TSTP Solution File: GRP101-1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : GRP101-1 : TPTP v8.1.2. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% Computer : n006.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 : Fri Sep 1 15:38:58 EDT 2023
% Result : Unsatisfiable 6.43s 1.35s
% Output : Refutation 6.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 38
% Number of leaves : 12
% Syntax : Number of formulae : 142 ( 32 unt; 0 def)
% Number of atoms : 326 ( 130 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 359 ( 175 ~; 177 |; 0 &)
% ( 7 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 4 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 9 ( 7 usr; 8 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 8 con; 0-2 aty)
% Number of variables : 168 (; 168 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f27372,plain,
$false,
inference(avatar_smt_refutation,[],[f231,f311,f324,f373,f393,f394,f395,f396,f947,f3318,f3320,f27215]) ).
fof(f27215,plain,
( spl0_1
| ~ spl0_4
| ~ spl0_7 ),
inference(avatar_contradiction_clause,[],[f27214]) ).
fof(f27214,plain,
( $false
| spl0_1
| ~ spl0_4
| ~ spl0_7 ),
inference(trivial_inequality_removal,[],[f27213]) ).
fof(f27213,plain,
( multiply(a3,multiply(b3,c3)) != multiply(a3,multiply(b3,c3))
| spl0_1
| ~ spl0_4
| ~ spl0_7 ),
inference(superposition,[],[f218,f20483]) ).
fof(f20483,plain,
( ! [X126,X127,X128] : multiply(multiply(X127,X126),X128) = multiply(X127,multiply(X126,X128))
| ~ spl0_4
| ~ spl0_7 ),
inference(superposition,[],[f18509,f18696]) ).
fof(f18696,plain,
( ! [X21,X22,X23] : multiply(double_divide(X23,X22),multiply(multiply(X22,X23),X21)) = X21
| ~ spl0_4
| ~ spl0_7 ),
inference(superposition,[],[f8219,f15489]) ).
fof(f15489,plain,
( ! [X10,X11,X12] : double_divide(X11,X10) = multiply(X12,double_divide(X12,multiply(X10,X11)))
| ~ spl0_4
| ~ spl0_7 ),
inference(superposition,[],[f2304,f2304]) ).
fof(f2304,plain,
( ! [X2,X0,X1] : multiply(multiply(multiply(X1,X0),X2),double_divide(X0,X1)) = X2
| ~ spl0_4
| ~ spl0_7 ),
inference(superposition,[],[f2303,f9]) ).
fof(f9,plain,
! [X2,X3] : multiply(X3,X2) = inverse(double_divide(X2,X3)),
inference(superposition,[],[f2,f3]) ).
fof(f3,axiom,
! [X0] : inverse(X0) = double_divide(X0,identity),
file('/export/starexec/sandbox/tmp/tmp.0T091Uydf2/Vampire---4.8_19412',inverse) ).
fof(f2,axiom,
! [X0,X1] : multiply(X0,X1) = double_divide(double_divide(X1,X0),identity),
file('/export/starexec/sandbox/tmp/tmp.0T091Uydf2/Vampire---4.8_19412',multiply) ).
fof(f2303,plain,
( ! [X2,X3] : multiply(multiply(inverse(X2),X3),X2) = X3
| ~ spl0_4
| ~ spl0_7 ),
inference(forward_demodulation,[],[f425,f1185]) ).
fof(f1185,plain,
( ! [X7] : inverse(X7) = double_divide(identity,X7)
| ~ spl0_4
| ~ spl0_7 ),
inference(forward_demodulation,[],[f1184,f3]) ).
fof(f1184,plain,
( ! [X7] : double_divide(identity,X7) = double_divide(X7,identity)
| ~ spl0_4
| ~ spl0_7 ),
inference(forward_demodulation,[],[f1183,f871]) ).
fof(f871,plain,
( ! [X1] : multiply(identity,X1) = X1
| ~ spl0_4
| ~ spl0_7 ),
inference(superposition,[],[f863,f13]) ).
fof(f13,plain,
! [X1] : inverse(inverse(X1)) = multiply(identity,X1),
inference(superposition,[],[f6,f3]) ).
