sF1
| ~ spl13_4 ),
inference(avatar_component_clause,[],[f75]) ).
fof(f75,plain,
( spl13_4
<=> sk_c7 = sF1 ),
introduced(avatar_definition,[new_symbols(naming,[spl13_4])]) ).
fof(f152,plain,
multiply(sF1,sk_c7) = sF10(sk_c1),
inference(superposition,[],[f46,f27]) ).
fof(f27,plain,
inverse(sk_c1) = sF1,
introduced(function_definition,[]) ).
fof(f597,plain,
( multiply(sk_c7,sk_c7) = sF10(sk_c4)
| ~ spl13_1 ),
inference(superposition,[],[f153,f63]) ).
fof(f695,plain,
( identity != sF10(sk_c4)
| ~ spl13_1
| ~ spl13_7
| ~ spl13_12
| ~ spl13_20 ),
inference(trivial_inequality_removal,[],[f694]) ).
fof(f694,plain,
( identity != sF10(sk_c4)
| identity != identity
| ~ spl13_1
| ~ spl13_7
| ~ spl13_12
| ~ spl13_20 ),
inference(superposition,[],[f542,f604]) ).
fof(f604,plain,
( identity = sF12(sk_c4)
| ~ spl13_1
| ~ spl13_7
| ~ spl13_20 ),
inference(forward_demodulation,[],[f603,f592]) ).
fof(f592,plain,
( identity = sF4
| ~ spl13_7
| ~ spl13_20 ),
inference(forward_demodulation,[],[f92,f241]) ).
fof(f542,plain,
( ! [X4] :
( identity != sF12(X4)
| identity != sF10(X4) )
| ~ spl13_12
| ~ spl13_20 ),
inference(forward_demodulation,[],[f541,f241]) ).
fof(f541,plain,
( ! [X4] :
( identity != sF12(X4)
| sk_c6 != sF10(X4) )
| ~ spl13_12
| ~ spl13_20 ),
inference(forward_demodulation,[],[f122,f241]) ).
fof(f578,plain,
( ~ spl13_2
| ~ spl13_4
| ~ spl13_5
| ~ spl13_8
| ~ spl13_12
| ~ spl13_20
| ~ spl13_24 ),
inference(avatar_contradiction_clause,[],[f577]) ).
fof(f577,plain,
( $false
| ~ spl13_2
| ~ spl13_4
| ~ spl13_5
| ~ spl13_8
| ~ spl13_12
| ~ spl13_20
| ~ spl13_24 ),
inference(subsumption_resolution,[],[f576,f158]) ).
fof(f158,plain,
identity = sF10(sk_c7),
inference(superposition,[],[f2,f46]) ).
fof(f576,plain,
( identity != sF10(sk_c7)
| ~ spl13_2
| ~ spl13_4
| ~ spl13_5
| ~ spl13_8
| ~ spl13_12
| ~ spl13_20
| ~ spl13_24 ),
inference(forward_demodulation,[],[f575,f512]) ).
fof(f512,plain,
( sk_c7 = sk_c2
| ~ spl13_2
| ~ spl13_4
| ~ spl13_5
| ~ spl13_8
| ~ spl13_20
| ~ spl13_24 ),
inference(superposition,[],[f1,f492]) ).
fof(f492,plain,
( sk_c7 = multiply(identity,sk_c2)
| ~ spl13_2
| ~ spl13_4
| ~ spl13_5
| ~ spl13_8
| ~ spl13_20
| ~ spl13_24 ),
inference(forward_demodulation,[],[f491,f241]) ).
fof(f491,plain,
( sk_c7 = multiply(sk_c6,sk_c2)
| ~ spl13_2
| ~ spl13_4
| ~ spl13_5
| ~ spl13_8
| ~ spl13_20
| ~ spl13_24 ),
inference(forward_demodulation,[],[f459,f484]) ).
