TSTP Solution File: GRP058-1 by Vampire---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : GRP058-1 : TPTP v8.1.2. Released v1.0.0.
% 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 : n004.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 : Thu Aug 31 01:20:57 EDT 2023
% Result : Unsatisfiable 1.83s 0.63s
% Output : Refutation 1.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 51
% Number of leaves : 5
% Syntax : Number of formulae : 126 ( 110 unt; 0 def)
% Number of atoms : 144 ( 120 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 32 ( 14 ~; 15 |; 0 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 12 ( 3 avg)
% Number of predicates : 5 ( 3 usr; 4 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 453 (; 453 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f6597,plain,
$false,
inference(avatar_smt_refutation,[],[f15,f2884,f6370,f6596]) ).
fof(f6596,plain,
spl0_2,
inference(avatar_contradiction_clause,[],[f6595]) ).
fof(f6595,plain,
( $false
| spl0_2 ),
inference(equality_resolution,[],[f6582]) ).
fof(f6582,plain,
( ! [X0,X1] : multiply(X1,inverse(X1)) != multiply(X0,inverse(X0))
| spl0_2 ),
inference(superposition,[],[f6550,f2597]) ).
fof(f2597,plain,
! [X171,X169] : multiply(X171,inverse(X171)) = multiply(inverse(X169),X169),
inference(backward_demodulation,[],[f2446,f2586]) ).
fof(f2586,plain,
! [X18,X19] : multiply(X18,inverse(inverse(multiply(X19,inverse(X19))))) = X18,
inference(backward_demodulation,[],[f1745,f2585]) ).
fof(f2585,plain,
! [X16,X17,X15] : inverse(multiply(multiply(X16,inverse(X16)),inverse(multiply(X17,inverse(multiply(X15,inverse(X15))))))) = X17,
inference(forward_demodulation,[],[f2573,f2011]) ).
fof(f2011,plain,
! [X170,X169] : multiply(X169,multiply(X170,inverse(X170))) = X169,
inference(forward_demodulation,[],[f1969,f1469]) ).
fof(f1469,plain,
! [X139,X134,X135] : multiply(multiply(X139,inverse(X139)),inverse(inverse(multiply(X134,multiply(X135,inverse(X135)))))) = X134,
inference(forward_demodulation,[],[f1458,f1323]) ).
fof(f1323,plain,
! [X324,X323,X326,X325] : multiply(multiply(multiply(X325,inverse(X325)),inverse(multiply(multiply(X324,inverse(X324)),X323))),multiply(X326,inverse(X326))) = inverse(X323),
inference(forward_demodulation,[],[f1229,f200]) ).
fof(f200,plain,
! [X11,X14,X12,X13] : inverse(X11) = multiply(X13,inverse(multiply(multiply(multiply(X12,inverse(X12)),multiply(X14,inverse(X14))),multiply(X11,X13)))),
inference(superposition,[],[f17,f185]) ).
fof(f185,plain,
! [X120,X123] : multiply(X120,inverse(X120)) = multiply(X123,inverse(X123)),
inference(forward_demodulation,[],[f149,f1]) ).
fof(f1,axiom,
! [X2,X3,X0,X1] : multiply(X0,inverse(multiply(X1,multiply(multiply(multiply(X2,inverse(X2)),inverse(multiply(X3,X1))),X0)))) = X3,
file('/export/starexec/sandbox2/tmp/tmp.iQqCUL4pOn/Vampire---4.8_22450',single_axiom) ).
fof(f149,plain,
! [X120,X121,X124,X125,X122,X123] : multiply(X120,inverse(X120)) = multiply(X124,inverse(multiply(inverse(multiply(X121,X122)),multiply(multiply(multiply(X125,inverse(X125)),inverse(multiply(multiply(X123,inverse(X123)),inverse(multiply(X121,X122))))),X124)))),
inference(superposition,[],[f1,f89]) ).
fof(f89,plain,
! [X2,X3,X1,X5] : multiply(multiply(X1,inverse(X1)),inverse(multiply(X2,X3))) = multiply(multiply(X5,inverse(X5)),inverse(multiply(X2,X3))),
inference(superposition,[],[f45,f17]) ).
fof(f45,plain,
! [X10,X11,X8,X9,X12] : multiply(multiply(X10,inverse(X10)),inverse(multiply(X9,multiply(X11,inverse(multiply(multiply(X8,multiply(X12,inverse(X12))),multiply(X9,X11))))))) = X8,
inference(superposition,[],[f1,f21]) ).
fof(f21,plain,
! [X2,X3,X0,X1,X4,X5] : multiply(multiply(multiply(X2,inverse(X2)),inverse(multiply(X3,X1))),multiply(X0,inverse(X0))) = multiply(X4,inverse(multiply(multiply(X3,multiply(X5,inverse(X5))),multiply(X1,X4)))),
inference(superposition,[],[f17,f1]) ).
fof(f17,plain,
! [X2,X3,X0,X1,X4] : multiply(X4,inverse(multiply(multiply(multiply(multiply(X2,inverse(X2)),inverse(multiply(X3,X1))),multiply(X0,inverse(X0))),multiply(X3,X4)))) = X1,
inference(superposition,[],[f1,f1]) ).