fof(f6,plain,
! [X0] : multiply(identity,X0) = double_divide(inverse(X0),identity),
inference(superposition,[],[f2,f3]) ).
fof(f863,plain,
( ! [X16] : inverse(inverse(X16)) = X16
| ~ spl0_4
| ~ spl0_7 ),
inference(forward_demodulation,[],[f840,f274]) ).
fof(f274,plain,
! [X0] : double_divide(double_divide(identity,double_divide(identity,inverse(X0))),inverse(identity)) = X0,
inference(superposition,[],[f119,f4]) ).
fof(f4,axiom,
! [X0] : identity = double_divide(X0,inverse(X0)),
file('/export/starexec/sandbox/tmp/tmp.0T091Uydf2/Vampire---4.8_19412',identity) ).
fof(f119,plain,
! [X0,X1] : double_divide(double_divide(identity,double_divide(double_divide(X1,inverse(X0)),inverse(X0))),inverse(identity)) = X1,
inference(superposition,[],[f52,f3]) ).
fof(f52,plain,
! [X2,X0,X1] : double_divide(double_divide(X0,double_divide(double_divide(X1,double_divide(X2,X0)),inverse(X2))),inverse(identity)) = X1,
inference(forward_demodulation,[],[f51,f3]) ).
fof(f51,plain,
! [X2,X0,X1] : double_divide(double_divide(X0,double_divide(double_divide(X1,double_divide(X2,X0)),double_divide(X2,identity))),inverse(identity)) = X1,
inference(forward_demodulation,[],[f1,f3]) ).
fof(f1,axiom,
! [X2,X0,X1] : double_divide(double_divide(X0,double_divide(double_divide(X1,double_divide(X2,X0)),double_divide(X2,identity))),double_divide(identity,identity)) = X1,
file('/export/starexec/sandbox/tmp/tmp.0T091Uydf2/Vampire---4.8_19412',single_axiom) ).
fof(f840,plain,
( ! [X16] : inverse(inverse(X16)) = double_divide(double_divide(identity,double_divide(identity,inverse(X16))),inverse(identity))
| ~ spl0_4
| ~ spl0_7 ),
inference(superposition,[],[f119,f801]) ).
fof(f801,plain,
( ! [X21] : identity = double_divide(inverse(X21),X21)
| ~ spl0_4
| ~ spl0_7 ),
inference(forward_demodulation,[],[f800,f229]) ).
fof(f229,plain,
( identity = inverse(identity)
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f228]) ).
fof(f228,plain,
( spl0_4
<=> identity = inverse(identity) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
fof(f800,plain,
( ! [X21] : inverse(identity) = double_divide(inverse(X21),X21)
| ~ spl0_4
| ~ spl0_7 ),
inference(forward_demodulation,[],[f799,f3]) ).
fof(f799,plain,
( ! [X21] : double_divide(identity,identity) = double_divide(inverse(X21),X21)
| ~ spl0_4
| ~ spl0_7 ),
inference(forward_demodulation,[],[f798,f392]) ).
fof(f392,plain,
( identity = multiply(identity,identity)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f390]) ).
fof(f390,plain,
( spl0_7
<=> identity = multiply(identity,identity) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
fof(f798,plain,
( ! [X21] : double_divide(multiply(identity,identity),identity) = double_divide(inverse(X21),X21)
| ~ spl0_4 ),
inference(forward_demodulation,[],[f754,f229]) ).
fof(f754,plain,
( ! [X21] : double_divide(multiply(identity,identity),inverse(identity)) = double_divide(inverse(X21),X21)
| ~ spl0_4 ),
inference(superposition,[],[f250,f648]) ).
fof(f648,plain,
( ! [X2] : identity = inverse(double_divide(inverse(X2),X2))
| ~ spl0_4 ),
inference(superposition,[],[f475,f3]) ).
fof(f475,plain,
( ! [X0] : identity = double_divide(double_divide(inverse(X0),X0),identity)
| ~ spl0_4 ),
inference(superposition,[],[f328,f274]) ).