fof(f484,plain,
( sk_c7 = multiply(sk_c2,identity)
| ~ spl13_2
| ~ spl13_4
| ~ spl13_5
| ~ spl13_8
| ~ spl13_20
| ~ spl13_24 ),
inference(forward_demodulation,[],[f483,f410]) ).
fof(f410,plain,
( sk_c7 = sk_c3
| ~ spl13_2
| ~ spl13_4
| ~ spl13_5
| ~ spl13_8
| ~ spl13_20
| ~ spl13_24 ),
inference(forward_demodulation,[],[f408,f146]) ).
fof(f146,plain,
sk_c7 = sF11(identity),
inference(superposition,[],[f1,f47]) ).
fof(f408,plain,
( sk_c3 = sF11(identity)
| ~ spl13_2
| ~ spl13_4
| ~ spl13_5
| ~ spl13_8
| ~ spl13_20
| ~ spl13_24 ),
inference(superposition,[],[f375,f241]) ).
fof(f375,plain,
( sk_c3 = sF11(sk_c6)
| ~ spl13_2
| ~ spl13_4
| ~ spl13_5
| ~ spl13_8
| ~ spl13_24 ),
inference(forward_demodulation,[],[f374,f351]) ).
fof(f351,plain,
( sk_c3 = multiply(sk_c3,sk_c6)
| ~ spl13_2
| ~ spl13_8 ),
inference(forward_demodulation,[],[f350,f67]) ).
fof(f67,plain,
( sk_c3 = sF8
| ~ spl13_2 ),
inference(avatar_component_clause,[],[f65]) ).
fof(f65,plain,
( spl13_2
<=> sk_c3 = sF8 ),
introduced(avatar_definition,[new_symbols(naming,[spl13_2])]) ).
fof(f350,plain,
( sk_c3 = multiply(sF8,sk_c6)
| ~ spl13_8 ),
inference(forward_demodulation,[],[f349,f43]) ).
fof(f43,plain,
inverse(sk_c2) = sF8,
introduced(function_definition,[]) ).
fof(f349,plain,
( sk_c3 = multiply(inverse(sk_c2),sk_c6)
| ~ spl13_8 ),
inference(forward_demodulation,[],[f331,f97]) ).
fof(f97,plain,
( sk_c6 = sF7
| ~ spl13_8 ),
inference(avatar_component_clause,[],[f95]) ).
fof(f95,plain,
( spl13_8
<=> sk_c6 = sF7 ),
introduced(avatar_definition,[new_symbols(naming,[spl13_8])]) ).
fof(f331,plain,
sk_c3 = multiply(inverse(sk_c2),sF7),
inference(superposition,[],[f302,f38]) ).
fof(f38,plain,
multiply(sk_c2,sk_c3) = sF7,
introduced(function_definition,[]) ).
fof(f374,plain,
( multiply(sk_c3,sk_c6) = sF11(sk_c6)
| ~ spl13_4
| ~ spl13_5
| ~ spl13_24 ),
inference(forward_demodulation,[],[f373,f47]) ).
fof(f373,plain,
( multiply(sk_c3,sk_c6) = multiply(sk_c6,sk_c7)
| ~ spl13_4
| ~ spl13_5
| ~ spl13_24 ),
inference(forward_demodulation,[],[f372,f259]) ).
fof(f372,plain,
( multiply(sk_c6,sk_c7) = multiply(sk_c3,sF10(sk_c1))
| ~ spl13_4
| ~ spl13_5 ),
inference(forward_demodulation,[],[f365,f165]) ).
fof(f165,plain,
( sF11(sk_c7) = sF10(sk_c1)
| ~ spl13_4 ),
inference(superposition,[],[f47,f163]) ).
fof(f365,plain,
( multiply(sk_c6,sk_c7) = multiply(sk_c3,sF11(sk_c7))
| ~ spl13_5 ),
inference(superposition,[],[f299,f47]) ).
fof(f299,plain,
( ! [X24] : multiply(sk_c3,multiply(sk_c7,X24)) = multiply(sk_c6,X24)
| ~ spl13_5 ),
inference(forward_demodulation,[],[f286,f83]) ).