fof(f1229,plain,
! [X324,X323,X322,X327,X328,X326,X325] : multiply(X327,inverse(multiply(multiply(multiply(X322,inverse(X322)),multiply(X328,inverse(X328))),multiply(X323,X327)))) = multiply(multiply(multiply(X325,inverse(X325)),inverse(multiply(multiply(X324,inverse(X324)),X323))),multiply(X326,inverse(X326))),
inference(superposition,[],[f21,f1055]) ).
fof(f1055,plain,
! [X32,X30,X33] : multiply(multiply(X32,inverse(X32)),X30) = multiply(multiply(X33,inverse(X33)),X30),
inference(superposition,[],[f89,f809]) ).
fof(f809,plain,
! [X8,X9,X7] : inverse(multiply(multiply(X8,inverse(X8)),inverse(multiply(X9,inverse(inverse(multiply(X7,inverse(X7)))))))) = X9,
inference(superposition,[],[f508,f1]) ).
fof(f508,plain,
! [X108,X107,X105] : inverse(X105) = multiply(X108,inverse(multiply(inverse(inverse(multiply(X107,inverse(X107)))),multiply(X105,X108)))),
inference(forward_demodulation,[],[f457,f399]) ).
fof(f399,plain,
! [X178,X176,X177,X175] : multiply(multiply(multiply(X177,inverse(X177)),inverse(multiply(multiply(X176,inverse(X176)),inverse(X175)))),multiply(X178,inverse(X178))) = inverse(inverse(X175)),
inference(forward_demodulation,[],[f354,f200]) ).
fof(f354,plain,
! [X180,X178,X179,X176,X174,X177,X175] : multiply(X179,inverse(multiply(multiply(multiply(X174,inverse(X174)),multiply(X180,inverse(X180))),multiply(inverse(X175),X179)))) = multiply(multiply(multiply(X177,inverse(X177)),inverse(multiply(multiply(X176,inverse(X176)),inverse(X175)))),multiply(X178,inverse(X178))),
inference(superposition,[],[f21,f114]) ).
fof(f114,plain,
! [X3,X4,X5] : multiply(multiply(X5,inverse(X5)),inverse(X3)) = multiply(multiply(X4,inverse(X4)),inverse(X3)),
inference(superposition,[],[f89,f1]) ).
fof(f457,plain,
! [X108,X109,X106,X107,X105,X110] : inverse(X105) = multiply(X108,inverse(multiply(multiply(multiply(multiply(X109,inverse(X109)),inverse(multiply(multiply(X106,inverse(X106)),inverse(multiply(X107,inverse(X107)))))),multiply(X110,inverse(X110))),multiply(X105,X108)))),
inference(superposition,[],[f17,f189]) ).
fof(f189,plain,
! [X2,X0,X1] : multiply(X2,inverse(X2)) = multiply(multiply(X1,inverse(X1)),inverse(multiply(X0,inverse(X0)))),
inference(superposition,[],[f185,f89]) ).
fof(f1458,plain,
! [X138,X139,X136,X134,X137,X135] : multiply(multiply(X139,inverse(X139)),inverse(multiply(multiply(multiply(X136,inverse(X136)),inverse(multiply(multiply(X137,inverse(X137)),multiply(X134,multiply(X135,inverse(X135)))))),multiply(X138,inverse(X138))))) = X134,
inference(superposition,[],[f45,f766]) ).
fof(f766,plain,
! [X3,X0,X4,X5] : multiply(X3,multiply(multiply(multiply(X4,inverse(X4)),inverse(multiply(multiply(X0,inverse(X0)),X3))),X5)) = X5,
inference(forward_demodulation,[],[f699,f214]) ).
fof(f214,plain,
! [X90,X91,X88,X89] : multiply(X90,inverse(multiply(inverse(X88),multiply(multiply(multiply(X91,inverse(X91)),inverse(multiply(X89,inverse(X89)))),X90)))) = X88,
inference(superposition,[],[f1,f185]) ).
fof(f699,plain,
! [X2,X3,X0,X1,X6,X4,X5] : multiply(X2,inverse(multiply(inverse(multiply(X3,multiply(multiply(multiply(X4,inverse(X4)),inverse(multiply(multiply(X0,inverse(X0)),X3))),X5))),multiply(multiply(multiply(X6,inverse(X6)),inverse(multiply(X1,inverse(X1)))),X2)))) = X5,
inference(superposition,[],[f16,f511]) ).
fof(f511,plain,
! [X127,X128] : inverse(multiply(X128,inverse(X128))) = inverse(multiply(X127,inverse(X127))),
inference(forward_demodulation,[],[f500,f215]) ).
fof(f215,plain,
! [X96,X94,X95,X92,X93] : inverse(X92) = multiply(X94,inverse(multiply(multiply(multiply(multiply(X95,inverse(X95)),inverse(multiply(X93,inverse(X93)))),multiply(X96,inverse(X96))),multiply(X92,X94)))),
inference(superposition,[],[f17,f185]) ).
fof(f500,plain,
! [X132,X127,X130,X131,X128,X129] : inverse(multiply(X128,inverse(X128))) = multiply(X130,inverse(multiply(multiply(multiply(multiply(X131,inverse(X131)),inverse(multiply(X129,inverse(X129)))),multiply(X132,inverse(X132))),multiply(multiply(X127,inverse(X127)),X130)))),
inference(superposition,[],[f17,f189]) ).