fof(f328,plain,
( ! [X2,X0,X1] : double_divide(double_divide(X0,double_divide(double_divide(X1,double_divide(X2,X0)),inverse(X2))),identity) = X1
| ~ spl0_4 ),
inference(superposition,[],[f52,f229]) ).
fof(f250,plain,
! [X0] : double_divide(multiply(identity,inverse(X0)),inverse(identity)) = X0,
inference(forward_demodulation,[],[f249,f13]) ).
fof(f249,plain,
! [X0] : double_divide(inverse(inverse(inverse(X0))),inverse(identity)) = X0,
inference(forward_demodulation,[],[f242,f3]) ).
fof(f242,plain,
! [X0] : double_divide(double_divide(inverse(inverse(X0)),identity),inverse(identity)) = X0,
inference(superposition,[],[f136,f4]) ).
fof(f136,plain,
! [X2,X3] : double_divide(double_divide(inverse(X2),double_divide(inverse(X3),inverse(X2))),inverse(identity)) = X3,
inference(forward_demodulation,[],[f120,f3]) ).
fof(f120,plain,
! [X2,X3] : double_divide(double_divide(inverse(X2),double_divide(double_divide(X3,identity),inverse(X2))),inverse(identity)) = X3,
inference(superposition,[],[f52,f4]) ).
fof(f1183,plain,
( ! [X7] : double_divide(identity,X7) = double_divide(multiply(identity,X7),identity)
| ~ spl0_4
| ~ spl0_7 ),
inference(forward_demodulation,[],[f1155,f536]) ).
fof(f536,plain,
( ! [X1] : multiply(identity,multiply(identity,X1)) = X1
| ~ spl0_4 ),
inference(superposition,[],[f331,f36]) ).
fof(f36,plain,
! [X2] : multiply(identity,multiply(identity,X2)) = double_divide(multiply(identity,inverse(X2)),identity),
inference(superposition,[],[f6,f23]) ).
fof(f23,plain,
! [X4] : multiply(identity,inverse(X4)) = inverse(multiply(identity,X4)),
inference(superposition,[],[f9,f6]) ).
fof(f331,plain,
( ! [X7] : double_divide(multiply(identity,inverse(X7)),identity) = X7
| ~ spl0_4 ),
inference(superposition,[],[f250,f229]) ).
fof(f1155,plain,
( ! [X7] : double_divide(multiply(identity,X7),identity) = multiply(identity,multiply(identity,double_divide(identity,X7)))
| ~ spl0_4
| ~ spl0_7 ),
inference(superposition,[],[f36,f1098]) ).
fof(f1098,plain,
( ! [X8] : inverse(double_divide(identity,X8)) = X8
| ~ spl0_4
| ~ spl0_7 ),
inference(superposition,[],[f1081,f3]) ).
fof(f1081,plain,
( ! [X20] : double_divide(double_divide(identity,X20),identity) = X20
| ~ spl0_4
| ~ spl0_7 ),
inference(forward_demodulation,[],[f1080,f871]) ).
fof(f1080,plain,
( ! [X20] : double_divide(double_divide(identity,multiply(identity,X20)),identity) = X20
| ~ spl0_4 ),
inference(forward_demodulation,[],[f1079,f9]) ).
fof(f1079,plain,
( ! [X20] : double_divide(double_divide(identity,inverse(double_divide(X20,identity))),identity) = X20
| ~ spl0_4 ),
inference(forward_demodulation,[],[f1078,f3]) ).
fof(f1078,plain,
( ! [X20] : double_divide(double_divide(identity,double_divide(double_divide(X20,identity),identity)),identity) = X20
| ~ spl0_4 ),
inference(forward_demodulation,[],[f1039,f229]) ).
fof(f1039,plain,
( ! [X20] : double_divide(double_divide(identity,double_divide(double_divide(X20,inverse(identity)),inverse(identity))),identity) = X20
| ~ spl0_4 ),
inference(superposition,[],[f816,f11]) ).
fof(f11,plain,
! [X1] : multiply(inverse(X1),X1) = inverse(identity),
inference(forward_demodulation,[],[f7,f3]) ).