fof(f83,plain,
( sk_c6 = sF5
| ~ spl13_5 ),
inference(avatar_component_clause,[],[f81]) ).
fof(f81,plain,
( spl13_5
<=> sk_c6 = sF5 ),
introduced(avatar_definition,[new_symbols(naming,[spl13_5])]) ).
fof(f286,plain,
! [X24] : multiply(sF5,X24) = multiply(sk_c3,multiply(sk_c7,X24)),
inference(superposition,[],[f3,f33]) ).
fof(f33,plain,
multiply(sk_c3,sk_c7) = sF5,
introduced(function_definition,[]) ).
fof(f483,plain,
( sk_c3 = multiply(sk_c2,identity)
| ~ spl13_2
| ~ spl13_4
| ~ spl13_5
| ~ spl13_8
| ~ spl13_20
| ~ spl13_24 ),
inference(forward_demodulation,[],[f482,f241]) ).
fof(f482,plain,
( sk_c3 = multiply(sk_c2,sk_c6)
| ~ spl13_2
| ~ spl13_4
| ~ spl13_5
| ~ spl13_8
| ~ spl13_24 ),
inference(forward_demodulation,[],[f481,f83]) ).
fof(f481,plain,
( sk_c3 = multiply(sk_c2,sF5)
| ~ spl13_2
| ~ spl13_4
| ~ spl13_5
| ~ spl13_8
| ~ spl13_24 ),
inference(forward_demodulation,[],[f480,f375]) ).
fof(f480,plain,
( multiply(sk_c2,sF5) = sF11(sk_c6)
| ~ spl13_8 ),
inference(forward_demodulation,[],[f457,f47]) ).
fof(f457,plain,
( multiply(sk_c2,sF5) = multiply(sk_c6,sk_c7)
| ~ spl13_8 ),
inference(superposition,[],[f309,f33]) ).
fof(f309,plain,
( ! [X23] : multiply(sk_c6,X23) = multiply(sk_c2,multiply(sk_c3,X23))
| ~ spl13_8 ),
inference(forward_demodulation,[],[f285,f97]) ).
fof(f285,plain,
! [X23] : multiply(sF7,X23) = multiply(sk_c2,multiply(sk_c3,X23)),
inference(superposition,[],[f3,f38]) ).
fof(f459,plain,
( multiply(sk_c6,sk_c2) = multiply(sk_c2,identity)
| ~ spl13_2
| ~ spl13_8 ),
inference(superposition,[],[f309,f130]) ).
fof(f130,plain,
( identity = multiply(sk_c3,sk_c2)
| ~ spl13_2 ),
inference(forward_demodulation,[],[f129,f67]) ).
fof(f129,plain,
identity = multiply(sF8,sk_c2),
inference(superposition,[],[f2,f43]) ).
fof(f575,plain,
( identity != sF10(sk_c2)
| ~ spl13_2
| ~ spl13_8
| ~ spl13_12
| ~ spl13_20 ),
inference(subsumption_resolution,[],[f561,f241]) ).
fof(f561,plain,
( identity != sk_c6
| identity != sF10(sk_c2)
| ~ spl13_2
| ~ spl13_8
| ~ spl13_12
| ~ spl13_20 ),
inference(superposition,[],[f542,f187]) ).
fof(f187,plain,
( sk_c6 = sF12(sk_c2)
| ~ spl13_2
| ~ spl13_8 ),
inference(forward_demodulation,[],[f186,f97]) ).
fof(f186,plain,
( sF12(sk_c2) = sF7
| ~ spl13_2 ),
inference(forward_demodulation,[],[f185,f38]) ).
fof(f185,plain,
( multiply(sk_c2,sk_c3) = sF12(sk_c2)
| ~ spl13_2 ),
inference(forward_demodulation,[],[f182,f67]) ).
fof(f182,plain,
multiply(sk_c2,sF8) = sF12(sk_c2),
inference(superposition,[],[f48,f43]) ).