fof(f16,plain,
! [X2,X3,X0,X1,X4,X5] : multiply(X4,inverse(multiply(inverse(multiply(X1,multiply(multiply(multiply(X2,inverse(X2)),inverse(multiply(X3,X1))),X0))),multiply(multiply(multiply(X5,inverse(X5)),inverse(X3)),X4)))) = X0,
inference(superposition,[],[f1,f1]) ).
fof(f1969,plain,
! [X170,X168,X169,X167] : multiply(multiply(X168,inverse(X168)),inverse(inverse(multiply(multiply(X169,multiply(X170,inverse(X170))),multiply(X167,inverse(X167)))))) = X169,
inference(backward_demodulation,[],[f506,f1844]) ).
fof(f1844,plain,
! [X2,X3,X0] : multiply(multiply(X3,inverse(X3)),multiply(inverse(multiply(X2,inverse(X2))),X0)) = X0,
inference(superposition,[],[f1469,f1588]) ).
fof(f1588,plain,
! [X18,X16,X17] : inverse(inverse(multiply(X16,multiply(X17,inverse(X17))))) = multiply(inverse(multiply(X18,inverse(X18))),X16),
inference(superposition,[],[f1405,f1469]) ).
fof(f1405,plain,
! [X24,X22,X23] : multiply(inverse(multiply(X22,inverse(X22))),multiply(multiply(X23,inverse(X23)),X24)) = X24,
inference(superposition,[],[f766,f189]) ).
fof(f506,plain,
! [X170,X168,X166,X169,X167,X165] : multiply(multiply(X168,inverse(X168)),inverse(multiply(multiply(X165,inverse(X165)),multiply(inverse(multiply(X166,inverse(X166))),inverse(multiply(multiply(X169,multiply(X170,inverse(X170))),multiply(X167,inverse(X167)))))))) = X169,
inference(superposition,[],[f45,f189]) ).
fof(f2573,plain,
! [X16,X14,X17,X15] : inverse(multiply(multiply(X16,inverse(X16)),inverse(multiply(X17,inverse(multiply(multiply(X15,inverse(X15)),multiply(X14,inverse(X14)))))))) = X17,
inference(backward_demodulation,[],[f2515,f2566]) ).
fof(f2566,plain,
! [X46,X44,X45] : inverse(multiply(inverse(X46),inverse(multiply(X44,X45)))) = multiply(multiply(X44,X45),X46),
inference(forward_demodulation,[],[f2565,f2468]) ).
fof(f2468,plain,
! [X181,X178,X177,X182] : multiply(multiply(X177,X178),X181) = multiply(X182,inverse(multiply(inverse(multiply(X178,X181)),multiply(inverse(X177),X182)))),
inference(backward_demodulation,[],[f2411,f2433]) ).
fof(f2433,plain,
! [X40,X39,X44] : multiply(X40,X44) = multiply(multiply(multiply(X39,inverse(X39)),X40),X44),
inference(backward_demodulation,[],[f1419,f2424]) ).
fof(f2424,plain,
! [X50,X51,X56,X54,X57,X55,X52,X53] : inverse(multiply(inverse(multiply(X53,multiply(multiply(multiply(X54,inverse(X54)),inverse(multiply(X55,X53))),X56))),multiply(multiply(multiply(X57,inverse(X57)),inverse(X55)),multiply(multiply(X50,inverse(X50)),inverse(multiply(X51,X52)))))) = multiply(multiply(X51,X52),X56),
inference(backward_demodulation,[],[f678,f2411]) ).
fof(f678,plain,
! [X50,X51,X58,X59,X56,X54,X57,X55,X52,X53] : inverse(multiply(inverse(multiply(X53,multiply(multiply(multiply(X54,inverse(X54)),inverse(multiply(X55,X53))),X56))),multiply(multiply(multiply(X57,inverse(X57)),inverse(X55)),multiply(multiply(X50,inverse(X50)),inverse(multiply(X51,X52)))))) = multiply(X58,inverse(multiply(inverse(multiply(X52,X56)),multiply(multiply(multiply(X59,inverse(X59)),inverse(X51)),X58)))),
inference(superposition,[],[f16,f16]) ).
fof(f1419,plain,
! [X40,X38,X41,X39,X44,X45,X42,X43] : inverse(multiply(inverse(multiply(X41,multiply(multiply(multiply(X42,inverse(X42)),inverse(multiply(X43,X41))),X44))),multiply(multiply(multiply(X45,inverse(X45)),inverse(X43)),multiply(multiply(X38,inverse(X38)),inverse(multiply(multiply(X39,inverse(X39)),X40)))))) = multiply(X40,X44),
inference(superposition,[],[f766,f16]) ).
fof(f2411,plain,
! [X181,X178,X177,X182,X183] : multiply(X182,inverse(multiply(inverse(multiply(X178,X181)),multiply(multiply(multiply(X183,inverse(X183)),inverse(X177)),X182)))) = multiply(multiply(X177,X178),X181),
inference(forward_demodulation,[],[f2403,f2384]) ).
fof(f2384,plain,
! [X10,X7] : multiply(multiply(X10,inverse(X10)),inverse(inverse(X7))) = X7,
inference(backward_demodulation,[],[f1577,f2368]) ).
fof(f2368,plain,
! [X62,X63,X64] : inverse(multiply(multiply(X62,inverse(X62)),inverse(multiply(multiply(X63,inverse(X63)),X64)))) = X64,
inference(backward_demodulation,[],[f1424,f2359]) ).