fof(f7,plain,
! [X1] : double_divide(identity,identity) = multiply(inverse(X1),X1),
inference(superposition,[],[f2,f4]) ).
fof(f816,plain,
( ! [X6,X4,X5] : double_divide(double_divide(identity,double_divide(double_divide(X6,multiply(X5,X4)),multiply(X5,X4))),identity) = X6
| ~ spl0_4 ),
inference(forward_demodulation,[],[f137,f229]) ).
fof(f137,plain,
! [X6,X4,X5] : double_divide(double_divide(identity,double_divide(double_divide(X6,multiply(X5,X4)),multiply(X5,X4))),inverse(identity)) = X6,
inference(forward_demodulation,[],[f121,f9]) ).
fof(f121,plain,
! [X6,X4,X5] : double_divide(double_divide(identity,double_divide(double_divide(X6,multiply(X5,X4)),inverse(double_divide(X4,X5)))),inverse(identity)) = X6,
inference(superposition,[],[f52,f2]) ).
fof(f425,plain,
( ! [X2,X3] : multiply(multiply(double_divide(identity,X2),X3),X2) = X3
| ~ spl0_4 ),
inference(superposition,[],[f360,f2]) ).
fof(f360,plain,
( ! [X10,X11] : double_divide(double_divide(X10,multiply(double_divide(identity,X10),X11)),identity) = X11
| ~ spl0_4 ),
inference(forward_demodulation,[],[f359,f9]) ).
fof(f359,plain,
( ! [X10,X11] : double_divide(double_divide(X10,inverse(double_divide(X11,double_divide(identity,X10)))),identity) = X11
| ~ spl0_4 ),
inference(forward_demodulation,[],[f344,f3]) ).
fof(f344,plain,
( ! [X10,X11] : double_divide(double_divide(X10,double_divide(double_divide(X11,double_divide(identity,X10)),identity)),identity) = X11
| ~ spl0_4 ),
inference(superposition,[],[f52,f229]) ).
fof(f8219,plain,
( ! [X31,X32,X33] : multiply(multiply(X33,double_divide(X31,X32)),multiply(X32,X31)) = X33
| ~ spl0_4
| ~ spl0_7 ),
inference(forward_demodulation,[],[f8218,f2454]) ).
fof(f2454,plain,
( ! [X26,X27] : double_divide(inverse(X26),inverse(X27)) = multiply(X27,X26)
| ~ spl0_4
| ~ spl0_7 ),
inference(superposition,[],[f2303,f2382]) ).
fof(f2382,plain,
( ! [X10,X9] : multiply(X10,double_divide(X10,inverse(X9))) = X9
| ~ spl0_4
| ~ spl0_7 ),
inference(forward_demodulation,[],[f2350,f864]) ).
fof(f864,plain,
( ! [X0,X1] : double_divide(X0,X1) = inverse(multiply(X1,X0))
| ~ spl0_4
| ~ spl0_7 ),
inference(superposition,[],[f863,f9]) ).
fof(f2350,plain,
( ! [X10,X9] : multiply(X10,inverse(multiply(inverse(X9),X10))) = X9
| ~ spl0_4
| ~ spl0_7 ),
inference(superposition,[],[f2334,f2303]) ).
fof(f2334,plain,
( ! [X12,X13] : multiply(multiply(X12,X13),inverse(X12)) = X13
| ~ spl0_4
| ~ spl0_7 ),
inference(forward_demodulation,[],[f2333,f536]) ).
fof(f2333,plain,
( ! [X12,X13] : multiply(multiply(multiply(identity,multiply(identity,X12)),X13),inverse(X12)) = X13
| ~ spl0_4
| ~ spl0_7 ),
inference(forward_demodulation,[],[f2310,f871]) ).
fof(f2310,plain,
( ! [X12,X13] : multiply(multiply(multiply(identity,multiply(identity,X12)),X13),multiply(identity,inverse(X12))) = X13
| ~ spl0_4
| ~ spl0_7 ),
inference(superposition,[],[f2303,f62]) ).