fof(f540,plain,
( spl13_25
| ~ spl13_2
| ~ spl13_4
| ~ spl13_5
| ~ spl13_8
| ~ spl13_20
| ~ spl13_24 ),
inference(avatar_split_clause,[],[f528,f258,f240,f95,f81,f75,f65,f262]) ).
fof(f262,plain,
( spl13_25
<=> sk_c7 = inverse(sk_c7) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_25])]) ).
fof(f528,plain,
( sk_c7 = inverse(sk_c7)
| ~ spl13_2
| ~ spl13_4
| ~ spl13_5
| ~ spl13_8
| ~ spl13_20
| ~ spl13_24 ),
inference(forward_demodulation,[],[f527,f410]) ).
fof(f527,plain,
( sk_c3 = inverse(sk_c7)
| ~ spl13_2
| ~ spl13_4
| ~ spl13_5
| ~ spl13_8
| ~ spl13_20
| ~ spl13_24 ),
inference(forward_demodulation,[],[f519,f67]) ).
fof(f519,plain,
( sF8 = inverse(sk_c7)
| ~ spl13_2
| ~ spl13_4
| ~ spl13_5
| ~ spl13_8
| ~ spl13_20
| ~ spl13_24 ),
inference(superposition,[],[f43,f512]) ).
fof(f402,plain,
( spl13_20
| ~ spl13_2
| ~ spl13_8 ),
inference(avatar_split_clause,[],[f399,f95,f65,f240]) ).
fof(f399,plain,
( identity = sk_c6
| ~ spl13_2
| ~ spl13_8 ),
inference(forward_demodulation,[],[f397,f2]) ).
fof(f397,plain,
( sk_c6 = multiply(inverse(sk_c3),sk_c3)
| ~ spl13_2
| ~ spl13_8 ),
inference(superposition,[],[f302,f351]) ).
fof(f360,plain,
( spl13_24
| ~ spl13_4
| ~ spl13_9 ),
inference(avatar_split_clause,[],[f355,f100,f75,f258]) ).
fof(f100,plain,
( spl13_9
<=> sk_c7 = sF2 ),
introduced(avatar_definition,[new_symbols(naming,[spl13_9])]) ).
fof(f355,plain,
( sk_c6 = sF10(sk_c1)
| ~ spl13_4
| ~ spl13_9 ),
inference(superposition,[],[f163,f342]) ).
fof(f342,plain,
( sk_c6 = multiply(sk_c7,sk_c7)
| ~ spl13_4
| ~ spl13_9 ),
inference(forward_demodulation,[],[f341,f77]) ).
fof(f341,plain,
( sk_c6 = multiply(sF1,sk_c7)
| ~ spl13_9 ),
inference(forward_demodulation,[],[f340,f27]) ).
fof(f340,plain,
( sk_c6 = multiply(inverse(sk_c1),sk_c7)
| ~ spl13_9 ),
inference(forward_demodulation,[],[f324,f102]) ).
fof(f102,plain,
( sk_c7 = sF2
| ~ spl13_9 ),
inference(avatar_component_clause,[],[f100]) ).
fof(f324,plain,
sk_c6 = multiply(inverse(sk_c1),sF2),
inference(superposition,[],[f302,f29]) ).
fof(f29,plain,
multiply(sk_c1,sk_c6) = sF2,
introduced(function_definition,[]) ).
fof(f270,plain,
( ~ spl13_7
| ~ spl13_26
| ~ spl13_11 ),
inference(avatar_split_clause,[],[f225,f118,f267,f90]) ).
fof(f118,plain,
( spl13_11
<=> ! [X6] :
( sk_c7 != inverse(X6)
| sk_c6 != sF11(X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_11])]) ).
fof(f225,plain,
( sk_c7 != inverse(sk_c4)
| sk_c6 != sF4
| ~ spl13_11 ),
inference(superposition,[],[f119,f148]) ).
fof(f148,plain,
sF4 = sF11(sk_c4),
inference(superposition,[],[f32,f47]) ).