fof(f2359,plain,
! [X119,X114,X115] : multiply(X119,multiply(multiply(X115,inverse(X115)),inverse(multiply(X114,inverse(X114))))) = X119,
inference(backward_demodulation,[],[f148,f2028]) ).
fof(f2028,plain,
! [X10,X11,X8,X9] : multiply(multiply(X10,inverse(X10)),inverse(multiply(X9,multiply(X11,inverse(multiply(X8,multiply(X9,X11))))))) = X8,
inference(backward_demodulation,[],[f45,f2011]) ).
fof(f148,plain,
! [X118,X119,X116,X117,X114,X115] : multiply(multiply(X116,inverse(X116)),inverse(multiply(X117,multiply(X118,inverse(multiply(multiply(X119,multiply(multiply(X115,inverse(X115)),inverse(multiply(X114,inverse(X114))))),multiply(X117,X118))))))) = X119,
inference(superposition,[],[f45,f89]) ).
fof(f1424,plain,
! [X65,X62,X63,X66,X64] : inverse(multiply(multiply(X62,inverse(X62)),inverse(multiply(multiply(X63,inverse(X63)),X64)))) = multiply(X64,multiply(multiply(X65,inverse(X65)),inverse(multiply(X66,inverse(X66))))),
inference(superposition,[],[f766,f189]) ).
fof(f1577,plain,
! [X10,X8,X9,X7] : multiply(multiply(X10,inverse(X10)),inverse(inverse(inverse(multiply(multiply(X8,inverse(X8)),inverse(multiply(multiply(X9,inverse(X9)),X7))))))) = X7,
inference(superposition,[],[f1469,f766]) ).
fof(f2403,plain,
! [X181,X178,X179,X177,X182,X183] : multiply(X182,inverse(multiply(inverse(multiply(X178,X181)),multiply(multiply(multiply(X183,inverse(X183)),inverse(X177)),X182)))) = multiply(multiply(multiply(X179,inverse(X179)),inverse(inverse(multiply(X177,X178)))),X181),
inference(backward_demodulation,[],[f1465,f2400]) ).
fof(f2400,plain,
! [X54,X57,X53] : multiply(multiply(X53,inverse(X53)),multiply(multiply(X54,inverse(X54)),X57)) = X57,
inference(forward_demodulation,[],[f2399,f2384]) ).
fof(f2399,plain,
! [X56,X54,X57,X53] : multiply(multiply(X53,inverse(X53)),multiply(multiply(multiply(X56,inverse(X56)),inverse(inverse(multiply(X54,inverse(X54))))),X57)) = X57,
inference(forward_demodulation,[],[f2390,f201]) ).
fof(f201,plain,
! [X16,X17,X15] : multiply(X17,inverse(multiply(inverse(X15),multiply(multiply(X16,inverse(X16)),X17)))) = X15,
inference(superposition,[],[f1,f185]) ).
fof(f2390,plain,
! [X56,X54,X57,X55,X52,X53] : multiply(X55,inverse(multiply(inverse(multiply(multiply(X53,inverse(X53)),multiply(multiply(multiply(X56,inverse(X56)),inverse(inverse(multiply(X54,inverse(X54))))),X57))),multiply(multiply(X52,inverse(X52)),X55)))) = X57,
inference(backward_demodulation,[],[f1752,f2384]) ).
fof(f1752,plain,
! [X58,X56,X54,X57,X55,X52,X53] : multiply(X55,inverse(multiply(inverse(multiply(multiply(X53,inverse(X53)),multiply(multiply(multiply(X56,inverse(X56)),inverse(inverse(multiply(X54,inverse(X54))))),X57))),multiply(multiply(multiply(X58,inverse(X58)),inverse(inverse(multiply(X52,inverse(X52))))),X55)))) = X57,
inference(superposition,[],[f16,f1423]) ).
fof(f1423,plain,
! [X59,X60,X61] : inverse(multiply(X60,inverse(X60))) = multiply(inverse(multiply(X59,inverse(X59))),multiply(X61,inverse(X61))),
inference(superposition,[],[f766,f189]) ).
fof(f1465,plain,
! [X180,X181,X178,X179,X176,X177,X182,X183] : multiply(multiply(multiply(X179,inverse(X179)),inverse(multiply(multiply(X180,inverse(X180)),multiply(multiply(X176,inverse(X176)),inverse(multiply(X177,X178)))))),X181) = multiply(X182,inverse(multiply(inverse(multiply(X178,X181)),multiply(multiply(multiply(X183,inverse(X183)),inverse(X177)),X182)))),
inference(superposition,[],[f16,f766]) ).
fof(f2565,plain,
! [X48,X46,X44,X45] : inverse(multiply(inverse(X46),inverse(multiply(X44,X45)))) = multiply(X48,inverse(multiply(inverse(multiply(X45,X46)),multiply(inverse(X44),X48)))),
inference(forward_demodulation,[],[f2404,f2433]) ).
fof(f2404,plain,
! [X48,X46,X49,X44,X45] : multiply(X48,inverse(multiply(inverse(multiply(X45,X46)),multiply(multiply(multiply(X49,inverse(X49)),inverse(X44)),X48)))) = inverse(multiply(inverse(X46),inverse(multiply(X44,X45)))),
inference(backward_demodulation,[],[f677,f2400]) ).