fof(f62,plain,
! [X6] : inverse(multiply(identity,inverse(X6))) = multiply(identity,multiply(identity,X6)),
inference(superposition,[],[f12,f6]) ).
fof(f12,plain,
! [X2,X3] : multiply(identity,double_divide(X2,X3)) = inverse(multiply(X3,X2)),
inference(forward_demodulation,[],[f8,f3]) ).
fof(f8,plain,
! [X2,X3] : multiply(identity,double_divide(X2,X3)) = double_divide(multiply(X3,X2),identity),
inference(superposition,[],[f2,f2]) ).
fof(f8218,plain,
( ! [X31,X32,X33] : multiply(double_divide(inverse(double_divide(X31,X32)),inverse(X33)),multiply(X32,X31)) = X33
| ~ spl0_4
| ~ spl0_7 ),
inference(forward_demodulation,[],[f8121,f3]) ).
fof(f8121,plain,
( ! [X31,X32,X33] : multiply(double_divide(inverse(double_divide(X31,X32)),double_divide(X33,identity)),multiply(X32,X31)) = X33
| ~ spl0_4
| ~ spl0_7 ),
inference(superposition,[],[f6224,f27]) ).
fof(f27,plain,
! [X6,X7] : identity = double_divide(double_divide(X6,X7),multiply(X7,X6)),
inference(superposition,[],[f4,f9]) ).
fof(f6224,plain,
( ! [X3,X4,X5] : multiply(double_divide(inverse(X5),double_divide(X4,double_divide(X5,X3))),X3) = X4
| ~ spl0_4
| ~ spl0_7 ),
inference(forward_demodulation,[],[f476,f1451]) ).
fof(f1451,plain,
( ! [X2,X3] : double_divide(X2,X3) = double_divide(X3,X2)
| ~ spl0_4
| ~ spl0_7 ),
inference(forward_demodulation,[],[f1450,f871]) ).
fof(f1450,plain,
( ! [X2,X3] : double_divide(X2,X3) = double_divide(X3,multiply(identity,X2))
| ~ spl0_4
| ~ spl0_7 ),
inference(forward_demodulation,[],[f1449,f863]) ).
fof(f1449,plain,
( ! [X2,X3] : double_divide(X3,multiply(identity,X2)) = inverse(inverse(double_divide(X2,X3)))
| ~ spl0_4
| ~ spl0_7 ),
inference(forward_demodulation,[],[f1448,f13]) ).
fof(f1448,plain,
( ! [X2,X3] : inverse(inverse(double_divide(X2,X3))) = double_divide(X3,inverse(inverse(X2)))
| ~ spl0_4
| ~ spl0_7 ),
inference(forward_demodulation,[],[f1447,f871]) ).
fof(f1447,plain,
( ! [X2,X3] : inverse(inverse(double_divide(X2,X3))) = multiply(identity,double_divide(X3,inverse(inverse(X2))))
| ~ spl0_4
| ~ spl0_7 ),
inference(forward_demodulation,[],[f1306,f1185]) ).
fof(f1306,plain,
( ! [X2,X3] : inverse(inverse(double_divide(X2,X3))) = multiply(identity,double_divide(X3,double_divide(identity,inverse(X2))))
| ~ spl0_4
| ~ spl0_7 ),
inference(superposition,[],[f1273,f801]) ).
fof(f1273,plain,
( ! [X14,X12,X13] : inverse(X13) = multiply(identity,double_divide(X12,double_divide(double_divide(X13,double_divide(X14,X12)),inverse(X14))))
| ~ spl0_4 ),
inference(forward_demodulation,[],[f147,f229]) ).
fof(f147,plain,
! [X14,X12,X13] : multiply(inverse(identity),double_divide(X12,double_divide(double_divide(X13,double_divide(X14,X12)),inverse(X14)))) = inverse(X13),
inference(forward_demodulation,[],[f135,f3]) ).
fof(f135,plain,
! [X14,X12,X13] : multiply(inverse(identity),double_divide(X12,double_divide(double_divide(X13,double_divide(X14,X12)),inverse(X14)))) = double_divide(X13,identity),
inference(superposition,[],[f2,f52]) ).