fof(f119,plain,
( ! [X6] :
( sk_c6 != sF11(X6)
| sk_c7 != inverse(X6) )
| ~ spl13_11 ),
inference(avatar_component_clause,[],[f118]) ).
fof(f265,plain,
( ~ spl13_24
| ~ spl13_25
| ~ spl13_4
| ~ spl13_11 ),
inference(avatar_split_clause,[],[f224,f118,f75,f262,f258]) ).
fof(f224,plain,
( sk_c7 != inverse(sk_c7)
| sk_c6 != sF10(sk_c1)
| ~ spl13_4
| ~ spl13_11 ),
inference(superposition,[],[f119,f165]) ).
fof(f220,plain,
( ~ spl13_4
| ~ spl13_9
| ~ spl13_10 ),
inference(avatar_contradiction_clause,[],[f219]) ).
fof(f219,plain,
( $false
| ~ spl13_4
| ~ spl13_9
| ~ spl13_10 ),
inference(subsumption_resolution,[],[f218,f77]) ).
fof(f218,plain,
( sk_c7 != sF1
| ~ spl13_9
| ~ spl13_10 ),
inference(superposition,[],[f194,f27]) ).
fof(f194,plain,
( inverse(sk_c1) != sk_c7
| ~ spl13_9
| ~ spl13_10 ),
inference(trivial_inequality_removal,[],[f192]) ).
fof(f192,plain,
( sk_c7 != sk_c7
| inverse(sk_c1) != sk_c7
| ~ spl13_9
| ~ spl13_10 ),
inference(superposition,[],[f116,f140]) ).
fof(f140,plain,
( sk_c7 = sF9(sk_c1)
| ~ spl13_9 ),
inference(forward_demodulation,[],[f134,f102]) ).
fof(f134,plain,
sF2 = sF9(sk_c1),
inference(superposition,[],[f45,f29]) ).
fof(f45,plain,
! [X7] : multiply(X7,sk_c6) = sF9(X7),
introduced(function_definition,[]) ).
fof(f116,plain,
( ! [X3] :
( sk_c7 != sF9(X3)
| sk_c7 != inverse(X3) )
| ~ spl13_10 ),
inference(avatar_component_clause,[],[f115]) ).
fof(f115,plain,
( spl13_10
<=> ! [X3] :
( sk_c7 != sF9(X3)
| sk_c7 != inverse(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_10])]) ).
fof(f208,plain,
( ~ spl13_15
| ~ spl13_3
| ~ spl13_10 ),
inference(avatar_split_clause,[],[f193,f115,f70,f205]) ).
fof(f193,plain,
( sk_c7 != sF3
| sk_c7 != inverse(sk_c5)
| ~ spl13_10 ),
inference(superposition,[],[f116,f139]) ).
fof(f139,plain,
sF9(sk_c5) = sF3,
inference(superposition,[],[f30,f45]) ).
fof(f123,plain,
( spl13_10
| spl13_11
| spl13_12
| spl13_10 ),
inference(avatar_split_clause,[],[f49,f115,f121,f118,f115]) ).
fof(f49,plain,
! [X3,X6,X7,X4] :
( sk_c7 != sF9(X7)
| sk_c6 != sF10(X4)
| sk_c7 != inverse(X6)
| sk_c7 != sF9(X3)
| sk_c7 != inverse(X7)
| sk_c6 != sF11(X6)
| sk_c6 != sF12(X4)
| sk_c7 != inverse(X3) ),
inference(definition_folding,[],[f25,f48,f47,f46,f45,f45]) ).
fof(f25,plain,
! [X3,X6,X7,X4] :
( sk_c7 != inverse(X3)
| sk_c7 != multiply(X7,sk_c6)
| sk_c7 != inverse(X7)
| sk_c7 != multiply(X3,sk_c6)
| sk_c6 != multiply(inverse(X4),sk_c7)
| sk_c7 != inverse(X6)
| sk_c6 != multiply(X6,sk_c7)
| sk_c6 != multiply(X4,inverse(X4)) ),
inference(equality_resolution,[],[f24]) ).