fof(f677,plain,
! [X48,X46,X49,X47,X44,X45,X43] : inverse(multiply(inverse(X46),multiply(multiply(X47,inverse(X47)),multiply(multiply(X43,inverse(X43)),inverse(multiply(X44,X45)))))) = multiply(X48,inverse(multiply(inverse(multiply(X45,X46)),multiply(multiply(multiply(X49,inverse(X49)),inverse(X44)),X48)))),
inference(superposition,[],[f16,f201]) ).
fof(f2515,plain,
! [X16,X14,X17,X15] : inverse(multiply(multiply(X16,inverse(X16)),inverse(multiply(X17,inverse(inverse(multiply(inverse(multiply(X14,inverse(X14))),inverse(multiply(X15,inverse(X15)))))))))) = X17,
inference(backward_demodulation,[],[f1011,f2433]) ).
fof(f1011,plain,
! [X16,X14,X17,X15,X13] : inverse(multiply(multiply(X16,inverse(X16)),inverse(multiply(X17,inverse(inverse(multiply(multiply(multiply(X13,inverse(X13)),inverse(multiply(X14,inverse(X14)))),inverse(multiply(X15,inverse(X15)))))))))) = X17,
inference(superposition,[],[f809,f515]) ).
fof(f515,plain,
! [X2,X0,X1] : inverse(multiply(X2,inverse(X2))) = inverse(multiply(multiply(X0,inverse(X0)),inverse(multiply(X1,inverse(X1))))),
inference(superposition,[],[f511,f511]) ).
fof(f1745,plain,
! [X18,X19,X16,X17] : multiply(inverse(multiply(multiply(X17,inverse(X17)),inverse(multiply(X18,inverse(multiply(X16,inverse(X16))))))),inverse(inverse(multiply(X19,inverse(X19))))) = X18,
inference(superposition,[],[f1,f1423]) ).
fof(f2446,plain,
! [X170,X171,X169] : multiply(X171,inverse(X171)) = multiply(inverse(multiply(X169,inverse(inverse(multiply(X170,inverse(X170)))))),X169),
inference(backward_demodulation,[],[f1076,f2433]) ).
fof(f1076,plain,
! [X170,X171,X168,X169] : multiply(X171,inverse(X171)) = multiply(multiply(multiply(X168,inverse(X168)),inverse(multiply(X169,inverse(inverse(multiply(X170,inverse(X170))))))),X169),
inference(superposition,[],[f185,f809]) ).
fof(f6550,plain,
( ! [X5] : multiply(inverse(a1),a1) != multiply(X5,inverse(X5))
| spl0_2 ),
inference(superposition,[],[f10,f2597]) ).
fof(f10,plain,
( multiply(inverse(a1),a1) != multiply(inverse(b1),b1)
| spl0_2 ),
inference(avatar_component_clause,[],[f8]) ).
fof(f8,plain,
( spl0_2
<=> multiply(inverse(a1),a1) = multiply(inverse(b1),b1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
fof(f6370,plain,
spl0_3,
inference(avatar_contradiction_clause,[],[f6369]) ).
fof(f6369,plain,
( $false
| spl0_3 ),
inference(trivial_inequality_removal,[],[f6368]) ).
fof(f6368,plain,
( a2 != a2
| spl0_3 ),
inference(forward_demodulation,[],[f6367,f2590]) ).
fof(f2590,plain,
! [X27,X23] : multiply(inverse(X23),multiply(X23,X27)) = X27,
inference(backward_demodulation,[],[f2435,f2586]) ).
fof(f2435,plain,
! [X27,X24,X23] : multiply(inverse(multiply(X23,inverse(inverse(multiply(X24,inverse(X24)))))),multiply(X23,X27)) = X27,
inference(backward_demodulation,[],[f1094,f2433]) ).
fof(f1094,plain,
! [X26,X27,X24,X23] : multiply(inverse(multiply(X23,inverse(inverse(multiply(X24,inverse(X24)))))),multiply(multiply(multiply(X26,inverse(X26)),X23),X27)) = X27,
inference(forward_demodulation,[],[f1054,f214]) ).
fof(f1054,plain,
! [X28,X26,X27,X24,X22,X25,X23] : multiply(X25,inverse(multiply(inverse(multiply(inverse(multiply(X23,inverse(inverse(multiply(X24,inverse(X24)))))),multiply(multiply(multiply(X26,inverse(X26)),X23),X27))),multiply(multiply(multiply(X28,inverse(X28)),inverse(multiply(X22,inverse(X22)))),X25)))) = X27,
inference(superposition,[],[f16,f809]) ).
fof(f6367,plain,
( a2 != multiply(inverse(b2),multiply(b2,a2))
| spl0_3 ),
inference(forward_demodulation,[],[f14,f2871]) ).
fof(f2871,plain,
! [X181,X178,X177] : multiply(multiply(X177,X178),X181) = multiply(X177,multiply(X178,X181)),
inference(backward_demodulation,[],[f2780,f2870]) ).
fof(f2870,plain,
! [X78,X79] : multiply(X78,X79) = inverse(multiply(inverse(X79),inverse(X78))),
inference(forward_demodulation,[],[f2643,f2773]) ).
fof(f2773,plain,
! [X3,X1,X4] : inverse(multiply(X3,X1)) = multiply(X4,inverse(multiply(X3,multiply(X1,X4)))),
inference(backward_demodulation,[],[f2706,f2766]) ).