fof(f476,plain,
( ! [X3,X4,X5] : multiply(double_divide(double_divide(X4,double_divide(X5,X3)),inverse(X5)),X3) = X4
| ~ spl0_4 ),
inference(superposition,[],[f328,f2]) ).
fof(f18509,plain,
( ! [X8,X6,X7] : multiply(X8,multiply(X7,multiply(double_divide(X7,X8),X6))) = X6
| ~ spl0_4
| ~ spl0_7 ),
inference(forward_demodulation,[],[f18330,f3120]) ).
fof(f3120,plain,
( ! [X2,X3] : multiply(X3,X2) = multiply(X2,X3)
| ~ spl0_4
| ~ spl0_7 ),
inference(superposition,[],[f1538,f9]) ).
fof(f1538,plain,
( ! [X2,X3] : multiply(X3,X2) = inverse(double_divide(X3,X2))
| ~ spl0_4
| ~ spl0_7 ),
inference(superposition,[],[f9,f1451]) ).
fof(f18330,plain,
( ! [X8,X6,X7] : multiply(X8,multiply(multiply(double_divide(X7,X8),X6),X7)) = X6
| ~ spl0_4
| ~ spl0_7 ),
inference(superposition,[],[f8219,f8362]) ).
fof(f8362,plain,
( ! [X31,X32,X30] : multiply(X31,double_divide(X30,multiply(double_divide(X30,X32),X31))) = X32
| ~ spl0_4
| ~ spl0_7 ),
inference(forward_demodulation,[],[f8361,f9]) ).
fof(f8361,plain,
( ! [X31,X32,X30] : multiply(X31,double_divide(X30,inverse(double_divide(X31,double_divide(X30,X32))))) = X32
| ~ spl0_4
| ~ spl0_7 ),
inference(forward_demodulation,[],[f8360,f2448]) ).
fof(f2448,plain,
( ! [X14,X13] : double_divide(X13,inverse(X14)) = multiply(X14,inverse(X13))
| ~ spl0_4
| ~ spl0_7 ),
inference(superposition,[],[f2334,f2382]) ).
fof(f8360,plain,
( ! [X31,X32,X30] : multiply(X31,multiply(double_divide(X31,double_divide(X30,X32)),inverse(X30))) = X32
| ~ spl0_4
| ~ spl0_7 ),
inference(forward_demodulation,[],[f8178,f9]) ).
fof(f8178,plain,
( ! [X31,X32,X30] : multiply(X31,inverse(double_divide(inverse(X30),double_divide(X31,double_divide(X30,X32))))) = X32
| ~ spl0_4
| ~ spl0_7 ),
inference(superposition,[],[f2334,f6224]) ).
fof(f218,plain,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| spl0_1 ),
inference(avatar_component_clause,[],[f216]) ).
fof(f216,plain,
( spl0_1
<=> multiply(multiply(a3,b3),c3) = multiply(a3,multiply(b3,c3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
fof(f3320,plain,
( spl0_2
| ~ spl0_4
| ~ spl0_7 ),
inference(avatar_contradiction_clause,[],[f3319]) ).
fof(f3319,plain,
( $false
| spl0_2
| ~ spl0_4
| ~ spl0_7 ),
inference(trivial_inequality_removal,[],[f3288]) ).
fof(f3288,plain,
( multiply(a4,b4) != multiply(a4,b4)
| spl0_2
| ~ spl0_4
| ~ spl0_7 ),
inference(superposition,[],[f222,f3120]) ).
fof(f222,plain,
( multiply(a4,b4) != multiply(b4,a4)
| spl0_2 ),
inference(avatar_component_clause,[],[f220]) ).
fof(f220,plain,
( spl0_2
<=> multiply(a4,b4) = multiply(b4,a4) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
fof(f3318,plain,
( spl0_2
| ~ spl0_4
| ~ spl0_7 ),
inference(avatar_contradiction_clause,[],[f3317]) ).