fof(f24,axiom,
! [X3,X6,X7,X4,X5] :
( inverse(X4) != X5
| sk_c7 != inverse(X3)
| sk_c7 != multiply(X7,sk_c6)
| sk_c7 != inverse(X7)
| sk_c7 != multiply(X3,sk_c6)
| sk_c6 != multiply(X5,sk_c7)
| sk_c7 != inverse(X6)
| sk_c6 != multiply(X6,sk_c7)
| sk_c6 != multiply(X4,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_21) ).
fof(f113,plain,
( spl13_6
| spl13_9 ),
inference(avatar_split_clause,[],[f42,f100,f85]) ).
fof(f42,plain,
( sk_c7 = sF2
| sk_c7 = sF6 ),
inference(definition_folding,[],[f10,f35,f29]) ).
fof(f10,axiom,
( sk_c7 = multiply(sk_c1,sk_c6)
| sk_c7 = inverse(sk_c5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_7) ).
fof(f112,plain,
( spl13_1
| spl13_9 ),
inference(avatar_split_clause,[],[f59,f100,f61]) ).
fof(f59,plain,
( sk_c7 = sF2
| sk_c7 = sF0 ),
inference(definition_folding,[],[f9,f26,f29]) ).
fof(f9,axiom,
( sk_c7 = multiply(sk_c1,sk_c6)
| sk_c7 = inverse(sk_c4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_6) ).
fof(f110,plain,
( spl13_7
| spl13_4 ),
inference(avatar_split_clause,[],[f58,f75,f90]) ).
fof(f58,plain,
( sk_c7 = sF1
| sk_c6 = sF4 ),
inference(definition_folding,[],[f4,f32,f27]) ).
fof(f4,axiom,
( inverse(sk_c1) = sk_c7
| multiply(sk_c4,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_1) ).
fof(f109,plain,
( spl13_2
| spl13_7 ),
inference(avatar_split_clause,[],[f53,f90,f65]) ).
fof(f53,plain,
( sk_c6 = sF4
| sk_c3 = sF8 ),
inference(definition_folding,[],[f16,f43,f32]) ).
fof(f16,axiom,
( multiply(sk_c4,sk_c7) = sk_c6
| sk_c3 = inverse(sk_c2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_13) ).
fof(f108,plain,
( spl13_8
| spl13_1 ),
inference(avatar_split_clause,[],[f41,f61,f95]) ).
fof(f41,plain,
( sk_c7 = sF0
| sk_c6 = sF7 ),
inference(definition_folding,[],[f13,f26,f38]) ).
fof(f13,axiom,
( sk_c6 = multiply(sk_c2,sk_c3)
| sk_c7 = inverse(sk_c4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_10) ).
fof(f107,plain,
( spl13_9
| spl13_7 ),
inference(avatar_split_clause,[],[f40,f90,f100]) ).
fof(f40,plain,
( sk_c6 = sF4
| sk_c7 = sF2 ),
inference(definition_folding,[],[f8,f29,f32]) ).
fof(f8,axiom,
( multiply(sk_c4,sk_c7) = sk_c6
| sk_c7 = multiply(sk_c1,sk_c6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_5) ).
fof(f105,plain,
( spl13_4
| spl13_6 ),
inference(avatar_split_clause,[],[f36,f85,f75]) ).
fof(f36,plain,
( sk_c7 = sF6
| sk_c7 = sF1 ),
inference(definition_folding,[],[f6,f27,f35]) ).
fof(f6,axiom,
( sk_c7 = inverse(sk_c5)
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_3) ).
fof(f104,plain,
( spl13_1
| spl13_5 ),
inference(avatar_split_clause,[],[f51,f81,f61]) ).
fof(f51,plain,
( sk_c6 = sF5
| sk_c7 = sF0 ),
inference(definition_folding,[],[f21,f33,f26]) ).
fof(f21,axiom,
( sk_c7 = inverse(sk_c4)
| sk_c6 = multiply(sk_c3,sk_c7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_18) ).