fof(f2766,plain,
! [X28,X29] : multiply(X28,X29) = inverse(inverse(multiply(X28,X29))),
inference(forward_demodulation,[],[f2765,f2726]) ).
fof(f2726,plain,
! [X57] : inverse(inverse(inverse(inverse(X57)))) = X57,
inference(forward_demodulation,[],[f2700,f2686]) ).
fof(f2686,plain,
! [X8,X7] : multiply(multiply(X8,inverse(X8)),X7) = inverse(inverse(X7)),
inference(backward_demodulation,[],[f2471,f2683]) ).
fof(f2683,plain,
! [X21,X22] : inverse(inverse(X21)) = multiply(inverse(multiply(X22,inverse(X22))),X21),
inference(forward_demodulation,[],[f2669,f2654]) ).
fof(f2654,plain,
! [X8,X6] : multiply(X8,inverse(multiply(X6,inverse(X6)))) = X8,
inference(forward_demodulation,[],[f2627,f2588]) ).
fof(f2588,plain,
! [X8,X9] : inverse(multiply(multiply(X8,inverse(X8)),inverse(X9))) = X9,
inference(backward_demodulation,[],[f809,f2586]) ).
fof(f2627,plain,
! [X8,X6,X7] : inverse(multiply(multiply(X7,inverse(X7)),inverse(multiply(X8,inverse(multiply(X6,inverse(X6))))))) = X8,
inference(backward_demodulation,[],[f1009,f2588]) ).
fof(f1009,plain,
! [X8,X6,X7,X5] : inverse(multiply(multiply(X7,inverse(X7)),inverse(multiply(X8,inverse(inverse(multiply(multiply(X5,inverse(X5)),inverse(multiply(X6,inverse(X6)))))))))) = X8,
inference(superposition,[],[f809,f511]) ).
fof(f2669,plain,
! [X21,X19,X22] : multiply(inverse(multiply(X22,inverse(X22))),X21) = inverse(inverse(multiply(X21,inverse(multiply(X19,inverse(X19)))))),
inference(backward_demodulation,[],[f2520,f2654]) ).
fof(f2520,plain,
! [X21,X19,X22,X20] : multiply(inverse(multiply(X22,inverse(X22))),X21) = inverse(inverse(multiply(X21,multiply(inverse(multiply(X19,inverse(X19))),inverse(multiply(X20,inverse(X20))))))),
inference(backward_demodulation,[],[f1783,f2433]) ).
fof(f1783,plain,
! [X21,X18,X19,X22,X20] : multiply(inverse(multiply(X22,inverse(X22))),X21) = inverse(inverse(multiply(X21,multiply(multiply(multiply(X18,inverse(X18)),inverse(multiply(X19,inverse(X19)))),inverse(multiply(X20,inverse(X20))))))),
inference(superposition,[],[f1588,f515]) ).
fof(f2471,plain,
! [X8,X6,X7] : multiply(multiply(X8,inverse(X8)),X7) = multiply(inverse(multiply(X6,inverse(X6))),X7),
inference(backward_demodulation,[],[f1098,f2433]) ).
fof(f1098,plain,
! [X8,X6,X7,X5] : multiply(multiply(X8,inverse(X8)),X7) = multiply(multiply(multiply(X5,inverse(X5)),inverse(multiply(X6,inverse(X6)))),X7),
inference(superposition,[],[f1055,f511]) ).
fof(f2700,plain,
! [X57,X53] : multiply(multiply(X53,inverse(X53)),inverse(inverse(X57))) = X57,
inference(backward_demodulation,[],[f2400,f2686]) ).
fof(f2765,plain,
! [X28,X29] : multiply(X28,X29) = inverse(inverse(inverse(inverse(inverse(inverse(multiply(X28,X29))))))),
inference(forward_demodulation,[],[f2715,f2706]) ).
fof(f2715,plain,
! [X31,X28,X29] : multiply(X28,X29) = inverse(inverse(inverse(multiply(X31,inverse(multiply(X28,multiply(X29,X31))))))),
inference(backward_demodulation,[],[f2559,f2686]) ).
fof(f2559,plain,
! [X31,X28,X29,X33] : multiply(X28,X29) = multiply(multiply(X33,inverse(X33)),inverse(multiply(X31,inverse(multiply(X28,multiply(X29,X31)))))),
inference(forward_demodulation,[],[f2536,f201]) ).
fof(f2536,plain,
! [X31,X28,X29,X35,X30,X33] : multiply(multiply(X33,inverse(X33)),inverse(multiply(X31,inverse(multiply(X28,multiply(X29,X31)))))) = multiply(X35,inverse(multiply(inverse(multiply(X28,X29)),multiply(multiply(X30,inverse(X30)),X35)))),
inference(backward_demodulation,[],[f2340,f2433]) ).
fof(f2340,plain,
! [X31,X28,X29,X27,X35,X30,X33] : multiply(multiply(X33,inverse(X33)),inverse(multiply(X31,inverse(multiply(X28,multiply(X29,X31)))))) = multiply(X35,inverse(multiply(multiply(multiply(X27,inverse(X27)),inverse(multiply(X28,X29))),multiply(multiply(X30,inverse(X30)),X35)))),
inference(forward_demodulation,[],[f2339,f2011]) ).