fof(f3317,plain,
( $false
| spl0_2
| ~ spl0_4
| ~ spl0_7 ),
inference(trivial_inequality_removal,[],[f3316]) ).
fof(f3316,plain,
( multiply(a4,b4) != multiply(a4,b4)
| spl0_2
| ~ spl0_4
| ~ spl0_7 ),
inference(superposition,[],[f222,f3120]) ).
fof(f947,plain,
( spl0_3
| ~ spl0_4
| ~ spl0_7 ),
inference(avatar_contradiction_clause,[],[f946]) ).
fof(f946,plain,
( $false
| spl0_3
| ~ spl0_4
| ~ spl0_7 ),
inference(trivial_inequality_removal,[],[f945]) ).
fof(f945,plain,
( a2 != a2
| spl0_3
| ~ spl0_4
| ~ spl0_7 ),
inference(superposition,[],[f226,f871]) ).
fof(f226,plain,
( a2 != multiply(identity,a2)
| spl0_3 ),
inference(avatar_component_clause,[],[f224]) ).
fof(f224,plain,
( spl0_3
<=> a2 = multiply(identity,a2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
fof(f396,plain,
( spl0_7
| ~ spl0_4
| ~ spl0_6 ),
inference(avatar_split_clause,[],[f388,f370,f228,f390]) ).
fof(f370,plain,
( spl0_6
<=> identity = double_divide(identity,identity) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
fof(f388,plain,
( identity = multiply(identity,identity)
| ~ spl0_4
| ~ spl0_6 ),
inference(forward_demodulation,[],[f387,f229]) ).
fof(f387,plain,
( inverse(identity) = multiply(identity,identity)
| ~ spl0_6 ),
inference(forward_demodulation,[],[f381,f3]) ).
fof(f381,plain,
( double_divide(identity,identity) = multiply(identity,identity)
| ~ spl0_6 ),
inference(superposition,[],[f2,f372]) ).
fof(f372,plain,
( identity = double_divide(identity,identity)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f370]) ).
fof(f395,plain,
( spl0_7
| ~ spl0_4
| ~ spl0_6 ),
inference(avatar_split_clause,[],[f386,f370,f228,f390]) ).
fof(f386,plain,
( identity = multiply(identity,identity)
| ~ spl0_4
| ~ spl0_6 ),
inference(forward_demodulation,[],[f380,f229]) ).
fof(f380,plain,
( inverse(identity) = multiply(identity,identity)
| ~ spl0_6 ),
inference(superposition,[],[f9,f372]) ).
fof(f394,plain,
( spl0_7
| ~ spl0_4 ),
inference(avatar_split_clause,[],[f354,f228,f390]) ).
fof(f354,plain,
( identity = multiply(identity,identity)
| ~ spl0_4 ),
inference(forward_demodulation,[],[f353,f229]) ).
fof(f353,plain,
( inverse(identity) = multiply(identity,identity)
| ~ spl0_4 ),
inference(forward_demodulation,[],[f336,f3]) ).
fof(f336,plain,
( double_divide(identity,identity) = multiply(identity,identity)
| ~ spl0_4 ),
inference(superposition,[],[f6,f229]) ).
fof(f393,plain,
( spl0_7
| ~ spl0_4 ),
inference(avatar_split_clause,[],[f337,f228,f390]) ).
fof(f337,plain,
( identity = multiply(identity,identity)
| ~ spl0_4 ),
inference(superposition,[],[f11,f229]) ).
fof(f373,plain,
( spl0_6
| ~ spl0_4 ),
inference(avatar_split_clause,[],[f335,f228,f370]) ).
fof(f335,plain,
( identity = double_divide(identity,identity)
| ~ spl0_4 ),
inference(superposition,[],[f4,f229]) ).
fof(f324,plain,
( spl0_4
| ~ spl0_5 ),
inference(avatar_contradiction_clause,[],[f323]) ).
fof(f323,plain,
( $false
| spl0_4
| ~ spl0_5 ),
inference(subsumption_resolution,[],[f322,f230]) ).