fof(f103,plain,
( spl13_3
| spl13_9 ),
inference(avatar_split_clause,[],[f31,f100,f70]) ).
fof(f31,plain,
( sk_c7 = sF2
| sk_c7 = sF3 ),
inference(definition_folding,[],[f11,f30,f29]) ).
fof(f11,axiom,
( sk_c7 = multiply(sk_c1,sk_c6)
| sk_c7 = multiply(sk_c5,sk_c6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_8) ).
fof(f98,plain,
( spl13_7
| spl13_8 ),
inference(avatar_split_clause,[],[f55,f95,f90]) ).
fof(f55,plain,
( sk_c6 = sF7
| sk_c6 = sF4 ),
inference(definition_folding,[],[f12,f38,f32]) ).
fof(f12,axiom,
( multiply(sk_c4,sk_c7) = sk_c6
| sk_c6 = multiply(sk_c2,sk_c3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_9) ).
fof(f93,plain,
( spl13_5
| spl13_7 ),
inference(avatar_split_clause,[],[f34,f90,f81]) ).
fof(f34,plain,
( sk_c6 = sF4
| sk_c6 = sF5 ),
inference(definition_folding,[],[f20,f33,f32]) ).
fof(f20,axiom,
( multiply(sk_c4,sk_c7) = sk_c6
| sk_c6 = multiply(sk_c3,sk_c7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_17) ).
fof(f79,plain,
( spl13_4
| spl13_3 ),
inference(avatar_split_clause,[],[f50,f70,f75]) ).
fof(f50,plain,
( sk_c7 = sF3
| sk_c7 = sF1 ),
inference(definition_folding,[],[f7,f30,f27]) ).
fof(f7,axiom,
( inverse(sk_c1) = sk_c7
| sk_c7 = multiply(sk_c5,sk_c6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_4) ).
fof(f78,plain,
( spl13_1
| spl13_4 ),
inference(avatar_split_clause,[],[f28,f75,f61]) ).
fof(f28,plain,
( sk_c7 = sF1
| sk_c7 = sF0 ),
inference(definition_folding,[],[f5,f27,f26]) ).
fof(f5,axiom,
( sk_c7 = inverse(sk_c4)
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_2) ).
fof(f68,plain,
( spl13_1
| spl13_2 ),
inference(avatar_split_clause,[],[f54,f65,f61]) ).
fof(f54,plain,
( sk_c3 = sF8
| sk_c7 = sF0 ),
inference(definition_folding,[],[f17,f43,f26]) ).
fof(f17,axiom,
( sk_c7 = inverse(sk_c4)
| sk_c3 = inverse(sk_c2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_14) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : GRP222-1 : TPTP v8.1.0. Released v2.5.0.
% 0.08/0.14 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.14/0.35 % Computer : n014.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Mon Aug 29 22:22:18 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.20/0.53 % (29950)ott+10_1:5_bd=off:tgt=full:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.20/0.53 % (29941)ott+33_1:4_s2a=on:tgt=ground:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.20/0.54 % (29950)First to succeed.
% 0.20/0.54 % (29964)ott+11_2:3_av=off:fde=unused:nwc=5.0:tgt=ground:i=177:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/177Mi)
% 0.20/0.55 % (29950)Refutation found. Thanks to Tanya!
% 0.20/0.55 % SZS status Unsatisfiable for theBenchmark
% 0.20/0.55 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.55 % (29950)------------------------------
% 0.20/0.55 % (29950)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.55 % (29950)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.55 % (29950)Termination reason: Refutation
% 0.20/0.55
% 0.20/0.55 % (29950)Memory used [KB]: 5884
% 0.20/0.55 % (29950)Time elapsed: 0.122 s
% 0.20/0.55 % (29950)Instructions burned: 25 (million)
% 0.20/0.55 % (29950)------------------------------
% 0.20/0.55 % (29950)------------------------------
% 0.20/0.55 % (29936)Success in time 0.187 s
%------------------------------------------------------------------------------