fof(f2339,plain,
! [X31,X28,X29,X36,X27,X35,X30,X33] : multiply(X35,inverse(multiply(multiply(multiply(multiply(X27,inverse(X27)),inverse(multiply(X28,X29))),multiply(X36,inverse(X36))),multiply(multiply(X30,inverse(X30)),X35)))) = multiply(multiply(X33,inverse(X33)),inverse(multiply(X31,inverse(multiply(X28,multiply(X29,X31)))))),
inference(forward_demodulation,[],[f2017,f2011]) ).
fof(f2017,plain,
! [X31,X28,X29,X36,X27,X34,X35,X30,X33] : multiply(X35,inverse(multiply(multiply(multiply(multiply(X27,inverse(X27)),inverse(multiply(X28,X29))),multiply(X36,inverse(X36))),multiply(multiply(X30,inverse(X30)),X35)))) = multiply(multiply(multiply(X33,inverse(X33)),inverse(multiply(X31,inverse(multiply(X28,multiply(X29,X31)))))),multiply(X34,inverse(X34))),
inference(backward_demodulation,[],[f31,f2011]) ).
fof(f31,plain,
! [X31,X28,X29,X36,X27,X34,X35,X32,X30,X33] : multiply(X35,inverse(multiply(multiply(multiply(multiply(X27,inverse(X27)),inverse(multiply(X28,X29))),multiply(X36,inverse(X36))),multiply(multiply(X30,inverse(X30)),X35)))) = multiply(multiply(multiply(X33,inverse(X33)),inverse(multiply(X31,inverse(multiply(multiply(X28,multiply(X32,inverse(X32))),multiply(X29,X31)))))),multiply(X34,inverse(X34))),
inference(superposition,[],[f21,f21]) ).
fof(f2706,plain,
! [X3,X1,X4] : multiply(X4,inverse(multiply(X3,multiply(X1,X4)))) = inverse(inverse(inverse(multiply(X3,X1)))),
inference(backward_demodulation,[],[f2330,f2686]) ).
fof(f2330,plain,
! [X2,X3,X1,X4] : multiply(multiply(X2,inverse(X2)),inverse(multiply(X3,X1))) = multiply(X4,inverse(multiply(X3,multiply(X1,X4)))),
inference(forward_demodulation,[],[f2012,f2011]) ).
fof(f2012,plain,
! [X2,X3,X0,X1,X4] : multiply(multiply(multiply(X2,inverse(X2)),inverse(multiply(X3,X1))),multiply(X0,inverse(X0))) = multiply(X4,inverse(multiply(X3,multiply(X1,X4)))),
inference(backward_demodulation,[],[f21,f2011]) ).
fof(f2643,plain,
! [X82,X78,X79] : multiply(X78,X79) = multiply(X82,inverse(multiply(inverse(X79),multiply(inverse(X78),X82)))),
inference(backward_demodulation,[],[f2467,f2588]) ).
fof(f2467,plain,
! [X82,X78,X79,X77] : inverse(multiply(multiply(X77,inverse(X77)),inverse(multiply(X78,X79)))) = multiply(X82,inverse(multiply(inverse(X79),multiply(inverse(X78),X82)))),
inference(backward_demodulation,[],[f2367,f2433]) ).
fof(f2367,plain,
! [X82,X83,X78,X79,X77] : inverse(multiply(multiply(X77,inverse(X77)),inverse(multiply(X78,X79)))) = multiply(X82,inverse(multiply(inverse(X79),multiply(multiply(multiply(X83,inverse(X83)),inverse(X78)),X82)))),
inference(backward_demodulation,[],[f682,f2359]) ).
fof(f682,plain,
! [X82,X83,X80,X78,X81,X79,X77] : inverse(multiply(multiply(X77,inverse(X77)),inverse(multiply(X78,X79)))) = multiply(X82,inverse(multiply(inverse(multiply(X79,multiply(multiply(X80,inverse(X80)),inverse(multiply(X81,inverse(X81)))))),multiply(multiply(multiply(X83,inverse(X83)),inverse(X78)),X82)))),
inference(superposition,[],[f16,f189]) ).
fof(f2780,plain,
! [X181,X178,X177] : multiply(multiply(X177,X178),X181) = inverse(multiply(inverse(multiply(X178,X181)),inverse(X177))),
inference(backward_demodulation,[],[f2752,f2766]) ).
fof(f2752,plain,
! [X181,X178,X177] : multiply(multiply(X177,X178),X181) = inverse(inverse(inverse(multiply(inverse(multiply(X178,X181)),inverse(X177))))),
inference(backward_demodulation,[],[f2468,f2706]) ).
fof(f14,plain,
( a2 != multiply(multiply(inverse(b2),b2),a2)
| spl0_3 ),
inference(avatar_component_clause,[],[f12]) ).
fof(f12,plain,
( spl0_3
<=> a2 = multiply(multiply(inverse(b2),b2),a2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
fof(f2884,plain,
spl0_1,
inference(avatar_contradiction_clause,[],[f2883]) ).
fof(f2883,plain,
( $false
| spl0_1 ),
inference(trivial_inequality_removal,[],[f2882]) ).
fof(f2882,plain,
( multiply(a3,multiply(b3,c3)) != multiply(a3,multiply(b3,c3))
| spl0_1 ),
inference(backward_demodulation,[],[f6,f2871]) ).
fof(f6,plain,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| spl0_1 ),
inference(avatar_component_clause,[],[f4]) ).
fof(f4,plain,
( spl0_1
<=> multiply(multiply(a3,b3),c3) = multiply(a3,multiply(b3,c3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
fof(f15,plain,
( ~ spl0_1
| ~ spl0_2
| ~ spl0_3 ),
inference(avatar_split_clause,[],[f2,f12,f8,f4]) ).
fof(f2,axiom,
( a2 != multiply(multiply(inverse(b2),b2),a2)
| multiply(inverse(a1),a1) != multiply(inverse(b1),b1)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) ),
file('/export/starexec/sandbox2/tmp/tmp.iQqCUL4pOn/Vampire---4.8_22450',prove_these_axioms) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : GRP058-1 : TPTP v8.1.2. Released v1.0.0.