fof(f230,plain,
( identity != inverse(identity)
| spl0_4 ),
inference(avatar_component_clause,[],[f228]) ).
fof(f322,plain,
( identity = inverse(identity)
| ~ spl0_5 ),
inference(forward_demodulation,[],[f313,f274]) ).
fof(f313,plain,
( inverse(identity) = double_divide(double_divide(identity,double_divide(identity,inverse(identity))),inverse(identity))
| ~ spl0_5 ),
inference(superposition,[],[f119,f310]) ).
fof(f310,plain,
( identity = double_divide(inverse(identity),inverse(identity))
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f308]) ).
fof(f308,plain,
( spl0_5
<=> identity = double_divide(inverse(identity),inverse(identity)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
fof(f311,plain,
spl0_5,
inference(avatar_split_clause,[],[f304,f308]) ).
fof(f304,plain,
identity = double_divide(inverse(identity),inverse(identity)),
inference(forward_demodulation,[],[f295,f3]) ).
fof(f295,plain,
identity = double_divide(double_divide(identity,identity),inverse(identity)),
inference(superposition,[],[f274,f4]) ).
fof(f231,plain,
( ~ spl0_1
| ~ spl0_2
| ~ spl0_3
| ~ spl0_4 ),
inference(avatar_split_clause,[],[f177,f228,f224,f220,f216]) ).
fof(f177,plain,
( identity != inverse(identity)
| a2 != multiply(identity,a2)
| multiply(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) ),
inference(forward_demodulation,[],[f5,f11]) ).
fof(f5,axiom,
( a2 != multiply(identity,a2)
| identity != multiply(inverse(a1),a1)
| multiply(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) ),
file('/export/starexec/sandbox/tmp/tmp.0T091Uydf2/Vampire---4.8_19412',prove_these_axioms) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.12 % Problem : GRP101-1 : TPTP v8.1.2. Bugfixed v2.7.0.
% 0.13/0.14 % Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.14/0.35 % Computer : n006.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 : Wed Aug 30 17:22:50 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.21/0.41 % (19698)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.42 % (19725)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on Vampire---4 for (793ds/0Mi)
% 0.21/0.42 % (19724)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on Vampire---4 for (846ds/0Mi)
% 0.21/0.42 % (19726)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on Vampire---4 for (569ds/0Mi)
% 0.21/0.42 % (19727)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on Vampire---4 for (533ds/0Mi)
% 0.21/0.42 % (19728)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on Vampire---4 for (531ds/0Mi)
% 0.21/0.42 % (19730)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on Vampire---4 for (497ds/0Mi)
% 0.21/0.42 % (19729)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on Vampire---4 for (522ds/0Mi)
% 0.21/0.42 TRYING [1]
% 0.21/0.42 TRYING [2]
% 0.21/0.42 TRYING [1]
% 0.21/0.42 TRYING [2]
% 0.21/0.42 TRYING [3]
% 0.21/0.43 TRYING [3]
% 0.21/0.43 TRYING [4]
% 0.21/0.45 TRYING [5]
% 0.21/0.46 TRYING [4]
% 0.21/0.51 TRYING [6]
% 4.58/1.12 TRYING [7]
% 5.10/1.13 TRYING [5]
% 5.48/1.34 % (19726)First to succeed.
% 6.43/1.35 % (19726)Refutation found. Thanks to Tanya!
% 6.43/1.35 % SZS status Unsatisfiable for Vampire---4
% 6.43/1.35 % SZS output start Proof for Vampire---4
% See solution above
% 6.43/1.35 % (19726)------------------------------
% 6.43/1.35 % (19726)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 6.43/1.35 % (19726)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 6.43/1.35 % (19726)Termination reason: Refutation
% 6.43/1.35
% 6.43/1.35 % (19726)Memory used [KB]: 32366
% 6.43/1.35 % (19726)Time elapsed: 0.927 s
% 6.43/1.35 % (19726)------------------------------
% 6.43/1.35 % (19726)------------------------------
% 6.43/1.35 % (19698)Success in time 0.987 s
% 6.43/1.35 % Vampire---4.8 exiting
%------------------------------------------------------------------------------