% 0.07/0.14 % Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.15/0.35 % Computer : n004.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Tue Aug 29 00:29:37 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.15/0.36 This is a CNF_UNS_RFO_PEQ_NUE problem
% 0.15/0.36 Running vampire_casc2023 --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/tmp/tmp.iQqCUL4pOn/Vampire---4.8_22450
% 0.15/0.36 % (22569)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.42 % (22574)lrs+3_20_av=off:bd=preordered:drc=off:fsd=off:fsr=off:fde=unused:irw=on:lcm=reverse:sos=theory:stl=315_961 on Vampire---4 for (961ds/0Mi)
% 0.21/0.42 % (22575)ott+1003_4:1_av=off:cond=on:drc=off:fsd=off:fsr=off:fde=none:gsp=on:nm=2:nwc=1.5:sos=all:sp=reverse_arity:tgt=full_871 on Vampire---4 for (871ds/0Mi)
% 0.21/0.42 % (22576)lrs-11_32_av=off:bd=off:bs=on:bsr=on:drc=off:flr=on:fsd=off:fsr=off:fde=none:gsp=on:irw=on:lcm=predicate:nm=4:sp=scramble:stl=125_825 on Vampire---4 for (825ds/0Mi)
% 0.21/0.42 % (22573)ott-4_11_av=off:bd=preordered:bce=on:drc=off:flr=on:fsr=off:lma=on:nwc=2.0:sp=occurrence:tgt=ground:urr=ec_only_1010 on Vampire---4 for (1010ds/0Mi)
% 0.21/0.42 % (22570)lrs+10_11_cond=on:drc=off:flr=on:fsr=off:gsp=on:gs=on:gsem=off:lma=on:msp=off:nm=4:nwc=1.5:nicw=on:sas=z3:sims=off:sp=scramble:stl=188_1169 on Vampire---4 for (1169ds/0Mi)
% 0.21/0.42 % (22577)ott+11_14_av=off:bs=on:bsr=on:cond=on:flr=on:fsd=off:fde=unused:gsp=on:nm=4:nwc=1.5:tgt=full_501 on Vampire---4 for (501ds/0Mi)
% 0.21/0.42 % (22575)Refutation not found, incomplete strategy% (22575)------------------------------
% 0.21/0.42 % (22575)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.21/0.42 % (22575)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.21/0.42 % (22575)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.42
% 0.21/0.42 % (22575)Memory used [KB]: 895
% 0.21/0.42 % (22575)Time elapsed: 0.003 s
% 0.21/0.42 % (22575)------------------------------
% 0.21/0.42 % (22575)------------------------------
% 0.21/0.42 % (22572)lrs-11_28_aac=none:afr=on:anc=none:bs=on:drc=off:fde=unused:gs=on:nm=2:nwc=1.3:sp=frequency:stl=188_1092 on Vampire---4 for (1092ds/0Mi)
% 0.21/0.48 % (22578)ott+4_40_av=off:bce=on:fsd=off:fde=unused:nm=4:nwc=1.1:sos=all:sp=frequency_375 on Vampire---4 for (375ds/0Mi)
% 0.21/0.48 % (22578)Refutation not found, incomplete strategy% (22578)------------------------------
% 0.21/0.48 % (22578)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.21/0.48 % (22578)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.21/0.48 % (22578)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.48
% 0.21/0.48 % (22578)Memory used [KB]: 895
% 0.21/0.48 % (22578)Time elapsed: 0.002 s
% 0.21/0.48 % (22578)------------------------------
% 0.21/0.48 % (22578)------------------------------
% 0.21/0.51 % (22579)lrs-11_16_av=off:bs=on:bsr=on:drc=off:fsd=off:fsr=off:nm=4:sp=scramble:tgt=ground:stl=62_367 on Vampire---4 for (367ds/0Mi)
% 1.83/0.63 % (22570)First to succeed.
% 1.83/0.63 % (22570)Refutation found. Thanks to Tanya!
% 1.83/0.63 % SZS status Unsatisfiable for Vampire---4
% 1.83/0.63 % SZS output start Proof for Vampire---4
% See solution above
% 1.83/0.63 % (22570)------------------------------
% 1.83/0.63 % (22570)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 1.83/0.63 % (22570)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 1.83/0.63 % (22570)Termination reason: Refutation
% 1.83/0.63
% 1.83/0.63 % (22570)Memory used [KB]: 11129
% 1.83/0.63 % (22570)Time elapsed: 0.209 s
% 1.83/0.63 % (22570)------------------------------
% 1.83/0.63 % (22570)------------------------------
% 1.83/0.63 % (22569)Success in time 0.266 s
% 1.83/0.63 % Vampire---4.8 exiting
%------------------------------------------------------------------------------